diff --git a/.coveragerc b/.coveragerc new file mode 100644 index 000000000..a5f7fcee8 --- /dev/null +++ b/.coveragerc @@ -0,0 +1,5 @@ +[report] +omit = + */python?.?/* + */site-packages/nose/* + *__init__* diff --git a/.github/workflows/python-app.yml b/.github/workflows/python-app.yml new file mode 100644 index 000000000..1eb737ecd --- /dev/null +++ b/.github/workflows/python-app.yml @@ -0,0 +1,36 @@ +# This workflow will install Python dependencies, run tests and lint with a single version of Python +# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions + +name: Python application + +on: + push: + branches: [ master ] + pull_request: + branches: [ master ] + +jobs: + build: + + runs-on: ubuntu-latest + + steps: + - uses: actions/checkout@v2 + - name: Set up Python 3.10 + uses: actions/setup-python@v2 + with: + python-version: "3.10" + - name: Install dependencies + run: | + python -m pip install --upgrade pip + pip install flake8 pytest + if [ -f requirements.txt ]; then pip install -r requirements.txt; fi + - name: Lint with flake8 + run: | + # stop the build if there are Python syntax errors or undefined names + flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics + # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide + flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics + - name: Test with pytest + run: | + python -m pytest diff --git a/.gitignore b/.gitignore index 43ae0e2a6..5152c3d1b 100755 --- a/.gitignore +++ b/.gitignore @@ -1,2 +1,19 @@ __pycache__/ *.py[cod] +*.iml +*.xml +.idea/ +.cache/ +.pytest_cache/ +.coverage +# Setuptools distribution folder. +/dist/ +# Python egg metadata, regenerated from source files by setuptools. +/*.egg-info +/*.egg +# docs +build/ +pythonenv3.8/ +.vscode/ +# Ignoring the virtual Environment when using GitHub Codespaces +.venv/ \ No newline at end of file diff --git a/.travis.yml b/.travis.yml new file mode 100644 index 000000000..94607d486 --- /dev/null +++ b/.travis.yml @@ -0,0 +1,30 @@ +group: travis_latest +dist: xenial # Travis CI's default distro +language: python +cache: + directories: + - $HOME/.cache/pip +matrix: + include: + - python: 3.6 + env: TOX_ENV=py36 + - python: 3.7 + env: TOX_ENV=py37 +install: + - pip install -r test_requirements.txt +before_script: + # run black to check if some files would need reformatting + - black --check . || true + # stop the build if there are Python syntax errors or undefined names + - flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics + # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide + - flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics +script: + # Check python install package + - pip install -e . + - tox -e $TOX_ENV + # Check python uninstall package + - pip uninstall -y algorithms +notifications: + on_success: change + on_failure: change # `always` will be the setting once code changes slow down diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md new file mode 100644 index 000000000..6eac6c029 --- /dev/null +++ b/CONTRIBUTING.md @@ -0,0 +1,66 @@ +# Contributing + +We love pull requests from everyone. By contributing to this repository, you +agree to abide by the [Code of Conduct](CODE_OF_CONDUCT.md). + +## Get Started + +* First [fork][fork] the repository and then clone it using: + + git clone git@github.com:your-username/algorithms.git + +* After that create a branch for your changes. For example: + * add_XXX if you will add new algorithms or data structures. + * fix_XXX if you will fix a bug on a certain algorithm or data structure. + * test_XXX if you wrote a test/s. + * doc_XXX if you added to or edited documentation. + +You may contribute by: +- implementing new algorithms in the repo. Be sure to keep it under +right section (e.g. [array](array), [dp](dp), etc). Make a new section for it if +it doesn't fall under any section. Make sure that your implementation works. +- optimizing or improving the existing algorithms. +- adding a different solution for the problem. +- finding and fixing bugs. +- adding examples to explain the algorithms better. +- adding test cases. +- improving documentation. + +## Pull Requests +Push to your fork and [submit a pull request][pr]. + +We will review and may suggest some changes or improvements or alternatives. +Some things that will increase the chance that your pull request is accepted: + +* All algorithms should be written in **Python 3**. +(There are a few algorithms still in _Python 2_ syntax. You can start by converting +[those][issue120] to _Python 3_.) +* Write clean and understandable code. +* Properly comment the code and briefly explain what the algorithm is doing in the [docstrings][docstr]. +* You may also explain the output using a minimal example. +* Try to also include a couple of test cases for the algorithm. +* Write a [good commit message][commit]. + + +## Issues +Submit a [new issue][newissue] if there is an algorithm to add, or if a bug was found in an existing algorithm. Before submitting a new issue please review the [existing issues][issues] to avoid creating duplicates. Also, consider resolving current issues or contributing to the discussion on an issue. + +## Collaborators +You can ask for any help or clarifications from the collaborators. +[Keon Kim](https://github.com/keon) + +[Rahul Goswami](https://github.com/goswami-rahul) + +[Ankit Agarwal](https://github.com/ankit167) + +[Hai Hoang Dang](https://github.com/danghai) + +[Saad](https://github.com/SaadBenn) + +[fork]: https://help.github.com/articles/fork-a-repo/ +[docstr]: https://www.python.org/dev/peps/pep-0257/#multi-line-docstrings +[commit]: http://tbaggery.com/2008/04/19/a-note-about-git-commit-messages.html +[pr]: https://github.com/keon/algorithms/compare/ +[newissue]: https://github.com/keon/algorithms/issues/new +[issue120]: https://github.com/keon/algorithms/issues/120 +[issues]: https://github.com/keon/algorithms/issues/ diff --git a/MANIFEST.in b/MANIFEST.in new file mode 100644 index 000000000..50af9b9c9 --- /dev/null +++ b/MANIFEST.in @@ -0,0 +1,3 @@ +include README.md +include LICENSE +include algorithms/* diff --git a/README.md b/README.md index 9b09e003b..65caeb5ca 100644 --- a/README.md +++ b/README.md @@ -1,212 +1,424 @@ +[![PyPI version](https://badge.fury.io/py/algorithms.svg)](https://badge.fury.io/py/algorithms) +[![Open Source Helpers](https://www.codetriage.com/keon/algorithms/badges/users.svg)](https://www.codetriage.com/keon/algorithms) +[![Build Status](https://travis-ci.org/keon/algorithms.svg?branch=master)](https://travis-ci.org/keon/algorithms) +[![Coverage Status](https://coveralls.io/repos/github/keon/algorithms/badge.svg?branch=master)](https://coveralls.io/github/keon/algorithms?branch=master) + +

+ Pythonic Data Structures and Algorithms ========================================= -Minimal and clean example implementations of data structures and algorithms in Python. +Minimal and clean example implementations of data structures and algorithms in Python 3. + +## Contributing +Thanks for your interest in contributing! There are many ways to contribute to this project. [Get started here](CONTRIBUTING.md) + +## Tests + +### Use unittest +For running all tests write down: + + $ python3 -m unittest discover tests + +For running some specific tests you can do this as following (Ex: sort): + + $ python3 -m unittest tests.test_sort + +### Use pytest +For running all tests write down: + $ python3 -m pytest tests + +## Install +If you want to use the API algorithms in your code, it is as simple as: + + $ pip3 install algorithms + +You can test by creating a python file: (Ex: use `merge_sort` in `sort`) + +```python3 +from algorithms.sort import merge_sort + +if __name__ == "__main__": + my_list = [1, 8, 3, 5, 6] + my_list = merge_sort(my_list) + print(my_list) +``` + +## Uninstall +If you want to uninstall algorithms, it is as simple as: + + $ pip3 uninstall -y algorithms ## List of Implementations -- [array](array) - - [circular_counter](array/circular_counter.py) - - [flatten](array/flatten.py) - - [garage](array/garage.py) - - [longest_non_repeat](array/longest_non_repeat.py/) - - [merge_intervals](array/merge_intervals.py) - - [missing_ranges](array/missing_ranges.py) - - [plus_one](array/plus_one.py) - - [rotate_array](array/rotate_array.py) - - [summary_ranges](array/summary_ranges.py) - - [three_sum](array/three_sum.py) - - [two_sum](array/two_sum.py) -- [backtrack](backtrack) - - [general_solution.md](backtrack/) - - [anagram](backtrack/anagram.py) - - [array_sum_combinations](backtrack/array_sum_combination.py) - - [combination_sum](backtrack/combination_sum.py) - - [expression_add_operators](backtrack/expression_add_operators.py) - - [factor_combinations](backtrack/factor_combinations.py) - - [generate_abbreviations](backtrack/generate_abbreviations.py) - - [generate_parenthesis](backtrack/generate_parenthesis.py) - - [letter_combination](backtrack/letter_combination.py) - - [palindrome_partitioning](backtrack/palindrome_partitioning.py) - - [pattern_match](backtrack/pattern_match.py) - - [permute](backtrack/permute.py) - - [permute_unique](backtrack/permute_unique.py) - - [subsets](backtrack/subsets.py) - - [subsets_unique](backtrack/subsets_unique.py) -- [bfs](bfs) - - [shortest_distance_from_all_buildings](bfs/shortest_distance_from_all_buildings.py) - - [word_ladder](bfs/word_ladder.py) -- [bit](bit) - - [bytes_int_conversion](bit/bytes_int_conversion.py) - - [count_ones](bit/count_ones.py) - - [find_missing_number](bit/find_missing_number.py) - - [power_of_two](bit/power_of_two.py) - - [reverse_bits](bit/reverse_bits.py) - - [single_number2](bit/single_number2.py) - - [single_number](bit/single_number.py) - - [subsets](bit/subsets.py) - - [add_without_operator](bit/add_without_operator.py) -- [calculator](calculator) - - [math_parser](calculator/math_parser.py) -- [dfs](dfs) - - [all_factors](dfs/all_factors.py) - - [count_islands](dfs/count_islands.py) - - [pacific_atlantic](dfs/pacific_atlantic.py) - - [sudoku_solver](dfs/sudoku_solver.py) - - [walls_and_gates](dfs/walls_and_gates.py) -- [dp](dp) - - [buy_sell_stock](dp/buy_sell_stock.py) - - [climbing_stairs](dp/climbing_stairs.py) - - [combination_sum](dp/combination_sum.py) - - [house_robber](dp/house_robber.py) - - [knapsack](dp/knapsack.py) - - [longest_increasing](dp/longest_increasing.py) - - [max_product_subarray](dp/max_product_subarray.py) - - [max_subarray](dp/max_subarray.py) - - [num_decodings](dp/num_decodings.py) - - [regex_matching](dp/regex_matching.py) - - [word_break](dp/word_break.py) -- [graph](graph) - - [2-sat](graph/satisfiability.py) - - [clone_graph](graph/clone_graph.py) - - [cycle_detection](graph/cycle_detection.py) - - [find_path](graph/find_path.py) - - [graph](graph/graph.py) - - [traversal](graph/traversal.py) - - [markov_chain](graph/markov_chain.py) -- [heap](heap) - - [merge_sorted_k_lists](heap/merge_sorted_k_lists.py) - - [skyline](heap/skyline.py) - - [sliding_window_max](heap/sliding_window_max.py) -- [linkedlist](linkedlist) - - [add_two_numbers](linkedlist/add_two_numbers.py) - - [copy_random_pointer](linkedlist/copy_random_pointer.py) - - [delete_node](linkedlist/delete_node.py) - - [first_cyclic_node](linkedlist/first_cyclic_node.py) - - [is_cyclic](linkedlist/is_cyclic.py) - - [is_palindrome](linkedlist/is_palindrome.py) - - [kth_to_last](linkedlist/kth_to_last.py) - - [linkedlist](linkedlist/linkedlist.py) - - [remove_duplicates](linkedlist/remove_duplicates.py) - - [reverse](linkedlist/reverse.py) - - [rotate_list](linkedlist/rotate_list.py) - - [swap_in_pairs](linkedlist/swap_in_pairs.py) -- [map](map) - - [hashtable](map/hashtable.py) - - [longest_common_subsequence](map/longest_common_subsequence.py) - - [randomized_set](map/randomized_set.py) - - [valid_sudoku](map/valid_sudoku.py) -- [math](math) - - [extended_gcd](math/extended_gcd.py) - - [gcd/lcm](math/gcd.py) - - [prime_test](math/prime_test.py) - - [primes_sieve_of_eratosthenes](math/primes_sieve_of_eratosthenes.py) - - [generate_strobogrammtic](math/generate_strobogrammtic.py) - - [is_strobogrammatic](math/is_strobogrammatic.py) - - [nth_digit](math/nth_digit.py) - - [rabin_miller](math/rabin_miller.py) - - [rsa](math/rsa.py) - - [sqrt_precision_factor](math/sqrt_precision_factor.py) - - [pythagoras](math/pythagoras.py) -- [matrix](matrix) - - [matrix_rotation.txt](matrix/matrix_rotation.txt) - - [copy_transform](matrix/copy_transform.py) - - [bomb_enemy](matrix/bomb_enemy.py) - - [rotate_image](matrix/rotate_image.py) - - [sparse_dot_vector](matrix/sparse_dot_vector.py) - - [sparse_mul](matrix/sparse_mul.py) - - [spiral_traversal](matrix/spiral_traversal.py) - - [count_paths](matrix/count_paths.py) -- [queue](queue) - - [max_sliding_window](queue/max_sliding_window.py) - - [moving_average](queue/moving_average.py) - - [queue](queue/queue.py) - - [reconstruct_queue](queue/reconstruct_queue.py) - - [zigzagiterator](queue/zigzagiterator.py) -- [search](search) - - [binary_search](search/binary_search.py) - - [count_elem](search/count_elem.py) - - [first_occurance](search/first_occurance.py) - - [last_occurance](search/last_occurance.py) -- [set](set) - - [randomized_set](set/randomized_set.py) - - [set_covering](set/set_covering.py) -- [sort](sort) - - [bubble_sort](sort/bubble_sort.py) - - [comb_sort](sort/comb_sort.py) - - [counting_sort](sort/counting_sort.py) - - [heap_sort](sort/heap_sort.py) - - [insertion_sort](sort/insertion_sort.py) - - [meeting_rooms](sort/meeting_rooms.py) - - [merge_sort](sort/merge_sort.py) - - [quick_sort](sort/quick_sort.py) - - [selection_sort](sort/selection_sort.py) - - [sort_colors](sort/sort_colors.py) - - [topsort](sort/topsort.py) - - [wiggle_sort](sort/wiggle_sort.py) -- [stack](stack) - - [longest_abs_path](stack/longest_abs_path.py) - - [simplify_path](stack/simplify_path.py) - - [stack](stack/stack.py) - - [valid_parenthesis](stack/valid_parenthesis.py) -- [string](string) - - [add_binary](string/add_binary.py) - - [breaking_bad](string/breaking_bad.py) - - [decode_string](string/decode_string.py) - - [encode_decode](string/encode_decode.py) - - [group_anagrams](string/group_anagrams.py) - - [int_to_roman](string/int_to_roman.py) - - [is_palindrome](string/is_palindrome.py) - - [license_number](string/license_number.py) - - [make_sentence](string/make_sentence.py) - - [multiply_strings](string/multiply_strings.py) - - [one_edit_distance](string/one_edit_distance.py) - - [rabin_karp](string/rabin_karp.py) - - [reverse_string](string/reverse_string.py) - - [reverse_vowel](string/reverse_vowel.py) - - [reverse_words](string/reverse_words.py) - - [roman_to_int](string/roman_to_int.py) - - [word_squares](string/word_squares.py) -- [tree](tree) - - [segment-tree](tree/Segment_Tree) - - [segment_tree](tree/Segment_Tree/segment_tree.py) - - [binary_tree_paths](tree/binary_tree_paths.py) - - [bintree2list](tree/bintree2list.py) - - [bst](tree/tree/bst) - - [array2bst](tree/bst/array2bst.py) - - [bst_closest_value](tree/bst/bst_closest_value.py) - - [BSTIterator](tree/bst/BSTIterator.py) - - [delete_node](tree/bst/delete_node.py) - - [is_bst](tree/bst/is_bst.py) - - [kth_smallest](tree/bst/kth_smallest.py) - - [lowest_common_ancestor](tree/bst/lowest_common_ancestor.py) - - [predecessor](tree/bst/predecessor.py) - - [serialize_deserialize](tree/bst/serialize_deserialize.py) - - [successor](tree/bst/successor.py) - - [unique_bst](tree/bst/unique_bst.py) - - [deepest_left](tree/deepest_left.py) - - [invert_tree](tree/invert_tree.py) - - [is_balanced](tree/is_balanced.py) - - [is_subtree](tree/is_subtree.py) - - [is_symmetric](tree/is_symmetric.py) - - [longest_consecutive](tree/longest_consecutive.py) - - [lowest_common_ancestor](tree/lowest_common_ancestor.py) - - [max_height](tree/max_height.py) - - [max_path_sum](tree/max_path_sum.py) - - [min_height](tree/min_height.py) - - [path_sum2](tree/path_sum2.py) - - [path_sum](tree/path_sum.py) - - [pretty_print](tree/pretty_print.py) - - [same_tree](tree/same_tree.py) - - [traversal](tree/traversal) - - [inorder](tree/traversal/inorder.py) - - [level_order](tree/traversal/level_order.py) - - [zigzag](tree/traversal/zigzag.py) - - [tree](tree/tree.py) - - [trie](tree/trie) - - [add_and_search](tree/trie/add_and_search.py) - - [trie](tree/trie/trie.py) -- [union-find](union-find) - - [count_islands](union-find/count_islands.py) +- [arrays](algorithms/arrays) + - [delete_nth](algorithms/arrays/delete_nth.py) + - [flatten](algorithms/arrays/flatten.py) + - [garage](algorithms/arrays/garage.py) + - [josephus_problem](algorithms/arrays/josephus.py) + - [limit](algorithms/arrays/limit.py) + - [longest_non_repeat](algorithms/arrays/longest_non_repeat.py/) + - [max_ones_index](algorithms/arrays/max_ones_index.py) + - [merge_intervals](algorithms/arrays/merge_intervals.py) + - [missing_ranges](algorithms/arrays/missing_ranges.py) + - [plus_one](algorithms/arrays/plus_one.py) + - [remove_duplicates](algorithms/arrays/remove_duplicates.py) + - [rotate](algorithms/arrays/rotate.py) + - [summarize_ranges](algorithms/arrays/summarize_ranges.py) + - [three_sum](algorithms/arrays/three_sum.py) + - [trimmean](algorithms/arrays/trimmean.py) + - [top_1](algorithms/arrays/top_1.py) + - [two_sum](algorithms/arrays/two_sum.py) + - [move_zeros](algorithms/arrays/move_zeros.py) + - [n_sum](algorithms/arrays/n_sum.py) +- [greedy](algorithms/greedy/) + - [max_contiguous_subsequence_sum](algorithms/greedy/max_contiguous_subsequence_sum.py) +- [automata](algorithms/automata) + - [DFA](algorithms/automata/dfa.py) +- [backtrack](algorithms/backtrack) + - [general_solution.md](algorithms/backtrack/) + - [add_operators](algorithms/backtrack/add_operators.py) + - [anagram](algorithms/backtrack/anagram.py) + - [array_sum_combinations](algorithms/backtrack/array_sum_combinations.py) + - [combination_sum](algorithms/backtrack/combination_sum.py) + - [factor_combinations](algorithms/backtrack/factor_combinations.py) + - [generate_abbreviations](algorithms/backtrack/generate_abbreviations.py) + - [generate_parenthesis](algorithms/backtrack/generate_parenthesis.py) + - [letter_combination](algorithms/backtrack/letter_combination.py) + - [palindrome_partitioning](algorithms/backtrack/palindrome_partitioning.py) + - [pattern_match](algorithms/backtrack/pattern_match.py) + - [permute](algorithms/backtrack/permute.py) + - [permute_unique](algorithms/backtrack/permute_unique.py) + - [subsets](algorithms/backtrack/subsets.py) + - [subsets_unique](algorithms/backtrack/subsets_unique.py) +- [bfs](algorithms/bfs) + - [maze_search](algorithms/bfs/maze_search.py) + - [shortest_distance_from_all_buildings](algorithms/bfs/shortest_distance_from_all_buildings.py) + - [word_ladder](algorithms/bfs/word_ladder.py) +- [bit](algorithms/bit) + - [add_bitwise_operator](algorithms/bit/add_bitwise_operator.py) + - [bit_operation](algorithms/bit/bit_operation.py) + - [bytes_int_conversion](algorithms/bit/bytes_int_conversion.py) + - [count_flips_to_convert](algorithms/bit/count_flips_to_convert.py) + - [count_ones](algorithms/bit/count_ones.py) + - [find_difference](algorithms/bit/find_difference.py) + - [find_missing_number](algorithms/bit/find_missing_number.py) + - [flip_bit_longest_sequence](algorithms/bit/flip_bit_longest_sequence.py) + - [power_of_two](algorithms/bit/power_of_two.py) + - [reverse_bits](algorithms/bit/reverse_bits.py) + - [single_number](algorithms/bit/single_number.py) + - [single_number2](algorithms/bit/single_number2.py) + - [single_number3](algorithms/bit/single_number3.py) + - [subsets](algorithms/bit/subsets.py) + - [swap_pair](algorithms/bit/swap_pair.py) + - [has_alternative_bit](algorithms/bit/has_alternative_bit.py) + - [insert_bit](algorithms/bit/insert_bit.py) + - [remove_bit](algorithms/bit/remove_bit.py) + - [binary_gap](algorithms/bit/binary_gap.py) +- [compression](algorithms/compression) + - [huffman_coding](algorithms/compression/huffman_coding.py) + - [rle_compression](algorithms/compression/rle_compression.py) + - [elias](algorithms/compression/elias.py) +- [dfs](algorithms/dfs) + - [all_factors](algorithms/dfs/all_factors.py) + - [count_islands](algorithms/dfs/count_islands.py) + - [pacific_atlantic](algorithms/dfs/pacific_atlantic.py) + - [sudoku_solver](algorithms/dfs/sudoku_solver.py) + - [walls_and_gates](algorithms/dfs/walls_and_gates.py) +- [distribution](algorithms/distribution) + - [histogram](algorithms/distribution/histogram.py) +- [dp](algorithms/dp) + - [buy_sell_stock](algorithms/dp/buy_sell_stock.py) + - [climbing_stairs](algorithms/dp/climbing_stairs.py) + - [coin_change](algorithms/dp/coin_change.py) + - [combination_sum](algorithms/dp/combination_sum.py) + - [egg_drop](algorithms/dp/egg_drop.py) + - [house_robber](algorithms/dp/house_robber.py) + - [int_divide](algorithms/dp/int_divide.py) + - [job_scheduling](algorithms/dp/job_scheduling.py) + - [knapsack](algorithms/dp/knapsack.py) + - [longest_increasing](algorithms/dp/longest_increasing.py) + - [matrix_chain_order](algorithms/dp/matrix_chain_order.py) + - [max_product_subarray](algorithms/dp/max_product_subarray.py) + - [max_subarray](algorithms/dp/max_subarray.py) + - [min_cost_path](algorithms/dp/min_cost_path.py) + - [num_decodings](algorithms/dp/num_decodings.py) + - [regex_matching](algorithms/dp/regex_matching.py) + - [rod_cut](algorithms/dp/rod_cut.py) + - [word_break](algorithms/dp/word_break.py) + - [fibonacci](algorithms/dp/fib.py) + - [hosoya triangle](algorithms/dp/hosoya_triangle.py) + - [K-Factor_strings](algorithms/dp/k_factor.py) + - [planting_trees](algorithms/dp/planting_trees.py) +- [graph](algorithms/graph) + - [check_bipartite](algorithms/graph/check_bipartite.py) + - [strongly_connected](algorithms/graph/check_digraph_strongly_connected.py) + - [clone_graph](algorithms/graph/clone_graph.py) + - [cycle_detection](algorithms/graph/cycle_detection.py) + - [find_all_cliques](algorithms/graph/find_all_cliques.py) + - [find_path](algorithms/graph/find_path.py) + - [graph](algorithms/graph/graph.py) + - [dijkstra](algorithms/graph/dijkstra.py) + - [markov_chain](algorithms/graph/markov_chain.py) + - [minimum_spanning_tree](algorithms/graph/minimum_spanning_tree.py) + - [satisfiability](algorithms/graph/satisfiability.py) + - [minimum_spanning_tree_prims](algorithms/graph/prims_minimum_spanning.py) + - [tarjan](algorithms/graph/tarjan.py) + - [traversal](algorithms/graph/traversal.py) + - [maximum_flow](algorithms/graph/maximum_flow.py) + - [maximum_flow_bfs](algorithms/graph/maximum_flow_bfs.py) + - [maximum_flow_dfs](algorithms/graph/maximum_flow_dfs.py) + - [all_pairs_shortest_path](algorithms/graph/all_pairs_shortest_path.py) + - [bellman_ford](algorithms/graph/bellman_ford.py) + - [Count Connected Components](algorithms/graph/count_connected_number_of_component.py) +- [heap](algorithms/heap) + - [merge_sorted_k_lists](algorithms/heap/merge_sorted_k_lists.py) + - [skyline](algorithms/heap/skyline.py) + - [sliding_window_max](algorithms/heap/sliding_window_max.py) + - [binary_heap](algorithms/heap/binary_heap.py) + - [k_closest_points](algorithms/heap/k_closest_points.py) +- [linkedlist](algorithms/linkedlist) + - [add_two_numbers](algorithms/linkedlist/add_two_numbers.py) + - [copy_random_pointer](algorithms/linkedlist/copy_random_pointer.py) + - [delete_node](algorithms/linkedlist/delete_node.py) + - [first_cyclic_node](algorithms/linkedlist/first_cyclic_node.py) + - [is_cyclic](algorithms/linkedlist/is_cyclic.py) + - [is_palindrome](algorithms/linkedlist/is_palindrome.py) + - [kth_to_last](algorithms/linkedlist/kth_to_last.py) + - [linkedlist](algorithms/linkedlist/linkedlist.py) + - [remove_duplicates](algorithms/linkedlist/remove_duplicates.py) + - [reverse](algorithms/linkedlist/reverse.py) + - [rotate_list](algorithms/linkedlist/rotate_list.py) + - [swap_in_pairs](algorithms/linkedlist/swap_in_pairs.py) + - [is_sorted](algorithms/linkedlist/is_sorted.py) + - [remove_range](algorithms/linkedlist/remove_range.py) +- [map](algorithms/map) + - [hashtable](algorithms/map/hashtable.py) + - [separate_chaining_hashtable](algorithms/map/separate_chaining_hashtable.py) + - [longest_common_subsequence](algorithms/map/longest_common_subsequence.py) + - [longest_palindromic_subsequence](algorithms/map/longest_palindromic_subsequence.py) + - [randomized_set](algorithms/map/randomized_set.py) + - [valid_sudoku](algorithms/map/valid_sudoku.py) + - [word_pattern](algorithms/map/word_pattern.py) + - [is_isomorphic](algorithms/map/is_isomorphic.py) + - [is_anagram](algorithms/map/is_anagram.py) +- [maths](algorithms/maths) + - [base_conversion](algorithms/maths/base_conversion.py) + - [chinese_remainder_theorem](algorithms/maths/chinese_remainder_theorem.py) + - [combination](algorithms/maths/combination.py) + - [cosine_similarity](algorithms/maths/cosine_similarity.py) + - [decimal_to_binary_ip](algorithms/maths/decimal_to_binary_ip.py) + - [diffie_hellman_key_exchange](algorithms/maths/diffie_hellman_key_exchange.py) + - [euler_totient](algorithms/maths/euler_totient.py) + - [extended_gcd](algorithms/maths/extended_gcd.py) + - [factorial](algorithms/maths/factorial.py) + - [find_order](algorithms/maths/find_order_simple.py) + - [find_primitive_root](algorithms/maths/find_primitive_root_simple.py) + - [gcd/lcm](algorithms/maths/gcd.py) + - [generate_strobogrammtic](algorithms/maths/generate_strobogrammtic.py) + - [hailstone](algorithms/maths/hailstone.py) + - [is_strobogrammatic](algorithms/maths/is_strobogrammatic.py) + - [krishnamurthy_number](algorithms/maths/krishnamurthy_number.py) + - [magic_number](algorithms/maths/magic_number.py) + - [modular_exponential](algorithms/maths/modular_exponential.py) + - [modular_inverse](algorithms/maths/modular_inverse.py) + - [next_bigger](algorithms/maths/next_bigger.py) + - [next_perfect_square](algorithms/maths/next_perfect_square.py) + - [nth_digit](algorithms/maths/nth_digit.py) + - [num_perfect_squares](algorithms/maths/num_perfect_squares.py) + - [polynomial](algorithms/maths/polynomial.py) + - [power](algorithms/maths/power.py) + - [prime_check](algorithms/maths/prime_check.py) + - [primes_sieve_of_eratosthenes](algorithms/maths/primes_sieve_of_eratosthenes.py) + - [pythagoras](algorithms/maths/pythagoras.py) + - [rabin_miller](algorithms/maths/rabin_miller.py) + - [recursive_binomial_coefficient](algorithms/maths/recursive_binomial_coefficient.py) + - [rsa](algorithms/maths/rsa.py) + - [sqrt_precision_factor](algorithms/maths/sqrt_precision_factor.py) + - [summing_digits](algorithms/maths/summing_digits.py) + - [symmetry_group_cycle_index](algorithms/maths/symmetry_group_cycle_index.py) +- [matrix](algorithms/matrix) + - [sudoku_validator](algorithms/matrix/sudoku_validator.py) + - [bomb_enemy](algorithms/matrix/bomb_enemy.py) + - [copy_transform](algorithms/matrix/copy_transform.py) + - [count_paths](algorithms/matrix/count_paths.py) + - [matrix_exponentiation](algorithms/matrix/matrix_exponentiation.py) + - [matrix_inversion](algorithms/matrix/matrix_inversion.py) + - [matrix_multiplication](algorithms/matrix/multiply.py) + - [rotate_image](algorithms/matrix/rotate_image.py) + - [search_in_sorted_matrix](algorithms/matrix/search_in_sorted_matrix.py) + - [sparse_dot_vector](algorithms/matrix/sparse_dot_vector.py) + - [sparse_mul](algorithms/matrix/sparse_mul.py) + - [spiral_traversal](algorithms/matrix/spiral_traversal.py) + - [crout_matrix_decomposition](algorithms/matrix/crout_matrix_decomposition.py) + - [cholesky_matrix_decomposition](algorithms/matrix/cholesky_matrix_decomposition.py) + - [sum_sub_squares](algorithms/matrix/sum_sub_squares.py) + - [sort_matrix_diagonally](algorithms/matrix/sort_matrix_diagonally.py) +- [queues](algorithms/queues) + - [max_sliding_window](algorithms/queues/max_sliding_window.py) + - [moving_average](algorithms/queues/moving_average.py) + - [queue](algorithms/queues/queue.py) + - [reconstruct_queue](algorithms/queues/reconstruct_queue.py) + - [zigzagiterator](algorithms/queues/zigzagiterator.py) +- [search](algorithms/search) + - [binary_search](algorithms/search/binary_search.py) + - [first_occurrence](algorithms/search/first_occurrence.py) + - [last_occurrence](algorithms/search/last_occurrence.py) + - [linear_search](algorithms/search/linear_search.py) + - [search_insert](algorithms/search/search_insert.py) + - [two_sum](algorithms/search/two_sum.py) + - [search_range](algorithms/search/search_range.py) + - [find_min_rotate](algorithms/search/find_min_rotate.py) + - [search_rotate](algorithms/search/search_rotate.py) + - [jump_search](algorithms/search/jump_search.py) + - [next_greatest_letter](algorithms/search/next_greatest_letter.py) + - [interpolation_search](algorithms/search/interpolation_search.py) +- [set](algorithms/set) + - [randomized_set](algorithms/set/randomized_set.py) + - [set_covering](algorithms/set/set_covering.py) + - [find_keyboard_row](algorithms/set/find_keyboard_row.py) +- [sort](algorithms/sort) + - [bitonic_sort](algorithms/sort/bitonic_sort.py) + - [bogo_sort](algorithms/sort/bogo_sort.py) + - [bubble_sort](algorithms/sort/bubble_sort.py) + - [bucket_sort](algorithms/sort/bucket_sort.py) + - [cocktail_shaker_sort](algorithms/sort/cocktail_shaker_sort.py) + - [comb_sort](algorithms/sort/comb_sort.py) + - [counting_sort](algorithms/sort/counting_sort.py) + - [cycle_sort](algorithms/sort/cycle_sort.py) + - [exchange_sort](algorithms/sort/exchange_sort.py) + - [gnome_sort](algorithms/sort/gnome_sort.py) + - [heap_sort](algorithms/sort/heap_sort.py) + - [insertion_sort](algorithms/sort/insertion_sort.py) + - [meeting_rooms](algorithms/sort/meeting_rooms.py) + - [merge_sort](algorithms/sort/merge_sort.py) + - [pancake_sort](algorithms/sort/pancake_sort.py) + - [pigeonhole_sort](algorithms/sort/pigeonhole_sort.py) + - [quick_sort](algorithms/sort/quick_sort.py) + - [radix_sort](algorithms/sort/radix_sort.py) + - [selection_sort](algorithms/sort/selection_sort.py) + - [shell_sort](algorithms/sort/shell_sort.py) + - [sort_colors](algorithms/sort/sort_colors.py) + - [stooge_sort](algorithms/sort/stooge_sort.py) + - [top_sort](algorithms/sort/top_sort.py) + - [wiggle_sort](algorithms/sort/wiggle_sort.py) +- [stack](algorithms/stack) + - [longest_abs_path](algorithms/stack/longest_abs_path.py) + - [simplify_path](algorithms/stack/simplify_path.py) + - [stack](algorithms/stack/stack.py) + - [valid_parenthesis](algorithms/stack/valid_parenthesis.py) + - [stutter](algorithms/stack/stutter.py) + - [switch_pairs](algorithms/stack/switch_pairs.py) + - [is_consecutive](algorithms/stack/is_consecutive.py) + - [remove_min](algorithms/stack/remove_min.py) + - [is_sorted](algorithms/stack/is_sorted.py) +- [streaming](algorithms/streaming) + - [1-sparse-recovery](algorithms/streaming/one_sparse_recovery.py) + - [misra-gries](algorithms/streaming/misra_gries.py) +- [strings](algorithms/strings) + - [fizzbuzz](algorithms/strings/fizzbuzz.py) + - [delete_reoccurring](algorithms/strings/delete_reoccurring.py) + - [strip_url_params](algorithms/strings/strip_url_params.py) + - [validate_coordinates](algorithms/strings/validate_coordinates.py) + - [domain_extractor](algorithms/strings/domain_extractor.py) + - [merge_string_checker](algorithms/strings/merge_string_checker.py) + - [add_binary](algorithms/strings/add_binary.py) + - [breaking_bad](algorithms/strings/breaking_bad.py) + - [decode_string](algorithms/strings/decode_string.py) + - [encode_decode](algorithms/strings/encode_decode.py) + - [group_anagrams](algorithms/strings/group_anagrams.py) + - [int_to_roman](algorithms/strings/int_to_roman.py) + - [is_palindrome](algorithms/strings/is_palindrome.py) + - [license_number](algorithms/strings/license_number.py) + - [make_sentence](algorithms/strings/make_sentence.py) + - [multiply_strings](algorithms/strings/multiply_strings.py) + - [one_edit_distance](algorithms/strings/one_edit_distance.py) + - [rabin_karp](algorithms/strings/rabin_karp.py) + - [reverse_string](algorithms/strings/reverse_string.py) + - [reverse_vowel](algorithms/strings/reverse_vowel.py) + - [reverse_words](algorithms/strings/reverse_words.py) + - [roman_to_int](algorithms/strings/roman_to_int.py) + - [word_squares](algorithms/strings/word_squares.py) + - [unique_morse](algorithms/strings/unique_morse.py) + - [judge_circle](algorithms/strings/judge_circle.py) + - [strong_password](algorithms/strings/strong_password.py) + - [caesar_cipher](algorithms/strings/caesar_cipher.py) + - [check_pangram](algorithms/strings/check_pangram.py) + - [contain_string](algorithms/strings/contain_string.py) + - [count_binary_substring](algorithms/strings/count_binary_substring.py) + - [repeat_string](algorithms/strings/repeat_string.py) + - [min_distance](algorithms/strings/min_distance.py) + - [longest_common_prefix](algorithms/strings/longest_common_prefix.py) + - [rotate](algorithms/strings/rotate.py) + - [first_unique_char](algorithms/strings/first_unique_char.py) + - [repeat_substring](algorithms/strings/repeat_substring.py) + - [atbash_cipher](algorithms/strings/atbash_cipher.py) + - [longest_palindromic_substring](algorithms/strings/longest_palindromic_substring.py) + - [knuth_morris_pratt](algorithms/strings/knuth_morris_pratt.py) + - [panagram](algorithms/strings/panagram.py) +- [tree](algorithms/tree) + - [bst](algorithms/tree/bst) + - [array_to_bst](algorithms/tree/bst/array_to_bst.py) + - [bst_closest_value](algorithms/tree/bst/bst_closest_value.py) + - [BSTIterator](algorithms/tree/bst/BSTIterator.py) + - [delete_node](algorithms/tree/bst/delete_node.py) + - [is_bst](algorithms/tree/bst/is_bst.py) + - [kth_smallest](algorithms/tree/bst/kth_smallest.py) + - [lowest_common_ancestor](algorithms/tree/bst/lowest_common_ancestor.py) + - [predecessor](algorithms/tree/bst/predecessor.py) + - [serialize_deserialize](algorithms/tree/bst/serialize_deserialize.py) + - [successor](algorithms/tree/bst/successor.py) + - [unique_bst](algorithms/tree/bst/unique_bst.py) + - [depth_sum](algorithms/tree/bst/depth_sum.py) + - [count_left_node](algorithms/tree/bst/count_left_node.py) + - [num_empty](algorithms/tree/bst/num_empty.py) + - [height](algorithms/tree/bst/height.py) + - [fenwick_tree](algorithms/tree/fenwick_tree/fenwick_tree.py) + - [red_black_tree](algorithms/tree/red_black_tree) + - [red_black_tree](algorithms/tree/red_black_tree/red_black_tree.py) + - [segment_tree](algorithms/tree/segment_tree) + - [segment_tree](algorithms/tree/segment_tree/segment_tree.py) + - [iterative_segment_tree](algorithms/tree/segment_tree/iterative_segment_tree.py) + - [traversal](algorithms/tree/traversal) + - [inorder](algorithms/tree/traversal/inorder.py) + - [level_order](algorithms/tree/traversal/level_order.py) + - [postorder](algorithms/tree/traversal/postorder.py) + - [preorder](algorithms/tree/traversal/preorder.py) + - [zigzag](algorithms/tree/traversal/zigzag.py) + - [trie](algorithms/tree/trie) + - [add_and_search](algorithms/tree/trie/add_and_search.py) + - [trie](algorithms/tree/trie/trie.py) + - [b_tree](algorithms/tree/b_tree.py) + - [binary_tree_paths](algorithms/tree/binary_tree_paths.py) + - [bin_tree_to_list](algorithms/tree/bin_tree_to_list.py) + - [construct_tree_preorder_postorder](algorithms/tree/construct_tree_postorder_preorder.py) + - [deepest_left](algorithms/tree/deepest_left.py) + - [invert_tree](algorithms/tree/invert_tree.py) + - [is_balanced](algorithms/tree/is_balanced.py) + - [is_subtree](algorithms/tree/is_subtree.py) + - [is_symmetric](algorithms/tree/is_symmetric.py) + - [longest_consecutive](algorithms/tree/longest_consecutive.py) + - [lowest_common_ancestor](algorithms/tree/lowest_common_ancestor.py) + - [max_height](algorithms/tree/max_height.py) + - [max_path_sum](algorithms/tree/max_path_sum.py) + - [min_height](algorithms/tree/min_height.py) + - [path_sum](algorithms/tree/path_sum.py) + - [path_sum2](algorithms/tree/path_sum2.py) + - [pretty_print](algorithms/tree/pretty_print.py) + - [same_tree](algorithms/tree/same_tree.py) + - [tree](algorithms/tree/tree.py) +- [unix](algorithms/unix) + - [path](algorithms/unix/path/) + - [join_with_slash](algorithms/unix/path/join_with_slash.py) + - [full_path](algorithms/unix/path/full_path.py) + - [split](algorithms/unix/path/split.py) + - [simplify_path](algorithms/unix/path/simplify_path.py) +- [unionfind](algorithms/unionfind) + - [count_islands](algorithms/unionfind/count_islands.py) + + +## Contributors +Thanks to [all the contributors](https://github.com/keon/algorithms/graphs/contributors) +who helped in building the repo. diff --git a/algorithms/__init__.py b/algorithms/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/arrays/__init__.py b/algorithms/arrays/__init__.py new file mode 100644 index 000000000..2632ca1c7 --- /dev/null +++ b/algorithms/arrays/__init__.py @@ -0,0 +1,19 @@ +from .delete_nth import * +from .flatten import * +from .garage import * +from .josephus import * +from .longest_non_repeat import * +from .max_ones_index import * +from .merge_intervals import * +from .missing_ranges import * +from .move_zeros import * +from .plus_one import * +from .rotate import * +from .summarize_ranges import * +from .three_sum import * +from .trimmean import * +from .top_1 import * +from .two_sum import * +from .limit import * +from .n_sum import * +from .remove_duplicates import * \ No newline at end of file diff --git a/algorithms/arrays/delete_nth.py b/algorithms/arrays/delete_nth.py new file mode 100644 index 000000000..8d768a4ed --- /dev/null +++ b/algorithms/arrays/delete_nth.py @@ -0,0 +1,32 @@ +""" +Given a list lst and a number N, create a new list +that contains each number of the list at most N times without reordering. + +For example if N = 2, and the input is [1,2,3,1,2,1,2,3], you take [1,2,3,1,2], +drop the next [1,2] since this would lead to 1 and 2 being in the result 3 times, and then take 3, +which leads to [1,2,3,1,2,3] +""" +import collections + + +# Time complexity O(n^2) +def delete_nth_naive(array, n): + ans = [] + for num in array: + if ans.count(num) < n: + ans.append(num) + return ans + + +# Time Complexity O(n), using hash tables. +def delete_nth(array, n): + result = [] + counts = collections.defaultdict(int) # keep track of occurrences + + for i in array: + + if counts[i] < n: + result.append(i) + counts[i] += 1 + + return result diff --git a/algorithms/arrays/flatten.py b/algorithms/arrays/flatten.py new file mode 100644 index 000000000..52f4ec56d --- /dev/null +++ b/algorithms/arrays/flatten.py @@ -0,0 +1,31 @@ +""" +Implement Flatten Arrays. +Given an array that may contain nested arrays, +produce a single resultant array. +""" +from collections.abc import Iterable + + +# return list +def flatten(input_arr, output_arr=None): + if output_arr is None: + output_arr = [] + for ele in input_arr: + if not isinstance(ele, str) and isinstance(ele, Iterable): + flatten(ele, output_arr) #tail-recursion + else: + output_arr.append(ele) #produce the result + return output_arr + + +# returns iterator +def flatten_iter(iterable): + """ + Takes as input multi dimensional iterable and + returns generator which produces one dimensional output. + """ + for element in iterable: + if not isinstance(element, str) and isinstance(element, Iterable): + yield from flatten_iter(element) + else: + yield element diff --git a/algorithms/arrays/garage.py b/algorithms/arrays/garage.py new file mode 100644 index 000000000..474655abd --- /dev/null +++ b/algorithms/arrays/garage.py @@ -0,0 +1,68 @@ +""" +There is a parking lot with only one empty spot. Given the initial state +of the parking lot and the final state. Each step we are only allowed to +move a car +out of its place and move it into the empty spot. +The goal is to find out the least movement needed to rearrange +the parking lot from the initial state to the final state. + +Say the initial state is an array: + +[1, 2, 3, 0, 4], +where 1, 2, 3, 4 are different cars, and 0 is the empty spot. + +And the final state is + +[0, 3, 2, 1, 4]. +We can swap 1 with 0 in the initial array to get [0, 2, 3, 1, 4] and so on. +Each step swap with 0 only. + +Edit: +Now also prints the sequence of changes in states. +Output of this example :- + +initial: [1, 2, 3, 0, 4] +final: [0, 3, 2, 1, 4] +Steps = 4 +Sequence : +0 2 3 1 4 +2 0 3 1 4 +2 3 0 1 4 +0 3 2 1 4 +""" + + +def garage(initial, final): + + initial = initial[::] # prevent changes in original 'initial' + seq = [] # list of each step in sequence + steps = 0 + while initial != final: + zero = initial.index(0) + if zero != final.index(0): # if zero isn't where it should be, + car_to_move = final[zero] # what should be where zero is, + pos = initial.index(car_to_move) # and where is it? + initial[zero], initial[pos] = initial[pos], initial[zero] + else: + for i in range(len(initial)): + if initial[i] != final[i]: + initial[zero], initial[i] = initial[i], initial[zero] + break + seq.append(initial[::]) + steps += 1 + + return steps, seq + # e.g.: 4, [{0, 2, 3, 1, 4}, {2, 0, 3, 1, 4}, + # {2, 3, 0, 1, 4}, {0, 3, 2, 1, 4}] + +""" +thus: +1 2 3 0 4 -- zero = 3, true, car_to_move = final[3] = 1, + pos = initial.index(1) = 0, switched [0], [3] +0 2 3 1 4 -- zero = 0, f, initial[1] != final[1], switched 0,1 +2 0 3 1 4 -- zero = 1, t, car_to_move = final[1] = 3, + pos = initial.index(3) = 2, switched [1], [2] +2 3 0 1 4 -- zero = 2, t, car_to_move = final[2] = 2, + pos = initial.index(2) = 0, switched [0], [2] +0 3 2 1 4 -- initial == final +""" \ No newline at end of file diff --git a/algorithms/arrays/josephus.py b/algorithms/arrays/josephus.py new file mode 100644 index 000000000..7805a388d --- /dev/null +++ b/algorithms/arrays/josephus.py @@ -0,0 +1,19 @@ +""" +There are people sitting in a circular fashion, +print every third member while removing them, +the next counter starts immediately after the member is removed. +Print till all the members are exhausted. + +For example: +Input: consider 123456789 members sitting in a circular fashion, +Output: 369485271 +""" + +def josephus(int_list, skip): + skip = skip - 1 # list starts with 0 index + idx = 0 + len_list = (len(int_list)) + while len_list > 0: + idx = (skip + idx) % len_list # hash index to every 3rd + yield int_list.pop(idx) + len_list -= 1 diff --git a/algorithms/arrays/limit.py b/algorithms/arrays/limit.py new file mode 100644 index 000000000..57f6561f8 --- /dev/null +++ b/algorithms/arrays/limit.py @@ -0,0 +1,25 @@ +""" +Sometimes you need to limit array result to use. Such as you only need the + value over 10 or, you need value under than 100. By use this algorithms, you + can limit your array to specific value + +If array, Min, Max value was given, it returns array that contains values of + given array which was larger than Min, and lower than Max. You need to give + 'unlimit' to use only Min or Max. + +ex) limit([1,2,3,4,5], None, 3) = [1,2,3] + +Complexity = O(n) +""" + +# tl:dr -- array slicing by value +def limit(arr, min_lim=None, max_lim=None): + if len(arr) == 0: + return arr + + if min_lim is None: + min_lim = min(arr) + if max_lim is None: + max_lim = max(arr) + + return list(filter(lambda x: (min_lim <= x <= max_lim), arr)) diff --git a/algorithms/arrays/longest_non_repeat.py b/algorithms/arrays/longest_non_repeat.py new file mode 100644 index 000000000..b25a952ca --- /dev/null +++ b/algorithms/arrays/longest_non_repeat.py @@ -0,0 +1,109 @@ +""" +Given a string, find the length of the longest substring +without repeating characters. + +Examples: +Given "abcabcbb", the answer is "abc", which the length is 3. +Given "bbbbb", the answer is "b", with the length of 1. +Given "pwwkew", the answer is "wke", with the length of 3. +Note that the answer must be a substring, +"pwke" is a subsequence and not a substring. +""" + + +def longest_non_repeat_v1(string): + """ + Find the length of the longest substring + without repeating characters. + """ + if string is None: + return 0 + dict = {} + max_length = 0 + j = 0 + for i in range(len(string)): + if string[i] in dict: + j = max(dict[string[i]], j) + dict[string[i]] = i + 1 + max_length = max(max_length, i - j + 1) + return max_length + +def longest_non_repeat_v2(string): + """ + Find the length of the longest substring + without repeating characters. + Uses alternative algorithm. + """ + if string is None: + return 0 + start, max_len = 0, 0 + used_char = {} + for index, char in enumerate(string): + if char in used_char and start <= used_char[char]: + start = used_char[char] + 1 + else: + max_len = max(max_len, index - start + 1) + used_char[char] = index + return max_len + +# get functions of above, returning the max_len and substring +def get_longest_non_repeat_v1(string): + """ + Find the length of the longest substring + without repeating characters. + Return max_len and the substring as a tuple + """ + if string is None: + return 0, '' + sub_string = '' + dict = {} + max_length = 0 + j = 0 + for i in range(len(string)): + if string[i] in dict: + j = max(dict[string[i]], j) + dict[string[i]] = i + 1 + if i - j + 1 > max_length: + max_length = i - j + 1 + sub_string = string[j: i + 1] + return max_length, sub_string + +def get_longest_non_repeat_v2(string): + """ + Find the length of the longest substring + without repeating characters. + Uses alternative algorithm. + Return max_len and the substring as a tuple + """ + if string is None: + return 0, '' + sub_string = '' + start, max_len = 0, 0 + used_char = {} + for index, char in enumerate(string): + if char in used_char and start <= used_char[char]: + start = used_char[char] + 1 + else: + if index - start + 1 > max_len: + max_len = index - start + 1 + sub_string = string[start: index + 1] + used_char[char] = index + return max_len, sub_string + +def get_longest_non_repeat_v3(string): + """ + Find the length of the longest substring + without repeating characters. + Uses window sliding approach. + Return max_len and the substring as a tuple + """ + longest_substring = '' + seen = set() + start_idx = 0 + for i in range(len(string)): + while string[i] in seen: + seen.remove(string[start_idx]) + start_idx += 1 + seen.add(string[i]) + longest_substring = max(longest_substring, string[start_idx: i+1], key=len) + return len(longest_substring), longest_substring diff --git a/algorithms/arrays/max_ones_index.py b/algorithms/arrays/max_ones_index.py new file mode 100644 index 000000000..40abdf505 --- /dev/null +++ b/algorithms/arrays/max_ones_index.py @@ -0,0 +1,43 @@ +""" +Find the index of 0 to be replaced with 1 to get +longest continuous sequence +of 1s in a binary array. +Returns index of 0 to be +replaced with 1 to get longest +continuous sequence of 1s. +If there is no 0 in array, then +it returns -1. + +e.g. +let input array = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1] +If we replace 0 at index 3 with 1, we get the longest continuous +sequence of 1s in the array. +So the function return => 3 +""" + + +def max_ones_index(arr): + + n = len(arr) + max_count = 0 + max_index = 0 + prev_zero = -1 + prev_prev_zero = -1 + + for curr in range(n): + + # If current element is 0, + # then calculate the difference + # between curr and prev_prev_zero + if arr[curr] == 0: + if curr - prev_prev_zero > max_count: + max_count = curr - prev_prev_zero + max_index = prev_zero + + prev_prev_zero = prev_zero + prev_zero = curr + + if n - prev_prev_zero > max_count: + max_index = prev_zero + + return max_index diff --git a/algorithms/arrays/merge_intervals.py b/algorithms/arrays/merge_intervals.py new file mode 100644 index 000000000..fae4162f6 --- /dev/null +++ b/algorithms/arrays/merge_intervals.py @@ -0,0 +1,77 @@ +""" +In mathematics, a (real) interval is a set of real + numbers with the property that any number that lies + between two numbers in the set is also included in the set. +""" + + +class Interval: + """ + A set of real numbers with methods to determine if other + numbers are included in the set. + Includes related methods to merge and print interval sets. + """ + def __init__(self, start=0, end=0): + self.start = start + self.end = end + + def __repr__(self): + return "Interval ({}, {})".format(self.start, self.end) + + def __iter__(self): + return iter(range(self.start, self.end)) + + def __getitem__(self, index): + if index < 0: + return self.end + index + return self.start + index + + def __len__(self): + return self.end - self.start + + def __contains__(self, item): + if self.start >= item >= self.end: + return True + return False + + def __eq__(self, other): + if self.start == other.start and self.end == other.end: + return True + return False + + def as_list(self): + """ Return interval as list. """ + return list(self) + + @staticmethod + def merge(intervals): + """ Merge two intervals into one. """ + out = [] + for i in sorted(intervals, key=lambda i: i.start): + if out and i.start <= out[-1].end: + out[-1].end = max(out[-1].end, i.end) + else: + out += i, + return out + + @staticmethod + def print_intervals(intervals): + """ Print out the intervals. """ + res = [] + for i in intervals: + res.append(repr(i)) + print("".join(res)) + + +def merge_intervals(intervals): + """ Merge intervals in the form of a list. """ + if intervals is None: + return None + intervals.sort(key=lambda i: i[0]) + out = [intervals.pop(0)] + for i in intervals: + if out[-1][-1] >= i[0]: + out[-1][-1] = max(out[-1][-1], i[-1]) + else: + out.append(i) + return out diff --git a/algorithms/arrays/missing_ranges.py b/algorithms/arrays/missing_ranges.py new file mode 100644 index 000000000..7f34bcd13 --- /dev/null +++ b/algorithms/arrays/missing_ranges.py @@ -0,0 +1,22 @@ +""" +Find missing ranges between low and high in the given array. +Ex) [3, 5] lo=1 hi=10 => answer: [(1, 2), (4, 4), (6, 10)] +""" + +def missing_ranges(arr, lo, hi): + + res = [] + start = lo + + for n in arr: + + if n == start: + start += 1 + elif n > start: + res.append((start, n-1)) + start = n + 1 + + if start <= hi: # after done iterating thru array, + res.append((start, hi)) # append remainder to list + + return res diff --git a/algorithms/arrays/move_zeros.py b/algorithms/arrays/move_zeros.py new file mode 100644 index 000000000..606afbfd5 --- /dev/null +++ b/algorithms/arrays/move_zeros.py @@ -0,0 +1,26 @@ +""" +Write an algorithm that takes an array and moves all of the zeros to the end, +preserving the order of the other elements. + move_zeros([false, 1, 0, 1, 2, 0, 1, 3, "a"]) + returns => [false, 1, 1, 2, 1, 3, "a", 0, 0] + +The time complexity of the below algorithm is O(n). +""" + + +# False == 0 is True +def move_zeros(array): + result = [] + zeros = 0 + + for i in array: + if i == 0 and type(i) != bool: # not using `not i` to avoid `False`, `[]`, etc. + zeros += 1 + else: + result.append(i) + + result.extend([0] * zeros) + return result + + +print(move_zeros([False, 1, 0, 1, 2, 0, 1, 3, "a"])) \ No newline at end of file diff --git a/algorithms/arrays/n_sum.py b/algorithms/arrays/n_sum.py new file mode 100644 index 000000000..da7ee3666 --- /dev/null +++ b/algorithms/arrays/n_sum.py @@ -0,0 +1,140 @@ +""" +Given an array of n integers, are there elements a, b, .. , n in nums +such that a + b + .. + n = target? + +Find all unique n-tuplets in the array which gives the sum of target. + +Example: + basic: + Given: + n = 4 + nums = [1, 0, -1, 0, -2, 2] + target = 0, + return [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]] + + advanced: + Given: + n = 2 + nums = [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], [-9, 5]] + target = -5 + def sum(a, b): + return [a[0] + b[1], a[1] + b[0]] + def compare(num, target): + if num[0] < target: + return -1 + elif if num[0] > target: + return 1 + else: + return 0 + return [[-9, 5], [8, 4]] +(TL:DR) because -9 + 4 = -5 +""" + + +def n_sum(n, nums, target, **kv): + """ + n: int + nums: list[object] + target: object + sum_closure: function, optional + Given two elements of nums, return sum of both. + compare_closure: function, optional + Given one object of nums and target, return -1, 1, or 0. + same_closure: function, optional + Given two object of nums, return bool. + return: list[list[object]] + + Note: + 1. type of sum_closure's return should be same + as type of compare_closure's first param + """ + + def sum_closure_default(a, b): + return a + b + + def compare_closure_default(num, target): + """ above, below, or right on? """ + if num < target: + return -1 + elif num > target: + return 1 + else: + return 0 + + def same_closure_default(a, b): + return a == b + + def n_sum(n, nums, target): + if n == 2: # want answers with only 2 terms? easy! + results = two_sum(nums, target) + else: + results = [] + prev_num = None + for index, num in enumerate(nums): + if prev_num is not None and \ + same_closure(prev_num, num): + continue + + prev_num = num + n_minus1_results = ( + n_sum( # recursive call + n - 1, # a + nums[index + 1:], # b + target - num # c + ) # x = n_sum( a, b, c ) + ) # n_minus1_results = x + + n_minus1_results = ( + append_elem_to_each_list(num, n_minus1_results) + ) + results += n_minus1_results + return union(results) + + def two_sum(nums, target): + nums.sort() + lt = 0 + rt = len(nums) - 1 + results = [] + while lt < rt: + sum_ = sum_closure(nums[lt], nums[rt]) + flag = compare_closure(sum_, target) + if flag == -1: + lt += 1 + elif flag == 1: + rt -= 1 + else: + results.append(sorted([nums[lt], nums[rt]])) + lt += 1 + rt -= 1 + while (lt < len(nums) and + same_closure(nums[lt - 1], nums[lt])): + lt += 1 + while (0 <= rt and + same_closure(nums[rt], nums[rt + 1])): + rt -= 1 + return results + + def append_elem_to_each_list(elem, container): + results = [] + for elems in container: + elems.append(elem) + results.append(sorted(elems)) + return results + + def union(duplicate_results): + results = [] + + if len(duplicate_results) != 0: + duplicate_results.sort() + results.append(duplicate_results[0]) + for result in duplicate_results[1:]: + if results[-1] != result: + results.append(result) + + return results + + sum_closure = kv.get('sum_closure', sum_closure_default) + same_closure = kv.get('same_closure', same_closure_default) + compare_closure = kv.get('compare_closure', compare_closure_default) + nums.sort() + return n_sum(n, nums, target) diff --git a/algorithms/arrays/plus_one.py b/algorithms/arrays/plus_one.py new file mode 100644 index 000000000..473b6c7d0 --- /dev/null +++ b/algorithms/arrays/plus_one.py @@ -0,0 +1,48 @@ +""" +Given a non-negative number represented as an array of digits, +adding one to each numeral. + +The digits are stored big-endian, such that the most significant +digit is at the head of the list. +""" + + +def plus_one_v1(digits): + """ + :type digits: List[int] + :rtype: List[int] + """ + digits[-1] = digits[-1] + 1 + res = [] + ten = 0 + i = len(digits)-1 + while i >= 0 or ten == 1: + summ = 0 + if i >= 0: + summ += digits[i] + if ten: + summ += 1 + res.append(summ % 10) + ten = summ // 10 + i -= 1 + return res[::-1] + + +def plus_one_v2(digits): + n = len(digits) + for i in range(n-1, -1, -1): + if digits[i] < 9: + digits[i] += 1 + return digits + digits[i] = 0 + digits.insert(0, 1) + return digits + + +def plus_one_v3(num_arr): + + for idx in reversed(list(enumerate(num_arr))): + num_arr[idx[0]] = (num_arr[idx[0]] + 1) % 10 + if num_arr[idx[0]]: + return num_arr + return [1] + num_arr diff --git a/algorithms/arrays/remove_duplicates.py b/algorithms/arrays/remove_duplicates.py new file mode 100644 index 000000000..1c0bc0a06 --- /dev/null +++ b/algorithms/arrays/remove_duplicates.py @@ -0,0 +1,18 @@ +""" +This algorithm removes any duplicates from an array and returns a new array with those duplicates +removed. + +For example: + +Input: [1, 1 ,1 ,2 ,2 ,3 ,4 ,4 ,"hey", "hey", "hello", True, True] +Output: [1, 2, 3, 4, 'hey', 'hello'] +""" + +def remove_duplicates(array): + new_array = [] + + for item in array: + if item not in new_array: + new_array.append(item) + + return new_array \ No newline at end of file diff --git a/algorithms/arrays/rotate.py b/algorithms/arrays/rotate.py new file mode 100644 index 000000000..974b511f3 --- /dev/null +++ b/algorithms/arrays/rotate.py @@ -0,0 +1,61 @@ +""" +Rotate an array of n elements to the right by k steps. + +For example, with n = 7 and k = 3, +the array [1,2,3,4,5,6,7] is rotated to [5,6,7,1,2,3,4]. + +Note: +Try to come up as many solutions as you can, +there are at least 3 different ways to solve this problem. +""" + + +def rotate_v1(array, k): + """ + Rotate the entire array 'k' times + T(n)- O(nk) + + :type array: List[int] + :type k: int + :rtype: void Do not return anything, modify array in-place instead. + """ + array = array[:] + n = len(array) + for i in range(k): # unused variable is not a problem + temp = array[n - 1] + for j in range(n-1, 0, -1): + array[j] = array[j - 1] + array[0] = temp + return array + + +def rotate_v2(array, k): + """ + Reverse segments of the array, followed by the entire array + T(n)- O(n) + :type array: List[int] + :type k: int + :rtype: void Do not return anything, modify nums in-place instead. + """ + array = array[:] + + def reverse(arr, a, b): + while a < b: + arr[a], arr[b] = arr[b], arr[a] + a += 1 + b -= 1 + + n = len(array) + k = k % n + reverse(array, 0, n - k - 1) + reverse(array, n - k, n - 1) + reverse(array, 0, n - 1) + return array + + +def rotate_v3(array, k): + if array is None: + return None + length = len(array) + k = k % length + return array[length - k:] + array[:length - k] diff --git a/algorithms/arrays/summarize_ranges.py b/algorithms/arrays/summarize_ranges.py new file mode 100644 index 000000000..58de7421a --- /dev/null +++ b/algorithms/arrays/summarize_ranges.py @@ -0,0 +1,25 @@ +""" +Given a sorted integer array without duplicates, +return the summary of its ranges. + +For example, given [0, 1, 2, 4, 5, 7], return [(0, 2), (4, 5), (7, 7)]. +""" + + +from typing import List + +def summarize_ranges(array: List[int]) -> List[str]: + res = [] + if len(array) == 1: + return [str(array[0])] + it = iter(array) + start = end = next(it) + for num in it: + if num - end == 1: + end = num + else: + res.append((start, end) if start != end else (start,)) + start = end = num + res.append((start, end) if start != end else (start,)) + return [f"{r[0]}-{r[1]}" if len(r) > 1 else str(r[0]) for r in res] + diff --git a/algorithms/arrays/three_sum.py b/algorithms/arrays/three_sum.py new file mode 100644 index 000000000..ccf3d2669 --- /dev/null +++ b/algorithms/arrays/three_sum.py @@ -0,0 +1,48 @@ +""" +Given an array S of n integers, are there three distinct elements +a, b, c in S such that a + b + c = 0? +Find all unique triplets in the array which gives the sum of zero. + +Note: The solution set must not contain duplicate triplets. + +For example, given array S = [-1, 0, 1, 2, -1, -4], + +A solution set is: +{ + (-1, 0, 1), + (-1, -1, 2) +} +""" + + +def three_sum(array): + """ + :param array: List[int] + :return: Set[ Tuple[int, int, int] ] + """ + res = set() + array.sort() + for i in range(len(array) - 2): + if i > 0 and array[i] == array[i - 1]: + continue + l, r = i + 1, len(array) - 1 + while l < r: + s = array[i] + array[l] + array[r] + if s > 0: + r -= 1 + elif s < 0: + l += 1 + else: + # found three sum + res.add((array[i], array[l], array[r])) + + # remove duplicates + while l < r and array[l] == array[l + 1]: + l += 1 + + while l < r and array[r] == array[r - 1]: + r -= 1 + + l += 1 + r -= 1 + return res diff --git a/algorithms/arrays/top_1.py b/algorithms/arrays/top_1.py new file mode 100644 index 000000000..71ac6b042 --- /dev/null +++ b/algorithms/arrays/top_1.py @@ -0,0 +1,37 @@ +""" +This algorithm receives an array and returns most_frequent_value +Also, sometimes it is possible to have multiple 'most_frequent_value's, +so this function returns a list. This result can be used to find a +representative value in an array. + +This algorithm gets an array, makes a dictionary of it, + finds the most frequent count, and makes the result list. + +For example: top_1([1, 1, 2, 2, 3, 4]) will return [1, 2] + +(TL:DR) Get mathematical Mode +Complexity: O(n) +""" +def top_1(arr): + values = {} + #reserve each value which first appears on keys + #reserve how many time each value appears by index number on values + result = [] + f_val = 0 + + for i in arr: + if i in values: + values[i] += 1 + else: + values[i] = 1 + + f_val = max(values.values()) + + for i in values.keys(): + if values[i] == f_val: + result.append(i) + else: + continue + + return result + \ No newline at end of file diff --git a/algorithms/arrays/trimmean.py b/algorithms/arrays/trimmean.py new file mode 100644 index 000000000..3d330a0e3 --- /dev/null +++ b/algorithms/arrays/trimmean.py @@ -0,0 +1,24 @@ +""" +When make reliable means, we need to neglect best and worst values. +For example, when making average score on athletes we need this option. +So, this algorithm affixes some percentage to neglect when making mean. +For example, if you suggest 20%, it will neglect the best 10% of values +and the worst 10% of values. + +This algorithm takes an array and percentage to neglect. After sorted, +if index of array is larger or smaller than desired ratio, we don't +compute it. + +Compleity: O(n) +""" +def trimmean(arr, per): + ratio = per/200 + # /100 for easy calculation by *, and /2 for easy adaption to best and worst parts. + cal_sum = 0 + # sum value to be calculated to trimmean. + arr.sort() + neg_val = int(len(arr)*ratio) + arr = arr[neg_val:len(arr)-neg_val] + for i in arr: + cal_sum += i + return cal_sum/len(arr) diff --git a/array/two_sum.py b/algorithms/arrays/two_sum.py similarity index 61% rename from array/two_sum.py rename to algorithms/arrays/two_sum.py index 29afd7919..2b6f1ed0b 100644 --- a/array/two_sum.py +++ b/algorithms/arrays/two_sum.py @@ -9,21 +9,15 @@ Given nums = [2, 7, 11, 15], target = 9, Because nums[0] + nums[1] = 2 + 7 = 9, - return [0, 1]. + return (0, 1) """ -def two_sum(nums:"List[int]", target:"int")->"List[int]": +def two_sum(array, target): dic = {} - for i, num in enumerate(nums): + for i, num in enumerate(array): if num in dic: - return [dic[num], i] + return dic[num], i else: dic[target - num] = i - - -if __name__ == "__main__": - arr = [3,2,4] - target = 6 - res = two_sum(arr, target) - print(res) + return None diff --git a/algorithms/automata/__init__.py b/algorithms/automata/__init__.py new file mode 100644 index 000000000..bef182c6f --- /dev/null +++ b/algorithms/automata/__init__.py @@ -0,0 +1 @@ +from .dfa import * diff --git a/algorithms/automata/dfa.py b/algorithms/automata/dfa.py new file mode 100644 index 000000000..34f73a4b4 --- /dev/null +++ b/algorithms/automata/dfa.py @@ -0,0 +1,17 @@ +def DFA(transitions, start, final, string): + + num = len(string) + num_final = len(final) + cur = start + + for i in range(num): + + if transitions[cur][string[i]] is None: + return False + else: + cur = transitions[cur][string[i]] + + for i in range(num_final): + if cur == final[i]: + return True + return False diff --git a/algorithms/backtrack/__init__.py b/algorithms/backtrack/__init__.py new file mode 100644 index 000000000..f8cdab753 --- /dev/null +++ b/algorithms/backtrack/__init__.py @@ -0,0 +1,15 @@ +from .add_operators import * +from .anagram import * +from .array_sum_combinations import * +from .combination_sum import * +from .factor_combinations import * +from .find_words import * +from .generate_abbreviations import * +from .generate_parenthesis import * +from .letter_combination import * +from .palindrome_partitioning import * +from .pattern_match import * +from .permute_unique import * +from .permute import * +from .subsets_unique import * +from .subsets import * diff --git a/algorithms/backtrack/add_operators.py b/algorithms/backtrack/add_operators.py new file mode 100644 index 000000000..7a847396c --- /dev/null +++ b/algorithms/backtrack/add_operators.py @@ -0,0 +1,45 @@ +""" +Given a string that contains only digits 0-9 and a target value, +return all possibilities to add binary operators (not unary) +, -, or * +between the digits so they prevuate to the target value. + +Examples: +"123", 6 -> ["1+2+3", "1*2*3"] +"232", 8 -> ["2*3+2", "2+3*2"] +"105", 5 -> ["1*0+5","10-5"] +"00", 0 -> ["0+0", "0-0", "0*0"] +"3456237490", 9191 -> [] +""" + + +def add_operators(num, target): + """ + :type num: str + :type target: int + :rtype: List[str] + """ + + def dfs(res, path, num, target, pos, prev, multed): + if pos == len(num): + if target == prev: + res.append(path) + return + for i in range(pos, len(num)): + if i != pos and num[pos] == '0': # all digits have to be used + break + cur = int(num[pos:i+1]) + if pos == 0: + dfs(res, path + str(cur), num, target, i+1, cur, cur) + else: + dfs(res, path + "+" + str(cur), num, target, + i+1, prev + cur, cur) + dfs(res, path + "-" + str(cur), num, target, + i+1, prev - cur, -cur) + dfs(res, path + "*" + str(cur), num, target, + i+1, prev - multed + multed * cur, multed * cur) + + res = [] + if not num: + return res + dfs(res, "", num, target, 0, 0, 0) + return res diff --git a/algorithms/backtrack/anagram.py b/algorithms/backtrack/anagram.py new file mode 100644 index 000000000..df3f4ab57 --- /dev/null +++ b/algorithms/backtrack/anagram.py @@ -0,0 +1,22 @@ +""" +Given two strings, determine if they are equal after reordering. + +Examples: +"apple", "pleap" -> True +"apple", "cherry" -> False +""" + + +def anagram(s1, s2): + c1 = [0] * 26 + c2 = [0] * 26 + + for c in s1: + pos = ord(c)-ord('a') + c1[pos] = c1[pos] + 1 + + for c in s2: + pos = ord(c)-ord('a') + c2[pos] = c2[pos] + 1 + + return c1 == c2 diff --git a/algorithms/backtrack/array_sum_combinations.py b/algorithms/backtrack/array_sum_combinations.py new file mode 100644 index 000000000..b152e4d11 --- /dev/null +++ b/algorithms/backtrack/array_sum_combinations.py @@ -0,0 +1,84 @@ +""" +WAP to take one element from each of the array add it to the target sum. +Print all those three-element combinations. + +/* +A = [1, 2, 3, 3] +B = [2, 3, 3, 4] +C = [2, 3, 3, 4] +target = 7 +*/ + +Result: +[[1, 2, 4], [1, 3, 3], [1, 3, 3], [1, 3, 3], [1, 3, 3], [1, 4, 2], + [2, 2, 3], [2, 2, 3], [2, 3, 2], [2, 3, 2], [3, 2, 2], [3, 2, 2]] +""" +import itertools +from functools import partial + + +def array_sum_combinations(A, B, C, target): + + def over(constructed_sofar): + sum = 0 + to_stop, reached_target = False, False + for elem in constructed_sofar: + sum += elem + if sum >= target or len(constructed_sofar) >= 3: + to_stop = True + if sum == target and 3 == len(constructed_sofar): + reached_target = True + return to_stop, reached_target + + def construct_candidates(constructed_sofar): + array = A + if 1 == len(constructed_sofar): + array = B + elif 2 == len(constructed_sofar): + array = C + return array + + def backtrack(constructed_sofar=[], res=[]): + to_stop, reached_target = over(constructed_sofar) + if to_stop: + if reached_target: + res.append(constructed_sofar) + return + candidates = construct_candidates(constructed_sofar) + + for candidate in candidates: + constructed_sofar.append(candidate) + backtrack(constructed_sofar[:], res) + constructed_sofar.pop() + + res = [] + backtrack([], res) + return res + + +def unique_array_sum_combinations(A, B, C, target): + """ + 1. Sort all the arrays - a,b,c. - This improves average time complexity. + 2. If c[i] < Sum, then look for Sum - c[i] in array a and b. + When pair found, insert c[i], a[j] & b[k] into the result list. + This can be done in O(n). + 3. Keep on doing the above procedure while going through complete c array. + + Complexity: O(n(m+p)) + """ + def check_sum(n, *nums): + if sum(x for x in nums) == n: + return (True, nums) + else: + return (False, nums) + + pro = itertools.product(A, B, C) + func = partial(check_sum, target) + sums = list(itertools.starmap(func, pro)) + + res = set() + for s in sums: + if s[0] is True and s[1] not in res: + res.add(s[1]) + + return list(res) diff --git a/backtrack/combination_sum.py b/algorithms/backtrack/combination_sum.py similarity index 58% rename from backtrack/combination_sum.py rename to algorithms/backtrack/combination_sum.py index 3ac87b6e9..4d4dfb176 100644 --- a/backtrack/combination_sum.py +++ b/algorithms/backtrack/combination_sum.py @@ -15,17 +15,19 @@ ] """ -def combinationSum(self, candidates, target): + +def combination_sum(candidates, target): + + def dfs(nums, target, index, path, res): + if target < 0: + return # backtracking + if target == 0: + res.append(path) + return + for i in range(index, len(nums)): + dfs(nums, target-nums[i], i, path+[nums[i]], res) + res = [] candidates.sort() - self.dfs(candidates, target, 0, [], res) + dfs(candidates, target, 0, [], res) return res - -def dfs(self, nums, target, index, path, res): - if target < 0: - return # backtracking - if target == 0: - res.append(path) - return - for i in range(index, len(nums)): - self.dfs(nums, target-nums[i], i, path+[nums[i]], res) diff --git a/backtrack/factor_combinations.py b/algorithms/backtrack/factor_combinations.py similarity index 69% rename from backtrack/factor_combinations.py rename to algorithms/backtrack/factor_combinations.py index 787c1cf25..3240b05a8 100644 --- a/backtrack/factor_combinations.py +++ b/algorithms/backtrack/factor_combinations.py @@ -3,7 +3,8 @@ 8 = 2 x 2 x 2; = 2 x 4. -Write a function that takes an integer n and return all possible combinations of its factors. +Write a function that takes an integer n +and return all possible combinations of its factors. Note: You may assume that n is always positive. @@ -34,27 +35,29 @@ ] """ -# Iterative: -def getFactors(self, n): +# Iterative: +def get_factors(n): todo, combis = [(n, 2, [])], [] while todo: n, i, combi = todo.pop() while i * i <= n: if n % i == 0: - combis += combi + [i, n/i], - todo += (n/i, i, combi+[i]), + combis.append(combi + [i, n//i]) + todo.append((n//i, i, combi+[i])) i += 1 return combis + # Recursive: +def recursive_get_factors(n): -def getFactors(self, n): def factor(n, i, combi, combis): while i * i <= n: if n % i == 0: - combis += combi + [i, n/i], - factor(n/i, i, combi+[i], combis) + combis.append(combi + [i, n//i]), + factor(n//i, i, combi+[i], combis) i += 1 return combis + return factor(n, 2, [], []) diff --git a/algorithms/backtrack/find_words.py b/algorithms/backtrack/find_words.py new file mode 100644 index 000000000..da6b6347a --- /dev/null +++ b/algorithms/backtrack/find_words.py @@ -0,0 +1,73 @@ +''' +Given a matrix of words and a list of words to search, +return a list of words that exists in the board +This is Word Search II on LeetCode + +board = [ + ['o','a','a','n'], + ['e','t','a','e'], + ['i','h','k','r'], + ['i','f','l','v'] + ] + +words = ["oath","pea","eat","rain"] +''' + + +def find_words(board, words): + + def backtrack(board, i, j, trie, pre, used, result): + ''' + backtrack tries to build each words from + the board and return all words found + + @param: board, the passed in board of characters + @param: i, the row index + @param: j, the column index + @param: trie, a trie of the passed in words + @param: pre, a buffer of currently build string that differs + by recursion stack + @param: used, a replica of the board except in booleans + to state whether a character has been used + @param: result, the resulting set that contains all words found + + @return: list of words found + ''' + + if '#' in trie: + result.add(pre) + + if i < 0 or i >= len(board) or j < 0 or j >= len(board[0]): + return + + if not used[i][j] and board[i][j] in trie: + used[i][j] = True + backtrack(board, i+1, j, trie[board[i][j]], + pre+board[i][j], used, result) + backtrack(board, i, j+1, trie[board[i][j]], + pre+board[i][j], used, result) + backtrack(board, i-1, j, trie[board[i][j]], + pre+board[i][j], used, result) + backtrack(board, i, j-1, trie[board[i][j]], + pre+board[i][j], used, result) + used[i][j] = False + + # make a trie structure that is essentially dictionaries of dictionaries + # that map each character to a potential next character + trie = {} + for word in words: + curr_trie = trie + for char in word: + if char not in curr_trie: + curr_trie[char] = {} + curr_trie = curr_trie[char] + curr_trie['#'] = '#' + + # result is a set of found words since we do not want repeats + result = set() + used = [[False]*len(board[0]) for _ in range(len(board))] + + for i in range(len(board)): + for j in range(len(board[0])): + backtrack(board, i, j, trie, '', used, result) + return list(result) diff --git a/algorithms/backtrack/generate_abbreviations.py b/algorithms/backtrack/generate_abbreviations.py new file mode 100644 index 000000000..674df93af --- /dev/null +++ b/algorithms/backtrack/generate_abbreviations.py @@ -0,0 +1,26 @@ +""" +given input word, return the list of abbreviations. +ex) +word => ['word', 'wor1', 'wo1d', 'wo2', 'w1rd', 'w1r1', 'w2d', 'w3', '1ord', '1or1', '1o1d', '1o2', '2rd', '2r1', '3d', '4'] +""" + + +def generate_abbreviations(word): + + def backtrack(result, word, pos, count, cur): + if pos == len(word): + if count > 0: + cur += str(count) + result.append(cur) + return + + if count > 0: # add the current word + backtrack(result, word, pos+1, 0, cur+str(count)+word[pos]) + else: + backtrack(result, word, pos+1, 0, cur+word[pos]) + # skip the current word + backtrack(result, word, pos+1, count+1, cur) + + result = [] + backtrack(result, word, 0, 0, "") + return result diff --git a/algorithms/backtrack/generate_parenthesis.py b/algorithms/backtrack/generate_parenthesis.py new file mode 100644 index 000000000..073cec96a --- /dev/null +++ b/algorithms/backtrack/generate_parenthesis.py @@ -0,0 +1,43 @@ +""" +Given n pairs of parentheses, write a function to generate +all combinations of well-formed parentheses. + +For example, given n = 3, a solution set is: + +[ + "((()))", + "(()())", + "(())()", + "()(())", + "()()()" +] +""" + + +def generate_parenthesis_v1(n): + def add_pair(res, s, left, right): + if left == 0 and right == 0: + res.append(s) + return + if right > 0: + add_pair(res, s + ")", left, right - 1) + if left > 0: + add_pair(res, s + "(", left - 1, right + 1) + + res = [] + add_pair(res, "", n, 0) + return res + + +def generate_parenthesis_v2(n): + def add_pair(res, s, left, right): + if left == 0 and right == 0: + res.append(s) + if left > 0: + add_pair(res, s + "(", left - 1, right) + if right > 0 and left < right: + add_pair(res, s + ")", left, right - 1) + + res = [] + add_pair(res, "", n, n) + return res diff --git a/backtrack/letter_combination.py b/algorithms/backtrack/letter_combination.py similarity index 75% rename from backtrack/letter_combination.py rename to algorithms/backtrack/letter_combination.py index f4a4c4e0b..09f8af826 100644 --- a/backtrack/letter_combination.py +++ b/algorithms/backtrack/letter_combination.py @@ -2,12 +2,22 @@ Given a digit string, return all possible letter combinations that the number could represent. +A mapping of digit to letters (just like on the telephone buttons) is given below: +2: "abc" +3: "def" +4: "ghi" +5: "jkl" +6: "mno" +7: "pqrs" +8: "tuv" +9: "wxyz" + Input:Digit string "23" Output: ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"]. """ -def letter_combinations(digits:"str")->"List[str]": +def letter_combinations(digits): if digits == "": return [] kmaps = { @@ -28,8 +38,3 @@ def letter_combinations(digits:"str")->"List[str]": tmp.append(an + char) ans = tmp return ans - - -if __name__ == "__main__": - digit_string = "23" - print(letter_combinations(digit_string)) diff --git a/algorithms/backtrack/palindrome_partitioning.py b/algorithms/backtrack/palindrome_partitioning.py new file mode 100644 index 000000000..10f1da94d --- /dev/null +++ b/algorithms/backtrack/palindrome_partitioning.py @@ -0,0 +1,45 @@ +""" It looks like you need to be looking not for all palindromic substrings, +but rather for all the ways you can divide the input string +up into palindromic substrings. +(There's always at least one way, +since one-character substrings are always palindromes.) + +ex) +'abcbab' => [['abcba', 'b'], ['a', 'bcb', 'a', 'b'], ['a', 'b', 'c', 'bab'], ['a', 'b', 'c', 'b', 'a', 'b']] +""" + + +def palindromic_substrings(s): + if not s: + return [[]] + results = [] + for i in range(len(s), 0, -1): + sub = s[:i] + if sub == sub[::-1]: + for rest in palindromic_substrings(s[i:]): + results.append([sub] + rest) + return results + + +""" +There's two loops. +The outer loop checks each length of initial substring +(in descending length order) to see if it is a palindrome. +If so, it recurses on the rest of the string and loops over the returned +values, adding the initial substring to +each item before adding it to the results. +""" + + +def palindromic_substrings_iter(s): + """ + A slightly more Pythonic approach with a recursive generator + """ + if not s: + yield [] + return + for i in range(len(s), 0, -1): + sub = s[:i] + if sub == sub[::-1]: + for rest in palindromic_substrings_iter(s[i:]): + yield [sub] + rest diff --git a/algorithms/backtrack/pattern_match.py b/algorithms/backtrack/pattern_match.py new file mode 100644 index 000000000..03a23a4e9 --- /dev/null +++ b/algorithms/backtrack/pattern_match.py @@ -0,0 +1,42 @@ +""" +Given a pattern and a string str, +find if str follows the same pattern. + +Here follow means a full match, such that there is a bijection between +a letter in pattern and a non-empty substring in str. + +Examples: +pattern = "abab", str = "redblueredblue" should return true. +pattern = "aaaa", str = "asdasdasdasd" should return true. +pattern = "aabb", str = "xyzabcxzyabc" should return false. +Notes: +You may assume both pattern and str contains only lowercase letters. +""" + + +def pattern_match(pattern, string): + """ + :type pattern: str + :type string: str + :rtype: bool + """ + def backtrack(pattern, string, dic): + + if len(pattern) == 0 and len(string) > 0: + return False + + if len(pattern) == len(string) == 0: + return True + + for end in range(1, len(string)-len(pattern)+2): + if pattern[0] not in dic and string[:end] not in dic.values(): + dic[pattern[0]] = string[:end] + if backtrack(pattern[1:], string[end:], dic): + return True + del dic[pattern[0]] + elif pattern[0] in dic and dic[pattern[0]] == string[:end]: + if backtrack(pattern[1:], string[end:], dic): + return True + return False + + return backtrack(pattern, string, {}) diff --git a/algorithms/backtrack/permute.py b/algorithms/backtrack/permute.py new file mode 100644 index 000000000..27c7d972f --- /dev/null +++ b/algorithms/backtrack/permute.py @@ -0,0 +1,54 @@ +""" +Given a collection of distinct numbers, return all possible permutations. + +For example, +[1,2,3] have the following permutations: +[ + [1,2,3], + [1,3,2], + [2,1,3], + [2,3,1], + [3,1,2], + [3,2,1] +] +""" + + +def permute(elements): + """ + returns a list with the permuations. + """ + if len(elements) <= 1: + return [elements] + else: + tmp = [] + for perm in permute(elements[1:]): + for i in range(len(elements)): + tmp.append(perm[:i] + elements[0:1] + perm[i:]) + return tmp + + +def permute_iter(elements): + """ + iterator: returns a perumation by each call. + """ + if len(elements) <= 1: + yield elements + else: + for perm in permute_iter(elements[1:]): + for i in range(len(elements)): + yield perm[:i] + elements[0:1] + perm[i:] + + +# DFS Version +def permute_recursive(nums): + def dfs(res, nums, path): + if not nums: + res.append(path) + for i in range(len(nums)): + print(nums[:i]+nums[i+1:]) + dfs(res, nums[:i]+nums[i+1:], path+[nums[i]]) + + res = [] + dfs(res, nums, []) + return res diff --git a/algorithms/backtrack/permute_unique.py b/algorithms/backtrack/permute_unique.py new file mode 100644 index 000000000..3b82e2c46 --- /dev/null +++ b/algorithms/backtrack/permute_unique.py @@ -0,0 +1,25 @@ +""" +Given a collection of numbers that might contain duplicates, +return all possible unique permutations. + +For example, +[1,1,2] have the following unique permutations: +[ + [1,1,2], + [1,2,1], + [2,1,1] +] +""" + + +def permute_unique(nums): + perms = [[]] + for n in nums: + new_perms = [] + for l in perms: + for i in range(len(l)+1): + new_perms.append(l[:i]+[n]+l[i:]) + if i < len(l) and l[i] == n: + break # handles duplication + perms = new_perms + return perms diff --git a/algorithms/backtrack/subsets.py b/algorithms/backtrack/subsets.py new file mode 100644 index 000000000..56eef44e8 --- /dev/null +++ b/algorithms/backtrack/subsets.py @@ -0,0 +1,59 @@ +""" +Given a set of distinct integers, nums, return all possible subsets. + +Note: The solution set must not contain duplicate subsets. + +For example, +If nums = [1,2,3], a solution is: + +[ + [3], + [1], + [2], + [1,2,3], + [1,3], + [2,3], + [1,2], + [] +] +""" + + +def subsets(nums): + """ + O(2**n) + """ + def backtrack(res, nums, stack, pos): + if pos == len(nums): + res.append(list(stack)) + else: + # take nums[pos] + stack.append(nums[pos]) + backtrack(res, nums, stack, pos+1) + stack.pop() + # dont take nums[pos] + backtrack(res, nums, stack, pos+1) + + res = [] + backtrack(res, nums, [], 0) + return res + + +""" +simplified backtrack + +def backtrack(res, nums, cur, pos): + if pos >= len(nums): + res.append(cur) + else: + backtrack(res, nums, cur+[nums[pos]], pos+1) + backtrack(res, nums, cur, pos+1) +""" + + +# Iteratively +def subsets_v2(nums): + res = [[]] + for num in sorted(nums): + res += [item+[num] for item in res] + return res diff --git a/algorithms/backtrack/subsets_unique.py b/algorithms/backtrack/subsets_unique.py new file mode 100644 index 000000000..da73a25ca --- /dev/null +++ b/algorithms/backtrack/subsets_unique.py @@ -0,0 +1,37 @@ +""" +Given a collection of integers that might contain duplicates, nums, +return all possible subsets. + +Note: The solution set must not contain duplicate subsets. + +For example, +If nums = [1,2,2], a solution is: + +[ + [2], + [1], + [1,2,2], + [2,2], + [1,2], + [] +] +""" + + +def subsets_unique(nums): + + def backtrack(res, nums, stack, pos): + if pos == len(nums): + res.add(tuple(stack)) + else: + # take + stack.append(nums[pos]) + backtrack(res, nums, stack, pos+1) + stack.pop() + + # don't take + backtrack(res, nums, stack, pos+1) + + res = set() + backtrack(res, nums, [], 0) + return list(res) diff --git a/algorithms/bfs/__init__.py b/algorithms/bfs/__init__.py new file mode 100644 index 000000000..e61e7dbe3 --- /dev/null +++ b/algorithms/bfs/__init__.py @@ -0,0 +1,4 @@ +from .count_islands import * +from .maze_search import * +from .shortest_distance_from_all_buildings import * +from .word_ladder import * diff --git a/algorithms/bfs/count_islands.py b/algorithms/bfs/count_islands.py new file mode 100644 index 000000000..5c9d00637 --- /dev/null +++ b/algorithms/bfs/count_islands.py @@ -0,0 +1,65 @@ +""" +This is a bfs-version of counting-islands problem in dfs section. +Given a 2d grid map of '1's (land) and '0's (water), +count the number of islands. +An island is surrounded by water and is formed by +connecting adjacent lands horizontally or vertically. +You may assume all four edges of the grid are all surrounded by water. + +Example 1: +11110 +11010 +11000 +00000 +Answer: 1 + +Example 2: +11000 +11000 +00100 +00011 +Answer: 3 + +Example 3: +111000 +110000 +100001 +001101 +001100 +Answer: 3 + +Example 4: +110011 +001100 +000001 +111100 +Answer: 5 +""" + + +def count_islands(grid): + row = len(grid) + col = len(grid[0]) + + num_islands = 0 + visited = [[0] * col for i in range(row)] + directions = [[-1, 0], [1, 0], [0, -1], [0, 1]] + queue = [] + + for i in range(row): + for j, num in enumerate(grid[i]): + if num == 1 and visited[i][j] != 1: + visited[i][j] = 1 + queue.append((i, j)) + while queue: + x, y = queue.pop(0) + for k in range(len(directions)): + nx_x = x + directions[k][0] + nx_y = y + directions[k][1] + if nx_x >= 0 and nx_y >= 0 and nx_x < row and nx_y < col: + if visited[nx_x][nx_y] != 1 and grid[nx_x][nx_y] == 1: + queue.append((nx_x, nx_y)) + visited[nx_x][nx_y] = 1 + num_islands += 1 + + return num_islands diff --git a/algorithms/bfs/maze_search.py b/algorithms/bfs/maze_search.py new file mode 100644 index 000000000..f7410d46e --- /dev/null +++ b/algorithms/bfs/maze_search.py @@ -0,0 +1,67 @@ +from collections import deque + +''' +BFS time complexity : O(|E| + |V|) +BFS space complexity : O(|E| + |V|) + +do BFS from (0,0) of the grid and get the minimum number of steps needed to get to the lower right column + +only step on the columns whose value is 1 + +if there is no path, it returns -1 + +Ex 1) +If grid is +[[1,0,1,1,1,1], + [1,0,1,0,1,0], + [1,0,1,0,1,1], + [1,1,1,0,1,1]], +the answer is: 14 + +Ex 2) +If grid is +[[1,0,0], + [0,1,1], + [0,1,1]], +the answer is: -1 +''' + +def maze_search(maze): + BLOCKED, ALLOWED = 0, 1 + UNVISITED, VISITED = 0, 1 + + initial_x, initial_y = 0, 0 + + if maze[initial_x][initial_y] == BLOCKED: + return -1 + + directions = [(0, -1), (0, 1), (-1, 0), (1, 0)] + + height, width = len(maze), len(maze[0]) + + target_x, target_y = height - 1, width - 1 + + queue = deque([(initial_x, initial_y, 0)]) + + is_visited = [[UNVISITED for w in range(width)] for h in range(height)] + is_visited[initial_x][initial_y] = VISITED + + while queue: + x, y, steps = queue.popleft() + + if x == target_x and y == target_y: + return steps + + for dx, dy in directions: + new_x = x + dx + new_y = y + dy + + if not (0 <= new_x < height and 0 <= new_y < width): + continue + + if maze[new_x][new_y] == ALLOWED and is_visited[new_x][new_y] == UNVISITED: + queue.append((new_x, new_y, steps + 1)) + is_visited[new_x][new_y] = VISITED + + return -1 + diff --git a/bfs/shortest_distance_from_all_buildings.py b/algorithms/bfs/shortest_distance_from_all_buildings.py similarity index 94% rename from bfs/shortest_distance_from_all_buildings.py rename to algorithms/bfs/shortest_distance_from_all_buildings.py index 48c41d063..4d4249cd2 100644 --- a/bfs/shortest_distance_from_all_buildings.py +++ b/algorithms/bfs/shortest_distance_from_all_buildings.py @@ -38,6 +38,3 @@ def bfs(grid, matrix, i, j, count): matrix[k][l][0] += step+1 matrix[k][l][1] = count+1 q.append((k, l, step+1)) - -grid = [[1,0,2,0,1],[0,0,0,0,0],[0,0,1,0,0]] -print(shortest_distance(grid)) diff --git a/algorithms/bfs/word_ladder.py b/algorithms/bfs/word_ladder.py new file mode 100644 index 000000000..6767571eb --- /dev/null +++ b/algorithms/bfs/word_ladder.py @@ -0,0 +1,72 @@ +""" +Given two words (begin_word and end_word), and a dictionary's word list, +find the length of shortest transformation sequence +from beginWord to endWord, such that: + +Only one letter can be changed at a time +Each intermediate word must exist in the word list +For example, + +Given: +begin_word = "hit" +end_word = "cog" +word_list = ["hot","dot","dog","lot","log"] +As one shortest transformation is "hit" -> "hot" -> "dot" -> "dog" -> "cog", +return its length 5. + +Note: +Return -1 if there is no such transformation sequence. +All words have the same length. +All words contain only lowercase alphabetic characters. +""" + + +def ladder_length(begin_word, end_word, word_list): + """ + Bidirectional BFS!!! + :type begin_word: str + :type end_word: str + :type word_list: Set[str] + :rtype: int + """ + if len(begin_word) != len(end_word): + return -1 # not possible + + if begin_word == end_word: + return 0 + + # when only differ by 1 character + if sum(c1 != c2 for c1, c2 in zip(begin_word, end_word)) == 1: + return 1 + + begin_set = set() + end_set = set() + begin_set.add(begin_word) + end_set.add(end_word) + result = 2 + while begin_set and end_set: + + if len(begin_set) > len(end_set): + begin_set, end_set = end_set, begin_set + + next_begin_set = set() + for word in begin_set: + for ladder_word in word_range(word): + if ladder_word in end_set: + return result + if ladder_word in word_list: + next_begin_set.add(ladder_word) + word_list.remove(ladder_word) + begin_set = next_begin_set + result += 1 + # print(begin_set) + # print(result) + return -1 + + +def word_range(word): + for ind in range(len(word)): + temp = word[ind] + for c in [chr(x) for x in range(ord('a'), ord('z') + 1)]: + if c != temp: + yield word[:ind] + c + word[ind + 1:] diff --git a/algorithms/bit/__init__.py b/algorithms/bit/__init__.py new file mode 100644 index 000000000..fa31d7ed8 --- /dev/null +++ b/algorithms/bit/__init__.py @@ -0,0 +1,19 @@ +from .add_bitwise_operator import * +from .count_ones import * +from .find_missing_number import * +from .power_of_two import * +from .reverse_bits import * +from .single_number import * +from .single_number2 import * +from .single_number3 import * +from .subsets import * +from .bit_operation import * +from .swap_pair import * +from .find_difference import * +from .has_alternative_bit import * +from .insert_bit import * +from .remove_bit import * +from .count_flips_to_convert import * +from .flip_bit_longest_sequence import * +from .binary_gap import * +from .bytes_int_conversion import * \ No newline at end of file diff --git a/bit/add_without_operator.py b/algorithms/bit/add_bitwise_operator.py similarity index 55% rename from bit/add_without_operator.py rename to algorithms/bit/add_bitwise_operator.py index a87b0f0d8..d9704decb 100644 --- a/bit/add_without_operator.py +++ b/algorithms/bit/add_bitwise_operator.py @@ -5,19 +5,10 @@ Input: 2 3 Output: 5 """ +def add_bitwise_operator(x, y): - -def addWithoutOperator(x, y): - while y != 0: + while y: carry = x & y x = x ^ y y = carry << 1 - print x - - -def main(): - x, y = map(int, raw_input().split()) - addWithoutOperator(x, y) - -if __name__ == '__main__': - main() + return x diff --git a/algorithms/bit/binary_gap.py b/algorithms/bit/binary_gap.py new file mode 100644 index 000000000..eed32208e --- /dev/null +++ b/algorithms/bit/binary_gap.py @@ -0,0 +1,57 @@ +""" +Given a positive integer N, find and return the longest distance between two +consecutive 1' in the binary representation of N. +If there are not two consecutive 1's, return 0 + +For example: +Input: 22 +Output: 2 +Explanation: +22 in binary is 10110 +In the binary representation of 22, there are three ones, and two consecutive pairs of 1's. +The first consecutive pair of 1's have distance 2. +The second consecutive pair of 1's have distance 1. +The answer is the largest of these two distances, which is 2 +""" + + +# 原方法为 binary_gap，但通过实验发现算法有误，不论是什么数，输出值最多为2。 +# 改进方法为binary_gap_improved。 +# The original method is binary_gap, +# but the experimental results show that the algorithm seems to be wrong, +# regardless of the number, the output value is up to 2. +# The improved method is binary_gap_improved. +def binary_gap(N): + last = None + ans = 0 + index = 0 + while N != 0: + if N & 1: + if last is not None: + ans = max(ans, index - last) + last = index + index = index + 1 + N = N >> 1 + return ans + + +def binary_gap_improved(N): + last = None + ans = 0 + index = 0 + while N != 0: + tes = N & 1 + if tes: + if last is not None: + ans = max(ans, index - last + 1) + else: + last = index + else: + last = index + 1 + index = index + 1 + N = N >> 1 + return ans + + +print(binary_gap(111)) +print(binary_gap_improved(111)) \ No newline at end of file diff --git a/algorithms/bit/bit_operation.py b/algorithms/bit/bit_operation.py new file mode 100644 index 000000000..58f7d7559 --- /dev/null +++ b/algorithms/bit/bit_operation.py @@ -0,0 +1,37 @@ +""" +Fundamental bit operation: + get_bit(num, i): get an exact bit at specific index + set_bit(num, i): set a bit at specific index + clear_bit(num, i): clear a bit at specific index + update_bit(num, i, bit): update a bit at specific index +""" + +""" +This function shifts 1 over by i bits, creating a value being like 0001000. By +performing an AND with num, we clear all bits other than the bit at bit i. +Finally we compare that to 0 +""" +def get_bit(num, i): + return (num & (1 << i)) != 0 + +""" +This function shifts 1 over by i bits, creating a value being like 0001000. By +performing an OR with num, only value at bit i will change. +""" +def set_bit(num, i): + return num | (1 << i) + +""" +This method operates in almost the reverse of set_bit +""" +def clear_bit(num, i): + mask = ~(1 << i) + return num & mask + +""" +To set the ith bit to value, we first clear the bit at position i by using a +mask. Then, we shift the intended value. Finally we OR these two numbers +""" +def update_bit(num, i, bit): + mask = ~(1 << i) + return (num & mask) | (bit << i) diff --git a/bit/bytes_int_conversion.py b/algorithms/bit/bytes_int_conversion.py similarity index 100% rename from bit/bytes_int_conversion.py rename to algorithms/bit/bytes_int_conversion.py diff --git a/algorithms/bit/count_flips_to_convert.py b/algorithms/bit/count_flips_to_convert.py new file mode 100644 index 000000000..375e68f21 --- /dev/null +++ b/algorithms/bit/count_flips_to_convert.py @@ -0,0 +1,19 @@ +""" +Write a function to determine the minimal number of bits you would need to +flip to convert integer A to integer B. +For example: +Input: 29 (or: 11101), 15 (or: 01111) +Output: 2 +""" + + +def count_flips_to_convert(a, b): + + diff = a ^ b + + # count number of ones in diff + count = 0 + while diff: + diff &= (diff - 1) + count += 1 + return count diff --git a/algorithms/bit/count_ones.py b/algorithms/bit/count_ones.py new file mode 100644 index 000000000..ac718f336 --- /dev/null +++ b/algorithms/bit/count_ones.py @@ -0,0 +1,32 @@ +""" +Write a function that takes an unsigned integer and +returns the number of '1' bits it has +(also known as the Hamming weight). + +For example, the 32-bit integer '11' has binary +representation 00000000000000000000000000001011, +so the function should return 3. + +T(n)- O(k) : k is the number of 1s present in binary representation. +NOTE: this complexity is better than O(log n). +e.g. for n = 00010100000000000000000000000000 +only 2 iterations are required. + +Number of loops is +equal to the number of 1s in the binary representation.""" +def count_ones_recur(n): + """Using Brian Kernighan's Algorithm. (Recursive Approach)""" + + if not n: + return 0 + return 1 + count_ones_recur(n & (n-1)) + + +def count_ones_iter(n): + """Using Brian Kernighan's Algorithm. (Iterative Approach)""" + + count = 0 + while n: + n &= (n-1) + count += 1 + return count diff --git a/algorithms/bit/find_difference.py b/algorithms/bit/find_difference.py new file mode 100644 index 000000000..67f2f0608 --- /dev/null +++ b/algorithms/bit/find_difference.py @@ -0,0 +1,28 @@ +""" +Given two strings s and t which consist of only lowercase letters. +String t is generated by random shuffling string s and then add one more letter +at a random position. Find the letter that was added in t. + +For example: +Input: +s = "abcd" +t = "abecd" +Output: 'e' + +Explanation: +'e' is the letter that was added. +""" + +""" +We use the characteristic equation of XOR. +A xor B xor C = A xor C xor B +If A == C, then A xor C = 0 +and then, B xor 0 = B +""" +def find_difference(s, t): + ret = 0 + for ch in s + t: + # ord(ch) return an integer representing the Unicode code point of that character + ret = ret ^ ord(ch) + # chr(i) Return the string representing a character whose Unicode code point is the integer i + return chr(ret) diff --git a/bit/find_missing_number.py b/algorithms/bit/find_missing_number.py similarity index 54% rename from bit/find_missing_number.py rename to algorithms/bit/find_missing_number.py index 115ce4855..2e47df4d1 100644 --- a/bit/find_missing_number.py +++ b/algorithms/bit/find_missing_number.py @@ -1,14 +1,14 @@ -def find_missing_number(nums): - """Returns the missing number from a sequence of unique integers +""" + Returns the missing number from a sequence of unique integers in range [0..n] in O(n) time and space. The difference between consecutive integers cannot be more than 1. If the sequence is already complete, the next integer in the sequence will be returned. - >>> find_missing_number(i for i in range(0, 10000) if i != 1234) - 1234 - >>> find_missing_number([4, 1, 3, 0, 6, 5, 2]) - 7 - """ + For example: + Input: nums = [4, 1, 3, 0, 6, 5, 2] + Output: 7 +""" +def find_missing_number(nums): missing = 0 for i, num in enumerate(nums): @@ -16,3 +16,12 @@ def find_missing_number(nums): missing ^= i + 1 return missing + + +def find_missing_number2(nums): + + num_sum = sum(nums) + n = len(nums) + total_sum = n*(n+1) // 2 + missing = total_sum - num_sum + return missing diff --git a/algorithms/bit/flip_bit_longest_sequence.py b/algorithms/bit/flip_bit_longest_sequence.py new file mode 100644 index 000000000..a952edb3e --- /dev/null +++ b/algorithms/bit/flip_bit_longest_sequence.py @@ -0,0 +1,30 @@ +""" +You have an integer and you can flip exactly one bit from a 0 to 1. +Write code to find the length of the longest sequence of 1s you could create. +For example: +Input: 1775 ( or: 11011101111) +Output: 8 +""" + + +def flip_bit_longest_seq(num): + + curr_len = 0 + prev_len = 0 + max_len = 0 + + while num: + if num & 1 == 1: # last digit is 1 + curr_len += 1 + + elif num & 1 == 0: # last digit is 0 + if num & 2 == 0: # second last digit is 0 + prev_len = 0 + else: + prev_len = curr_len + curr_len = 0 + + max_len = max(max_len, prev_len + curr_len) + num = num >> 1 # right shift num + + return max_len + 1 diff --git a/algorithms/bit/has_alternative_bit.py b/algorithms/bit/has_alternative_bit.py new file mode 100644 index 000000000..ade2f56a6 --- /dev/null +++ b/algorithms/bit/has_alternative_bit.py @@ -0,0 +1,38 @@ +""" +Given a positive integer, check whether it has alternating bits: namely, +if two adjacent bits will always have different values. + +For example: +Input: 5 +Output: True because the binary representation of 5 is: 101. + +Input: 7 +Output: False because the binary representation of 7 is: 111. + +Input: 11 +Output: False because the binary representation of 11 is: 1011. + +Input: 10 +Output: True because The binary representation of 10 is: 1010. +""" + +# Time Complexity - O(number of bits in n) +def has_alternative_bit(n): + first_bit = 0 + second_bit = 0 + while n: + first_bit = n & 1 + if n >> 1: + second_bit = (n >> 1) & 1 + if not first_bit ^ second_bit: + return False + else: + return True + n = n >> 1 + return True + +# Time Complexity - O(1) +def has_alternative_bit_fast(n): + mask1 = int('aaaaaaaa', 16) # for bits ending with zero (...1010) + mask2 = int('55555555', 16) # for bits ending with one (...0101) + return mask1 == (n + (n ^ mask1)) or mask2 == (n + (n ^ mask2)) diff --git a/algorithms/bit/insert_bit.py b/algorithms/bit/insert_bit.py new file mode 100644 index 000000000..a86e042f4 --- /dev/null +++ b/algorithms/bit/insert_bit.py @@ -0,0 +1,44 @@ +""" +Insertion: + +insert_one_bit(num, bit, i): insert exact one bit at specific position +For example: + +Input: num = 10101 (21) +insert_one_bit(num, 1, 2): 101101 (45) +insert_one_bit(num, 0, 2): 101001 (41) +insert_one_bit(num, 1, 5): 110101 (53) +insert_one_bit(num, 1, 0): 101011 (43) + +insert_mult_bits(num, bits, len, i): insert multiple bits with len at specific position +For example: + +Input: num = 101 (5) +insert_mult_bits(num, 7, 3, 1): 101111 (47) +insert_mult_bits(num, 7, 3, 0): 101111 (47) +insert_mult_bits(num, 7, 3, 3): 111101 (61) +""" + +""" +Insert exact one bit at specific position + +Algorithm: +1. Create a mask having bit from i to the most significant bit, and append the new bit at 0 position +2. Keep the bit from 0 position to i position ( like 000...001111) +3. Merge mask and num +""" +def insert_one_bit(num, bit, i): + # Create mask + mask = num >> i + mask = (mask << 1) | bit + mask = mask << i + # Keep the bit from 0 position to i position + right = ((1 << i) - 1) & num + return right | mask + +def insert_mult_bits(num, bits, len, i): + mask = num >> i + mask = (mask << len) | bits + mask = mask << i + right = ((1 << i) - 1) & num + return right | mask diff --git a/bit/power_of_two.py b/algorithms/bit/power_of_two.py similarity index 98% rename from bit/power_of_two.py rename to algorithms/bit/power_of_two.py index bdb629471..01587788a 100644 --- a/bit/power_of_two.py +++ b/algorithms/bit/power_of_two.py @@ -1,8 +1,6 @@ """ given an integer, write a function to determine if it is a power of two """ - - def is_power_of_two(n): """ :type n: int diff --git a/algorithms/bit/remove_bit.py b/algorithms/bit/remove_bit.py new file mode 100644 index 000000000..b302cf986 --- /dev/null +++ b/algorithms/bit/remove_bit.py @@ -0,0 +1,15 @@ +""" +Remove_bit(num, i): remove a bit at specific position. +For example: + +Input: num = 10101 (21) +remove_bit(num, 2): output = 1001 (9) +remove_bit(num, 4): output = 101 (5) +remove_bit(num, 0): output = 1010 (10) +""" + +def remove_bit(num, i): + mask = num >> (i + 1) + mask = mask << i + right = ((1 << i) - 1) & num + return mask | right diff --git a/bit/reverse_bits.py b/algorithms/bit/reverse_bits.py similarity index 99% rename from bit/reverse_bits.py rename to algorithms/bit/reverse_bits.py index 06beebf39..410c63d57 100644 --- a/bit/reverse_bits.py +++ b/algorithms/bit/reverse_bits.py @@ -6,8 +6,6 @@ return 964176192 (represented in binary as 00111001011110000010100101000000). """ - - def reverse_bits(n): m = 0 i = 0 diff --git a/bit/single_number.py b/algorithms/bit/single_number.py similarity index 61% rename from bit/single_number.py rename to algorithms/bit/single_number.py index 756c3d79e..6e0b6f705 100644 --- a/bit/single_number.py +++ b/algorithms/bit/single_number.py @@ -2,14 +2,18 @@ Given an array of integers, every element appears twice except for one. Find that single one. +NOTE: This also works for finding a number occurring odd + number of times, where all the other numbers appear + even number of times. + Note: Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory? """ - - def single_number(nums): """ + Returns single number, if found. + Else if all numbers appear twice, returns 0. :type nums: List[int] :rtype: int """ diff --git a/bit/single_number2.py b/algorithms/bit/single_number2.py similarity index 70% rename from bit/single_number2.py rename to algorithms/bit/single_number2.py index 8646b2149..2f0e36c59 100644 --- a/bit/single_number2.py +++ b/algorithms/bit/single_number2.py @@ -6,10 +6,9 @@ Note: Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory? -""" -""" +Solution: 32 bits for each integer. Consider 1 bit in it, the sum of each integer's corresponding bit (except for the single number) @@ -19,24 +18,6 @@ In this way, you get the 32 bits of the single number. """ - -def single_number(nums): - """ - :type nums: List[int] - :rtype: int - """ - res = 0 - for i in range(0, 32): - count = 0 - for num in nums: - if ((num >> i) & 1): - count += 1 - res |= ((count % 3) << i) - if res >= 2**31: - res -= 2**32 - return res - - # Another awesome answer def single_number2(nums): ones, twos = 0, 0 diff --git a/algorithms/bit/single_number3.py b/algorithms/bit/single_number3.py new file mode 100644 index 000000000..5182bd271 --- /dev/null +++ b/algorithms/bit/single_number3.py @@ -0,0 +1,49 @@ +""" +Given an array of numbers nums, +in which exactly two elements appear only once +and all the other elements appear exactly twice. +Find the two elements that appear only once. +Limitation: Time Complexity: O(N) and Space Complexity O(1) + +For example: + +Given nums = [1, 2, 1, 3, 2, 5], return [3, 5]. + +Note: +The order of the result is not important. +So in the above example, [5, 3] is also correct. + + +Solution: +1. Use XOR to cancel out the pairs and isolate A^B +2. It is guaranteed that at least 1 bit exists in A^B since + A and B are different numbers. ex) 010 ^ 111 = 101 +3. Single out one bit R (right most bit in this solution) to use it as a pivot +4. Divide all numbers into two groups. + One group with a bit in the position R + One group without a bit in the position R +5. Use the same strategy we used in step 1 to isolate A and B from each group. +""" + + +def single_number3(nums): + """ + :type nums: List[int] + :rtype: List[int] + """ + # isolate a^b from pairs using XOR + ab = 0 + for n in nums: + ab ^= n + + # isolate right most bit from a^b + right_most = ab & (-ab) + + # isolate a and b from a^b + a, b = 0, 0 + for n in nums: + if n & right_most: + a ^= n + else: + b ^= n + return [a, b] diff --git a/bit/subsets.py b/algorithms/bit/subsets.py similarity index 76% rename from bit/subsets.py rename to algorithms/bit/subsets.py index 8eafd79f4..6d5a0a284 100644 --- a/bit/subsets.py +++ b/algorithms/bit/subsets.py @@ -7,45 +7,31 @@ For example, If nums = [1,2,3], a solution is: -[ - [3], - [1], - [2], - [1,2,3], - [1,3], - [2,3], - [1,2], - [] -] +{ + (1, 2), + (1, 3), + (1,), + (2,), + (3,), + (1, 2, 3), + (), + (2, 3) +} """ - - -def subnets(nums): - nums.sort() - total = 2 ** len(nums) # or 1 << len(nums) - res = [] * total +def subsets(nums): + """ + :param nums: List[int] + :return: Set[tuple] + """ + n = len(nums) + total = 1 << n + res = set() for i in range(total): - res.append([]) - - for i in range(len(nums)): - for j in range(total): - if ((j >> i) & 1) > 0: # i & 1 << j - res[j].append(nums[i]) - return res - + subset = tuple(num for j, num in enumerate(nums) if i & 1 << j) + res.add(subset) -def subsets2(self, nums): - res = [] - nums.sort() - for i in range(1 << len(nums)): - tmp = [] - for j in range(len(nums)): - if i & 1 << j: # if i >> j & 1: - tmp.append(nums[j]) - res.append(tmp) return res - """ this explanation is from leet_nik @ leetcode This is an amazing solution. Learnt a lot. diff --git a/algorithms/bit/swap_pair.py b/algorithms/bit/swap_pair.py new file mode 100644 index 000000000..c1bf75811 --- /dev/null +++ b/algorithms/bit/swap_pair.py @@ -0,0 +1,21 @@ +""" +Swap_pair: A function swap odd and even bits in an integer with as few instructions +as possible (Ex bit and bit 1 are swapped, bit 2 and bit 3 are swapped) + +For example: +22: 010110 --> 41: 101001 +10: 1010 --> 5 : 0101 +""" + +""" +We can approach this as operating on the odds bit first, and then the even bits. +We can mask all odd bits with 10101010 in binary ('AA') then shift them right by 1 +Similarly, we mask all even bit with 01010101 in binary ('55') then shift them left +by 1. Finally, we merge these two values by OR operation. +""" +def swap_pair(num): + # odd bit arithmetic right shift 1 bit + odd = (num & int('AAAAAAAA', 16)) >> 1 + # even bit left shift 1 bit + even = (num & int('55555555', 16)) << 1 + return odd | even diff --git a/algorithms/compression/__init__.py b/algorithms/compression/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/compression/elias.py b/algorithms/compression/elias.py new file mode 100644 index 000000000..974fc3772 --- /dev/null +++ b/algorithms/compression/elias.py @@ -0,0 +1,53 @@ +""" +Elias γ code or Elias gamma code is a universal code +encoding positive integers. +It is used most commonly when coding integers whose +upper-bound cannot be determined beforehand. +Elias δ code or Elias delta code is a universal code + encoding the positive integers, +that includes Elias γ code when calculating. +Both were developed by Peter Elias. + +""" +from math import log + +log2 = lambda x: log(x, 2) + +# Calculates the binary number +def binary(x, l=1): + fmt = '{0:0%db}' % l + return fmt.format(x) + +# Calculates the unary number +def unary(x): + return (x-1)*'1'+'0' + +def elias_generic(lencoding, x): + """ + The compressed data is calculated in two parts. + The first part is the unary number of 1 + ⌊log2(x)⌋. + The second part is the binary number of x - 2^(⌊log2(x)⌋). + For the final result we add these two parts. + """ + if x == 0: + return '0' + + first_part = 1 + int(log2(x)) + + a = x - 2**(int(log2(x))) + + k = int(log2(x)) + + return lencoding(first_part) + binary(a, k) + +def elias_gamma(x): + """ + For the first part we put the unary number of x. + """ + return elias_generic(unary, x) + +def elias_delta(x): + """ + For the first part we put the elias_g of the number. + """ + return elias_generic(elias_gamma, x) diff --git a/algorithms/compression/huffman_coding.py b/algorithms/compression/huffman_coding.py new file mode 100644 index 000000000..44effb19c --- /dev/null +++ b/algorithms/compression/huffman_coding.py @@ -0,0 +1,328 @@ +""" +Huffman coding is an efficient method of compressing data without losing information. +This algorithm analyzes the symbols that appear in a message. +Symbols that appear more often will be encoded as a shorter-bit string +while symbols that aren't used as much will be encoded as longer strings. +""" + +from collections import defaultdict, deque +import heapq + + +class Node: + def __init__(self, frequency=0, sign=None, left=None, right=None): + self.frequency = frequency + self.sign = sign + self.left = left + self.right = right + + def __lt__(self, other): + return self.frequency < other.frequency + + def __gt__(self, other): + return self.frequency > other.frequency + + def __eq__(self, other): + return self.frequency == other.frequency + + def __str__(self): + return "".format(self.sign, self.frequency) + + def __repr__(self): + return "".format(self.sign, self.frequency) + + +class HuffmanReader: + def __init__(self, file): + self.file = file + self.buffer = [] + self.is_last_byte = False + + def get_number_of_additional_bits_in_the_last_byte(self) -> int: + bin_num = self.get_bit() + self.get_bit() + self.get_bit() + return int(bin_num, 2) + + def load_tree(self) -> Node: + """ + Load tree from file + + :return: + """ + node_stack = deque() + queue_leaves = deque() + root = Node() + + current_node = root + is_end_of_tree = False + while not is_end_of_tree: + current_bit = self.get_bit() + if current_bit == "0": + current_node.left = Node() + current_node.right = Node() + node_stack.append(current_node.right) # going to left node, right push on stack + current_node = current_node.left + else: + queue_leaves.append(current_node) + if node_stack: + current_node = node_stack.pop() + else: + is_end_of_tree = True + + self._fill_tree(queue_leaves) + + return root + + def _fill_tree(self, leaves_queue): + """ + Load values to tree after reading tree + :param leaves_queue: + :return: + """ + leaves_queue.reverse() + while leaves_queue: + node = leaves_queue.pop() + s = int(self.get_byte(), 2) + node.sign = s + + def _load_byte(self, buff_limit=8) -> bool: + """ + Load next byte is buffer is less than buff_limit + :param buff_limit: + :return: True if there is enough bits in buffer to read + """ + if len(self.buffer) <= buff_limit: + byte = self.file.read(1) + + if not byte: + return False + + i = int.from_bytes(byte, "big") + self.buffer.extend(list("{0:08b}".format(i))) + + return True + + def get_bit(self, buff_limit=8): + if self._load_byte(buff_limit): + bit = self.buffer.pop(0) + return bit + else: + return -1 + + def get_byte(self): + if self._load_byte(): + byte_list = self.buffer[:8] + self.buffer = self.buffer[8:] + + return "".join(byte_list) + else: + return -1 + + +class HuffmanWriter: + def __init__(self, file): + self.file = file + self.buffer = "" + self.saved_bits = 0 + + def write_char(self, char): + self.write_int(ord(char)) + + def write_int(self, num): + bin_int = "{0:08b}".format(num) + self.write_bits(bin_int) + + def write_bits(self, bits): + self.saved_bits += len(bits) + + self.buffer += bits + + while len(self.buffer) >= 8: + i = int(self.buffer[:8], 2) + self.file.write(bytes([i])) + self.buffer = self.buffer[8:] + + def save_tree(self, tree): + """ + Generate and save tree code to file + :param tree: + :return: + """ + signs = [] + tree_code = "" + + def get_code_tree(T): + nonlocal tree_code + if T.sign is not None: + signs.append(T.sign) + if T.left: + tree_code += "0" + get_code_tree(T.left) + if T.right: + tree_code += "1" + get_code_tree(T.right) + + get_code_tree(tree) + self.write_bits(tree_code + "1") # "1" indicates that tree ended (it will be needed to load the tree) + for int_sign in signs: + self.write_int(int_sign) + + def _save_information_about_additional_bits(self, additional_bits: int): + """ + Overwrite first three bits in the file + :param additional_bits: number of bits that were appended to fill last byte + :return: + """ + self.file.seek(0) + first_byte_raw = self.file.read(1) + self.file.seek(0) + first_byte = "{0:08b}".format(int.from_bytes(first_byte_raw, "big")) + # overwrite first three bits + first_byte = first_byte[3:] + first_byte = "{0:03b}".format(additional_bits) + first_byte + + self.write_bits(first_byte) + + def close(self): + additional_bits = 8 - len(self.buffer) + if additional_bits != 8: # buffer is empty, no need to append extra "0" + self.write_bits("0" * additional_bits) + self._save_information_about_additional_bits(additional_bits) + + +class TreeFinder: + """ + Class to help find signs in tree + """ + + def __init__(self, tree): + self.root = tree + self.current_node = tree + self.found = None + + def find(self, bit): + """ + Find sign in tree + :param bit: + :return: True if sign is found + """ + if bit == "0": + self.current_node = self.current_node.left + elif bit == "1": + self.current_node = self.current_node.right + else: + self._reset() + return True + + if self.current_node.sign is not None: + self._reset(self.current_node.sign) + return True + else: + return False + + def _reset(self, found=""): + self.found = found + self.current_node = self.root + + +class HuffmanCoding: + def __init__(self): + pass + + @staticmethod + def decode_file(file_in_name, file_out_name): + with open(file_in_name, "rb") as file_in, open(file_out_name, "wb") as file_out: + reader = HuffmanReader(file_in) + additional_bits = reader.get_number_of_additional_bits_in_the_last_byte() + tree = reader.load_tree() + + HuffmanCoding._decode_and_write_signs_to_file(file_out, reader, tree, additional_bits) + + print("File decoded.") + + @staticmethod + def _decode_and_write_signs_to_file(file, reader: HuffmanReader, tree: Node, additional_bits: int): + tree_finder = TreeFinder(tree) + is_end_of_file = False + + while not is_end_of_file: + bit = reader.get_bit() + if bit != -1: + while not tree_finder.find(bit): # read whole code + bit = reader.get_bit(0) + file.write(bytes([tree_finder.found])) + else: # There is last byte in buffer to parse + is_end_of_file = True + last_byte = reader.buffer + last_byte = last_byte[:-additional_bits] # remove additional "0" used to fill byte + for bit in last_byte: + if tree_finder.find(bit): + file.write(bytes([tree_finder.found])) + + @staticmethod + def encode_file(file_in_name, file_out_name): + with open(file_in_name, "rb") as file_in, open(file_out_name, mode="wb+") as file_out: + signs_frequency = HuffmanCoding._get_char_frequency(file_in) + file_in.seek(0) + tree = HuffmanCoding._create_tree(signs_frequency) + codes = HuffmanCoding._generate_codes(tree) + + writer = HuffmanWriter(file_out) + writer.write_bits("000") # leave space to save how many bits will be appended to fill the last byte + writer.save_tree(tree) + HuffmanCoding._encode_and_write_signs_to_file(file_in, writer, codes) + writer.close() + + print("File encoded.") + + @staticmethod + def _encode_and_write_signs_to_file(file, writer: HuffmanWriter, codes: dict): + sign = file.read(1) + while sign: + int_char = int.from_bytes(sign, "big") + writer.write_bits(codes[int_char]) + sign = file.read(1) + + @staticmethod + def _get_char_frequency(file) -> dict: + is_end_of_file = False + signs_frequency = defaultdict(lambda: 0) + while not is_end_of_file: + prev_pos = file.tell() + sign = file.read(1) + curr_pos = file.tell() + if prev_pos == curr_pos: + is_end_of_file = True + else: + signs_frequency[int.from_bytes(sign, "big")] += 1 + + return signs_frequency + + @staticmethod + def _generate_codes(tree: Node) -> dict: + codes = dict() + HuffmanCoding._go_through_tree_and_create_codes(tree, "", codes) + return codes + + @staticmethod + def _create_tree(signs_frequency: dict) -> Node: + nodes = [Node(frequency=frequency, sign=char_int) for char_int, frequency in signs_frequency.items()] + heapq.heapify(nodes) + + while len(nodes) > 1: + left = heapq.heappop(nodes) + right = heapq.heappop(nodes) + new_node = Node(frequency=left.frequency + right.frequency, left=left, right=right) + heapq.heappush(nodes, new_node) + + return nodes[0] # root + + @staticmethod + def _go_through_tree_and_create_codes(tree: Node, code: str, dict_codes: dict): + if tree.sign is not None: + dict_codes[tree.sign] = code + + if tree.left: + HuffmanCoding._go_through_tree_and_create_codes(tree.left, code + "0", dict_codes) + + if tree.right: + HuffmanCoding._go_through_tree_and_create_codes(tree.right, code + "1", dict_codes) diff --git a/algorithms/compression/rle_compression.py b/algorithms/compression/rle_compression.py new file mode 100644 index 000000000..b6c6df44d --- /dev/null +++ b/algorithms/compression/rle_compression.py @@ -0,0 +1,58 @@ +""" +Run-length encoding (RLE) is a simple compression algorithm +that gets a stream of data as the input and returns a +sequence of counts of consecutive data values in a row. +When decompressed the data will be fully recovered as RLE +is a lossless data compression. +""" + +def encode_rle(input): + """ + Gets a stream of data and compresses it + under a Run-Length Encoding. + :param input: The data to be encoded. + :return: The encoded string. + """ + if not input: return '' + + encoded_str = '' + prev_ch = '' + count = 1 + + for ch in input: + + # Check If the subsequent character does not match + if ch != prev_ch: + # Add the count and character + if prev_ch: + encoded_str += str(count) + prev_ch + # Reset the count and set the character + count = 1 + prev_ch = ch + else: + # Otherwise increment the counter + count += 1 + else: + return encoded_str + (str(count) + prev_ch) + + +def decode_rle(input): + """ + Gets a stream of data and decompresses it + under a Run-Length Decoding. + :param input: The data to be decoded. + :return: The decoded string. + """ + decode_str = '' + count = '' + + for ch in input: + # If not numerical + if not ch.isdigit(): + # Expand it for the decoding + decode_str += ch * int(count) + count = '' + else: + # Add it in the counter + count += ch + return decode_str diff --git a/algorithms/dfs/__init__.py b/algorithms/dfs/__init__.py new file mode 100644 index 000000000..043414c1e --- /dev/null +++ b/algorithms/dfs/__init__.py @@ -0,0 +1,6 @@ +from .all_factors import * +from .count_islands import * +from .pacific_atlantic import * +from .sudoku_solver import * +from .walls_and_gates import * +from .maze_search import * diff --git a/dfs/all_factors.py b/algorithms/dfs/all_factors.py similarity index 52% rename from dfs/all_factors.py rename to algorithms/dfs/all_factors.py index fbed6edb9..13438d41f 100644 --- a/dfs/all_factors.py +++ b/algorithms/dfs/all_factors.py @@ -27,10 +27,30 @@ [2, 2, 2, 4], [2, 2, 2, 2, 2], """ - - def get_factors(n): + """[summary] + + Arguments: + n {[int]} -- [to analysed number] + + Returns: + [list of lists] -- [all factors of the number n] + """ + def factor(n, i, combi, res): + """[summary] + helper function + + Arguments: + n {[int]} -- [number] + i {[int]} -- [to tested divisor] + combi {[list]} -- [catch divisors] + res {[list]} -- [all factors of the number n] + + Returns: + [list] -- [res] + """ + while i * i <= n: if n % i == 0: res += combi + [i, int(n/i)], @@ -40,22 +60,44 @@ def factor(n, i, combi, res): return factor(n, 2, [], []) -def get_factors_iterative1(self, n): +def get_factors_iterative1(n): + """[summary] + Computes all factors of n. + Translated the function get_factors(...) in + a call-stack modell. + + Arguments: + n {[int]} -- [to analysed number] + + Returns: + [list of lists] -- [all factors] + """ + todo, res = [(n, 2, [])], [] while todo: n, i, combi = todo.pop() while i * i <= n: if n % i == 0: - res += combi + [i, n/i], - todo += (n/i, i, combi+[i]), + res += combi + [i, n//i], + todo.append((n//i, i, combi+[i])), i += 1 return res def get_factors_iterative2(n): + """[summary] + analog as above + + Arguments: + n {[int]} -- [description] + + Returns: + [list of lists] -- [all factors of n] + """ + ans, stack, x = [], [], 2 while True: - if x > n / x: + if x > n // x: if not stack: return ans ans.append(stack + [n]) @@ -64,10 +106,6 @@ def get_factors_iterative2(n): x += 1 elif n % x == 0: stack.append(x) - n /= x + n //= x else: x += 1 - - -if __name__ == "__main__": - print(get_factors(32)) diff --git a/dfs/count_islands.py b/algorithms/dfs/count_islands.py similarity index 62% rename from dfs/count_islands.py rename to algorithms/dfs/count_islands.py index 5c4711526..21bcee85a 100644 --- a/dfs/count_islands.py +++ b/algorithms/dfs/count_islands.py @@ -24,21 +24,21 @@ def num_islands(grid): count = 0 - for i, row in enumerate(grid): + for i in range(len(grid)): for j, col in enumerate(grid[i]): - if col == '1': - DFS(grid, i, j) + if col == 1: + dfs(grid, i, j) count += 1 return count -def DFS(grid, i, j): - if (i < 0 or i >= len(grid)) or (j < 0 or len(grid[0])): +def dfs(grid, i, j): + if (i < 0 or i >= len(grid)) or (j < 0 or j >= len(grid[0])): return - if grid[i][j] != '1': + if grid[i][j] != 1: return - grid[i][j] = '0' - DFS(grid, i+1, j) - DFS(grid, i-1, j) - DFS(grid, i, j+1) - DFS(grid, i, j-1) + grid[i][j] = 0 + dfs(grid, i+1, j) + dfs(grid, i-1, j) + dfs(grid, i, j+1) + dfs(grid, i, j-1) diff --git a/algorithms/dfs/maze_search.py b/algorithms/dfs/maze_search.py new file mode 100644 index 000000000..f644fd5a6 --- /dev/null +++ b/algorithms/dfs/maze_search.py @@ -0,0 +1,55 @@ +''' +Find shortest path from top left column to the right lowest column using DFS. +only step on the columns whose value is 1 +if there is no path, it returns -1 +(The first column(top left column) is not included in the answer.) + +Ex 1) +If maze is +[[1,0,1,1,1,1], + [1,0,1,0,1,0], + [1,0,1,0,1,1], + [1,1,1,0,1,1]], +the answer is: 14 + +Ex 2) +If maze is +[[1,0,0], + [0,1,1], + [0,1,1]], +the answer is: -1 +''' + + +def find_path(maze): + cnt = dfs(maze, 0, 0, 0, -1) + return cnt + + +def dfs(maze, i, j, depth, cnt): + directions = [(0, -1), (0, 1), (-1, 0), (1, 0)] + + row = len(maze) + col = len(maze[0]) + + if i == row - 1 and j == col - 1: + if cnt == -1: + cnt = depth + else: + if cnt > depth: + cnt = depth + return cnt + + maze[i][j] = 0 + + for k in range(len(directions)): + nx_i = i + directions[k][0] + nx_j = j + directions[k][1] + + if nx_i >= 0 and nx_i < row and nx_j >= 0 and nx_j < col: + if maze[nx_i][nx_j] == 1: + cnt = dfs(maze, nx_i, nx_j, depth + 1, cnt) + + maze[i][j] = 1 + + return cnt diff --git a/dfs/pacific_atlantic.py b/algorithms/dfs/pacific_atlantic.py similarity index 79% rename from dfs/pacific_atlantic.py rename to algorithms/dfs/pacific_atlantic.py index 38f2c5cbe..984aa26ba 100644 --- a/dfs/pacific_atlantic.py +++ b/algorithms/dfs/pacific_atlantic.py @@ -42,24 +42,24 @@ def pacific_atlantic(matrix): atlantic = [[False for _ in range (n)] for _ in range(m)] pacific = [[False for _ in range (n)] for _ in range(m)] for i in range(n): - DFS(pacific, matrix, float("-inf"), i, 0) - DFS(atlantic, matrix, float("-inf"), i, m-1) + dfs(pacific, matrix, float("-inf"), i, 0) + dfs(atlantic, matrix, float("-inf"), i, m-1) for i in range(m): - DFS(pacific, matrix, float("-inf"), 0, i) - DFS(atlantic, matrix, float("-inf"), n-1, i) + dfs(pacific, matrix, float("-inf"), 0, i) + dfs(atlantic, matrix, float("-inf"), n-1, i) for i in range(n): for j in range(m): if pacific[i][j] and atlantic[i][j]: res.append([i, j]) return res -def DFS(grid, matrix, height, i, j): +def dfs(grid, matrix, height, i, j): if i < 0 or i >= len(matrix) or j < 0 or j >= len(matrix[0]): return if grid[i][j] or matrix[i][j] < height: return grid[i][j] = True - DFS(grid, matrix, matrix[i][j], i-1, j) - DFS(grid, matrix, matrix[i][j], i+1, j) - DFS(grid, matrix, matrix[i][j], i, j-1) - DFS(grid, matrix, matrix[i][j], i, j+1) + dfs(grid, matrix, matrix[i][j], i-1, j) + dfs(grid, matrix, matrix[i][j], i+1, j) + dfs(grid, matrix, matrix[i][j], i, j-1) + dfs(grid, matrix, matrix[i][j], i, j+1) diff --git a/algorithms/dfs/sudoku_solver.py b/algorithms/dfs/sudoku_solver.py new file mode 100644 index 000000000..e7ba9aa02 --- /dev/null +++ b/algorithms/dfs/sudoku_solver.py @@ -0,0 +1,95 @@ +""" +It's similar to how human solve Sudoku. + +create a hash table (dictionary) val to store possible values in every location. +Each time, start from the location with fewest possible values, choose one value +from it and then update the board and possible values at other locations. +If this update is valid, keep solving (DFS). If this update is invalid (leaving +zero possible values at some locations) or this value doesn't lead to the +solution, undo the updates and then choose the next value. +Since we calculated val at the beginning and start filling the board from the +location with fewest possible values, the amount of calculation and thus the +runtime can be significantly reduced: + + +The run time is 48-68 ms on LeetCode OJ, which seems to be among the fastest +python solutions here. + + +The PossibleVals function may be further simplified/optimized, but it works just +fine for now. (it would look less lengthy if we are allowed to use numpy array +for the board lol). +""" +class Sudoku: + def __init__ (self, board, row, col): + self.board = board + self.row = row + self.col = col + self.val = self.possible_values() + + def possible_values(self): + a = "123456789" + d, val = {}, {} + for i in range(self.row): + for j in range(self.col): + ele = self.board[i][j] + if ele != ".": + d[("r", i)] = d.get(("r", i), []) + [ele] + d[("c", j)] = d.get(("c", j), []) + [ele] + d[(i//3, j//3)] = d.get((i//3, j//3), []) + [ele] + else: + val[(i,j)] = [] + for (i,j) in val.keys(): + inval = d.get(("r",i),[])+d.get(("c",j),[])+d.get((i/3,j/3),[]) + val[(i,j)] = [n for n in a if n not in inval ] + return val + + def solve(self): + if len(self.val)==0: + return True + kee = min(self.val.keys(), key=lambda x: len(self.val[x])) + nums = self.val[kee] + for n in nums: + update = {kee:self.val[kee]} + if self.valid_one(n, kee, update): # valid choice + if self.solve(): # keep solving + return True + self.undo(kee, update) # invalid choice or didn't solve it => undo + return False + + def valid_one(self, n, kee, update): + self.board[kee[0]][kee[1]] = n + del self.val[kee] + i, j = kee + for ind in self.val.keys(): + if n in self.val[ind]: + if ind[0]==i or ind[1]==j or (ind[0]/3,ind[1]/3)==(i/3,j/3): + update[ind] = n + self.val[ind].remove(n) + if len(self.val[ind])==0: + return False + return True + + def undo(self, kee, update): + self.board[kee[0]][kee[1]]="." + for k in update: + if k not in self.val: + self.val[k]= update[k] + else: + self.val[k].append(update[k]) + return None + + def __str__(self): + """[summary] + Generates a board representation as string. + + Returns: + [str] -- [board representation] + """ + + resp = "" + for i in range(self.row): + for j in range(self.col): + resp += " {0} ".format(self.board[i][j]) + resp += "\n" + return resp diff --git a/algorithms/dfs/walls_and_gates.py b/algorithms/dfs/walls_and_gates.py new file mode 100644 index 000000000..0369203d9 --- /dev/null +++ b/algorithms/dfs/walls_and_gates.py @@ -0,0 +1,38 @@ +""" +You are given a m x n 2D grid initialized with these three possible values: + -1: A wall or an obstacle. + 0: A gate. + INF: Infinity means an empty room. We use the value 2^31 - 1 = 2147483647 to represent INF + as you may assume that the distance to a gate is less than 2147483647. +Fill the empty room with distance to its nearest gate. +If it is impossible to reach a gate, it should be filled with INF. + +For example, given the 2D grid: + INF -1 0 INF + INF INF INF -1 + INF -1 INF -1 + 0 -1 INF INF +After running your function, the 2D grid should be: + 3 -1 0 1 + 2 2 1 -1 + 1 -1 2 -1 + 0 -1 3 4 +""" + +def walls_and_gates(rooms): + for i in range(len(rooms)): + for j in range(len(rooms[0])): + if rooms[i][j] == 0: + dfs(rooms, i, j, 0) + + +def dfs(rooms, i, j, depth): + if (i < 0 or i >= len(rooms)) or (j < 0 or j >= len(rooms[0])): + return # out of bounds + if rooms[i][j] < depth: + return # crossed + rooms[i][j] = depth + dfs(rooms, i+1, j, depth+1) + dfs(rooms, i-1, j, depth+1) + dfs(rooms, i, j+1, depth+1) + dfs(rooms, i, j-1, depth+1) diff --git a/algorithms/distribution/__init__.py b/algorithms/distribution/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/distribution/histogram.py b/algorithms/distribution/histogram.py new file mode 100644 index 000000000..7bcdc7f47 --- /dev/null +++ b/algorithms/distribution/histogram.py @@ -0,0 +1,28 @@ +""" +Histogram function. + +Histogram is an accurate representation of the distribution of numerical data. +It is an estimate of the probability distribution of a continuous variable. +https://en.wikipedia.org/wiki/Histogram + +Example: + list_1 = [3, 3, 2, 1] + :return {1: 1, 2: 1, 3: 2} + + list_2 = [2, 3, 5, 5, 5, 6, 4, 3, 7] + :return {2: 1, 3: 2, 4: 1, 5: 3, 6: 1, 7: 1} +""" + + +def get_histogram(input_list: list) -> dict: + """ + Get histogram representation + :param input_list: list with different and unordered values + :return histogram: dict with histogram of input_list + """ + # Create dict to store histogram + histogram = {} + # For each list value, add one to the respective histogram dict position + for i in input_list: + histogram[i] = histogram.get(i, 0) + 1 + return histogram diff --git a/algorithms/dp/__init__.py b/algorithms/dp/__init__.py new file mode 100644 index 000000000..442120282 --- /dev/null +++ b/algorithms/dp/__init__.py @@ -0,0 +1,23 @@ +from .buy_sell_stock import * +from .climbing_stairs import * +from .coin_change import * +from .combination_sum import * +from .edit_distance import * +from .egg_drop import * +from .fib import * +from .hosoya_triangle import * +from .house_robber import * +from .job_scheduling import * +from .knapsack import * +from .longest_increasing import * +from .matrix_chain_order import * +from .max_product_subarray import * +from .max_subarray import * +from .min_cost_path import * +from .num_decodings import * +from .regex_matching import * +from .rod_cut import * +from .word_break import * +from .int_divide import * +from .k_factor import * +from .planting_trees import * diff --git a/dp/buy_sell_stock.py b/algorithms/dp/buy_sell_stock.py similarity index 100% rename from dp/buy_sell_stock.py rename to algorithms/dp/buy_sell_stock.py diff --git a/algorithms/dp/climbing_stairs.py b/algorithms/dp/climbing_stairs.py new file mode 100644 index 000000000..9b90ae15c --- /dev/null +++ b/algorithms/dp/climbing_stairs.py @@ -0,0 +1,36 @@ +""" +You are climbing a stair case. +It takes `steps` number of steps to reach to the top. + +Each time you can either climb 1 or 2 steps. +In how many distinct ways can you climb to the top? + +Note: Given argument `steps` will be a positive integer. +""" + + +# O(n) space + +def climb_stairs(steps): + """ + :type steps: int + :rtype: int + """ + arr = [1, 1] + for _ in range(1, steps): + arr.append(arr[-1] + arr[-2]) + return arr[-1] + + +# the above function can be optimized as: +# O(1) space + +def climb_stairs_optimized(steps): + """ + :type steps: int + :rtype: int + """ + a_steps = b_steps = 1 + for _ in range(steps): + a_steps, b_steps = b_steps, a_steps + b_steps + return a_steps diff --git a/algorithms/dp/coin_change.py b/algorithms/dp/coin_change.py new file mode 100644 index 000000000..379753b06 --- /dev/null +++ b/algorithms/dp/coin_change.py @@ -0,0 +1,34 @@ +""" +Problem +Given a value `value`, if we want to make change for `value` cents, and we have infinite +supply of each of coins = {S1, S2, .. , Sm} valued `coins`, how many ways can we make the change? +The order of `coins` doesn't matter. +For example, for `value` = 4 and `coins` = [1, 2, 3], there are four solutions: +[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3]. +So output should be 4. + +For `value` = 10 and `coins` = [2, 5, 3, 6], there are five solutions: + +[2, 2, 2, 2, 2], [2, 2, 3, 3], [2, 2, 6], [2, 3, 5] and [5, 5]. +So the output should be 5. + +Time complexity: O(n * m) where n is the `value` and m is the number of `coins` +Space complexity: O(n) +""" + +def count(coins, value): + """ Find number of combination of `coins` that adds upp to `value` + + Keyword arguments: + coins -- int[] + value -- int + """ + # initialize dp array and set base case as 1 + dp_array = [1] + [0] * value + + # fill dp in a bottom up manner + for coin in coins: + for i in range(coin, value+1): + dp_array[i] += dp_array[i-coin] + + return dp_array[value] diff --git a/algorithms/dp/combination_sum.py b/algorithms/dp/combination_sum.py new file mode 100644 index 000000000..aaf0749e8 --- /dev/null +++ b/algorithms/dp/combination_sum.py @@ -0,0 +1,74 @@ +""" +Given an integer array with all positive numbers and no duplicates, +find the number of possible combinations that +add up to a positive integer target. + +Example: + +nums = [1, 2, 3] +target = 4 + +The possible combination ways are: +(1, 1, 1, 1) +(1, 1, 2) +(1, 2, 1) +(1, 3) +(2, 1, 1) +(2, 2) +(3, 1) + +Note that different sequences are counted as different combinations. + +Therefore the output is 7. +Follow up: +What if negative numbers are allowed in the given array? +How does it change the problem? +What limitation we need to add to the question to allow negative numbers? + +""" + +DP = None + +def helper_topdown(nums, target): + """Generates DP and finds result. + + Keyword arguments: + nums -- positive integer array without duplicates + target -- integer describing what a valid combination should add to + """ + if DP[target] != -1: + return DP[target] + res = 0 + for num in nums: + if target >= num: + res += helper_topdown(nums, target - num) + DP[target] = res + return res + + +def combination_sum_topdown(nums, target): + """Find number of possible combinations in nums that add up to target, in top-down manner. + + Keyword arguments: + nums -- positive integer array without duplicates + target -- integer describing what a valid combination should add to + """ + global DP + DP = [-1] * (target + 1) + DP[0] = 1 + return helper_topdown(nums, target) + +def combination_sum_bottom_up(nums, target): + """Find number of possible combinations in nums that add up to target, in bottom-up manner. + + Keyword arguments: + nums -- positive integer array without duplicates + target -- integer describing what a valid combination should add to + """ + combs = [0] * (target + 1) + combs[0] = 1 + for i in range(0, len(combs)): + for num in nums: + if i - num >= 0: + combs[i] += combs[i - num] + return combs[target] diff --git a/algorithms/dp/edit_distance.py b/algorithms/dp/edit_distance.py new file mode 100644 index 000000000..caf56eedc --- /dev/null +++ b/algorithms/dp/edit_distance.py @@ -0,0 +1,69 @@ +"""The edit distance between two words is the minimum number +of letter insertions, letter deletions, and letter substitutions +required to transform one word into another. + +For example, the edit distance between FOOD and MONEY is at +most four: + +FOOD -> MOOD -> MOND -> MONED -> MONEY + +Given two words A and B, find the minimum number of operations +required to transform one string into the other. +In other words, find the edit distance between A and B. + +Thought process: + +Let edit(i, j) denote the edit distance between +the prefixes A[1..i] and B[1..j]. + +Then, the function satifies the following recurrence: + +edit(i, j) = i if j = 0 + j if i = 0 + min(edit(i-1, j) + 1, + edit(i, j-1), + 1, + edit(i-1, j-1) + cost) otherwise + +There are two base cases, both of which occur when one string is empty +and the other is not. +1. To convert an empty string A into a string B of length n, +perform n insertions. +2. To convert a string A of length m into an empty string B, +perform m deletions. + +Here, the cost is 1 if a substitution is required, +or 0 if both chars in words A and B are the same at +indexes i and j, respectively. + +To find the edit distance between two words A and B, +we need to find edit(length_a, length_b). + +Time: O(length_a*length_b) +Space: O(length_a*length_b) +""" + + +def edit_distance(word_a, word_b): + """Finds edit distance between word_a and word_b + + Kwyword arguments: + word_a -- string + word_b -- string + """ + + length_a, length_b = len(word_a) + 1, len(word_b) + 1 + + edit = [[0 for _ in range(length_b)] for _ in range(length_a)] + + for i in range(1, length_a): + edit[i][0] = i + + for j in range(1, length_b): + edit[0][j] = j + + for i in range(1, length_a): + for j in range(1, length_b): + cost = 0 if word_a[i - 1] == word_b[j - 1] else 1 + edit[i][j] = min(edit[i - 1][j] + 1, edit[i][j - 1] + 1, edit[i - 1][j - 1] + cost) + + return edit[-1][-1] # this is the same as edit[length_a][length_b] diff --git a/algorithms/dp/egg_drop.py b/algorithms/dp/egg_drop.py new file mode 100644 index 000000000..dfa232019 --- /dev/null +++ b/algorithms/dp/egg_drop.py @@ -0,0 +1,58 @@ +""" +You are given K eggs, and you have access to a building with N floors +from 1 to N. Each egg is identical in function, and if an egg breaks, +you cannot drop it again. You know that there exists a floor F with +0 <= F <= N such that any egg dropped at a floor higher than F will +break, and any egg dropped at or below floor F will not break. +Each move, you may take an egg (if you have an unbroken one) and drop +it from any floor X (with 1 <= X <= N). Your goal is to know with +certainty what the value of F is. What is the minimum number of moves +that you need to know with certainty what F is, regardless of the +initial value of F? + +Example: +Input: K = 1, N = 2 +Output: 2 +Explanation: +Drop the egg from floor 1. If it breaks, we know with certainty that F = 0. +Otherwise, drop the egg from floor 2. If it breaks, we know with +certainty that F = 1. +If it didn't break, then we know with certainty F = 2. +Hence, we needed 2 moves in the worst case to know what F is with certainty. +""" + +# A Dynamic Programming based Python Program for the Egg Dropping Puzzle +INT_MAX = 32767 + + +def egg_drop(n, k): + """ + Keyword arguments: + n -- number of floors + k -- number of eggs + """ + # A 2D table where entery eggFloor[i][j] will represent minimum + # number of trials needed for i eggs and j floors. + egg_floor = [[0 for _ in range(k + 1)] for _ in range(n + 1)] + + # We need one trial for one floor and 0 trials for 0 floors + for i in range(1, n+1): + egg_floor[i][1] = 1 + egg_floor[i][0] = 0 + + # We always need j trials for one egg and j floors. + for j in range(1, k+1): + egg_floor[1][j] = j + + # Fill rest of the entries in table using optimal substructure + # property + for i in range(2, n+1): + for j in range(2, k+1): + egg_floor[i][j] = INT_MAX + for x in range(1, j+1): + res = 1 + max(egg_floor[i-1][x-1], egg_floor[i][j-x]) + if res < egg_floor[i][j]: + egg_floor[i][j] = res + + # eggFloor[n][k] holds the result + return egg_floor[n][k] diff --git a/algorithms/dp/fib.py b/algorithms/dp/fib.py new file mode 100644 index 000000000..08fa8ea02 --- /dev/null +++ b/algorithms/dp/fib.py @@ -0,0 +1,92 @@ +''' +In mathematics, the Fibonacci numbers, commonly denoted Fn, +form a sequence, called the Fibonacci sequence, +such that each number is the sum of the two preceding ones, +starting from 0 and 1. +That is, + F0=0 , F1=1 +and + Fn= F(n-1) + F(n-2) +The Fibonacci numbers are the numbers in the following integer sequence. + 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……. + +In mathematical terms, the sequence Fn of Fibonacci numbers is +defined by the recurrence relation + +Here, given a number n, print n-th Fibonacci Number. +''' + + +def fib_recursive(n): + """[summary] + Computes the n-th fibonacci number recursive. + Problem: This implementation is very slow. + approximate O(2^n) + + Arguments: + n {[int]} -- [description] + + Returns: + [int] -- [description] + """ + + # precondition + assert n >= 0, 'n must be a positive integer' + + if n <= 1: + return n + return fib_recursive(n-1) + fib_recursive(n-2) + +# print(fib_recursive(35)) # => 9227465 (slow) + + +def fib_list(n): + """[summary] + This algorithm computes the n-th fibbonacci number + very quick. approximate O(n) + The algorithm use dynamic programming. + + Arguments: + n {[int]} -- [description] + + Returns: + [int] -- [description] + """ + + # precondition + assert n >= 0, 'n must be a positive integer' + + list_results = [0, 1] + for i in range(2, n+1): + list_results.append(list_results[i-1] + list_results[i-2]) + return list_results[n] + +# print(fib_list(100)) # => 354224848179261915075 + + +def fib_iter(n): + """[summary] + Works iterative approximate O(n) + + Arguments: + n {[int]} -- [description] + + Returns: + [int] -- [description] + """ + + # precondition + assert n >= 0, 'n must be positive integer' + + fib_1 = 0 + fib_2 = 1 + res = 0 + if n <= 1: + return n + for _ in range(n-1): + res = fib_1 + fib_2 + fib_1 = fib_2 + fib_2 = res + return res + +# print(fib_iter(100)) # => 354224848179261915075 diff --git a/algorithms/dp/hosoya_triangle.py b/algorithms/dp/hosoya_triangle.py new file mode 100644 index 000000000..a63deaf48 --- /dev/null +++ b/algorithms/dp/hosoya_triangle.py @@ -0,0 +1,56 @@ +""" +Hosoya triangle (originally Fibonacci triangle) is a triangular arrangement +of numbers, where if you take any number it is the sum of 2 numbers above. +First line is always 1, and second line is always {1 1}. + +This printHosoya function takes argument n which is the height of the triangle +(number of lines). + +For example: +printHosoya( 6 ) would return: +1 +1 1 +2 1 2 +3 2 2 3 +5 3 4 3 5 +8 5 6 6 5 8 + +The complexity is O(n^3). + +""" + +def hosoya(height, width): + """ Calculates the hosoya triangle + + height -- height of the triangle + """ + if (width == 0) and (height in (0,1)): + return 1 + if (width == 1) and (height in (1,2)): + return 1 + if height > width: + return hosoya(height - 1, width) + hosoya(height - 2, width) + if width == height: + return hosoya(height - 1, width - 1) + hosoya(height - 2, width - 2) + return 0 + +def print_hosoya(height): + """Prints the hosoya triangle + + height -- height of the triangle + """ + for i in range(height): + for j in range(i + 1): + print(hosoya(i, j) , end = " ") + print ("\n", end = "") + +def hosoya_testing(height): + """Test hosoya function + + height -- height of the triangle + """ + res = [] + for i in range(height): + for j in range(i + 1): + res.append(hosoya(i, j)) + return res diff --git a/dp/house_robber.py b/algorithms/dp/house_robber.py similarity index 81% rename from dp/house_robber.py rename to algorithms/dp/house_robber.py index 88baaa9c4..5a359f93d 100644 --- a/dp/house_robber.py +++ b/algorithms/dp/house_robber.py @@ -15,11 +15,5 @@ def house_robber(houses): last, now = 0, 0 for house in houses: - tmp = now - now = max(last + house, now) - last = tmp + last, now = now, max(last + house, now) return now - -houses = [1, 2, 16, 3, 15, 3, 12, 1] - -print(house_robber(houses)) diff --git a/algorithms/dp/int_divide.py b/algorithms/dp/int_divide.py new file mode 100644 index 000000000..37c9a44e1 --- /dev/null +++ b/algorithms/dp/int_divide.py @@ -0,0 +1,55 @@ +""" +Given positive integer decompose, find an algorithm to find the number of +non-negative number division, or decomposition. + +The complexity is O(n^2). + +Example 1: +Input: 4 +Output: 5 +Explaination: +4=4 +4=3+1 +4=2+2 +4=2+1+1 +4=1+1+1+1 + +Example : +Input: 7 +Output: 15 +Explaination: +7=7 +7=6+1 +7=5+2 +7=5+1+1 +7=4+3 +7=4+2+1 +7=4+1+1+1 +7=3+3+1 +7=3+2+2 +7=3+2+1+1 +7=3+1+1+1+1 +7=2+2+2+1 +7=2+2+1+1+1 +7=2+1+1+1+1+1 +7=1+1+1+1+1+1+1 + +""" + + +def int_divide(decompose): + """Find number of decompositions from `decompose` + + decompose -- integer + """ + arr = [[0 for i in range(decompose + 1)] for j in range(decompose + 1)] + arr[1][1] = 1 + for i in range(1, decompose + 1): + for j in range(1, decompose + 1): + if i < j: + arr[i][j] = arr[i][i] + elif i == j: + arr[i][j] = 1 + arr[i][j - 1] + else: + arr[i][j] = arr[i][j - 1] + arr[i - j][j] + return arr[decompose][decompose] diff --git a/algorithms/dp/job_scheduling.py b/algorithms/dp/job_scheduling.py new file mode 100644 index 000000000..b822c032c --- /dev/null +++ b/algorithms/dp/job_scheduling.py @@ -0,0 +1,68 @@ +""" +Python program for weighted job scheduling using Dynamic +Programming and Binary Search +""" + +class Job: + """ + Class to represent a job + """ + def __init__(self, start, finish, profit): + self.start = start + self.finish = finish + self.profit = profit + +def binary_search(job, start_index): + """ + A Binary Search based function to find the latest job + (before current job) that doesn't conflict with current + job. "index" is index of the current job. This function + returns -1 if all jobs before index conflict with it. + The array jobs[] is sorted in increasing order of finish + time. + """ + + left = 0 + right = start_index - 1 + + # Perform binary Search iteratively + while left <= right: + mid = (left + right) // 2 + if job[mid].finish <= job[start_index].start: + if job[mid + 1].finish <= job[start_index].start: + left = mid + 1 + else: + return mid + else: + right = mid - 1 + return -1 + +def schedule(job): + """ + The main function that returns the maximum possible + profit from given array of jobs + """ + + # Sort jobs according to finish time + job = sorted(job, key = lambda j: j.finish) + + # Create an array to store solutions of subproblems. table[i] + # stores the profit for jobs till arr[i] (including arr[i]) + length = len(job) + table = [0 for _ in range(length)] + + table[0] = job[0].profit + + # Fill entries in table[] using recursive property + for i in range(1, length): + + # Find profit including the current job + incl_prof = job[i].profit + pos = binary_search(job, i) + if pos != -1: + incl_prof += table[pos] + + # Store maximum of including and excluding + table[i] = max(incl_prof, table[i - 1]) + + return table[length-1] diff --git a/algorithms/dp/k_factor.py b/algorithms/dp/k_factor.py new file mode 100644 index 000000000..c072f7541 --- /dev/null +++ b/algorithms/dp/k_factor.py @@ -0,0 +1,85 @@ +''' +The K factor of a string is defined as the number of times 'abba' appears as a +substring. Given two numbers `length` and `k_factor`, find the number of +strings of length `length` with 'K factor' = `k_factor`. + +The algorithms is as follows: + +dp[length][k_factor] will be a 4 element array, wherein each element can be the +number of strings of length `length` and 'K factor' = `k_factor` which belong +to the criteria represented by that index: + + - dp[length][k_factor][0] can be the number of strings of length `length` + and K-factor = `k_factor` which end with substring 'a' + + - dp[length][k_factor][1] can be the number of strings of length `length` + and K-factor = `k_factor` which end with substring 'ab' + + - dp[length][k_factor][2] can be the number of strings of length `length` + and K-factor = `k_factor` which end with substring 'abb' + + - dp[length][k_factor][3] can be the number of strings of `length` and + K-factor = `k_factor` which end with anything other than the above + substrings (anything other than 'a' 'ab' 'abb') + +Example inputs + +length=4 k_factor=1 no of strings = 1 +length=7 k_factor=1 no of strings = 70302 +length=10 k_factor=2 no of strings = 74357 + +''' + +def find_k_factor(length, k_factor): + """Find the number of strings of length `length` with K factor = `k_factor`. + + Keyword arguments: + length -- integer + k_factor -- integer + """ + mat=[[[0 for i in range(4)]for j in range((length-1)//3+2)]for k in range(length+1)] + if 3*k_factor+1>length: + return 0 + #base cases + mat[1][0][0]=1 + mat[1][0][1]=0 + mat[1][0][2]=0 + mat[1][0][3]=25 + + for i in range(2,length+1): + for j in range((length-1)//3+2): + if j==0: + #adding a at the end + mat[i][j][0]=mat[i-1][j][0]+mat[i-1][j][1]+mat[i-1][j][3] + + #adding b at the end + mat[i][j][1]=mat[i-1][j][0] + mat[i][j][2]=mat[i-1][j][1] + + #adding any other lowercase character + mat[i][j][3]=mat[i-1][j][0]*24+mat[i-1][j][1]*24+mat[i-1][j][2]*25+mat[i-1][j][3]*25 + + elif 3*j+1 sequence[j]: + counts[i] = max(counts[i], counts[j] + 1) + print(counts) + return max(counts) + + +def longest_increasing_subsequence_optimized(sequence): + """ + Optimized dynamic programming algorithm for + couting the length of the longest increasing subsequence + using segment tree data structure to achieve better complexity + if max element is larger than 10^5 then use + longest_increasing_subsequence_optimied2() instead + type sequence: list[int] + rtype: int + """ + max_seq = max(sequence) + tree = [0] * (max_seq<<2) + + def update(pos, left, right, target, vertex): + if left == right: + tree[pos] = vertex + return + mid = (left+right)>>1 + if target <= mid: + update(pos<<1, left, mid, target, vertex) + else: + update((pos<<1)|1, mid+1, right, target, vertex) + tree[pos] = max_seq(tree[pos<<1], tree[(pos<<1)|1]) + + def get_max(pos, left, right, start, end): + if left > end or right < start: + return 0 + if left >= start and right <= end: + return tree[pos] + mid = (left+right)>>1 + return max_seq(get_max(pos<<1, left, mid, start, end), + get_max((pos<<1)|1, mid+1, right, start, end)) + ans = 0 + for element in sequence: + cur = get_max(1, 0, max_seq, 0, element-1)+1 + ans = max_seq(ans, cur) + update(1, 0, max_seq, element, cur) + return ans + + +def longest_increasing_subsequence_optimized2(sequence): + """ + Optimized dynamic programming algorithm for + counting the length of the longest increasing subsequence + using segment tree data structure to achieve better complexity + type sequence: list[int] + rtype: int + """ + length = len(sequence) + tree = [0] * (length<<2) + sorted_seq = sorted((x, -i) for i, x in enumerate(sequence)) + def update(pos, left, right, target, vertex): + if left == right: + tree[pos] = vertex + return + mid = (left+right)>>1 + if target <= mid: + vertex(pos<<1, left, mid, target, vertex) + else: + vertex((pos<<1)|1, mid+1, right, target, vertex) + tree[pos] = max(tree[pos<<1], tree[(pos<<1)|1]) + + def get_max(pos, left, right, start, end): + if left > end or right < start: + return 0 + if left >= start and right <= end: + return tree[pos] + mid = (left+right)>>1 + return max(get_max(pos<<1, left, mid, start, end), + get_max((pos<<1)|1, mid+1, right, start, end)) + ans = 0 + for tup in sorted_seq: + i = -tup[1] + cur = get_max(1, 0, length-1, 0, i-1)+1 + ans = max(ans, cur) + update(1, 0, length-1, i, cur) + return ans diff --git a/algorithms/dp/matrix_chain_order.py b/algorithms/dp/matrix_chain_order.py new file mode 100644 index 000000000..dd2ef7bd9 --- /dev/null +++ b/algorithms/dp/matrix_chain_order.py @@ -0,0 +1,61 @@ +''' +Dynamic Programming +Implementation of matrix Chain Multiplication +Time Complexity: O(n^3) +Space Complexity: O(n^2) +''' +INF = float("inf") + + +def matrix_chain_order(array): + """Finds optimal order to multiply matrices + + array -- int[] + """ + n = len(array) + matrix = [[0 for x in range(n)] for x in range(n)] + sol = [[0 for x in range(n)] for x in range(n)] + for chain_length in range(2, n): + for a in range(1, n-chain_length+1): + b = a+chain_length-1 + + matrix[a][b] = INF + for c in range(a, b): + cost = matrix[a][c] + matrix[c+1][b] + array[a-1]*array[c]*array[b] + if cost < matrix[a][b]: + matrix[a][b] = cost + sol[a][b] = c + return matrix, sol +# Print order of matrix with Ai as matrix + +def print_optimal_solution(optimal_solution,i,j): + """Print the solution + + optimal_solution -- int[][] + i -- int[] + j -- int[] + """ + if i==j: + print("A" + str(i),end = " ") + else: + print("(", end=" ") + print_optimal_solution(optimal_solution, i, optimal_solution[i][j]) + print_optimal_solution(optimal_solution, optimal_solution[i][j]+1, j) + print(")", end=" ") + + +def main(): + """ + Testing for matrix_chain_ordering + """ + array=[30,35,15,5,10,20,25] + length=len(array) + #Size of matrix created from above array will be + # 30*35 35*15 15*5 5*10 10*20 20*25 + matrix, optimal_solution = matrix_chain_order(array) + + print("No. of Operation required: "+str((matrix[1][length-1]))) + print_optimal_solution(optimal_solution,1,length-1) + +if __name__ == '__main__': + main() diff --git a/dp/max_product_subarray.py b/algorithms/dp/max_product_subarray.py similarity index 73% rename from dp/max_product_subarray.py rename to algorithms/dp/max_product_subarray.py index 69b0dacf3..7a9beac63 100644 --- a/dp/max_product_subarray.py +++ b/algorithms/dp/max_product_subarray.py @@ -5,6 +5,7 @@ For example, given the array [2,3,-2,4], the contiguous subarray [2,3] has the largest product = 6. """ +from functools import reduce def max_product(nums): @@ -13,15 +14,15 @@ def max_product(nums): :rtype: int """ lmin = lmax = gmax = nums[0] - for i in range(len(nums)): - t1 = nums[i] * lmax - t2 = nums[i] * lmin - lmax = max(max(t1, t2), nums[i]) - lmin = min(min(t1, t2), nums[i]) + for num in nums: + t_1 = num * lmax + t_2 = num * lmin + lmax = max(max(t_1, t_2), num) + lmin = min(min(t_1, t_2), num) gmax = max(gmax, lmax) -''' +""" Another approach that would print max product and the subarray Examples: @@ -33,19 +34,21 @@ def max_product(nums): #=> max_product_so_far: 24, [-4, -3, -2, -1] subarray_with_max_product([-3,0,1]) #=> max_product_so_far: 1, [1] -''' +""" + def subarray_with_max_product(arr): ''' arr is list of positive/negative numbers ''' - l = len(arr) + length = len(arr) product_so_far = max_product_end = 1 max_start_i = 0 so_far_start_i = so_far_end_i = 0 all_negative_flag = True - for i in range(l): + for i in range(length): max_product_end *= arr[i] - if arr[i] > 0: all_negative_flag = False + if arr[i] > 0: + all_negative_flag = False if max_product_end <= 0: max_product_end = arr[i] @@ -55,10 +58,9 @@ def subarray_with_max_product(arr): product_so_far = max_product_end so_far_end_i = i so_far_start_i = max_start_i - + if all_negative_flag: - print "max_product_so_far: %s, %s" % \ - (reduce(lambda x, y: x * y, arr), arr) + print(f"max_product_so_far: {reduce(lambda x, y: x * y, arr)}, {arr}") + else: - print "max_product_so_far: %s, %s" % (product_so_far,\ - arr[so_far_start_i:so_far_end_i + 1]) + print(f"max_product_so_far: {product_so_far},{arr[so_far_start_i:so_far_end_i + 1]}") diff --git a/dp/max_subarray.py b/algorithms/dp/max_subarray.py similarity index 100% rename from dp/max_subarray.py rename to algorithms/dp/max_subarray.py diff --git a/algorithms/dp/min_cost_path.py b/algorithms/dp/min_cost_path.py new file mode 100644 index 000000000..7771e1e0f --- /dev/null +++ b/algorithms/dp/min_cost_path.py @@ -0,0 +1,58 @@ +""" +author @goswami-rahul + +To find minimum cost path +from station 0 to station N-1, +where cost of moving from ith station to jth station is given as: + +Matrix of size (N x N) +where Matrix[i][j] denotes the cost of moving from +station i --> station j for i < j + +NOTE that values where Matrix[i][j] and i > j does not +mean anything, and hence represented by -1 or INF + +For the input below (cost matrix), +Minimum cost is obtained as from { 0 --> 1 --> 3} + = cost[0][1] + cost[1][3] = 65 +the Output will be: + +The Minimum cost to reach station 4 is 65 + +Time Complexity: O(n^2) +Space Complexity: O(n) +""" + +INF = float("inf") + + +def min_cost(cost): + """Find minimum cost. + + Keyword arguments: + cost -- matrix containing costs + """ + length = len(cost) + # dist[i] stores minimum cost from 0 --> i. + dist = [INF] * length + + dist[0] = 0 # cost from 0 --> 0 is zero. + + for i in range(length): + for j in range(i+1,length): + dist[j] = min(dist[j], dist[i] + cost[i][j]) + + return dist[length-1] + + +if __name__ == '__main__': + costs = [ [ 0, 15, 80, 90], # cost[i][j] is the cost of + [-1, 0, 40, 50], # going from i --> j + [-1, -1, 0, 70], + [-1, -1, -1, 0] ] # cost[i][j] = -1 for i > j + TOTAL_LEN = len(costs) + + mcost = min_cost(costs) + assert mcost == 65 + + print(f"The minimum cost to reach station {TOTAL_LEN} is {mcost}") diff --git a/dp/num_decodings.py b/algorithms/dp/num_decodings.py similarity index 52% rename from dp/num_decodings.py rename to algorithms/dp/num_decodings.py index 541db6edf..87cd3e3dc 100644 --- a/dp/num_decodings.py +++ b/algorithms/dp/num_decodings.py @@ -17,33 +17,37 @@ """ -def num_decodings(s): +def num_decodings(enc_mes): """ :type s: str :rtype: int """ - if not s or s[0] == "0": + if not enc_mes or enc_mes[0] == "0": return 0 - wo_last, wo_last_two = 1, 1 - for i in range(1, len(s)): - x = wo_last if s[i] != "0" else 0 - y = wo_last_two if int(s[i-1:i+1]) < 27 and s[i-1] != "0" else 0 - wo_last_two = wo_last - wo_last = x+y - return wo_last + last_char, last_two_chars = 1, 1 + for i in range(1, len(enc_mes)): + last = last_char if enc_mes[i] != "0" else 0 + last_two = last_two_chars if int(enc_mes[i-1:i+1]) < 27 and enc_mes[i-1] != "0" else 0 + last_two_chars = last_char + last_char = last+last_two + return last_char -def num_decodings2(s): - if not s or s.startswith('0'): +def num_decodings2(enc_mes): + """ + :type s: str + :rtype: int + """ + if not enc_mes or enc_mes.startswith('0'): return 0 stack = [1, 1] - for i in range(1, len(s)): - if s[i] == '0': - if s[i-1] == '0' or s[i-1] > '2': + for i in range(1, len(enc_mes)): + if enc_mes[i] == '0': + if enc_mes[i-1] == '0' or enc_mes[i-1] > '2': # only '10', '20' is valid return 0 stack.append(stack[-2]) - elif 9 < int(s[i-1:i+1]) < 27: + elif 9 < int(enc_mes[i-1:i+1]) < 27: # '01 - 09' is not allowed stack.append(stack[-2]+stack[-1]) else: diff --git a/algorithms/dp/planting_trees.py b/algorithms/dp/planting_trees.py new file mode 100644 index 000000000..ee8394b8e --- /dev/null +++ b/algorithms/dp/planting_trees.py @@ -0,0 +1,49 @@ +""" +An even number of trees are left along one side of a country road. You've been +assigned the job to plant these trees at an even interval on both sides of the +road. The length and width of the road are variable, and a pair of trees must +be planted at the beginning (at 0) and at the end (at length) of the road. Only +one tree can be moved at a time. The goal is to calculate the lowest amount of +distance that the trees have to be moved before they are all in a valid +position. +""" + +from math import sqrt + +def planting_trees(trees, length, width): + """ + Returns the minimum distance that trees have to be moved before they + are all in a valid state. + + Parameters: + tree (list): A sorted list of integers with all trees' + position along the road. + length (int): An integer with the length of the road. + width (int): An integer with the width of the road. + + Returns: + A float number with the total distance trees have been moved. + """ + trees = [0] + trees + + n_pairs = int(len(trees)/2) + + space_between_pairs = length/(n_pairs-1) + + target_locations = [location*space_between_pairs for location in range(n_pairs)] + + cmatrix = [[0 for _ in range(n_pairs+1)] for _ in range(n_pairs+1)] + for r_i in range(1, n_pairs+1): + cmatrix[r_i][0] = cmatrix[r_i-1][0] + sqrt( + width + abs(trees[r_i]-target_locations[r_i-1])**2) + for l_i in range(1, n_pairs+1): + cmatrix[0][l_i] = cmatrix[0][l_i-1] + abs(trees[l_i]-target_locations[l_i-1]) + + for r_i in range(1, n_pairs+1): + for l_i in range(1, n_pairs+1): + cmatrix[r_i][l_i] = min( + cmatrix[r_i-1][l_i] + sqrt(width + (trees[l_i + r_i]-target_locations[r_i-1])**2), + cmatrix[r_i][l_i-1] + abs(trees[l_i + r_i]-target_locations[l_i-1]) + ) + + return cmatrix[n_pairs][n_pairs] diff --git a/algorithms/dp/regex_matching.py b/algorithms/dp/regex_matching.py new file mode 100644 index 000000000..3b65e3594 --- /dev/null +++ b/algorithms/dp/regex_matching.py @@ -0,0 +1,61 @@ +""" +Implement regular expression matching with support for '.' and '*'. + +'.' Matches any single character. +'*' Matches zero or more of the preceding element. + +The matching should cover the entire input string (not partial). + +The function prototype should be: +bool is_match(const char *s, const char *p) + +Some examples: +is_match("aa","a") → false +is_match("aa","aa") → true +is_match("aaa","aa") → false +is_match("aa", "a*") → true +is_match("aa", ".*") → true +is_match("ab", ".*") → true +is_match("aab", "c*a*b") → true +""" + +def is_match(str_a, str_b): + """Finds if `str_a` matches `str_b` + + Keyword arguments: + str_a -- string + str_b -- string + """ + len_a, len_b = len(str_a) + 1, len(str_b) + 1 + matches = [[False] * len_b for _ in range(len_a)] + + # Match empty string with empty pattern + matches[0][0] = True + + # Match empty string with .* + for i, element in enumerate(str_b[1:], 2): + matches[0][i] = matches[0][i - 2] and element == '*' + + for i, char_a in enumerate(str_a, 1): + for j, char_b in enumerate(str_b, 1): + if char_b != '*': + # The previous character has matched and the current one + # has to be matched. Two possible matches: the same or . + matches[i][j] = matches[i - 1][j - 1] and \ + char_b in (char_a, '.') + else: + # Horizontal look up [j - 2]. + # Not use the character before *. + matches[i][j] |= matches[i][j - 2] + + # Vertical look up [i - 1]. + # Use at least one character before *. + # p a b * + # s 1 0 0 0 + # a 0 1 0 1 + # b 0 0 1 1 + # b 0 0 0 ? + if char_a == str_b[j - 2] or str_b[j - 2] == '.': + matches[i][j] |= matches[i - 1][j] + + return matches[-1][-1] diff --git a/algorithms/dp/rod_cut.py b/algorithms/dp/rod_cut.py new file mode 100644 index 000000000..d9259e862 --- /dev/null +++ b/algorithms/dp/rod_cut.py @@ -0,0 +1,28 @@ +"""A Dynamic Programming solution for Rod cutting problem +""" + +INT_MIN = -32767 + +def cut_rod(price): + """ + Returns the best obtainable price for a rod of length n and + price[] as prices of different pieces + """ + n = len(price) + val = [0]*(n+1) + + # Build the table val[] in bottom up manner and return + # the last entry from the table + for i in range(1, n+1): + max_val = INT_MIN + for j in range(i): + max_val = max(max_val, price[j] + val[i-j-1]) + val[i] = max_val + + return val[n] + +# Driver program to test above functions +arr = [1, 5, 8, 9, 10, 17, 17, 20] +print("Maximum Obtainable Value is " + str(cut_rod(arr))) + +# This code is contributed by Bhavya Jain diff --git a/dp/word_break.py b/algorithms/dp/word_break.py similarity index 55% rename from dp/word_break.py rename to algorithms/dp/word_break.py index ea244dc68..f520456b0 100644 --- a/dp/word_break.py +++ b/algorithms/dp/word_break.py @@ -1,44 +1,41 @@ """ Given a non-empty string s and a dictionary wordDict containing a list of non-empty words, -determine if s can be segmented into a space-separated +determine if word can be segmented into a space-separated sequence of one or more dictionary words. You may assume the dictionary does not contain duplicate words. For example, given -s = "leetcode", +word = "leetcode", dict = ["leet", "code"]. Return true because "leetcode" can be segmented as "leet code". -""" - -""" -s = abc word_dict = ["a","bc"] +word = abc word_dict = ["a","bc"] True False False False """ # TC: O(N^2) SC: O(N) -def word_break(s, word_dict): +def word_break(word, word_dict): """ - :type s: str + :type word: str :type word_dict: Set[str] :rtype: bool """ - dp = [False] * (len(s)+1) - dp[0] = True - for i in range(1, len(s)+1): + dp_array = [False] * (len(word)+1) + dp_array[0] = True + for i in range(1, len(word)+1): for j in range(0, i): - if dp[j] and s[j:i] in word_dict: - dp[i] = True + if dp_array[j] and word[j:i] in word_dict: + dp_array[i] = True break - return dp[-1] + return dp_array[-1] if __name__ == "__main__": - s = "keonkim" + STR = "keonkim" dic = ["keon", "kim"] - print(word_break(s, dic)) + print(word_break(str, dic)) diff --git a/algorithms/graph/__init__.py b/algorithms/graph/__init__.py new file mode 100644 index 000000000..1f52f9bdb --- /dev/null +++ b/algorithms/graph/__init__.py @@ -0,0 +1,12 @@ +""" +Collection of algorithms on graphs. +""" + +from .tarjan import * +from .check_bipartite import * +from .maximum_flow import * +from .maximum_flow_bfs import * +from .maximum_flow_dfs import * +from .all_pairs_shortest_path import * +from .bellman_ford import * +from .prims_minimum_spanning import * diff --git a/algorithms/graph/all_pairs_shortest_path.py b/algorithms/graph/all_pairs_shortest_path.py new file mode 100644 index 000000000..d8e6feca3 --- /dev/null +++ b/algorithms/graph/all_pairs_shortest_path.py @@ -0,0 +1,42 @@ +""" +Given a n*n adjacency array. +it will give you all pairs shortest path length. +use deepcopy to preserve the original information. + +Time complexity : O(E^3) + +example + +a = [[0 , 0.1 , 0.101, 0.142, 0.277], + [0.465, 0 , 0.191, 0.192, 0.587], + [0.245, 0.554, 0 , 0.333, 0.931], + [1.032, 0.668, 0.656, 0 , 0.151], + [0.867, 0.119, 0.352, 0.398, 0]] + +result + +[[0 , 0.1 , 0.101, 0.142, 0.277], + [0.436, 0 , 0.191, 0.192, 0.343], + [0.245, 0.345, 0 , 0.333, 0.484], + [0.706, 0.27 , 0.461, 0 , 0.151], + [0.555, 0.119, 0.31 , 0.311, 0]] + +""" +import copy + +def all_pairs_shortest_path(adjacency_matrix): + """ + Given a matrix of the edge weights between respective nodes, returns a + matrix containing the shortest distance distance between the two nodes. + """ + + new_array = copy.deepcopy(adjacency_matrix) + + size = len(new_array) + for k in range(size): + for i in range(size): + for j in range(size): + if new_array[i][j] > new_array[i][k] + new_array[k][j]: + new_array[i][j] = new_array[i][k] + new_array[k][j] + + return new_array diff --git a/algorithms/graph/bellman_ford.py b/algorithms/graph/bellman_ford.py new file mode 100644 index 000000000..ea1e0465b --- /dev/null +++ b/algorithms/graph/bellman_ford.py @@ -0,0 +1,48 @@ +""" +Determination of single-source shortest-path. +""" + +def bellman_ford(graph, source): + """ + This Bellman-Ford Code is for determination whether we can get + shortest path from given graph or not for single-source shortest-paths problem. + In other words, if given graph has any negative-weight cycle that is reachable + from the source, then it will give answer False for "no solution exits". + For argument graph, it should be a dictionary type + such as + graph = { + 'a': {'b': 6, 'e': 7}, + 'b': {'c': 5, 'd': -4, 'e': 8}, + 'c': {'b': -2}, + 'd': {'a': 2, 'c': 7}, + 'e': {'b': -3} + } + """ + weight = {} + pre_node = {} + + initialize_single_source(graph, source, weight, pre_node) + + for _ in range(1, len(graph)): + for node in graph: + for adjacent in graph[node]: + if weight[adjacent] > weight[node] + graph[node][adjacent]: + weight[adjacent] = weight[node] + graph[node][adjacent] + pre_node[adjacent] = node + + for node in graph: + for adjacent in graph[node]: + if weight[adjacent] > weight[node] + graph[node][adjacent]: + return False + + return True + +def initialize_single_source(graph, source, weight, pre_node): + """ + Initialize data structures for Bellman-Ford algorithm. + """ + for node in graph: + weight[node] = float('inf') + pre_node[node] = None + + weight[source] = 0 diff --git a/algorithms/graph/check_bipartite.py b/algorithms/graph/check_bipartite.py new file mode 100644 index 000000000..51a84ab4c --- /dev/null +++ b/algorithms/graph/check_bipartite.py @@ -0,0 +1,40 @@ +""" +Bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets. +(https://en.wikipedia.org/wiki/Bipartite_graph) +""" + +def check_bipartite(adj_list): + """ + Determine if the given graph is bipartite. + + Time complexity is O(|E|) + Space complexity is O(|V|) + """ + + vertices = len(adj_list) + + # Divide vertexes in the graph into set_type 0 and 1 + # Initialize all set_types as -1 + set_type = [-1 for v in range(vertices)] + set_type[0] = 0 + + queue = [0] + + while queue: + current = queue.pop(0) + + # If there is a self-loop, it cannot be bipartite + if adj_list[current][current]: + return False + + for adjacent in range(vertices): + if adj_list[current][adjacent]: + if set_type[adjacent] == set_type[current]: + return False + + if set_type[adjacent] == -1: + # set type of u opposite of v + set_type[adjacent] = 1 - set_type[current] + queue.append(adjacent) + + return True diff --git a/algorithms/graph/check_digraph_strongly_connected.py b/algorithms/graph/check_digraph_strongly_connected.py new file mode 100644 index 000000000..03dd6ab79 --- /dev/null +++ b/algorithms/graph/check_digraph_strongly_connected.py @@ -0,0 +1,69 @@ +""" +In a directed graph, a strongly connected component is a set of vertices such +that for any pairs of vertices u and v there exists a path (u-...-v) that +connects them. A graph is strongly connected if it is a single strongly +connected component. +""" + +from collections import defaultdict + +class Graph: + """ + A directed graph where edges are one-way (a two-way edge can be represented by using two edges). + """ + + def __init__(self,vertex_count): + """ + Create a new graph with vertex_count vertices. + """ + + self.vertex_count = vertex_count + self.graph = defaultdict(list) + + def add_edge(self,source,target): + """ + Add an edge going from source to target + """ + self.graph[source].append(target) + + def dfs(self): + """ + Determine if all nodes are reachable from node 0 + """ + visited = [False] * self.vertex_count + self.dfs_util(0,visited) + if visited == [True]*self.vertex_count: + return True + return False + + def dfs_util(self,source,visited): + """ + Determine if all nodes are reachable from the given node + """ + visited[source] = True + for adjacent in self.graph[source]: + if not visited[adjacent]: + self.dfs_util(adjacent,visited) + + def reverse_graph(self): + """ + Create a new graph where every edge a->b is replaced with an edge b->a + """ + reverse_graph = Graph(self.vertex_count) + for source, adjacent in self.graph.items(): + for target in adjacent: + # Note: we reverse the order of arguments + # pylint: disable=arguments-out-of-order + reverse_graph.add_edge(target,source) + return reverse_graph + + + def is_strongly_connected(self): + """ + Determine if the graph is strongly connected. + """ + if self.dfs(): + reversed_graph = self.reverse_graph() + if reversed_graph.dfs(): + return True + return False diff --git a/algorithms/graph/clone_graph.py b/algorithms/graph/clone_graph.py new file mode 100644 index 000000000..84d0324cf --- /dev/null +++ b/algorithms/graph/clone_graph.py @@ -0,0 +1,123 @@ +r""" +Clone an undirected graph. Each node in the graph contains a label and a list +of its neighbors. + + +OJ's undirected graph serialization: +Nodes are labeled uniquely. + +We use # as a separator for each node, and , as a separator for node label and +each neighbor of the node. +As an example, consider the serialized graph {0,1,2#1,2#2,2}. + +The graph has a total of three nodes, and therefore contains three parts as +separated by #. + +First node is labeled as 0. Connect node 0 to both nodes 1 and 2. +Second node is labeled as 1. Connect node 1 to node 2. +Third node is labeled as 2. Connect node 2 to node 2 (itself), thus forming a +self-cycle. +Visually, the graph looks like the following: + + 1 + / \ + / \ + 0 --- 2 + / \ + \_/ +""" +import collections + + +class UndirectedGraphNode: + """ + A node in an undirected graph. Contains a label and a list of neighbouring + nodes (initially empty). + """ + + def __init__(self, label): + self.label = label + self.neighbors = [] + + def shallow_copy(self): + """ + Return a shallow copy of this node (ignoring any neighbors) + """ + return UndirectedGraphNode(self.label) + + def add_neighbor(self, node): + """ + Adds a new neighbor + """ + self.neighbors.append(node) + + +def clone_graph1(node): + """ + Returns a new graph as seen from the given node using a breadth first search (BFS). + """ + if not node: + return None + node_copy = node.shallow_copy() + dic = {node: node_copy} + queue = collections.deque([node]) + while queue: + node = queue.popleft() + for neighbor in node.neighbors: + if neighbor not in dic: # neighbor is not visited + neighbor_copy = neighbor.shallow_copy() + dic[neighbor] = neighbor_copy + dic[node].add_neighbor(neighbor_copy) + queue.append(neighbor) + else: + dic[node].add_neighbor(dic[neighbor]) + return node_copy + + +def clone_graph2(node): + """ + Returns a new graph as seen from the given node using an iterative depth first search (DFS). + """ + if not node: + return None + node_copy = node.shallow_copy() + dic = {node: node_copy} + stack = [node] + while stack: + node = stack.pop() + for neighbor in node.neighbors: + if neighbor not in dic: + neighbor_copy = neighbor.shallow_copy() + dic[neighbor] = neighbor_copy + dic[node].add_neighbor(neighbor_copy) + stack.append(neighbor) + else: + dic[node].add_neighbor(dic[neighbor]) + return node_copy + + +def clone_graph(node): + """ + Returns a new graph as seen from the given node using a recursive depth first search (DFS). + """ + if not node: + return None + node_copy = node.shallow_copy() + dic = {node: node_copy} + dfs(node, dic) + return node_copy + + +def dfs(node, dic): + """ + Clones a graph using a recursive depth first search. Stores the clones in + the dictionary, keyed by the original nodes. + """ + for neighbor in node.neighbors: + if neighbor not in dic: + neighbor_copy = neighbor.shallow_copy() + dic[neighbor] = neighbor_copy + dic[node].add_neighbor(neighbor_copy) + dfs(neighbor, dic) + else: + dic[node].add_neighbor(dic[neighbor]) diff --git a/algorithms/graph/count_connected_number_of_component.py b/algorithms/graph/count_connected_number_of_component.py new file mode 100644 index 000000000..a58eda6c3 --- /dev/null +++ b/algorithms/graph/count_connected_number_of_component.py @@ -0,0 +1,59 @@ +#count connected no of component using DFS +''' +In graph theory, a component, sometimes called a connected component, +of an undirected graph is a subgraph in which any +two vertices are connected to each other by paths. + +Example: + + + 1 3------------7 + | + | + 2--------4 + | | + | | output = 2 + 6--------5 + +''' + +# Code is Here + +def dfs(source,visited,adjacency_list): + ''' Function that performs DFS ''' + + visited[source] = True + for child in adjacency_list[source]: + if not visited[child]: + dfs(child,visited,adjacency_list) + +def count_components(adjacency_list,size): + ''' + Function that counts the Connected components on bases of DFS. + return type : int + ''' + + count = 0 + visited = [False]*(size+1) + for i in range(1,size+1): + if not visited[i]: + dfs(i,visited,adjacency_list) + count+=1 + return count + +def main(): + """ + Example application + """ + node_count,edge_count = map(int, input("Enter the Number of Nodes and Edges \n").split(' ')) + adjacency = [[] for _ in range(node_count+1)] + for _ in range(edge_count): + print("Enter the edge's Nodes in form of `source target`\n") + source,target = map(int,input().split(' ')) + adjacency[source].append(target) + adjacency[target].append(source) + print("Total number of Connected Components are : ", count_components(adjacency,node_count)) + +# Driver code +if __name__ == '__main__': + main() diff --git a/graph/cycle_detection.py b/algorithms/graph/cycle_detection.py similarity index 61% rename from graph/cycle_detection.py rename to algorithms/graph/cycle_detection.py index 61cf61c1f..0821b1c0a 100644 --- a/graph/cycle_detection.py +++ b/algorithms/graph/cycle_detection.py @@ -9,27 +9,22 @@ class TraversalState(Enum): + """ + For a given node: + - WHITE: has not been visited yet + - GRAY: is currently being investigated for a cycle + - BLACK: is not part of a cycle + """ WHITE = 0 GRAY = 1 BLACK = 2 - -example_graph_with_cycle = {'A': ['B', 'C'], - 'B': ['D'], - 'C': ['F'], - 'D': ['E', 'F'], - 'E': ['B'], - 'F': []} - -example_graph_without_cycle = {'A': ['B', 'C'], - 'B': ['D', 'E'], - 'C': ['F'], - 'D': ['E'], - 'E': [], - 'F': []} - - def is_in_cycle(graph, traversal_states, vertex): + """ + Determines if the given vertex is in a cycle. + + :param: traversal_states: for each vertex, the state it is in + """ if traversal_states[vertex] == TraversalState.GRAY: return True traversal_states[vertex] = TraversalState.GRAY @@ -41,12 +36,20 @@ def is_in_cycle(graph, traversal_states, vertex): def contains_cycle(graph): + """ + Determines if there is a cycle in the given graph. + The graph should be given as a dictionary: + + graph = {'A': ['B', 'C'], + 'B': ['D'], + 'C': ['F'], + 'D': ['E', 'F'], + 'E': ['B'], + 'F': []} + """ traversal_states = {vertex: TraversalState.WHITE for vertex in graph} for vertex, state in traversal_states.items(): if (state == TraversalState.WHITE and is_in_cycle(graph, traversal_states, vertex)): return True return False - -print(contains_cycle(example_graph_with_cycle)) -print(contains_cycle(example_graph_without_cycle)) diff --git a/algorithms/graph/dijkstra.py b/algorithms/graph/dijkstra.py new file mode 100644 index 000000000..e5022e3af --- /dev/null +++ b/algorithms/graph/dijkstra.py @@ -0,0 +1,49 @@ +""" +Dijkstra's single-source shortest-path algorithm +""" + +class Dijkstra(): + """ + A fully connected directed graph with edge weights + """ + + def __init__(self, vertex_count): + self.vertex_count = vertex_count + self.graph = [[0 for _ in range(vertex_count)] for _ in range(vertex_count)] + + def min_distance(self, dist, min_dist_set): + """ + Find the vertex that is closest to the visited set + """ + min_dist = float("inf") + for target in range(self.vertex_count): + if min_dist_set[target]: + continue + if dist[target] < min_dist: + min_dist = dist[target] + min_index = target + return min_index + + def dijkstra(self, src): + """ + Given a node, returns the shortest distance to every other node + """ + dist = [float("inf")] * self.vertex_count + dist[src] = 0 + min_dist_set = [False] * self.vertex_count + + for _ in range(self.vertex_count): + #minimum distance vertex that is not processed + source = self.min_distance(dist, min_dist_set) + + #put minimum distance vertex in shortest tree + min_dist_set[source] = True + + #Update dist value of the adjacent vertices + for target in range(self.vertex_count): + if self.graph[source][target] <= 0 or min_dist_set[target]: + continue + if dist[target] > dist[source] + self.graph[source][target]: + dist[target] = dist[source] + self.graph[source][target] + + return dist diff --git a/graph/find_all_cliques.py b/algorithms/graph/find_all_cliques.py similarity index 62% rename from graph/find_all_cliques.py rename to algorithms/graph/find_all_cliques.py index 10f7a24eb..f1db16ed5 100644 --- a/graph/find_all_cliques.py +++ b/algorithms/graph/find_all_cliques.py @@ -1,12 +1,19 @@ -# takes dict of sets -# each key is a vertex -# value is set of all edges connected to vertex -# returns list of lists (each sub list is a maximal clique) -# implementation of the basic algorithm described in: -# Bron, Coen; Kerbosch, Joep (1973), "Algorithm 457: finding all cliques of an undirected graph", - +""" +Finds all cliques in an undirected graph. A clique is a set of vertices in the +graph such that the subgraph is fully connected (ie. for any pair of nodes in +the subgraph there is an edge between them). +""" def find_all_cliques(edges): + """ + takes dict of sets + each key is a vertex + value is set of all edges connected to vertex + returns list of lists (each sub list is a maximal clique) + implementation of the basic algorithm described in: + Bron, Coen; Kerbosch, Joep (1973), "Algorithm 457: finding all cliques of an undirected graph", + """ + def expand_clique(candidates, nays): nonlocal compsub if not candidates and not nays: diff --git a/graph/find_path.py b/algorithms/graph/find_path.py similarity index 68% rename from graph/find_path.py rename to algorithms/graph/find_path.py index 5008da05a..253e43ca3 100644 --- a/graph/find_path.py +++ b/algorithms/graph/find_path.py @@ -1,14 +1,14 @@ -myGraph = {'A': ['B', 'C'], - 'B': ['C', 'D'], - 'C': ['D', 'F'], - 'D': ['C'], - 'E': ['F'], - 'F': ['C']} +""" +Functions for finding paths in graphs. +""" -# find path from start to end using recursion with backtracking +# pylint: disable=dangerous-default-value def find_path(graph, start, end, path=[]): + """ + Find a path between two nodes using recursion and backtracking. + """ path = path + [start] - if (start == end): + if start == end: return path if not start in graph: return None @@ -18,14 +18,16 @@ def find_path(graph, start, end, path=[]): return newpath return None -# find all path +# pylint: disable=dangerous-default-value def find_all_path(graph, start, end, path=[]): + """ + Find all paths between two nodes using recursion and backtracking + """ path = path + [start] - print(path) - if (start == end): + if start == end: return [path] if not start in graph: - return None + return [] paths = [] for node in graph[start]: if node not in path: @@ -35,6 +37,9 @@ def find_all_path(graph, start, end, path=[]): return paths def find_shortest_path(graph, start, end, path=[]): + """ + find the shortest path between two nodes + """ path = path + [start] if start == end: return path @@ -43,11 +48,8 @@ def find_shortest_path(graph, start, end, path=[]): shortest = None for node in graph[start]: if node not in path: - newpath = find_shortest_path(graph, start, end, path) + newpath = find_shortest_path(graph, node, end, path) if newpath: if not shortest or len(newpath) < len(shortest): shortest = newpath return shortest - -print(find_all_path(myGraph, 'A', 'F')) -# print(find_shortest_path(myGraph, 'A', 'D')) diff --git a/algorithms/graph/graph.py b/algorithms/graph/graph.py new file mode 100644 index 000000000..5d4305933 --- /dev/null +++ b/algorithms/graph/graph.py @@ -0,0 +1,111 @@ +""" +These are classes to represent a Graph and its elements. +It can be shared across graph algorithms. +""" + +class Node: + """ + A node/vertex in a graph. + """ + + def __init__(self, name): + self.name = name + + @staticmethod + def get_name(obj): + """ + Return the name of the node + """ + if isinstance(obj, Node): + return obj.name + if isinstance(obj, str): + return obj + return'' + + def __eq__(self, obj): + return self.name == self.get_name(obj) + + def __repr__(self): + return self.name + + def __hash__(self): + return hash(self.name) + + def __ne__(self, obj): + return self.name != self.get_name(obj) + + def __lt__(self, obj): + return self.name < self.get_name(obj) + + def __le__(self, obj): + return self.name <= self.get_name(obj) + + def __gt__(self, obj): + return self.name > self.get_name(obj) + + def __ge__(self, obj): + return self.name >= self.get_name(obj) + + def __bool__(self): + return self.name + +class DirectedEdge: + """ + A directed edge in a directed graph. + Stores the source and target node of the edge. + """ + + def __init__(self, node_from, node_to): + self.source = node_from + self.target = node_to + + def __eq__(self, obj): + if isinstance(obj, DirectedEdge): + return obj.source == self.source and obj.target == self.target + return False + + def __repr__(self): + return f"({self.source} -> {self.target})" + +class DirectedGraph: + """ + A directed graph. + Stores a set of nodes, edges and adjacency matrix. + """ + + # pylint: disable=dangerous-default-value + def __init__(self, load_dict={}): + self.nodes = [] + self.edges = [] + self.adjacency_list = {} + + if load_dict and isinstance(load_dict, dict): + for vertex in load_dict: + node_from = self.add_node(vertex) + self.adjacency_list[node_from] = [] + for neighbor in load_dict[vertex]: + node_to = self.add_node(neighbor) + self.adjacency_list[node_from].append(node_to) + self.add_edge(vertex, neighbor) + + def add_node(self, node_name): + """ + Add a new named node to the graph. + """ + try: + return self.nodes[self.nodes.index(node_name)] + except ValueError: + node = Node(node_name) + self.nodes.append(node) + return node + + def add_edge(self, node_name_from, node_name_to): + """ + Add a new edge to the graph between two nodes. + """ + try: + node_from = self.nodes[self.nodes.index(node_name_from)] + node_to = self.nodes[self.nodes.index(node_name_to)] + self.edges.append(DirectedEdge(node_from, node_to)) + except ValueError: + pass diff --git a/algorithms/graph/markov_chain.py b/algorithms/graph/markov_chain.py new file mode 100644 index 000000000..78c50bd12 --- /dev/null +++ b/algorithms/graph/markov_chain.py @@ -0,0 +1,39 @@ +""" +Implements a markov chain. Chains are described using a dictionary: + + my_chain = { + 'A': {'A': 0.6, + 'E': 0.4}, + 'E': {'A': 0.7, + 'E': 0.3} + } +""" + +import random + +def __choose_state(state_map): + """ + Choose the next state randomly + """ + choice = random.random() + probability_reached = 0 + for state, probability in state_map.items(): + probability_reached += probability + if probability_reached > choice: + return state + return None + +def next_state(chain, current_state): + """ + Given a markov-chain, randomly chooses the next state given the current state. + """ + next_state_map = chain.get(current_state) + return __choose_state(next_state_map) + +def iterating_markov_chain(chain, state): + """ + Yield a sequence of states given a markov chain and the initial state + """ + while True: + state = next_state(chain, state) + yield state diff --git a/algorithms/graph/maximum_flow.py b/algorithms/graph/maximum_flow.py new file mode 100644 index 000000000..b46e70790 --- /dev/null +++ b/algorithms/graph/maximum_flow.py @@ -0,0 +1,149 @@ +""" +Given the capacity, source and sink of a graph, +computes the maximum flow from source to sink. +Input : capacity, source, sink +Output : maximum flow from source to sink +Capacity is a two-dimensional array that is v*v. +capacity[i][j] implies the capacity of the edge from i to j. +If there is no edge from i to j, capacity[i][j] should be zero. +""" + +from queue import Queue + +# pylint: disable=too-many-arguments +def dfs(capacity, flow, visit, vertices, idx, sink, current_flow = 1 << 63): + """ + Depth First Search implementation for Ford-Fulkerson algorithm. + """ + + # DFS function for ford_fulkerson algorithm. + if idx == sink: + return current_flow + visit[idx] = True + for nxt in range(vertices): + if not visit[nxt] and flow[idx][nxt] < capacity[idx][nxt]: + available_flow = min(current_flow, capacity[idx][nxt]-flow[idx][nxt]) + tmp = dfs(capacity, flow, visit, vertices, nxt, sink, available_flow) + if tmp: + flow[idx][nxt] += tmp + flow[nxt][idx] -= tmp + return tmp + return 0 + +def ford_fulkerson(capacity, source, sink): + """ + Computes maximum flow from source to sink using DFS. + Time Complexity : O(Ef) + E is the number of edges and f is the maximum flow in the graph. + """ + vertices = len(capacity) + ret = 0 + flow = [[0]*vertices for _ in range(vertices)] + while True: + visit = [False for _ in range(vertices)] + tmp = dfs(capacity, flow, visit, vertices, source, sink) + if tmp: + ret += tmp + else: + break + return ret + +def edmonds_karp(capacity, source, sink): + """ + Computes maximum flow from source to sink using BFS. + Time complexity : O(V*E^2) + V is the number of vertices and E is the number of edges. + """ + vertices = len(capacity) + ret = 0 + flow = [[0]*vertices for _ in range(vertices)] + while True: + tmp = 0 + queue = Queue() + visit = [False for _ in range(vertices)] + par = [-1 for _ in range(vertices)] + visit[source] = True + queue.put((source, 1 << 63)) + # Finds new flow using BFS. + while queue.qsize(): + front = queue.get() + idx, current_flow = front + if idx == sink: + tmp = current_flow + break + for nxt in range(vertices): + if not visit[nxt] and flow[idx][nxt] < capacity[idx][nxt]: + visit[nxt] = True + par[nxt] = idx + queue.put((nxt, min(current_flow, capacity[idx][nxt]-flow[idx][nxt]))) + if par[sink] == -1: + break + ret += tmp + parent = par[sink] + idx = sink + # Update flow array following parent starting from sink. + while parent != -1: + flow[parent][idx] += tmp + flow[idx][parent] -= tmp + idx = parent + parent = par[parent] + return ret + +def dinic_bfs(capacity, flow, level, source, sink): + """ + BFS function for Dinic algorithm. + Check whether sink is reachable only using edges that is not full. + """ + vertices = len(capacity) + queue = Queue() + queue.put(source) + level[source] = 0 + while queue.qsize(): + front = queue.get() + for nxt in range(vertices): + if level[nxt] == -1 and flow[front][nxt] < capacity[front][nxt]: + level[nxt] = level[front] + 1 + queue.put(nxt) + return level[sink] != -1 + +def dinic_dfs(capacity, flow, level, idx, sink, work, current_flow = 1 << 63): + """ + DFS function for Dinic algorithm. + Finds new flow using edges that is not full. + """ + if idx == sink: + return current_flow + vertices = len(capacity) + while work[idx] < vertices: + nxt = work[idx] + if level[nxt] == level[idx] + 1 and flow[idx][nxt] < capacity[idx][nxt]: + available_flow = min(current_flow, capacity[idx][nxt] - flow[idx][nxt]) + tmp = dinic_dfs(capacity, flow, level, nxt, sink, work, available_flow) + if tmp > 0: + flow[idx][nxt] += tmp + flow[nxt][idx] -= tmp + return tmp + work[idx] += 1 + return 0 + +def dinic(capacity, source, sink): + """ + Computes maximum flow from source to sink using Dinic algorithm. + Time complexity : O(V^2*E) + V is the number of vertices and E is the number of edges. + """ + vertices = len(capacity) + flow = [[0]*vertices for i in range(vertices)] + ret = 0 + while True: + level = [-1 for i in range(vertices)] + work = [0 for i in range(vertices)] + if not dinic_bfs(capacity, flow, level, source, sink): + break + while True: + tmp = dinic_dfs(capacity, flow, level, source, sink, work) + if tmp > 0: + ret += tmp + else: + break + return ret diff --git a/algorithms/graph/maximum_flow_bfs.py b/algorithms/graph/maximum_flow_bfs.py new file mode 100644 index 000000000..bd056c8d3 --- /dev/null +++ b/algorithms/graph/maximum_flow_bfs.py @@ -0,0 +1,87 @@ +""" +Given a n*n adjacency array. +it will give you a maximum flow. +This version use BFS to search path. + +Assume the first is the source and the last is the sink. + +Time complexity - O(Ef) + +example + +graph = [[0, 16, 13, 0, 0, 0], + [0, 0, 10, 12, 0, 0], + [0, 4, 0, 0, 14, 0], + [0, 0, 9, 0, 0, 20], + [0, 0, 0, 7, 0, 4], + [0, 0, 0, 0, 0, 0]] + +answer should be + +23 + +""" +import copy +import queue +import math + +def maximum_flow_bfs(adjacency_matrix): + """ + Get the maximum flow through a graph using a breadth first search + """ + #initial setting + new_array = copy.deepcopy(adjacency_matrix) + total = 0 + + while True: + #setting min to max_value + min_flow = math.inf + #save visited nodes + visited = [0]*len(new_array) + #save parent nodes + path = [0]*len(new_array) + + #initialize queue for BFS + bfs = queue.Queue() + + #initial setting + visited[0] = 1 + bfs.put(0) + + #BFS to find path + while bfs.qsize() > 0: + #pop from queue + src = bfs.get() + for k in range(len(new_array)): + #checking capacity and visit + if(new_array[src][k] > 0 and visited[k] == 0 ): + #if not, put into queue and chage to visit and save path + visited[k] = 1 + bfs.put(k) + path[k] = src + + #if there is no path from src to sink + if visited[len(new_array) - 1] == 0: + break + + #initial setting + tmp = len(new_array) - 1 + + #Get minimum flow + while tmp != 0: + #find minimum flow + if min_flow > new_array[path[tmp]][tmp]: + min_flow = new_array[path[tmp]][tmp] + tmp = path[tmp] + + #initial setting + tmp = len(new_array) - 1 + + #reduce capacity + while tmp != 0: + new_array[path[tmp]][tmp] = new_array[path[tmp]][tmp] - min_flow + tmp = path[tmp] + + total = total + min_flow + + return total diff --git a/algorithms/graph/maximum_flow_dfs.py b/algorithms/graph/maximum_flow_dfs.py new file mode 100644 index 000000000..e27c4e851 --- /dev/null +++ b/algorithms/graph/maximum_flow_dfs.py @@ -0,0 +1,88 @@ +""" +Given a n*n adjacency array. +it will give you a maximum flow. +This version use DFS to search path. + +Assume the first is the source and the last is the sink. + +Time complexity - O(Ef) + +example + +graph = [[0, 16, 13, 0, 0, 0], + [0, 0, 10, 12, 0, 0], + [0, 4, 0, 0, 14, 0], + [0, 0, 9, 0, 0, 20], + [0, 0, 0, 7, 0, 4], + [0, 0, 0, 0, 0, 0]] + +answer should be + +23 + +""" +import copy +import math + +def maximum_flow_dfs(adjacency_matrix): + """ + Get the maximum flow through a graph using a depth first search + """ + + #initial setting + new_array = copy.deepcopy(adjacency_matrix) + total = 0 + + while True: + #setting min to max_value + min = math.inf + #save visited nodes + visited = [0]*len(new_array) + #save parent nodes + path = [0]*len(new_array) + + #initialize stack for DFS + stack = [] + + #initial setting + visited[0] = 1 + stack.append(0) + + #DFS to find path + while len(stack) > 0: + #pop from queue + src = stack.pop() + for k in range(len(new_array)): + #checking capacity and visit + if new_array[src][k] > 0 and visited[k] == 0: + #if not, put into queue and chage to visit and save path + visited[k] = 1 + stack.append(k) + path[k] = src + + #if there is no path from src to sink + if visited[len(new_array) - 1] == 0: + break + + #initial setting + tmp = len(new_array) - 1 + + #Get minimum flow + while tmp != 0: + #find minimum flow + if min > new_array[path[tmp]][tmp]: + min = new_array[path[tmp]][tmp] + tmp = path[tmp] + + #initial setting + tmp = len(new_array) - 1 + + #reduce capacity + while tmp != 0: + new_array[path[tmp]][tmp] = new_array[path[tmp]][tmp] - min + tmp = path[tmp] + + total = total + min + + return total + diff --git a/algorithms/graph/minimum_spanning_tree.py b/algorithms/graph/minimum_spanning_tree.py new file mode 100644 index 000000000..d53a957ca --- /dev/null +++ b/algorithms/graph/minimum_spanning_tree.py @@ -0,0 +1,151 @@ +""" +Minimum spanning tree (MST) is going to use an undirected graph +""" + +import sys + +# pylint: disable=too-few-public-methods +class Edge: + """ + An edge of an undirected graph + """ + + def __init__(self, source, target, weight): + self.source = source + self.target = target + self.weight = weight + + +class DisjointSet: + """ + The disjoint set is represented with an list of integers where + is the parent of the node at position . + If = , it's a root, or a head, of a set + """ + + def __init__(self, size): + """ + Args: + n (int): Number of vertices in the graph + """ + + self.parent = [None] * size # Contains wich node is the parent of the node at poisition + self.size = [1] * size # Contains size of node at index , used to optimize merge + for i in range(size): + self.parent[i] = i # Make all nodes his own parent, creating n sets. + + def merge_set(self, node1, node2): + """ + Args: + node1, node2 (int): Indexes of nodes whose sets will be merged. + """ + + # Get the set of nodes at position and + # If and are the roots, this will be constant O(1) + node1 = self.find_set(node1) + node2 = self.find_set(node2) + + # Join the shortest node to the longest, minimizing tree size (faster find) + if self.size[node1] < self.size[node2]: + self.parent[node1] = node2 # Merge set(a) and set(b) + self.size[node2] += self.size[node1] # Add size of old set(a) to set(b) + else: + self.parent[node2] = node1 # Merge set(b) and set(a) + self.size[node1] += self.size[node2] # Add size of old set(b) to set(a) + + def find_set(self, node): + """ + Get the root element of the set containing + """ + if self.parent[node] != node: + # Very important, memoize result of the + # recursion in the list to optimize next + # calls and make this operation practically constant, O(1) + self.parent[node] = self.find_set(self.parent[node]) + + # node it's the set root, so we can return that index + return self.parent[node] + + +def kruskal(vertex_count, edges, forest): + """ + Args: + vertex_count (int): Number of vertices in the graph + edges (list of Edge): Edges of the graph + forest (DisjointSet): DisjointSet of the vertices + Returns: + int: sum of weights of the minnimum spanning tree + + Kruskal algorithm: + This algorithm will find the optimal graph with less edges and less + total weight to connect all vertices (MST), the MST will always contain + n-1 edges because it's the minimum required to connect n vertices. + + Procedure: + Sort the edges (criteria: less weight). + Only take edges of nodes in different sets. + If we take a edge, we need to merge the sets to discard these. + After repeat this until select n-1 edges, we will have the complete MST. + """ + edges.sort(key=lambda edge: edge.weight) + + mst = [] # List of edges taken, minimum spanning tree + + for edge in edges: + set_u = forest.find_set(edge.u) # Set of the node + set_v = forest.find_set(edge.v) # Set of the node + if set_u != set_v: + forest.merge_set(set_u, set_v) + mst.append(edge) + if len(mst) == vertex_count-1: + # If we have selected n-1 edges, all the other + # edges will be discarted, so, we can stop here + break + + return sum([edge.weight for edge in mst]) + + +def main(): + """ + Test. How input works: + Input consists of different weighted, connected, undirected graphs. + line 1: + integers n, m + lines 2..m+2: + edge with the format -> node index u, node index v, integer weight + + Samples of input: + + 5 6 + 1 2 3 + 1 3 8 + 2 4 5 + 3 4 2 + 3 5 4 + 4 5 6 + + 3 3 + 2 1 20 + 3 1 20 + 2 3 100 + + Sum of weights of the optimal paths: + 14, 40 + """ + for size in sys.stdin: + vertex_count, edge_count = map(int, size.split()) + forest = DisjointSet(edge_count) + edges = [None] * edge_count # Create list of size + + # Read edges from input + for i in range(edge_count): + source, target, weight = map(int, input().split()) + source -= 1 # Convert from 1-indexed to 0-indexed + target -= 1 # Convert from 1-indexed to 0-indexed + edges[i] = Edge(source, target, weight) + + # After finish input and graph creation, use Kruskal algorithm for MST: + print("MST weights sum:", kruskal(vertex_count, edges, forest)) + +if __name__ == "__main__": + main() diff --git a/algorithms/graph/path_between_two_vertices_in_digraph.py b/algorithms/graph/path_between_two_vertices_in_digraph.py new file mode 100644 index 000000000..4bf290253 --- /dev/null +++ b/algorithms/graph/path_between_two_vertices_in_digraph.py @@ -0,0 +1,51 @@ +""" +Determine if there is a path between nodes in a graph +""" + +from collections import defaultdict + + +class Graph: + """ + A directed graph + """ + + def __init__(self,vertex_count): + self.vertex_count = vertex_count + self.graph = defaultdict(list) + self.has_path = False + + def add_edge(self,source,target): + """ + Add a new directed edge to the graph + """ + self.graph[source].append(target) + + def dfs(self,source,target): + """ + Determine if there is a path from source to target using a depth first search + """ + visited = [False] * self.vertex_count + self.dfsutil(visited,source,target,) + + def dfsutil(self,visited,source,target): + """ + Determine if there is a path from source to target using a depth first search. + :param: visited should be an array of booleans determining if the + corresponding vertex has been visited already + """ + visited[source] = True + for i in self.graph[source]: + if target in self.graph[source]: + self.has_path = True + return + if not visited[i]: + self.dfsutil(visited,source,i) + + def is_reachable(self,source,target): + """ + Determine if there is a path from source to target + """ + self.has_path = False + self.dfs(source,target) + return self.has_path diff --git a/algorithms/graph/prims_minimum_spanning.py b/algorithms/graph/prims_minimum_spanning.py new file mode 100644 index 000000000..af7cb4357 --- /dev/null +++ b/algorithms/graph/prims_minimum_spanning.py @@ -0,0 +1,42 @@ +''' +This Prim's Algorithm Code is for finding weight of minimum spanning tree +of a connected graph. +For argument graph, it should be a dictionary type such as: + + graph = { + 'a': [ [3, 'b'], [8,'c'] ], + 'b': [ [3, 'a'], [5, 'd'] ], + 'c': [ [8, 'a'], [2, 'd'], [4, 'e'] ], + 'd': [ [5, 'b'], [2, 'c'], [6, 'e'] ], + 'e': [ [4, 'c'], [6, 'd'] ] + } + +where 'a','b','c','d','e' are nodes (these can be 1,2,3,4,5 as well) +''' + + +import heapq # for priority queue + +def prims_minimum_spanning(graph_used): + """ + Prim's algorithm to find weight of minimum spanning tree + """ + vis=[] + heap=[[0,1]] + prim = set() + mincost=0 + + while len(heap) > 0: + cost, node = heapq.heappop(heap) + if node in vis: + continue + + mincost += cost + prim.add(node) + vis.append(node) + + for distance, adjacent in graph_used[node]: + if adjacent not in vis: + heapq.heappush(heap, [distance, adjacent]) + + return mincost diff --git a/graph/satisfiability.py b/algorithms/graph/satisfiability.py similarity index 54% rename from graph/satisfiability.py rename to algorithms/graph/satisfiability.py index ad166c964..0cae8ee92 100644 --- a/graph/satisfiability.py +++ b/algorithms/graph/satisfiability.py @@ -1,45 +1,49 @@ -''' +""" Given a formula in conjunctive normal form (2-CNF), finds a way to assign True/False values to all variables to satisfy all clauses, or reports there is no solution. https://en.wikipedia.org/wiki/2-satisfiability -''' -''' Format: +Format: - each clause is a pair of literals - each literal in the form (name, is_neg) where name is an arbitrary identifier, and is_neg is true if the literal is negated -''' -formula = [(('x', False), ('y', False)), - (('y', True), ('y', True)), - (('a', False), ('b', False)), - (('a', True), ('c', True)), - (('c', False), ('b', True))] +""" +def dfs_transposed(vertex, graph, order, visited): + """ + Perform a depth first search traversal of the graph starting at the given vertex. + Stores the order in which nodes were visited to the list, in transposed order. + """ + visited[vertex] = True -def dfs_transposed(v, graph, order, vis): - vis[v] = True + for adjacent in graph[vertex]: + if not visited[adjacent]: + dfs_transposed(adjacent, graph, order, visited) - for u in graph[v]: - if not vis[u]: - dfs_transposed(u, graph, order, vis) + order.append(vertex) - order.append(v) +def dfs(vertex, current_comp, vertex_scc, graph, visited): + """ + Perform a depth first search traversal of the graph starting at the given vertex. + Records all visited nodes as being of a certain strongly connected component. + """ + visited[vertex] = True + vertex_scc[vertex] = current_comp -def dfs(v, current_comp, vertex_scc, graph, vis): - vis[v] = True - vertex_scc[v] = current_comp - - for u in graph[v]: - if not vis[u]: - dfs(u, current_comp, vertex_scc, graph, vis) + for adjacent in graph[vertex]: + if not visited[adjacent]: + dfs(adjacent, current_comp, vertex_scc, graph, visited) def add_edge(graph, vertex_from, vertex_to): + """ + Add a directed edge to the graph. + """ if vertex_from not in graph: graph[vertex_from] = [] @@ -49,26 +53,26 @@ def add_edge(graph, vertex_from, vertex_to): def scc(graph): ''' Computes the strongly connected components of a graph ''' order = [] - vis = {vertex: False for vertex in graph} + visited = {vertex: False for vertex in graph} graph_transposed = {vertex: [] for vertex in graph} - for (v, neighbours) in graph.iteritems(): - for u in neighbours: - add_edge(graph_transposed, u, v) + for (source, neighbours) in graph.iteritems(): + for target in neighbours: + add_edge(graph_transposed, target, source) - for v in graph: - if not vis[v]: - dfs_transposed(v, graph_transposed, order, vis) + for vertex in graph: + if not visited[vertex]: + dfs_transposed(vertex, graph_transposed, order, visited) - vis = {vertex: False for vertex in graph} + visited = {vertex: False for vertex in graph} vertex_scc = {} current_comp = 0 - for v in reversed(order): - if not vis[v]: + for vertex in reversed(order): + if not visited[vertex]: # Each dfs will visit exactly one component - dfs(v, current_comp, vertex_scc, graph, vis) + dfs(vertex, current_comp, vertex_scc, graph, visited) current_comp += 1 return vertex_scc @@ -91,6 +95,9 @@ def build_graph(formula): def solve_sat(formula): + """ + Solves the 2-SAT problem + """ graph = build_graph(formula) vertex_scc = scc(graph) @@ -118,8 +125,21 @@ def solve_sat(formula): return value -if __name__ == '__main__': + +def main(): + """ + Entry point for testing + """ + formula = [(('x', False), ('y', False)), + (('y', True), ('y', True)), + (('a', False), ('b', False)), + (('a', True), ('c', True)), + (('c', False), ('b', True))] + result = solve_sat(formula) - for (variable, assign) in result.iteritems(): - print variable, ":", assign + for (variable, assign) in result.items(): + print(f"{variable}:{assign}") + +if __name__ == '__main__': + main() diff --git a/algorithms/graph/strongly_connected_components_kosaraju.py b/algorithms/graph/strongly_connected_components_kosaraju.py new file mode 100644 index 000000000..0c82a7af6 --- /dev/null +++ b/algorithms/graph/strongly_connected_components_kosaraju.py @@ -0,0 +1,81 @@ +""" +Implementing strongly connected components in a graph using Kosaraju's algorithm. +https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm +""" + + +class Kosaraju: + """ + Kosaraju's algorithm use depth first search approach to find strongly connected components in a directed graph. + Approach: + 1. Make a DFS call to keep track of finish time of each vertex. + 2. Tranpose the original graph. ie 1->2 transpose is 1<-2 + 3. Make another DFS call to calculate strongly connected components. + """ + + def dfs(self, i, V, adj, visited, stk): + visited[i] = 1 + + for x in adj[i]: + if visited[x] == -1: + self.dfs(x, V, adj, visited, stk) + + stk.append(i) + + def kosaraju(self, V, adj): + + stk, visited = [], [-1]*(V+1) + + for i in range(V): + if visited[i] == -1: + self.dfs(i, V, adj, visited, stk) + + stk.reverse() + res = stk.copy() + + ans, visited1 = 0, [-1]*(V+1) + + adj1 = [[] for x in range(V)] + + for i in range(len(adj)): + for x in adj[i]: + adj1[x].append(i) + + for i in range(len(res)): + if visited1[res[i]] == -1: + ans += 1 + self.dfs(res[i], V, adj1, visited1, stk) + + return ans + + +def main(): + """ + Let's look at the sample input. + + 6 7 #no of vertex, no of edges + 0 2 #directed edge 0->2 + 1 0 + 2 3 + 3 1 + 3 4 + 4 5 + 5 4 + + calculating no of strongly connected compnenets in a directed graph. + answer should be: 2 + 1st strong component: 0->2->3->1->0 + 2nd strongly connected component: 4->5->4 + """ + V, E = map(int, input().split()) + adj = [[] for x in range(V)] + + for i in range(E): + u, v = map(int, input().split()) + adj[u].append(v) + + print(Kosaraju().kosaraju(V, adj)) + + +if __name__ == '__main__': + main() diff --git a/algorithms/graph/tarjan.py b/algorithms/graph/tarjan.py new file mode 100644 index 000000000..ebc69326c --- /dev/null +++ b/algorithms/graph/tarjan.py @@ -0,0 +1,65 @@ +""" +Implements Tarjan's algorithm for finding strongly connected components +in a graph. +https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm +""" +from algorithms.graph.graph import DirectedGraph + + +# pylint: disable=too-few-public-methods +class Tarjan: + """ + A directed graph used for finding strongly connected components + """ + def __init__(self, dict_graph): + self.graph = DirectedGraph(dict_graph) + self.index = 0 + self.stack = [] + + # Runs Tarjan + # Set all node index to None + for vertex in self.graph.nodes: + vertex.index = None + + self.sccs = [] + for vertex in self.graph.nodes: + if vertex.index is None: + self.strongconnect(vertex, self.sccs) + + def strongconnect(self, vertex, sccs): + """ + Given a vertex, adds all successors of the given vertex to the same connected component + """ + # Set the depth index for v to the smallest unused index + vertex.index = self.index + vertex.lowlink = self.index + self.index += 1 + self.stack.append(vertex) + vertex.on_stack = True + + # Consider successors of v + for adjacent in self.graph.adjacency_list[vertex]: + if adjacent.index is None: + # Successor w has not yet been visited; recurse on it + self.strongconnect(adjacent, sccs) + vertex.lowlink = min(vertex.lowlink, adjacent.lowlink) + elif adjacent.on_stack: + # Successor w is in stack S and hence in the current SCC + # If w is not on stack, then (v, w) is a cross-edge in the DFS + # tree and must be ignored + # Note: The next line may look odd - but is correct. + # It says w.index not w.lowlink; that is deliberate and from the original paper + vertex.lowlink = min(vertex.lowlink, adjacent.index) + + # If v is a root node, pop the stack and generate an SCC + if vertex.lowlink == vertex.index: + # start a new strongly connected component + scc = [] + while True: + adjacent = self.stack.pop() + adjacent.on_stack = False + scc.append(adjacent) + if adjacent == vertex: + break + scc.sort() + sccs.append(scc) diff --git a/algorithms/graph/transitive_closure_dfs.py b/algorithms/graph/transitive_closure_dfs.py new file mode 100644 index 000000000..ca7e43a1b --- /dev/null +++ b/algorithms/graph/transitive_closure_dfs.py @@ -0,0 +1,55 @@ +""" +Finds the transitive closure of a graph. + +reference: https://en.wikipedia.org/wiki/Transitive_closure#In_graph_theory +""" + +class Graph: + """ + This class represents a directed graph using adjacency lists + """ + def __init__(self, vertices): + # No. of vertices + self.vertex_count = vertices + + # default dictionary to store graph + self.graph = {} + + # To store transitive closure + self.closure = [[0 for j in range(vertices)] for i in range(vertices)] + + def add_edge(self, source, target): + """ + Adds a directed edge to the graph + """ + if source in self.graph: + self.graph[source].append(target) + else: + self.graph[source] = [target] + + def dfs_util(self, source, target): + """ + A recursive DFS traversal function that finds + all reachable vertices for source + """ + + # Mark reachability from source to target as true. + self.closure[source][target] = 1 + + # Find all the vertices reachable through target + for adjacent in self.graph[target]: + if self.closure[source][adjacent] == 0: + self.dfs_util(source, adjacent) + + def transitive_closure(self): + """ + The function to find transitive closure. It uses + recursive dfs_util() + """ + + # Call the recursive helper function to print DFS + # traversal starting from all vertices one by one + for i in range(self.vertex_count): + self.dfs_util(i, i) + + return self.closure diff --git a/algorithms/graph/traversal.py b/algorithms/graph/traversal.py new file mode 100644 index 000000000..19ae14154 --- /dev/null +++ b/algorithms/graph/traversal.py @@ -0,0 +1,48 @@ +""" +Different ways to traverse a graph +""" + +# dfs and bfs are the ultimately same except that they are visiting nodes in +# different order. To simulate this ordering we would use stack for dfs and +# queue for bfs. +# + +def dfs_traverse(graph, start): + """ + Traversal by depth first search. + """ + visited, stack = set(), [start] + while stack: + node = stack.pop() + if node not in visited: + visited.add(node) + for next_node in graph[node]: + if next_node not in visited: + stack.append(next_node) + return visited + +def bfs_traverse(graph, start): + """ + Traversal by breadth first search. + """ + visited, queue = set(), [start] + while queue: + node = queue.pop(0) + if node not in visited: + visited.add(node) + for next_node in graph[node]: + if next_node not in visited: + queue.append(next_node) + return visited + +def dfs_traverse_recursive(graph, start, visited=None): + """ + Traversal by recursive depth first search. + """ + if visited is None: + visited = set() + visited.add(start) + for next_node in graph[start]: + if next_node not in visited: + dfs_traverse_recursive(graph, next_node, visited) + return visited diff --git a/algorithms/greedy/__init__.py b/algorithms/greedy/__init__.py new file mode 100644 index 000000000..66184782e --- /dev/null +++ b/algorithms/greedy/__init__.py @@ -0,0 +1 @@ +from .max_contiguous_subsequence_sum import * diff --git a/algorithms/greedy/max_contiguous_subsequence_sum.py b/algorithms/greedy/max_contiguous_subsequence_sum.py new file mode 100644 index 000000000..c5eae3d6e --- /dev/null +++ b/algorithms/greedy/max_contiguous_subsequence_sum.py @@ -0,0 +1,42 @@ +''' +Algorithm used => Kadane's Algorithm + +kadane's algorithm is used for finding the maximum sum of contiguous subsequence in a sequence. +It is considered a greedy/dp algorithm but I think they more greedy than dp +here are some of the examples to understand the use case more clearly +Example1 => [-2, 3, 8, -1, 4] +result => {3, 8, -1, 4} => 14 +Example2 => [-1, 1, 0] +result => {1} => 1 +Example3 => [-1, -3, -4] +result => -1 +Example1 => [-2, 3, 8, -12, 8, 4] +result => {8, 4} => 12 +Basic Algorithm Idea + If the sum of the current contiguous subsequence after adding the value at the current position is less than the value + at the current position then we know that it will be better if we start the current contiguous subsequence from this position. + Else we add the value at the current position to the current contiguous subsequence. +Note + In the implementation, the contiguous subsequence has at least one element. + If it can have 0 elements then the result will be max(max_till_now, 0) +''' + + +def max_contiguous_subsequence_sum(arr) -> int: + arr_size = len(arr) + + if arr_size == 0: + return 0 + + max_till_now = arr[0] + curr_sub_sum = 0 + + for i in range(0, arr_size): + if curr_sub_sum + arr[i] < arr[i]: + curr_sub_sum = arr[i] + else: + curr_sub_sum += arr[i] + + max_till_now = max(max_till_now, curr_sub_sum) + + return max_till_now diff --git a/algorithms/heap/__init__.py b/algorithms/heap/__init__.py new file mode 100644 index 000000000..9ea682d09 --- /dev/null +++ b/algorithms/heap/__init__.py @@ -0,0 +1,5 @@ +from .binary_heap import * +from .skyline import * +from .sliding_window_max import * +from .merge_sorted_k_lists import * +from .k_closest_points import * diff --git a/algorithms/heap/binary_heap.py b/algorithms/heap/binary_heap.py new file mode 100644 index 000000000..776e315f6 --- /dev/null +++ b/algorithms/heap/binary_heap.py @@ -0,0 +1,122 @@ +r""" +Binary Heap. A min heap is a complete binary tree where each node is smaller than +its children. The root, therefore, is the minimum element in the tree. The min +heap uses an array to represent the data and operation. For example a min heap: + + 4 + / \ + 50 7 + / \ / +55 90 87 + +Heap [0, 4, 50, 7, 55, 90, 87] + +Method in class: insert, remove_min +For example insert(2) in a min heap: + + 4 4 2 + / \ / \ / \ + 50 7 --> 50 2 --> 50 4 + / \ / \ / \ / \ / \ / \ +55 90 87 2 55 90 87 7 55 90 87 7 + +For example remove_min() in a min heap: + + 4 87 7 + / \ / \ / \ + 50 7 --> 50 7 --> 50 87 + / \ / / \ / \ +55 90 87 55 90 55 90 + +""" +from abc import ABCMeta, abstractmethod + + +class AbstractHeap(metaclass=ABCMeta): + """Abstract Class for Binary Heap.""" + + def __init__(self): + """Pass.""" + + @abstractmethod + def perc_up(self, i): + """Pass.""" + + @abstractmethod + def insert(self, val): + """Pass.""" + + @abstractmethod + def perc_down(self, i): + """Pass.""" + + @abstractmethod + def min_child(self, i): + """Pass.""" + + @abstractmethod + def remove_min(self): + """Pass.""" + + +class BinaryHeap(AbstractHeap): + """Binary Heap Class""" + + def __init__(self): + self.current_size = 0 + self.heap = [(0)] + + def perc_up(self, i): + while i // 2 > 0: + if self.heap[i] < self.heap[i // 2]: + # Swap value of child with value of its parent + self.heap[i], self.heap[i//2] = self.heap[i//2], self.heap[i] + i = i // 2 + + def insert(self, val): + """ + Method insert always start by inserting the element at the bottom. + It inserts rightmost spot so as to maintain the complete tree property. + Then, it fixes the tree by swapping the new element with its parent, + until it finds an appropriate spot for the element. It essentially + perc_up the minimum element + Complexity: O(logN) + """ + self.heap.append(val) + self.current_size = self.current_size + 1 + self.perc_up(self.current_size) + + """ + Method min_child returns the index of smaller of 2 children of parent at index i + """ + + def min_child(self, i): + if 2 * i + 1 > self.current_size: # No right child + return 2 * i + if self.heap[2 * i] > self.heap[2 * i + 1]: + return 2 * i + 1 + return 2 * i + + def perc_down(self, i): + while 2 * i < self.current_size: + min_child = self.min_child(i) + if self.heap[min_child] < self.heap[i]: + # Swap min child with parent + self.heap[min_child], self.heap[i] = self.heap[i], self.heap[min_child] + i = min_child + """ + Remove Min method removes the minimum element and swap it with the last + element in the heap( the bottommost, rightmost element). Then, it + perc_down this element, swapping it with one of its children until the + min heap property is restored + Complexity: O(logN) + """ + + def remove_min(self): + ret = self.heap[1] # the smallest value at beginning + # Replace it by the last value + self.heap[1] = self.heap[self.current_size] + self.current_size = self.current_size - 1 + self.heap.pop() + self.perc_down(1) + return ret diff --git a/algorithms/heap/k_closest_points.py b/algorithms/heap/k_closest_points.py new file mode 100644 index 000000000..6a4e03604 --- /dev/null +++ b/algorithms/heap/k_closest_points.py @@ -0,0 +1,48 @@ +"""Given a list of points, find the k closest to the origin. + +Idea: Maintain a max heap of k elements. +We can iterate through all points. +If a point p has a smaller distance to the origin than the top element of a +heap, we add point p to the heap and remove the top element. +After iterating through all points, our heap contains the k closest points to +the origin. +""" + + +from heapq import heapify, heappushpop + + +def k_closest(points, k, origin=(0, 0)): + # Time: O(k+(n-k)logk) + # Space: O(k) + """Initialize max heap with first k points. + Python does not support a max heap; thus we can use the default min heap + where the keys (distance) are negated. + """ + heap = [(-distance(p, origin), p) for p in points[:k]] + heapify(heap) + + """ + For every point p in points[k:], + check if p is smaller than the root of the max heap; + if it is, add p to heap and remove root. Reheapify. + """ + for point in points[k:]: + dist = distance(point, origin) + + heappushpop(heap, (-dist, point)) # heappushpop does conditional check + """Same as: + if d < -heap[0][0]: + heappush(heap, (-d,p)) + heappop(heap) + + Note: heappushpop is more efficient than separate push and pop calls. + Each heappushpop call takes O(logk) time. + """ + + return [point for nd, point in heap] # return points in heap + + +def distance(point, origin=(0, 0)): + """ Calculates the distance for a point from origo""" + return (point[0] - origin[0])**2 + (point[1] - origin[1])**2 diff --git a/algorithms/heap/merge_sorted_k_lists.py b/algorithms/heap/merge_sorted_k_lists.py new file mode 100644 index 000000000..f3600c447 --- /dev/null +++ b/algorithms/heap/merge_sorted_k_lists.py @@ -0,0 +1,72 @@ +""" +Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity. +""" + + +from heapq import heappop, heapreplace, heapify +from queue import PriorityQueue + + +# Definition for singly-linked list. +class ListNode(object): + """ ListNode Class""" + + def __init__(self, val): + self.val = val + self.next = None + + +def merge_k_lists(lists): + """ Merge Lists """ + dummy = node = ListNode(0) + list_h = [(n.val, n) for n in lists if n] + heapify(list_h) + while list_h: + _, n_val = list_h[0] + if n_val.next is None: + heappop(list_h) # only change heap size when necessary + else: + heapreplace(list_h, (n_val.next.val, n_val.next)) + node.next = n_val + node = node.next + + return dummy.next + + +def merge_k_lists(lists): + """ Merge List """ + dummy = ListNode(None) + curr = dummy + q = PriorityQueue() + for node in lists: + if node: + q.put((node.val, node)) + while not q.empty(): + curr.next = q.get()[1] # These two lines seem to + curr = curr.next # be equivalent to :- curr = q.get()[1] + if curr.next: + q.put((curr.next.val, curr.next)) + return dummy.next + + +""" +I think my code's complexity is also O(nlogk) and not using heap or priority queue, +n means the total elements and k means the size of list. + +The mergeTwoLists function in my code comes from the problem Merge Two Sorted Lists +whose complexity obviously is O(n), n is the sum of length of l1 and l2. + +To put it simpler, assume the k is 2^x, So the progress of combination is like a full binary tree, +from bottom to top. So on every level of tree, the combination complexity is n, +because every level have all n numbers without repetition. +The level of tree is x, ie log k. So the complexity is O(n log k). + +for example, 8 ListNode, and the length of every ListNode is x1, x2, +x3, x4, x5, x6, x7, x8, total is n. + +on level 3: x1+x2, x3+x4, x5+x6, x7+x8 sum: n + +on level 2: x1+x2+x3+x4, x5+x6+x7+x8 sum: n + +on level 1: x1+x2+x3+x4+x5+x6+x7+x8 sum: n +""" diff --git a/heap/skyline.py b/algorithms/heap/skyline.py similarity index 85% rename from heap/skyline.py rename to algorithms/heap/skyline.py index b3ab5cc70..c666703f3 100644 --- a/heap/skyline.py +++ b/algorithms/heap/skyline.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- """ A city's skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. @@ -33,22 +34,21 @@ into one in the final output as such: [...[2 3], [4 5], [12 7], ...] """ - import heapq -def get_skyline(LRH): +def get_skyline(lrh): """ Wortst Time Complexity: O(NlogN) :type buildings: List[List[int]] :rtype: List[List[int]] """ skyline, live = [], [] - i, n = 0, len(LRH) + i, n = 0, len(lrh) while i < n or live: - if not live or i < n and LRH[i][0] <= -live[0][1]: - x = LRH[i][0] - while i < n and LRH[i][0] == x: - heapq.heappush(live, (-LRH[i][2], -LRH[i][1])) + if not live or i < n and lrh[i][0] <= -live[0][1]: + x = lrh[i][0] + while i < n and lrh[i][0] == x: + heapq.heappush(live, (-lrh[i][2], -lrh[i][1])) i += 1 else: x = -live[0][1] @@ -58,9 +58,3 @@ def get_skyline(LRH): if not skyline or height != skyline[-1][1]: skyline += [x, height], return skyline - -buildings = [ [2, 9, 10], [3, 7, 15], [5, 12, 12], [15, 20, 10], [19, 24, 8] ] -# [ [2 10], [3 15], [7 12], [12 0], [15 10], [20 8], [24, 0] ] -print(get_skyline(buildings)) - - diff --git a/heap/sliding_window_max.py b/algorithms/heap/sliding_window_max.py similarity index 100% rename from heap/sliding_window_max.py rename to algorithms/heap/sliding_window_max.py diff --git a/algorithms/linkedlist/__init__.py b/algorithms/linkedlist/__init__.py new file mode 100644 index 000000000..1c9c3b9fc --- /dev/null +++ b/algorithms/linkedlist/__init__.py @@ -0,0 +1,9 @@ +from .reverse import * +from .is_sorted import * +from .remove_range import * +from .swap_in_pairs import * +from .rotate_list import * +from .is_cyclic import * +from .merge_two_list import * +from .is_palindrome import * +from .copy_random_pointer import * diff --git a/algorithms/linkedlist/add_two_numbers.py b/algorithms/linkedlist/add_two_numbers.py new file mode 100644 index 000000000..02f7eff6b --- /dev/null +++ b/algorithms/linkedlist/add_two_numbers.py @@ -0,0 +1,132 @@ +""" +You are given two non-empty linked lists representing +two non-negative integers. The digits are stored in reverse order +and each of their nodes contain a single digit. +Add the two numbers and return it as a linked list. + +You may assume the two numbers do not contain any leading zero, +except the number 0 itself. + +Input: (2 -> 4 -> 3) + (5 -> 6 -> 4) +Output: 7 -> 0 -> 8 +""" + +import unittest + + +class Node: + def __init__(self, x): + self.val = x + self.next = None + + +def add_two_numbers(left: Node, right: Node) -> Node: + head = Node(0) + current = head + sum = 0 + while left or right: + print("adding: ", left.val, right.val) + sum //= 10 + if left: + sum += left.val + left = left.next + if right: + sum += right.val + right = right.next + current.next = Node(sum % 10) + current = current.next + if sum // 10 == 1: + current.next = Node(1) + return head.next + + +def convert_to_list(number: int) -> Node: + """ + converts a positive integer into a (reversed) linked list. + for example: give 112 + result 2 -> 1 -> 1 + """ + if number >= 0: + head = Node(0) + current = head + remainder = number % 10 + quotient = number // 10 + + while quotient != 0: + current.next = Node(remainder) + current = current.next + remainder = quotient % 10 + quotient //= 10 + current.next = Node(remainder) + return head.next + else: + print("number must be positive!") + + +def convert_to_str(l: Node) -> str: + """ + converts the non-negative number list into a string. + """ + result = "" + while l: + result += str(l.val) + l = l.next + return result + + +class TestSuite(unittest.TestCase): + """ + testsuite for the linked list structure and + the adding function, above. + """ + + def test_convert_to_str(self): + number1 = Node(2) + number1.next = Node(4) + number1.next.next = Node(3) + self.assertEqual("243", convert_to_str(number1)) + + def test_add_two_numbers(self): + # 1. test case + number1 = Node(2) + number1.next = Node(4) + number1.next.next = Node(3) + number2 = Node(5) + number2.next = Node(6) + number2.next.next = Node(4) + result = convert_to_str(add_two_numbers(number1, number2)) + self.assertEqual("708", result) + + # 2. test case + number3 = Node(1) + number3.next = Node(1) + number3.next.next = Node(9) + number4 = Node(1) + number4.next = Node(0) + number4.next.next = Node(1) + result = convert_to_str(add_two_numbers(number3, number4)) + self.assertEqual("2101", result) + + # 3. test case + number5 = Node(1) + number6 = Node(0) + result = convert_to_str(add_two_numbers(number5, number6)) + self.assertEqual("1", result) + + # 4. test case + number7 = Node(9) + number7.next = Node(1) + number7.next.next = Node(1) + number8 = Node(1) + number8.next = Node(0) + number8.next.next = Node(1) + result = convert_to_str(add_two_numbers(number7, number8)) + self.assertEqual("022", result) + + def test_convert_to_list(self): + result = convert_to_str(convert_to_list(112)) + self.assertEqual("211", result) + + +if __name__ == "__main__": + unittest.main() diff --git a/linkedlist/copy_random_pointer.py b/algorithms/linkedlist/copy_random_pointer.py similarity index 58% rename from linkedlist/copy_random_pointer.py rename to algorithms/linkedlist/copy_random_pointer.py index 7e2718bf5..b3ef4628d 100644 --- a/linkedlist/copy_random_pointer.py +++ b/algorithms/linkedlist/copy_random_pointer.py @@ -4,11 +4,21 @@ Return a deep copy of the list. """ +from collections import defaultdict -class Solution: -# @param head, a RandomListNode -# @return a RandomListNode -def copyRandomList(self, head): + +class RandomListNode(object): + def __init__(self, label): + self.label = label + self.next = None + self.random = None + + +def copy_random_pointer_v1(head): + """ + :type head: RandomListNode + :rtype: RandomListNode + """ dic = dict() m = n = head while m: @@ -20,12 +30,14 @@ def copyRandomList(self, head): n = n.next return dic.get(head) -#O(n) -class Solution: -# @param head, a RandomListNode -# @return a RandomListNode -def copyRandomList(self, head): - copy = collections.defaultdict(lambda: RandomListNode(0)) + +# O(n) +def copy_random_pointer_v2(head): + """ + :type head: RandomListNode + :rtype: RandomListNode + """ + copy = defaultdict(lambda: RandomListNode(0)) copy[None] = None node = head while node: diff --git a/algorithms/linkedlist/delete_node.py b/algorithms/linkedlist/delete_node.py new file mode 100644 index 000000000..302b52918 --- /dev/null +++ b/algorithms/linkedlist/delete_node.py @@ -0,0 +1,63 @@ +""" +Write a function to delete a node (except the tail) +in a singly linked list, given only access to that node. + +Supposed the linked list is 1 -> 2 -> 3 -> 4 and +you are given the third node with value 3, +the linked list should become 1 -> 2 -> 4 after calling your function. +""" +import unittest + + +class Node: + def __init__(self, x): + self.val = x + self.next = None + + +def delete_node(node): + if node is None or node.next is None: + raise ValueError + node.val = node.next.val + node.next = node.next.next + + +class TestSuite(unittest.TestCase): + + def test_delete_node(self): + + # make linkedlist 1 -> 2 -> 3 -> 4 + head = Node(1) + curr = head + for i in range(2, 6): + curr.next = Node(i) + curr = curr.next + + # node3 = 3 + node3 = head.next.next + + # after delete_node => 1 -> 2 -> 4 + delete_node(node3) + + curr = head + self.assertEqual(1, curr.val) + + curr = curr.next + self.assertEqual(2, curr.val) + + curr = curr.next + self.assertEqual(4, curr.val) + + curr = curr.next + self.assertEqual(5, curr.val) + + tail = curr + self.assertIsNone(tail.next) + + self.assertRaises(ValueError, delete_node, tail) + self.assertRaises(ValueError, delete_node, tail.next) + + +if __name__ == '__main__': + + unittest.main() diff --git a/algorithms/linkedlist/first_cyclic_node.py b/algorithms/linkedlist/first_cyclic_node.py new file mode 100644 index 000000000..9ab7f88f7 --- /dev/null +++ b/algorithms/linkedlist/first_cyclic_node.py @@ -0,0 +1,64 @@ +""" + Given a linked list, find the first node of a cycle in it. + 1 -> 2 -> 3 -> 4 -> 5 -> 1 => 1 + A -> B -> C -> D -> E -> C => C + + Note: The solution is a direct implementation + Floyd's cycle-finding algorithm (Floyd's Tortoise and Hare). +""" +import unittest + + +class Node: + + def __init__(self, x): + self.val = x + self.next = None + + +def first_cyclic_node(head): + """ + :type head: Node + :rtype: Node + """ + runner = walker = head + while runner and runner.next: + runner = runner.next.next + walker = walker.next + if runner is walker: + break + + if runner is None or runner.next is None: + return None + + walker = head + while runner is not walker: + runner, walker = runner.next, walker.next + return runner + + +class TestSuite(unittest.TestCase): + + def test_first_cyclic_node(self): + + # create linked list => A -> B -> C -> D -> E -> C + head = Node('A') + head.next = Node('B') + curr = head.next + + cyclic_node = Node('C') + curr.next = cyclic_node + + curr = curr.next + curr.next = Node('D') + curr = curr.next + curr.next = Node('E') + curr = curr.next + curr.next = cyclic_node + + self.assertEqual('C', first_cyclic_node(head).val) + + +if __name__ == '__main__': + + unittest.main() diff --git a/algorithms/linkedlist/intersection.py b/algorithms/linkedlist/intersection.py new file mode 100644 index 000000000..71c4c1c61 --- /dev/null +++ b/algorithms/linkedlist/intersection.py @@ -0,0 +1,101 @@ +""" + This function takes two lists and returns the node they have in common, if any. + In this example: + 1 -> 3 -> 5 + \ + 7 -> 9 -> 11 + / + 2 -> 4 -> 6 + ...we would return 7. + Note that the node itself is the unique identifier, not the value of the node. + """ +import unittest + + +class Node(object): + def __init__(self, val=None): + self.val = val + self.next = None + + +def intersection(h1, h2): + + count = 0 + flag = None + h1_orig = h1 + h2_orig = h2 + + while h1 or h2: + count += 1 + + if not flag and (h1.next is None or h2.next is None): + # We hit the end of one of the lists, set a flag for this + flag = (count, h1.next, h2.next) + + if h1: + h1 = h1.next + if h2: + h2 = h2.next + + long_len = count # Mark the length of the longer of the two lists + short_len = flag[0] + + if flag[1] is None: + shorter = h1_orig + longer = h2_orig + elif flag[2] is None: + shorter = h2_orig + longer = h1_orig + + while longer and shorter: + + while long_len > short_len: + # force the longer of the two lists to "catch up" + longer = longer.next + long_len -= 1 + + if longer == shorter: + # The nodes match, return the node + return longer + else: + longer = longer.next + shorter = shorter.next + + return None + + +class TestSuite(unittest.TestCase): + + def test_intersection(self): + + # create linked list as: + # 1 -> 3 -> 5 + # \ + # 7 -> 9 -> 11 + # / + # 2 -> 4 -> 6 + a1 = Node(1) + b1 = Node(3) + c1 = Node(5) + d = Node(7) + a2 = Node(2) + b2 = Node(4) + c2 = Node(6) + e = Node(9) + f = Node(11) + + a1.next = b1 + b1.next = c1 + c1.next = d + a2.next = b2 + b2.next = c2 + c2.next = d + d.next = e + e.next = f + + self.assertEqual(7, intersection(a1, a2).val) + + +if __name__ == '__main__': + + unittest.main() diff --git a/linkedlist/is_cyclic.py b/algorithms/linkedlist/is_cyclic.py similarity index 84% rename from linkedlist/is_cyclic.py rename to algorithms/linkedlist/is_cyclic.py index e9be312c6..70d2c6616 100644 --- a/linkedlist/is_cyclic.py +++ b/algorithms/linkedlist/is_cyclic.py @@ -4,7 +4,11 @@ Follow up: Can you solve it without using extra space? """ +class Node: + def __init__(self, x): + self.val = x + self.next = None def is_cyclic(head): """ diff --git a/algorithms/linkedlist/is_palindrome.py b/algorithms/linkedlist/is_palindrome.py new file mode 100644 index 000000000..c9f2bc18c --- /dev/null +++ b/algorithms/linkedlist/is_palindrome.py @@ -0,0 +1,89 @@ +def is_palindrome(head): + if not head: + return True + # split the list to two parts + fast, slow = head.next, head + while fast and fast.next: + fast = fast.next.next + slow = slow.next + second = slow.next + slow.next = None # Don't forget here! But forget still works! + # reverse the second part + node = None + while second: + nxt = second.next + second.next = node + node = second + second = nxt + # compare two parts + # second part has the same or one less node + while node: + if node.val != head.val: + return False + node = node.next + head = head.next + return True + + +def is_palindrome_stack(head): + if not head or not head.next: + return True + + # 1. Get the midpoint (slow) + slow = fast = cur = head + while fast and fast.next: + fast, slow = fast.next.next, slow.next + + # 2. Push the second half into the stack + stack = [slow.val] + while slow.next: + slow = slow.next + stack.append(slow.val) + + # 3. Comparison + while stack: + if stack.pop() != cur.val: + return False + cur = cur.next + + return True + + +def is_palindrome_dict(head): + """ + This function builds up a dictionary where the keys are the values of the list, + and the values are the positions at which these values occur in the list. + We then iterate over the dict and if there is more than one key with an odd + number of occurrences, bail out and return False. + Otherwise, we want to ensure that the positions of occurrence sum to the + value of the length of the list - 1, working from the outside of the list inward. + For example: + Input: 1 -> 1 -> 2 -> 3 -> 2 -> 1 -> 1 + d = {1: [0,1,5,6], 2: [2,4], 3: [3]} + '3' is the middle outlier, 2+4=6, 0+6=6 and 5+1=6 so we have a palindrome. + """ + if not head or not head.next: + return True + d = {} + pos = 0 + while head: + if head.val in d.keys(): + d[head.val].append(pos) + else: + d[head.val] = [pos] + head = head.next + pos += 1 + checksum = pos - 1 + middle = 0 + for v in d.values(): + if len(v) % 2 != 0: + middle += 1 + else: + step = 0 + for i in range(0, len(v)): + if v[i] + v[len(v) - 1 - step] != checksum: + return False + step += 1 + if middle > 1: + return False + return True diff --git a/algorithms/linkedlist/is_sorted.py b/algorithms/linkedlist/is_sorted.py new file mode 100644 index 000000000..978c5a69b --- /dev/null +++ b/algorithms/linkedlist/is_sorted.py @@ -0,0 +1,19 @@ +""" +Given a linked list, is_sort function returns true if the list is in sorted +(increasing) order and return false otherwise. An empty list is considered +to be sorted. + +For example: +Null :List is sorted +1 2 3 4 :List is sorted +1 2 -1 3 :List is not sorted +""" +def is_sorted(head): + if not head: + return True + current = head + while current.next: + if current.val > current.next.val: + return False + current = current.next + return True diff --git a/algorithms/linkedlist/kth_to_last.py b/algorithms/linkedlist/kth_to_last.py new file mode 100644 index 000000000..fb70a5c16 --- /dev/null +++ b/algorithms/linkedlist/kth_to_last.py @@ -0,0 +1,120 @@ +class Node(): + def __init__(self, val=None): + self.val = val + self.next = None + + +def kth_to_last_eval(head, k): + """ + This is a suboptimal, hacky method using eval(), which is not + safe for user input. We guard against danger by ensuring k in an int + """ + if not isinstance(k, int) or not head.val: + return False + + nexts = '.'.join(['next' for n in range(1, k+1)]) + seeker = str('.'.join(['head', nexts])) + + while head: + if eval(seeker) is None: + return head + else: + head = head.next + + return False + + +def kth_to_last_dict(head, k): + """ + This is a brute force method where we keep a dict the size of the list + Then we check it for the value we need. If the key is not in the dict, + our and statement will short circuit and return False + """ + if not (head and k > -1): + return False + d = dict() + count = 0 + while head: + d[count] = head + head = head.next + count += 1 + return len(d)-k in d and d[len(d)-k] + + +def kth_to_last(head, k): + """ + This is an optimal method using iteration. + We move p1 k steps ahead into the list. + Then we move p1 and p2 together until p1 hits the end. + """ + if not (head or k > -1): + return False + p1 = head + p2 = head + for i in range(1, k+1): + if p1 is None: + # Went too far, k is not valid + raise IndexError + p1 = p1.next + while p1: + p1 = p1.next + p2 = p2.next + return p2 + + +def print_linked_list(head): + string = "" + while head.next: + string += head.val + " -> " + head = head.next + string += head.val + print(string) + + +def test(): + # def make_test_li + # A A B C D C F G + a1 = Node("A") + a2 = Node("A") + b = Node("B") + c1 = Node("C") + d = Node("D") + c2 = Node("C") + f = Node("F") + g = Node("G") + a1.next = a2 + a2.next = b + b.next = c1 + c1.next = d + d.next = c2 + c2.next = f + f.next = g + print_linked_list(a1) + + # test kth_to_last_eval + kth = kth_to_last_eval(a1, 4) + try: + assert kth.val == "D" + except AssertionError as e: + e.args += ("Expecting D, got %s" % kth.val,) + raise + + # test kth_to_last_dict + kth = kth_to_last_dict(a1, 4) + try: + assert kth.val == "D" + except AssertionError as e: + e.args += ("Expecting D, got %s" % kth.val,) + raise + + # test kth_to_last + kth = kth_to_last(a1, 4) + try: + assert kth.val == "D" + except AssertionError as e: + e.args += ("Expecting D, got %s" % kth.val,) + raise + print("all passed.") + +if __name__ == '__main__': + test() diff --git a/linkedlist/linkedlist.py b/algorithms/linkedlist/linkedlist.py similarity index 93% rename from linkedlist/linkedlist.py rename to algorithms/linkedlist/linkedlist.py index 1b921c926..c7b8e0c4a 100644 --- a/linkedlist/linkedlist.py +++ b/algorithms/linkedlist/linkedlist.py @@ -3,7 +3,7 @@ # in comparison, arrays require O(n) time to do the same thing. # Linked lists can continue to expand without having to specify # their size ahead of time (remember our lectures on Array sizing -# form the Array Sequence section of the course!) +# from the Array Sequence section of the course!) # Cons # To access an element in a linked list, you need to take O(k) time diff --git a/algorithms/linkedlist/merge_two_list.py b/algorithms/linkedlist/merge_two_list.py new file mode 100644 index 000000000..6be44f33e --- /dev/null +++ b/algorithms/linkedlist/merge_two_list.py @@ -0,0 +1,37 @@ +""" +Merge two sorted linked lists and return it as a new list. The new list should +be made by splicing together the nodes of the first two lists. + +For example: +Input: 1->2->4, 1->3->4 +Output: 1->1->2->3->4->4 +""" +class Node: + + def __init__(self, x): + self.val = x + self.next = None + +def merge_two_list(l1, l2): + ret = cur = Node(0) + while l1 and l2: + if l1.val < l2.val: + cur.next = l1 + l1 = l1.next + else: + cur.next = l2 + l2 = l2.next + cur = cur.next + cur.next = l1 or l2 + return ret.next + +# recursively +def merge_two_list_recur(l1, l2): + if not l1 or not l2: + return l1 or l2 + if l1.val < l2.val: + l1.next = merge_two_list_recur(l1.next, l2) + return l1 + else: + l2.next = merge_two_list_recur(l1, l2.next) + return l2 diff --git a/algorithms/linkedlist/partition.py b/algorithms/linkedlist/partition.py new file mode 100644 index 000000000..8078f3321 --- /dev/null +++ b/algorithms/linkedlist/partition.py @@ -0,0 +1,76 @@ +""" +Write code to partition a linked list around a value x, such that all nodes less +than x come before all nodes greater than or equal to x. If x is contained +within the list, the values of x only need to be after the elements less than x. +The partition element x can appear anywhere in the "right partition"; +it does not need to appear between the left and right partitions. + +3 -> 5 -> 8 -> 5 -> 10 -> 2 -> 1 [partition=5] +3 -> 1 -> 2 -> 10 -> 5 -> 5 -> 8 + +We assume the values of all linked list nodes are int and that x in an int. +""" + + +class Node(): + def __init__(self, val=None): + self.val = int(val) + self.next = None + + +def print_linked_list(head): + string = "" + while head.next: + string += str(head.val) + " -> " + head = head.next + string += str(head.val) + print(string) + + +def partition(head, x): + left = None + right = None + prev = None + current = head + while current: + if int(current.val) >= x: + if not right: + right = current + else: + if not left: + left = current + else: + prev.next = current.next + left.next = current + left = current + left.next = right + if prev and prev.next is None: + break + # cache previous value in case it needs to be pointed elsewhere + prev = current + current = current.next + + +def test(): + a = Node("3") + b = Node("5") + c = Node("8") + d = Node("5") + e = Node("10") + f = Node("2") + g = Node("1") + + a.next = b + b.next = c + c.next = d + d.next = e + e.next = f + f.next = g + + print_linked_list(a) + partition(a, 5) + print_linked_list(a) + + +if __name__ == '__main__': + test() diff --git a/linkedlist/remove_duplicates.py b/algorithms/linkedlist/remove_duplicates.py similarity index 86% rename from linkedlist/remove_duplicates.py rename to algorithms/linkedlist/remove_duplicates.py index 683fd4f4d..ba18aecf2 100644 --- a/linkedlist/remove_duplicates.py +++ b/algorithms/linkedlist/remove_duplicates.py @@ -3,7 +3,7 @@ def __init__(self, val = None): self.val = val self.next = None -def removeDups(head): +def remove_dups(head): """ Time Complexity: O(N) Space Complexity: O(N) @@ -18,7 +18,7 @@ def removeDups(head): prev = head head = head.next -def removeDupsWithoutSet(head): +def remove_dups_wothout_set(head): """ Time Complexity: O(N^2) Space Complexity: O(1) @@ -33,7 +33,7 @@ def removeDupsWithoutSet(head): runner = runner.next current = current.next -def printLinkedList(head): +def print_linked_list(head): string = "" while head.next: string += head.val + " -> " @@ -60,8 +60,7 @@ def printLinkedList(head): c2.next = f f.next = g -removeDups(a1) -printLinkedList(a1) -removeDupsWithoutSet(a1) -printLinkedList(a1) - +remove_dups(a1) +print_linked_list(a1) +remove_dups_wothout_set(a1) +print_linked_list(a1) diff --git a/algorithms/linkedlist/remove_range.py b/algorithms/linkedlist/remove_range.py new file mode 100644 index 000000000..ba7c1443e --- /dev/null +++ b/algorithms/linkedlist/remove_range.py @@ -0,0 +1,28 @@ +""" +Given a linked list, remove_range function accepts a starting and ending index +as parameters and removes the elements at those indexes (inclusive) from the list + +For example: +List: [8, 13, 17, 4, 9, 12, 98, 41, 7, 23, 0, 92] +remove_range(list, 3, 8); +List becomes: [8, 13, 17, 23, 0, 92] + +legal range of the list (0 < start index < end index < size of list). +""" +def remove_range(head, start, end): + assert(start <= end) + # Case: remove node at head + if start == 0: + for i in range(0, end+1): + if head != None: + head = head.next + else: + current = head + # Move pointer to start position + for i in range(0,start-1): + current = current.next + # Remove data until the end + for i in range(0, end-start + 1): + if current != None and current.next != None: + current.next = current.next.next + return head diff --git a/linkedlist/reverse.py b/algorithms/linkedlist/reverse.py similarity index 81% rename from linkedlist/reverse.py rename to algorithms/linkedlist/reverse.py index dcc77cb0c..c41b81a8b 100644 --- a/linkedlist/reverse.py +++ b/algorithms/linkedlist/reverse.py @@ -1,8 +1,10 @@ """ -Reverse a singly linked list. -""" - +Reverse a singly linked list. For example: +1 --> 2 --> 3 --> 4 +After reverse: +4 --> 3 --> 2 --> 1 +""" # # Iterative solution # T(n)- O(n) @@ -36,6 +38,6 @@ def reverse_list_recursive(head): return head p = head.next head.next = None - revrest = self.reverse(p) + revrest = reverse_list_recursive(p) p.next = head return revrest diff --git a/linkedlist/rotate_list.py b/algorithms/linkedlist/rotate_list.py similarity index 100% rename from linkedlist/rotate_list.py rename to algorithms/linkedlist/rotate_list.py diff --git a/algorithms/linkedlist/swap_in_pairs.py b/algorithms/linkedlist/swap_in_pairs.py new file mode 100644 index 000000000..7f82f5b1e --- /dev/null +++ b/algorithms/linkedlist/swap_in_pairs.py @@ -0,0 +1,30 @@ +""" +Given a linked list, swap every two adjacent nodes +and return its head. + +For example, +Given 1->2->3->4, you should return the list as 2->1->4->3. + +Your algorithm should use only constant space. +You may not modify the values in the list, +only nodes itself can be changed. +""" +class Node(object): + def __init__(self, x): + self.val = x + self.next = None + +def swap_pairs(head): + if not head: + return head + start = Node(0) + start.next = head + current = start + while current.next and current.next.next: + first = current.next + second = current.next.next + first.next = second.next + current.next = second + current.next.next = first + current = current.next.next + return start.next diff --git a/algorithms/map/__init__.py b/algorithms/map/__init__.py new file mode 100644 index 000000000..931c0e776 --- /dev/null +++ b/algorithms/map/__init__.py @@ -0,0 +1,6 @@ +from .hashtable import * +from .separate_chaining_hashtable import * +from .word_pattern import * +from .is_isomorphic import * +from .is_anagram import * +from .longest_palindromic_subsequence import * diff --git a/map/hashtable.py b/algorithms/map/hashtable.py similarity index 63% rename from map/hashtable.py rename to algorithms/map/hashtable.py index 1de554737..f579c0b0d 100644 --- a/map/hashtable.py +++ b/algorithms/map/hashtable.py @@ -1,6 +1,3 @@ -from unittest import TestCase - - class HashTable(object): """ HashMap Data Type @@ -120,81 +117,3 @@ def __resize(self): for key, value in zip(keys, values): if key is not self._empty and key is not self._deleted: self.put(key, value) - - -class TestHashTable(TestCase): - def test_one_entry(self): - m = HashTable(10) - m.put(1, '1') - self.assertEqual('1', m.get(1)) - - def test_add_entry_bigger_than_table_size(self): - m = HashTable(10) - m.put(11, '1') - self.assertEqual('1', m.get(11)) - - def test_get_none_if_key_missing_and_hash_collision(self): - m = HashTable(10) - m.put(1, '1') - self.assertEqual(None, m.get(11)) - - def test_two_entries_with_same_hash(self): - m = HashTable(10) - m.put(1, '1') - m.put(11, '11') - self.assertEqual('1', m.get(1)) - self.assertEqual('11', m.get(11)) - - def test_get_on_full_table_does_halts(self): - # and does not search forever - m = HashTable(10) - for i in range(10, 20): - m.put(i, i) - self.assertEqual(None, m.get(1)) - - def test_delete_key(self): - m = HashTable(10) - m.put(1, 1) - m.del_(1) - self.assertEqual(None, m.get(1)) - - def test_delete_key_and_reassign(self): - m = HashTable(10) - m.put(1, 1) - del m[1] - m.put(1, 2) - self.assertEqual(2, m.get(1)) - - def test_assigning_to_full_table_throws_error(self): - m = HashTable(3) - m.put(1, 1) - m.put(2, 2) - m.put(3, 3) - with self.assertRaises(ValueError): - m.put(4, 4) - - def test_len_trivial(self): - m = HashTable(10) - self.assertEqual(0, len(m)) - for i in range(10): - m.put(i, i) - self.assertEqual(i + 1, len(m)) - - def test_len_after_deletions(self): - m = HashTable(10) - m.put(1, 1) - self.assertEqual(1, len(m)) - m.del_(1) - self.assertEqual(0, len(m)) - m.put(11, 42) - self.assertEqual(1, len(m)) - - def test_resizable_hash_table(self): - m = ResizableHashTable() - self.assertEqual(ResizableHashTable.MIN_SIZE, m.size) - for i in range(ResizableHashTable.MIN_SIZE): - m.put(i, 'foo') - self.assertEqual(ResizableHashTable.MIN_SIZE * 2, m.size) - self.assertEqual('foo', m.get(1)) - self.assertEqual('foo', m.get(3)) - self.assertEqual('foo', m.get(ResizableHashTable.MIN_SIZE - 1)) diff --git a/algorithms/map/is_anagram.py b/algorithms/map/is_anagram.py new file mode 100644 index 000000000..066d8c20f --- /dev/null +++ b/algorithms/map/is_anagram.py @@ -0,0 +1,29 @@ +""" +Given two strings s and t , write a function to determine if t is an anagram of s. + +Example 1: +Input: s = "anagram", t = "nagaram" +Output: true + +Example 2: +Input: s = "rat", t = "car" +Output: false + +Note: +You may assume the string contains only lowercase alphabets. + +Reference: https://leetcode.com/problems/valid-anagram/description/ +""" +def is_anagram(s, t): + """ + :type s: str + :type t: str + :rtype: bool + """ + maps = {} + mapt = {} + for i in s: + maps[i] = maps.get(i, 0) + 1 + for i in t: + mapt[i] = mapt.get(i, 0) + 1 + return maps == mapt diff --git a/algorithms/map/is_isomorphic.py b/algorithms/map/is_isomorphic.py new file mode 100644 index 000000000..62342e5e4 --- /dev/null +++ b/algorithms/map/is_isomorphic.py @@ -0,0 +1,40 @@ +""" +Given two strings s and t, determine if they are isomorphic. +Two strings are isomorphic if the characters in s can be replaced to get t. +All occurrences of a character must be replaced with another character while +preserving the order of characters. No two characters may map to the same +character but a character may map to itself. + +Example 1: +Input: s = "egg", t = "add" +Output: true + +Example 2: +Input: s = "foo", t = "bar" +Output: false + +Example 3: +Input: s = "paper", t = "title" +Output: true +Reference: https://leetcode.com/problems/isomorphic-strings/description/ +""" +def is_isomorphic(s, t): + """ + :type s: str + :type t: str + :rtype: bool + """ + if len(s) != len(t): + return False + dict = {} + set_value = set() + for i in range(len(s)): + if s[i] not in dict: + if t[i] in set_value: + return False + dict[s[i]] = t[i] + set_value.add(t[i]) + else: + if dict[s[i]] != t[i]: + return False + return True diff --git a/map/longest_common_subsequence.py b/algorithms/map/longest_common_subsequence.py similarity index 81% rename from map/longest_common_subsequence.py rename to algorithms/map/longest_common_subsequence.py index 247b238e1..631b19d0e 100644 --- a/map/longest_common_subsequence.py +++ b/algorithms/map/longest_common_subsequence.py @@ -1,14 +1,14 @@ """ Given string a and b, with b containing all distinct characters, -find the longest common subsequence's +find the longest common sub sequence's length. -length. Expected complexity O(nlogn). +Expected complexity O(n logn). """ def max_common_sub_string(s1, s2): # Assuming s2 has all unique chars - s2dic = {s2[i]: i for i in xrange(len(s2))} + s2dic = {s2[i]: i for i in range(len(s2))} maxr = 0 subs = '' i = 0 diff --git a/algorithms/map/longest_palindromic_subsequence.py b/algorithms/map/longest_palindromic_subsequence.py new file mode 100644 index 000000000..767e78f44 --- /dev/null +++ b/algorithms/map/longest_palindromic_subsequence.py @@ -0,0 +1,29 @@ +def longest_palindromic_subsequence(s): + + k = len(s) + olist = [0] * k # 申请长度为n的列表，并初始化 + nList = [0] * k # 同上 + logestSubStr = "" + logestLen = 0 + + for j in range(0, k): + for i in range(0, j + 1): + if j - i <= 1: + if s[i] == s[j]: + nList[i] = 1 # 当 j 时，第 i 个子串为回文子串 + len_t = j - i + 1 + if logestLen < len_t: # 判断长度 + logestSubStr = s[i:j + 1] + logestLen = len_t + else: + if s[i] == s[j] and olist[i+1]: # 当j-i>1时，判断s[i]是否等于s[j]，并判断当j-1时，第i+1个子串是否为回文子串 + nList[i] = 1 # 当 j 时，第 i 个子串为回文子串 + len_t = j - i + 1 + if logestLen < len_t: + logestSubStr = s[i:j + 1] + logestLen = len_t + olist = nList # 覆盖旧的列表 + nList = [0] * k # 新的列表清空 + # ~ from icecream import ic + # ~ ic(s, logestSubStr) + return logestLen#, logestSubStr diff --git a/map/randomized_set.py b/algorithms/map/randomized_set.py similarity index 100% rename from map/randomized_set.py rename to algorithms/map/randomized_set.py diff --git a/algorithms/map/separate_chaining_hashtable.py b/algorithms/map/separate_chaining_hashtable.py new file mode 100644 index 000000000..fecb251fa --- /dev/null +++ b/algorithms/map/separate_chaining_hashtable.py @@ -0,0 +1,84 @@ +import unittest + + +class Node(object): + def __init__(self, key=None, value=None, next=None): + self.key = key + self.value = value + self.next = next + + +class SeparateChainingHashTable(object): + """ + HashTable Data Type: + By having each bucket contain a linked list of elements that are hashed to that bucket. + + Usage: + >>> table = SeparateChainingHashTable() # Create a new, empty map. + >>> table.put('hello', 'world') # Add a new key-value pair. + >>> len(table) # Return the number of key-value pairs stored in the map. + 1 + >>> table.get('hello') # Get value by key. + 'world' + >>> del table['hello'] # Equivalent to `table.del_('hello')`, deleting key-value pair. + >>> table.get('hello') is None # Return `None` if a key doesn't exist. + True + """ + _empty = None + + def __init__(self, size=11): + self.size = size + self._len = 0 + self._table = [self._empty] * size + + def put(self, key, value): + hash_ = self.hash(key) + node_ = self._table[hash_] + if node_ is self._empty: + self._table[hash_] = Node(key, value) + else: + while node_.next is not None: + if node_.key == key: + node_.value = value + return + node_ = node_.next + node_.next = Node(key, value) + self._len += 1 + + def get(self, key): + hash_ = self.hash(key) + node_ = self._table[hash_] + while node_ is not self._empty: + if node_.key == key: + return node_.value + node_ = node_.next + return None + + def del_(self, key): + hash_ = self.hash(key) + node_ = self._table[hash_] + pre_node = None + while node_ is not None: + if node_.key == key: + if pre_node is None: + self._table[hash_] = node_.next + else: + pre_node.next = node_.next + self._len -= 1 + pre_node = node_ + node_ = node_.next + + def hash(self, key): + return hash(key) % self.size + + def __len__(self): + return self._len + + def __getitem__(self, key): + return self.get(key) + + def __delitem__(self, key): + return self.del_(key) + + def __setitem__(self, key, value): + self.put(key, value) diff --git a/map/valid_sudoku.py b/algorithms/map/valid_sudoku.py similarity index 100% rename from map/valid_sudoku.py rename to algorithms/map/valid_sudoku.py diff --git a/algorithms/map/word_pattern.py b/algorithms/map/word_pattern.py new file mode 100644 index 000000000..bee2f7a91 --- /dev/null +++ b/algorithms/map/word_pattern.py @@ -0,0 +1,40 @@ +""" +Given a pattern and a string str, find if str follows the same pattern. +Here follow means a full match, such that there is a bijection between a +letter in pattern and a non-empty word in str. + +Example 1: +Input: pattern = "abba", str = "dog cat cat dog" +Output: true + +Example 2: +Input:pattern = "abba", str = "dog cat cat fish" +Output: false + +Example 3: +Input: pattern = "aaaa", str = "dog cat cat dog" +Output: false + +Example 4: +Input: pattern = "abba", str = "dog dog dog dog" +Output: false +Notes: +You may assume pattern contains only lowercase letters, and str contains lowercase letters separated by a single space. +Reference: https://leetcode.com/problems/word-pattern/description/ +""" +def word_pattern(pattern, str): + dict = {} + set_value = set() + list_str = str.split() + if len(list_str) != len(pattern): + return False + for i in range(len(pattern)): + if pattern[i] not in dict: + if list_str[i] in set_value: + return False + dict[pattern[i]] = list_str[i] + set_value.add(list_str[i]) + else: + if dict[pattern[i]] != list_str[i]: + return False + return True diff --git a/algorithms/maths/__init__.py b/algorithms/maths/__init__.py new file mode 100644 index 000000000..d5499b094 --- /dev/null +++ b/algorithms/maths/__init__.py @@ -0,0 +1,28 @@ +""" +Collection of mathematical algorithms and functions. +""" +from .base_conversion import * +from .decimal_to_binary_ip import * +from .euler_totient import * +from .extended_gcd import * +from .factorial import * +from .gcd import * +from .generate_strobogrammtic import * +from .is_strobogrammatic import * +from .modular_exponential import * +from .next_perfect_square import * +from .prime_check import * +from .primes_sieve_of_eratosthenes import * +from .pythagoras import * +from .rabin_miller import * +from .rsa import * +from .combination import * +from .cosine_similarity import * +from .find_order_simple import * +from .find_primitive_root_simple import * +from .diffie_hellman_key_exchange import * +from .num_digits import * +from .power import * +from .magic_number import * +from .krishnamurthy_number import * +from .num_perfect_squares import * diff --git a/algorithms/maths/base_conversion.py b/algorithms/maths/base_conversion.py new file mode 100644 index 000000000..6badf749e --- /dev/null +++ b/algorithms/maths/base_conversion.py @@ -0,0 +1,49 @@ +""" +Integer base conversion algorithm + +int_to_base(5, 2) return '101'. +base_to_int('F', 16) return 15. + +""" + +import string + +def int_to_base(num, base): + """ + :type num: int + :type base: int + :rtype: str + """ + is_negative = False + if num == 0: + return '0' + if num < 0: + is_negative = True + num *= -1 + digit = string.digits + string.ascii_uppercase + res = '' + while num > 0: + res += digit[num % base] + num //= base + if is_negative: + return '-' + res[::-1] + return res[::-1] + + +def base_to_int(str_to_convert, base): + """ + Note : You can use int() built-in function instead of this. + :type str_to_convert: str + :type base: int + :rtype: int + """ + + digit = {} + for ind, char in enumerate(string.digits + string.ascii_uppercase): + digit[char] = ind + multiplier = 1 + res = 0 + for char in str_to_convert[::-1]: + res += digit[char] * multiplier + multiplier *= base + return res diff --git a/algorithms/maths/chinese_remainder_theorem.py b/algorithms/maths/chinese_remainder_theorem.py new file mode 100644 index 000000000..256e60f16 --- /dev/null +++ b/algorithms/maths/chinese_remainder_theorem.py @@ -0,0 +1,46 @@ +""" +Solves system of equations using the chinese remainder theorem if possible. +""" +from typing import List +from algorithms.maths.gcd import gcd + +def solve_chinese_remainder(nums : List[int], rems : List[int]): + """ + Computes the smallest x that satisfies the chinese remainder theorem + for a system of equations. + The system of equations has the form: + x % nums[0] = rems[0] + x % nums[1] = rems[1] + ... + x % nums[k - 1] = rems[k - 1] + Where k is the number of elements in nums and rems, k > 0. + All numbers in nums needs to be pariwise coprime otherwise an exception is raised + returns x: the smallest value for x that satisfies the system of equations + """ + if not len(nums) == len(rems): + raise Exception("nums and rems should have equal length") + if not len(nums) > 0: + raise Exception("Lists nums and rems need to contain at least one element") + for num in nums: + if not num > 1: + raise Exception("All numbers in nums needs to be > 1") + if not _check_coprime(nums): + raise Exception("All pairs of numbers in nums are not coprime") + k = len(nums) + x = 1 + while True: + i = 0 + while i < k: + if x % nums[i] != rems[i]: + break + i += 1 + if i == k: + return x + x += 1 + +def _check_coprime(list_to_check : List[int]): + for ind, num in enumerate(list_to_check): + for num2 in list_to_check[ind + 1:]: + if gcd(num, num2) != 1: + return False + return True diff --git a/algorithms/maths/combination.py b/algorithms/maths/combination.py new file mode 100644 index 000000000..998536056 --- /dev/null +++ b/algorithms/maths/combination.py @@ -0,0 +1,19 @@ +""" +Functions to calculate nCr (ie how many ways to choose r items from n items) +""" +def combination(n, r): + """This function calculates nCr.""" + if n == r or r == 0: + return 1 + return combination(n-1, r-1) + combination(n-1, r) + +def combination_memo(n, r): + """This function calculates nCr using memoization method.""" + memo = {} + def recur(n, r): + if n == r or r == 0: + return 1 + if (n, r) not in memo: + memo[(n, r)] = recur(n - 1, r - 1) + recur(n - 1, r) + return memo[(n, r)] + return recur(n, r) diff --git a/algorithms/maths/cosine_similarity.py b/algorithms/maths/cosine_similarity.py new file mode 100644 index 000000000..3ee7fcdd8 --- /dev/null +++ b/algorithms/maths/cosine_similarity.py @@ -0,0 +1,43 @@ +""" +Calculate cosine similarity between given two 1d list. +Two list must have the same length. + +Example: +cosine_similarity([1, 1, 1], [1, 2, -1]) # output : 0.47140452079103173 +""" +import math + + +def _l2_distance(vec): + """ + Calculate l2 distance from two given vectors. + """ + norm = 0. + for element in vec: + norm += element * element + norm = math.sqrt(norm) + return norm + + +def cosine_similarity(vec1, vec2): + """ + Calculate cosine similarity between given two vectors + :type vec1: list + :type vec2: list + """ + if len(vec1) != len(vec2): + raise ValueError("The two vectors must be the same length. Got shape " + str(len(vec1)) + + " and " + str(len(vec2))) + + norm_a = _l2_distance(vec1) + norm_b = _l2_distance(vec2) + + similarity = 0. + + # Calculate the dot product of two vectors + for vec1_element, vec2_element in zip(vec1, vec2): + similarity += vec1_element * vec2_element + + similarity /= (norm_a * norm_b) + + return similarity diff --git a/algorithms/maths/decimal_to_binary_ip.py b/algorithms/maths/decimal_to_binary_ip.py new file mode 100644 index 000000000..04e65e83c --- /dev/null +++ b/algorithms/maths/decimal_to_binary_ip.py @@ -0,0 +1,35 @@ +""" +Given an ip address in dotted-decimal representation, determine the +binary representation. For example, +decimal_to_binary(255.0.0.5) returns 11111111.00000000.00000000.00000101 +accepts string +returns string +""" + +def decimal_to_binary_util(val): + """ + Convert 8-bit decimal number to binary representation + :type val: str + :rtype: str + """ + bits = [128, 64, 32, 16, 8, 4, 2, 1] + val = int(val) + binary_rep = '' + for bit in bits: + if val >= bit: + binary_rep += str(1) + val -= bit + else: + binary_rep += str(0) + + return binary_rep + +def decimal_to_binary_ip(ip): + """ + Convert dotted-decimal ip address to binary representation with help of decimal_to_binary_util + """ + values = ip.split('.') + binary_list = [] + for val in values: + binary_list.append(decimal_to_binary_util(val)) + return '.'.join(binary_list) diff --git a/algorithms/maths/diffie_hellman_key_exchange.py b/algorithms/maths/diffie_hellman_key_exchange.py new file mode 100644 index 000000000..b70b000af --- /dev/null +++ b/algorithms/maths/diffie_hellman_key_exchange.py @@ -0,0 +1,184 @@ +""" +Algorithms for performing diffie-hellman key exchange. +""" +import math +from random import randint + + +""" +Code from /algorithms/maths/prime_check.py, +written by 'goswami-rahul' and 'Hai Honag Dang' +""" +def prime_check(num): + """Return True if num is a prime number + Else return False. + """ + + if num <= 1: + return False + if num == 2 or num == 3: + return True + if num % 2 == 0 or num % 3 == 0: + return False + j = 5 + while j * j <= num: + if num % j == 0 or num % (j + 2) == 0: + return False + j += 6 + return True + + +""" +For positive integer n and given integer a that satisfies gcd(a, n) = 1, +the order of a modulo n is the smallest positive integer k that satisfies +pow (a, k) % n = 1. In other words, (a^k) ≡ 1 (mod n). +Order of certain number may or may not exist. If not, return -1. +""" +def find_order(a, n): + if (a == 1) & (n == 1): + # Exception Handeling : 1 is the order of of 1 + return 1 + if math.gcd(a, n) != 1: + print ("a and n should be relative prime!") + return -1 + for i in range(1, n): + if pow(a, i) % n == 1: + return i + return -1 + + +""" +Euler's totient function, also known as phi-function ϕ(n), +counts the number of integers between 1 and n inclusive, +which are coprime to n. +(Two numbers are coprime if their greatest common divisor (GCD) equals 1). +Code from /algorithms/maths/euler_totient.py, written by 'goswami-rahul' +""" +def euler_totient(n): + """Euler's totient function or Phi function. + Time Complexity: O(sqrt(n)).""" + result = n + for i in range(2, int(n ** 0.5) + 1): + if n % i == 0: + while n % i == 0: + n //= i + result -= result // i + if n > 1: + result -= result // n + return result + +""" +For positive integer n and given integer a that satisfies gcd(a, n) = 1, +a is the primitive root of n, if a's order k for n satisfies k = ϕ(n). +Primitive roots of certain number may or may not be exist. +If so, return empty list. +""" + +def find_primitive_root(n): + """ Returns all primitive roots of n. """ + if n == 1: + # Exception Handeling : 0 is the only primitive root of 1 + return [0] + phi = euler_totient(n) + p_root_list = [] + for i in range (1, n): + if math.gcd(i, n) != 1: + # To have order, a and n must be relative prime with each other. + continue + order = find_order(i, n) + if order == phi: + p_root_list.append(i) + return p_root_list + + +""" +Diffie-Hellman key exchange is the method that enables +two entities (in here, Alice and Bob), not knowing each other, +to share common secret key through not-encrypted communication network. +This method use the property of one-way function (discrete logarithm) +For example, given a, b and n, it is easy to calculate x +that satisfies (a^b) ≡ x (mod n). +However, it is very hard to calculate x that satisfies (a^x) ≡ b (mod n). +For using this method, large prime number p and its primitive root a +must be given. +""" + +def alice_private_key(p): + """Alice determine her private key + in the range of 1 ~ p-1. + This must be kept in secret""" + return randint(1, p-1) + + +def alice_public_key(a_pr_k, a, p): + """Alice calculate her public key + with her private key. + This is open to public""" + return pow(a, a_pr_k) % p + + +def bob_private_key(p): + """Bob determine his private key + in the range of 1 ~ p-1. + This must be kept in secret""" + return randint(1, p-1) + + +def bob_public_key(b_pr_k, a, p): + """Bob calculate his public key + with his private key. + This is open to public""" + return pow(a, b_pr_k) % p + + +def alice_shared_key(b_pu_k, a_pr_k, p): + """ Alice calculate secret key shared with Bob, + with her private key and Bob's public key. + This must be kept in secret""" + return pow(b_pu_k, a_pr_k) % p + + +def bob_shared_key(a_pu_k, b_pr_k, p): + """ Bob calculate secret key shared with Alice, + with his private key and Alice's public key. + This must be kept in secret""" + return pow(a_pu_k, b_pr_k) % p + + +def diffie_hellman_key_exchange(a, p, option = None): + """ Perform diffie-helmman key exchange. """ + if option is not None: + # Print explanation of process when option parameter is given + option = 1 + if prime_check(p) is False: + print(f"{p} is not a prime number") + # p must be large prime number + return False + try: + p_root_list = find_primitive_root(p) + p_root_list.index(a) + except ValueError: + print(f"{a} is not a primitive root of {p}") + # a must be primitive root of p + return False + + a_pr_k = alice_private_key(p) + a_pu_k = alice_public_key(a_pr_k, a, p) + + b_pr_k = bob_private_key(p) + b_pu_k = bob_public_key(b_pr_k, a, p) + + if option == 1: + print(f"Alice's private key: {a_pr_k}") + print(f"Alice's public key: {a_pu_k}") + print(f"Bob's private key: {b_pr_k}") + print(f"Bob's public key: {b_pu_k}") + + # In here, Alice send her public key to Bob, and Bob also send his public key to Alice. + + a_sh_k = alice_shared_key(b_pu_k, a_pr_k, p) + b_sh_k = bob_shared_key(a_pu_k, b_pr_k, p) + print (f"Shared key calculated by Alice = {a_sh_k}") + print (f"Shared key calculated by Bob = {b_sh_k}") + + return a_sh_k == b_sh_k diff --git a/algorithms/maths/euler_totient.py b/algorithms/maths/euler_totient.py new file mode 100644 index 000000000..f29d382ff --- /dev/null +++ b/algorithms/maths/euler_totient.py @@ -0,0 +1,18 @@ +""" +Euler's totient function, also known as phi-function ϕ(n), +counts the number of integers between 1 and n inclusive, +which are coprime to n. +(Two numbers are coprime if their greatest common divisor (GCD) equals 1). +""" +def euler_totient(n): + """Euler's totient function or Phi function. + Time Complexity: O(sqrt(n)).""" + result = n + for i in range(2, int(n ** 0.5) + 1): + if n % i == 0: + while n % i == 0: + n //= i + result -= result // i + if n > 1: + result -= result // n + return result diff --git a/algorithms/maths/extended_gcd.py b/algorithms/maths/extended_gcd.py new file mode 100644 index 000000000..a0e9cbc12 --- /dev/null +++ b/algorithms/maths/extended_gcd.py @@ -0,0 +1,24 @@ +""" +Provides extended GCD functionality for finding co-prime numbers s and t such that: +num1 * s + num2 * t = GCD(num1, num2). +Ie the coefficients of Bézout's identity. +""" +def extended_gcd(num1, num2): + """Extended GCD algorithm. + Return s, t, g + such that num1 * s + num2 * t = GCD(num1, num2) + and s and t are co-prime. + """ + + old_s, s = 1, 0 + old_t, t = 0, 1 + old_r, r = num1, num2 + + while r != 0: + quotient = old_r / r + + old_r, r = r, old_r - quotient * r + old_s, s = s, old_s - quotient * s + old_t, t = t, old_t - quotient * t + + return old_s, old_t, old_r diff --git a/algorithms/maths/factorial.py b/algorithms/maths/factorial.py new file mode 100644 index 000000000..f5e3ea5a2 --- /dev/null +++ b/algorithms/maths/factorial.py @@ -0,0 +1,35 @@ +""" +Calculates the factorial with the added functionality of calculating it modulo mod. +""" +def factorial(n, mod=None): + """Calculates factorial iteratively. + If mod is not None, then return (n! % mod) + Time Complexity - O(n)""" + if not (isinstance(n, int) and n >= 0): + raise ValueError("'n' must be a non-negative integer.") + if mod is not None and not (isinstance(mod, int) and mod > 0): + raise ValueError("'mod' must be a positive integer") + result = 1 + if n == 0: + return 1 + for i in range(2, n+1): + result *= i + if mod: + result %= mod + return result + + +def factorial_recur(n, mod=None): + """Calculates factorial recursively. + If mod is not None, then return (n! % mod) + Time Complexity - O(n)""" + if not (isinstance(n, int) and n >= 0): + raise ValueError("'n' must be a non-negative integer.") + if mod is not None and not (isinstance(mod, int) and mod > 0): + raise ValueError("'mod' must be a positive integer") + if n == 0: + return 1 + result = n * factorial(n - 1, mod) + if mod: + result %= mod + return result diff --git a/algorithms/maths/fft.py b/algorithms/maths/fft.py new file mode 100644 index 000000000..6f6697421 --- /dev/null +++ b/algorithms/maths/fft.py @@ -0,0 +1,32 @@ +""" +Implementation of the Cooley-Tukey, which is the most common FFT algorithm. + +Input: an array of complex values which has a size of N, where N is an integer power of 2 +Output: an array of complex values which is the discrete fourier transform of the input + +Example 1 +Input: [2.0+2j, 1.0+3j, 3.0+1j, 2.0+2j] +Output: [8+8j, 2j, 2-2j, -2+0j] + + +Pseudocode: https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm +""" +from cmath import exp, pi + +def fft(x): + """ Recursive implementation of the Cooley-Tukey""" + N = len(x) + if N == 1: + return x + + # get the elements at even/odd indices + even = fft(x[0::2]) + odd = fft(x[1::2]) + + y = [0 for i in range(N)] + for k in range(N//2): + q = exp(-2j*pi*k/N)*odd[k] + y[k] = even[k] + q + y[k + N//2] = even[k] - q + + return y diff --git a/algorithms/maths/find_order_simple.py b/algorithms/maths/find_order_simple.py new file mode 100644 index 000000000..8f69773c7 --- /dev/null +++ b/algorithms/maths/find_order_simple.py @@ -0,0 +1,27 @@ +""" +For positive integer n and given integer a that satisfies gcd(a, n) = 1, +the order of a modulo n is the smallest positive integer k that satisfies +pow (a, k) % n = 1. In other words, (a^k) ≡ 1 (mod n). +Order of a certain number may or may not be exist. If not, return -1. + +Total time complexity O(nlog(n)): +O(n) for iteration loop, +O(log(n)) for built-in power function +""" + +import math + +def find_order(a, n): + """ + Find order for positive integer n and given integer a that satisfies gcd(a, n) = 1. + """ + if (a == 1) & (n == 1): + # Exception Handeling : 1 is the order of of 1 + return 1 + if math.gcd(a, n) != 1: + print ("a and n should be relative prime!") + return -1 + for i in range(1, n): + if pow(a, i) % n == 1: + return i + return -1 diff --git a/algorithms/maths/find_primitive_root_simple.py b/algorithms/maths/find_primitive_root_simple.py new file mode 100644 index 000000000..366f40191 --- /dev/null +++ b/algorithms/maths/find_primitive_root_simple.py @@ -0,0 +1,67 @@ +""" +Function to find the primitive root of a number. +""" +import math + +""" +For positive integer n and given integer a that satisfies gcd(a, n) = 1, +the order of a modulo n is the smallest positive integer k that satisfies +pow (a, k) % n = 1. In other words, (a^k) ≡ 1 (mod n). +Order of certain number may or may not be exist. If so, return -1. +""" +def find_order(a, n): + """ + Find order for positive integer n and given integer a that satisfies gcd(a, n) = 1. + Time complexity O(nlog(n)) + """ + if (a == 1) & (n == 1): + # Exception Handeling : 1 is the order of of 1 + return 1 + if math.gcd(a, n) != 1: + print ("a and n should be relative prime!") + return -1 + for i in range(1, n): + if pow(a, i) % n == 1: + return i + return -1 + +""" +Euler's totient function, also known as phi-function ϕ(n), +counts the number of integers between 1 and n inclusive, +which are coprime to n. +(Two numbers are coprime if their greatest common divisor (GCD) equals 1). +Code from /algorithms/maths/euler_totient.py, written by 'goswami-rahul' +""" +def euler_totient(n): + """Euler's totient function or Phi function. + Time Complexity: O(sqrt(n)).""" + result = n + for i in range(2, int(n ** 0.5) + 1): + if n % i == 0: + while n % i == 0: + n //= i + result -= result // i + if n > 1: + result -= result // n + return result + +""" +For positive integer n and given integer a that satisfies gcd(a, n) = 1, +a is the primitive root of n, if a's order k for n satisfies k = ϕ(n). +Primitive roots of certain number may or may not exist. +If so, return empty list. +""" +def find_primitive_root(n): + if n == 1: + # Exception Handeling : 0 is the only primitive root of 1 + return [0] + phi = euler_totient(n) + p_root_list = [] + """ It will return every primitive roots of n. """ + for i in range (1, n): + #To have order, a and n must be relative prime with each other. + if math.gcd(i, n) == 1: + order = find_order(i, n) + if order == phi: + p_root_list.append(i) + return p_root_list diff --git a/algorithms/maths/gcd.py b/algorithms/maths/gcd.py new file mode 100644 index 000000000..189eae100 --- /dev/null +++ b/algorithms/maths/gcd.py @@ -0,0 +1,63 @@ +""" +Functions for calculating the greatest common divisor of two integers or +their least common multiple. +""" + +def gcd(a, b): + """Computes the greatest common divisor of integers a and b using + Euclid's Algorithm. + gcd{𝑎,𝑏}=gcd{−𝑎,𝑏}=gcd{𝑎,−𝑏}=gcd{−𝑎,−𝑏} + See proof: https://proofwiki.org/wiki/GCD_for_Negative_Integers + """ + a_int = isinstance(a, int) + b_int = isinstance(b, int) + a = abs(a) + b = abs(b) + if not(a_int or b_int): + raise ValueError("Input arguments are not integers") + + if (a == 0) or (b == 0) : + raise ValueError("One or more input arguments equals zero") + + while b != 0: + a, b = b, a % b + return a + +def lcm(a, b): + """Computes the lowest common multiple of integers a and b.""" + return abs(a) * abs(b) / gcd(a, b) + +""" +Given a positive integer x, computes the number of trailing zero of x. +Example +Input : 34(100010) + ~~~~~^ +Output : 1 + +Input : 40(101000) + ~~~^^^ +Output : 3 +""" +def trailing_zero(x): + count = 0 + while x and not x & 1: + count += 1 + x >>= 1 + return count + +""" +Given two non-negative integer a and b, +computes the greatest common divisor of a and b using bitwise operator. +""" +def gcd_bit(a, b): + """ Similar to gcd but uses bitwise operators and less error handling.""" + tza = trailing_zero(a) + tzb = trailing_zero(b) + a >>= tza + b >>= tzb + while b: + if a < b: + a, b = b, a + a -= b + a >>= trailing_zero(a) + return a << min(tza, tzb) diff --git a/math/generate_strobogrammtic.py b/algorithms/maths/generate_strobogrammtic.py similarity index 77% rename from math/generate_strobogrammtic.py rename to algorithms/maths/generate_strobogrammtic.py index f5589ac7e..d051865fb 100644 --- a/math/generate_strobogrammtic.py +++ b/algorithms/maths/generate_strobogrammtic.py @@ -8,15 +8,13 @@ Given n = 2, return ["11","69","88","96"]. """ - def gen_strobogrammatic(n): """ + Given n, generate all strobogrammatic numbers of length n. :type n: int :rtype: List[str] """ - result = helper(n, n) - return result - + return helper(n, n) def helper(n, length): if n == 0: @@ -34,8 +32,7 @@ def helper(n, length): result.append("6" + middle + "9") return result - -def strobogrammaticInRange(low, high): +def strobogrammatic_in_range(low, high): """ :type low: str :type high: str @@ -43,19 +40,19 @@ def strobogrammaticInRange(low, high): """ res = [] count = 0 - for i in range(len(low), len(high)+1): + low_len = len(low) + high_len = len(high) + for i in range(low_len, high_len + 1): res.extend(helper2(i, i)) for perm in res: - if len(perm) == len(low) and int(perm) < int(low): + if len(perm) == low_len and int(perm) < int(low): continue - elif len(perm) == len(high) and int(perm) > int(high): + if len(perm) == high_len and int(perm) > int(high): continue - else: - count += 1 + count += 1 return count - -def helper2(self, n, length): +def helper2(n, length): if n == 0: return [""] if n == 1: diff --git a/algorithms/maths/hailstone.py b/algorithms/maths/hailstone.py new file mode 100644 index 000000000..77261ac5e --- /dev/null +++ b/algorithms/maths/hailstone.py @@ -0,0 +1,21 @@ +""" +Implementation of hailstone function which generates a sequence for some n by following these rules: +* n == 1 : done +* n is even : the next n = n/2 +* n is odd : the next n = 3n + 1 +""" + +def hailstone(n): + """ + Return the 'hailstone sequence' from n to 1 + n: The starting point of the hailstone sequence + """ + + sequence = [n] + while n > 1: + if n%2 != 0: + n = 3*n + 1 + else: + n = int(n/2) + sequence.append(n) + return sequence diff --git a/math/is_strobogrammatic.py b/algorithms/maths/is_strobogrammatic.py similarity index 72% rename from math/is_strobogrammatic.py rename to algorithms/maths/is_strobogrammatic.py index e42e87980..b849ddac4 100644 --- a/math/is_strobogrammatic.py +++ b/algorithms/maths/is_strobogrammatic.py @@ -18,9 +18,13 @@ def is_strobogrammatic(num): i = 0 j = len(num) - 1 while i <= j: - x = comb.find(num[i]+num[j]) - if x == -1: + if comb.find(num[i]+num[j]) == -1: return False i += 1 j -= 1 return True + + +def is_strobogrammatic2(num: str): + """Another implementation.""" + return num == num[::-1].replace('6', '#').replace('9', '6').replace('#', '9') diff --git a/algorithms/maths/krishnamurthy_number.py b/algorithms/maths/krishnamurthy_number.py new file mode 100644 index 000000000..1d41721b1 --- /dev/null +++ b/algorithms/maths/krishnamurthy_number.py @@ -0,0 +1,46 @@ +""" +A Krishnamurthy number is a number whose sum total of the factorials of each digit is equal to the +number itself. + +The following are some examples of Krishnamurthy numbers: + +"145" is a Krishnamurthy Number because, +1! + 4! + 5! = 1 + 24 + 120 = 145 + +"40585" is also a Krishnamurthy Number. +4! + 0! + 5! + 8! + 5! = 40585 + +"357" or "25965" is NOT a Krishnamurthy Number +3! + 5! + 7! = 6 + 120 + 5040 != 357 + +The following function will check if a number is a Krishnamurthy Number or not and return a +boolean value. +""" + + +def find_factorial(n): + """ Calculates the factorial of a given number n """ + fact = 1 + while n != 0: + fact *= n + n -= 1 + return fact + + +def krishnamurthy_number(n): + if n == 0: + return False + sum_of_digits = 0 # will hold sum of FACTORIAL of digits + temp = n + + while temp != 0: + + # get the factorial of of the last digit of n and add it to sum_of_digits + sum_of_digits += find_factorial(temp % 10) + + # replace value of temp by temp/10 + # i.e. will remove the last digit from temp + temp //= 10 + + # returns True if number is krishnamurthy + return sum_of_digits == n diff --git a/algorithms/maths/magic_number.py b/algorithms/maths/magic_number.py new file mode 100644 index 000000000..6107753d2 --- /dev/null +++ b/algorithms/maths/magic_number.py @@ -0,0 +1,33 @@ +""" +Magic Number +A number is said to be a magic number, +if summing the digits of the number and then recursively repeating this process for the given sum +untill the number becomes a single digit number equal to 1. + +Example: + Number = 50113 => 5+0+1+1+3=10 => 1+0=1 [This is a Magic Number] + Number = 1234 => 1+2+3+4=10 => 1+0=1 [This is a Magic Number] + Number = 199 => 1+9+9=19 => 1+9=10 => 1+0=1 [This is a Magic Number] + Number = 111 => 1+1+1=3 [This is NOT a Magic Number] + +The following function checks for Magic numbers and returns a Boolean accordingly. +""" + +def magic_number(n): + """ Checks if n is a magic number """ + total_sum = 0 + + # will end when n becomes 0 + # AND + # sum becomes single digit. + while n > 0 or total_sum > 9: + # when n becomes 0 but we have a total_sum, + # we update the value of n with the value of the sum digits + if n == 0: + n = total_sum # only when sum of digits isn't single digit + total_sum = 0 + total_sum += n % 10 + n //= 10 + + # Return true if sum becomes 1 + return total_sum == 1 diff --git a/algorithms/maths/modular_exponential.py b/algorithms/maths/modular_exponential.py new file mode 100644 index 000000000..f0e58de8f --- /dev/null +++ b/algorithms/maths/modular_exponential.py @@ -0,0 +1,18 @@ +def modular_exponential(base, exponent, mod): + """Computes (base ^ exponent) % mod. + Time complexity - O(log n) + Use similar to Python in-built function pow.""" + if exponent < 0: + raise ValueError("Exponent must be positive.") + base %= mod + result = 1 + + while exponent > 0: + # If the last bit is 1, add 2^k. + if exponent & 1: + result = (result * base) % mod + exponent = exponent >> 1 + # Utilize modular multiplication properties to combine the computed mod C values. + base = (base * base) % mod + + return result diff --git a/algorithms/maths/modular_inverse.py b/algorithms/maths/modular_inverse.py new file mode 100644 index 000000000..c6f849d7d --- /dev/null +++ b/algorithms/maths/modular_inverse.py @@ -0,0 +1,34 @@ +# extended_gcd(a, b) modified from +# https://github.com/keon/algorithms/blob/master/algorithms/maths/extended_gcd.py + +def extended_gcd(a: int, b: int) -> [int, int, int]: + """Extended GCD algorithm. + Return s, t, g + such that a * s + b * t = GCD(a, b) + and s and t are co-prime. + """ + + old_s, s = 1, 0 + old_t, t = 0, 1 + old_r, r = a, b + + while r != 0: + quotient = old_r // r + + old_r, r = r, old_r - quotient * r + old_s, s = s, old_s - quotient * s + old_t, t = t, old_t - quotient * t + + return old_s, old_t, old_r + + +def modular_inverse(a: int, m: int) -> int: + """ + Returns x such that a * x = 1 (mod m) + a and m must be coprime + """ + + s, _, g = extended_gcd(a, m) + if g != 1: + raise ValueError("a and m must be coprime") + return s % m diff --git a/algorithms/maths/next_bigger.py b/algorithms/maths/next_bigger.py new file mode 100644 index 000000000..a159da197 --- /dev/null +++ b/algorithms/maths/next_bigger.py @@ -0,0 +1,64 @@ +""" +I just bombed an interview and made pretty much zero +progress on my interview question. + +Given a number, find the next higher number which has the +exact same set of digits as the original number. +For example: given 38276 return 38627. + given 99999 return -1. (no such number exists) + +Condensed mathematical description: + +Find largest index i such that array[i − 1] < array[i]. +(If no such i exists, then this is already the last permutation.) + +Find largest index j such that j ≥ i and array[j] > array[i − 1]. + +Swap array[j] and array[i − 1]. + +Reverse the suffix starting at array[i]. + +""" +import unittest + + +def next_bigger(num): + + digits = [int(i) for i in str(num)] + idx = len(digits) - 1 + + while idx >= 1 and digits[idx-1] >= digits[idx]: + idx -= 1 + + if idx == 0: + return -1 # no such number exists + + pivot = digits[idx-1] + swap_idx = len(digits) - 1 + + while pivot >= digits[swap_idx]: + swap_idx -= 1 + + digits[swap_idx], digits[idx-1] = digits[idx-1], digits[swap_idx] + digits[idx:] = digits[:idx-1:-1] # prefer slicing instead of reversed(digits[idx:]) + + return int(''.join(str(x) for x in digits)) + + +class TestSuite(unittest.TestCase): + + def test_next_bigger(self): + + self.assertEqual(next_bigger(38276), 38627) + self.assertEqual(next_bigger(12345), 12354) + self.assertEqual(next_bigger(1528452), 1528524) + self.assertEqual(next_bigger(138654), 143568) + + self.assertEqual(next_bigger(54321), -1) + self.assertEqual(next_bigger(999), -1) + self.assertEqual(next_bigger(5), -1) + + +if __name__ == '__main__': + + unittest.main() diff --git a/algorithms/maths/next_perfect_square.py b/algorithms/maths/next_perfect_square.py new file mode 100644 index 000000000..be2d24a24 --- /dev/null +++ b/algorithms/maths/next_perfect_square.py @@ -0,0 +1,17 @@ +""" +This program will look for the next perfect square. +Check the argument to see if it is a perfect square itself, if it is not then return -1 otherwise +look for the next perfect square. +for instance if you pass 121 then the script should return the next perfect square which is 144. +""" + +def find_next_square(sq): + root = sq ** 0.5 + if root.is_integer(): + return (root + 1)**2 + return -1 + +def find_next_square2(sq): + """ Alternative method, works by evaluating anything non-zero as True (0.000001 --> True) """ + root = sq**0.5 + return -1 if root % 1 else (root+1)**2 diff --git a/algorithms/maths/nth_digit.py b/algorithms/maths/nth_digit.py new file mode 100644 index 000000000..f6454e940 --- /dev/null +++ b/algorithms/maths/nth_digit.py @@ -0,0 +1,17 @@ +def find_nth_digit(n): + """find the nth digit of given number. + 1. find the length of the number where the nth digit is from. + 2. find the actual number where the nth digit is from + 3. find the nth digit and return + """ + length = 1 + count = 9 + start = 1 + while n > length * count: + n -= length * count + length += 1 + count *= 10 + start *= 10 + start += (n-1) / length + s = str(start) + return int(s[(n-1) % length]) diff --git a/algorithms/maths/num_digits.py b/algorithms/maths/num_digits.py new file mode 100644 index 000000000..4ecd5c7c3 --- /dev/null +++ b/algorithms/maths/num_digits.py @@ -0,0 +1,12 @@ +""" +num_digits() method will return the number of digits of a number in O(1) time using +math.log10() method. +""" + +import math + +def num_digits(n): + n=abs(n) + if n==0: + return 1 + return int(math.log10(n))+1 diff --git a/algorithms/maths/num_perfect_squares.py b/algorithms/maths/num_perfect_squares.py new file mode 100644 index 000000000..e02eeb768 --- /dev/null +++ b/algorithms/maths/num_perfect_squares.py @@ -0,0 +1,47 @@ +""" +Given an integer num_perfect_squares will return the minimum amount of perfect squares are required +to sum to the specified number. Lagrange's four-square theorem gives us that the answer will always +be between 1 and 4 (https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem). + +Some examples: +Number | Perfect Squares representation | Answer +-------|--------------------------------|-------- +9 | 3^2 | 1 +10 | 3^2 + 1^2 | 2 +12 | 2^2 + 2^2 + 2^2 | 3 +31 | 5^2 + 2^2 + 1^2 + 1^2 | 4 +""" + +import math + +def num_perfect_squares(number): + """ + Returns the smallest number of perfect squares that sum to the specified number. + :return: int between 1 - 4 + """ + # If the number is a perfect square then we only need 1 number. + if int(math.sqrt(number))**2 == number: + return 1 + + # We check if https://en.wikipedia.org/wiki/Legendre%27s_three-square_theorem holds and divide + # the number accordingly. Ie. if the number can be written as a sum of 3 squares (where the + # 0^2 is allowed), which is possible for all numbers except those of the form: 4^a(8b + 7). + while number > 0 and number % 4 == 0: + number /= 4 + + # If the number is of the form: 4^a(8b + 7) it can't be expressed as a sum of three (or less + # excluding the 0^2) perfect squares. If the number was of that form, the previous while loop + # divided away the 4^a, so by now it would be of the form: 8b + 7. So check if this is the case + # and return 4 since it neccessarily must be a sum of 4 perfect squares, in accordance + # with https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem. + if number % 8 == 7: + return 4 + + # By now we know that the number wasn't of the form 4^a(8b + 7) so it can be expressed as a sum + # of 3 or less perfect squares. Try first to express it as a sum of 2 perfect squares, and if + # that fails, we know finally that it can be expressed as a sum of 3 perfect squares. + for i in range(1, int(math.sqrt(number)) + 1): + if int(math.sqrt(number - i**2))**2 == number - i**2: + return 2 + + return 3 diff --git a/algorithms/maths/polynomial.py b/algorithms/maths/polynomial.py new file mode 100644 index 000000000..81faf2b7e --- /dev/null +++ b/algorithms/maths/polynomial.py @@ -0,0 +1,575 @@ +# from __future__ import annotations + +from fractions import Fraction +from typing import Dict, Union, Set, Iterable +from numbers import Rational +from functools import reduce + + +class Monomial: + """ + A simple Monomial class to + record the details of all variables + that a typical monomial is composed of. + """ + def __init__(self, variables: Dict[int, int], coeff: Union[int, float, Fraction, None]= None) -> None: + ''' + Create a monomial in the given variables: + Examples: + + Monomial({1:1}) = (a_1)^1 + + Monomial({ + 1:3, + 2:2, + 4:1, + 5:0 + }, 12) = 12(a_1)^3(a_2)^2(a_4) + + Monomial({}) = 0 + + Monomial({2:3, 3:-1}, 1.5) = (3/2)(a_2)^3(a_3)^(-1) + + ''' + self.variables = dict() + + if coeff is None: + if len(variables) == 0: + coeff = Fraction(0, 1) + else: + coeff = Fraction(1, 1) + elif coeff == 0: + self.coeff = Fraction(0, 1) + return + + if len(variables) == 0: + self.coeff = Monomial._rationalize_if_possible(coeff) + return + + for i in variables: + if variables[i] != 0: + self.variables[i] = variables[i] + self.coeff = Monomial._rationalize_if_possible(coeff) + + @staticmethod + def _rationalize_if_possible(num): + ''' + A helper for converting numbers + to Fraction only when possible. + ''' + if isinstance(num, Rational): + res = Fraction(num, 1) + return Fraction(res.numerator, res.denominator) + else: + return num + + # def equal_upto_scalar(self, other: Monomial) -> bool: + def equal_upto_scalar(self, other) -> bool: + """ + Return True if other is a monomial + and is equivalent to self up to a scalar + multiple. + """ + if not isinstance(other, Monomial): + raise ValueError('Can only compare monomials.') + return other.variables == self.variables + + # def __add__(self, other: Union[int, float, Fraction, Monomial]): + def __add__(self, other: Union[int, float, Fraction]): + """ + Define the addition of two + monomials or the addition of + a monomial with an int, float, or a Fraction. + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + return self.__add__(Monomial({}, Monomial._rationalize_if_possible(other))) + + if not isinstance(other, Monomial): + raise ValueError('Can only add monomials, ints, floats, or Fractions.') + + if self.variables == other.variables: + mono = {i: self.variables[i] for i in self.variables} + return Monomial(mono, Monomial._rationalize_if_possible(self.coeff + other.coeff)).clean() + + # If they don't share same variables then by the definition, + # if they are added, the result becomes a polynomial and not a monomial. + # Thus, raise ValueError in that case. + + raise ValueError(f'Cannot add {str(other)} to {self.__str__()} because they don\'t have same variables.') + + # def __eq__(self, other: Monomial) -> bool: + def __eq__(self, other) -> bool: + """ + Return True if two monomials + are equal upto a scalar multiple. + """ + return self.equal_upto_scalar(other) and self.coeff == other.coeff + + # def __mul__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial: + def __mul__(self, other: Union[int, float, Fraction]): + """ + Multiply two monomials and merge the variables + in both of them. + + Examples: + + Monomial({1:1}) * Monomial({1: -3, 2: 1}) = (a_1)^(-2)(a_2) + Monomial({3:2}) * 2.5 = (5/2)(a_3)^2 + + """ + if isinstance(other, float) or isinstance(other, int) or isinstance(other, Fraction): + mono = {i: self.variables[i] for i in self.variables} + return Monomial(mono, Monomial._rationalize_if_possible(self.coeff * other)).clean() + + if not isinstance(other, Monomial): + raise ValueError('Can only multiply monomials, ints, floats, or Fractions.') + else: + mono = {i: self.variables[i] for i in self.variables} + for i in other.variables: + if i in mono: + mono[i] += other.variables[i] + else: + mono[i] = other.variables[i] + + temp = dict() + for k in mono: + if mono[k] != 0: + temp[k] = mono[k] + + return Monomial(temp, Monomial._rationalize_if_possible(self.coeff * other.coeff)).clean() + + # def inverse(self) -> Monomial: + def inverse(self): + """ + Compute the inverse of a monomial. + + Examples: + + Monomial({1:1, 2:-1, 3:2}, 2.5).inverse() = Monomial({1:-1, 2:1, 3:-2} ,2/5) + + + """ + mono = {i: self.variables[i] for i in self.variables if self.variables[i] != 0} + for i in mono: + mono[i] *= -1 + if self.coeff == 0: + raise ValueError("Coefficient must not be 0.") + return Monomial(mono, Monomial._rationalize_if_possible(1/self.coeff)).clean() + + # def __truediv__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial: + def __truediv__(self, other: Union[int, float, Fraction]): + """ + Compute the division between two monomials + or a monomial and some other datatype + like int/float/Fraction. + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + mono = {i: self.variables[i] for i in self.variables} + if other == 0: + raise ValueError('Cannot divide by 0.') + return Monomial(mono, Monomial._rationalize_if_possible(self.coeff / other)).clean() + + o = other.inverse() + return self.__mul__(o) + + # def __floordiv__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial: + def __floordiv__(self, other: Union[int, float, Fraction]): + """ + For monomials, + floor div is the same as true div. + """ + return self.__truediv__(other) + + # def clone(self) -> Monomial: + def clone(self): + """ + Clone the monomial. + """ + temp_variables = {i: self.variables[i] for i in self.variables} + return Monomial(temp_variables, Monomial._rationalize_if_possible(self.coeff)).clean() + + # def clean(self) -> Monomial: + def clean(self): + """ + Clean the monomial by dropping any variables that have power 0. + """ + temp_variables = {i: self.variables[i] for i in self.variables if self.variables[i] != 0} + return Monomial(temp_variables, Monomial._rationalize_if_possible(self.coeff)) + + # def __sub__(self, other: Union[int, float, Fraction, Monomial]) -> Monomial: + def __sub__(self, other: Union[int, float, Fraction]): + """ + Compute the subtraction + of a monomial and a datatype + such as int, float, Fraction, or Monomial. + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + mono = {i: self.variables[i] for i in self.variables if self.variables[i] != 0} + if len(mono) != 0: + raise ValueError('Can only subtract like monomials.') + other_term = Monomial(mono, Monomial._rationalize_if_possible(other)) + return self.__sub__(other_term) + if not isinstance(other, Monomial): + raise ValueError('Can only subtract monomials') + return self.__add__(other.__mul__(Fraction(-1, 1))) + + def __hash__(self) -> int: + """ + Define the hash of a monomial + by the underlying variables. + + If hashing is implemented in O(v*log(v)) + where v represents the number of + variables in the monomial, + then search queries for the + purposes of simplification of a + polynomial can be performed in + O(v*log(v)) as well; much better than + the length of the polynomial. + """ + arr = [] + for i in sorted(self.variables): + if self.variables[i] > 0: + for _ in range(self.variables[i]): + arr.append(i) + return hash(tuple(arr)) + + def all_variables(self) -> Set: + """ + Get the set of all variables + present in the monomial. + """ + return set(sorted(self.variables.keys())) + + def substitute(self, substitutions: Union[int, float, Fraction, Dict[int, Union[int, float, Fraction]]]) -> Fraction: + """ + Substitute the variables in the + monomial for values defined by + the substitutions dictionary. + """ + if isinstance(substitutions, int) or isinstance(substitutions, float) or isinstance(substitutions, Fraction): + substitutions = {v: Monomial._rationalize_if_possible(substitutions) for v in self.all_variables()} + else: + if not self.all_variables().issubset(set(substitutions.keys())): + raise ValueError('Some variables didn\'t receive their values.') + if self.coeff == 0: + return Fraction(0, 1) + ans = Monomial._rationalize_if_possible(self.coeff) + for k in self.variables: + ans *= Monomial._rationalize_if_possible(substitutions[k]**self.variables[k]) + return Monomial._rationalize_if_possible(ans) + + def __str__(self) -> str: + """ + Get a string representation of + the monomial. + """ + if len(self.variables) == 0: + return str(self.coeff) + + result = str(self.coeff) + result += '(' + for i in self.variables: + temp = 'a_{}'.format(str(i)) + if self.variables[i] > 1: + temp = '(' + temp + ')**{}'.format(self.variables[i]) + elif self.variables[i] < 0: + temp = '(' + temp + ')**(-{})'.format(-self.variables[i]) + elif self.variables[i] == 0: + continue + else: + temp = '(' + temp + ')' + result += temp + return result + ')' + + +class Polynomial: + """ + A simple implementation + of a polynomial class that + records the details about two polynomials + that are potentially comprised of multiple + variables. + """ + def __init__(self, monomials: Iterable[Union[int, float, Fraction, Monomial]]) -> None: + ''' + Create a polynomial in the given variables: + Examples: + + Polynomial([ + Monomial({1:1}, 2), + Monomial({2:3, 1:-1}, -1), + math.pi, + Fraction(-1, 2) + ]) = (a_1)^2 + (-1)(a_2)^3(a_1)^(-1) + 2.6415926536 + + Polynomial([]) = 0 + + ''' + self.monomials = set() + for m in monomials: + if any(map(lambda x: isinstance(m, x), [int, float, Fraction])): + self.monomials |= {Monomial({}, m)} + elif isinstance(m, Monomial): + self.monomials |= {m} + else: + raise ValueError('Iterable should have monomials, int, float, or Fraction.') + self.monomials -= {Monomial({}, 0)} + + @staticmethod + def _rationalize_if_possible(num): + ''' + A helper for converting numbers + to Fraction only when possible. + ''' + if isinstance(num, Rational): + res = Fraction(num, 1) + return Fraction(res.numerator, res.denominator) + else: + return num + + + # def __add__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: + def __add__(self, other: Union[int, float, Fraction, Monomial]): + """ + Add a given poylnomial to a copy of self. + + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + return self.__add__(Monomial({}, Polynomial._rationalize_if_possible(other))) + elif isinstance(other, Monomial): + monos = {m.clone() for m in self.monomials} + + for _own_monos in monos: + if _own_monos.equal_upto_scalar(other): + scalar = _own_monos.coeff + monos -= {_own_monos} + temp_variables = {i: other.variables[i] for i in other.variables} + monos |= {Monomial(temp_variables, Polynomial._rationalize_if_possible(scalar + other.coeff))} + return Polynomial([z for z in monos]) + + monos |= {other.clone()} + return Polynomial([z for z in monos]) + elif isinstance(other, Polynomial): + temp = list(z for z in {m.clone() for m in self.all_monomials()}) + + p = Polynomial(temp) + for o in other.all_monomials(): + p = p.__add__(o.clone()) + return p + else: + raise ValueError('Can only add int, float, Fraction, Monomials, or Polynomials to Polynomials.') + + # def __sub__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: + def __sub__(self, other: Union[int, float, Fraction, Monomial]): + """ + Subtract the given polynomial + from a copy of self. + + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + return self.__sub__(Monomial({}, Polynomial._rationalize_if_possible(other))) + elif isinstance(other, Monomial): + monos = {m.clone() for m in self.all_monomials()} + for _own_monos in monos: + if _own_monos.equal_upto_scalar(other): + scalar = _own_monos.coeff + monos -= {_own_monos} + temp_variables = {i: other.variables[i] for i in other.variables} + monos |= {Monomial(temp_variables, Polynomial._rationalize_if_possible(scalar - other.coeff))} + return Polynomial([z for z in monos]) + + to_insert = other.clone() + to_insert.coeff *= -1 + + monos |= {to_insert} + return Polynomial([z for z in monos]) + + elif isinstance(other, Polynomial): + p = Polynomial(list(z for z in {m.clone() for m in self.all_monomials()})) + for o in other.all_monomials(): + p = p.__sub__(o.clone()) + return p + + else: + raise ValueError('Can only subtract int, float, Fraction, Monomials, or Polynomials from Polynomials.') + return + + # def __mul__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: + def __mul__(self, other: Union[int, float, Fraction, Monomial]): + """ + Multiply a given polynomial + to a copy of self. + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + result = Polynomial([]) + monos = {m.clone() for m in self.all_monomials()} + for m in monos: + result = result.__add__(m.clone()*other) + return result + elif isinstance(other, Monomial): + result = Polynomial([]) + monos = {m.clone() for m in self.all_monomials()} + for m in monos: + result = result.__add__(m.clone() * other) + return result + elif isinstance(other, Polynomial): + temp_self = {m.clone() for m in self.all_monomials()} + temp_other = {m.clone() for m in other.all_monomials()} + + result = Polynomial([]) + + for i in temp_self: + for j in temp_other: + result = result.__add__(i * j) + + return result + else: + raise ValueError('Can only multiple int, float, Fraction, Monomials, or Polynomials with Polynomials.') + + # def __floordiv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: + def __floordiv__(self, other: Union[int, float, Fraction, Monomial]): + """ + For Polynomials, floordiv is the same + as truediv. + """ + return self.__truediv__(other) + + # def __truediv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: + def __truediv__(self, other: Union[int, float, Fraction, Monomial]): + """ + For Polynomial division, no remainder is provided. Must use poly_long_division() to capture remainder + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + return self.__truediv__( Monomial({}, other) ) + elif isinstance(other, Monomial): + poly_temp = reduce(lambda acc, val: acc + val, map(lambda x: x / other, [z for z in self.all_monomials()]), Polynomial([Monomial({}, 0)])) + return poly_temp + elif isinstance(other, Polynomial): + # Call long division + quotient, remainder = self.poly_long_division(other) + return quotient # Return just the quotient, remainder is ignored here + + raise ValueError('Can only divide a polynomial by an int, float, Fraction, Monomial, or Polynomial.') + + return + + # def clone(self) -> Polynomial: + def clone(self): + """ + Clone the polynomial. + """ + return Polynomial(list({m.clone() for m in self.all_monomials()})) + + def variables(self) -> Set: + """ + Get all the variables present + in this polynomials. + """ + res = set() + for i in self.all_monomials(): + res |= {j for j in i.variables} + res = list(res) + # res.sort() + return set(res) + + def all_monomials(self) -> Iterable[Monomial]: + """ + Get the monomials of this polynomial. + """ + return {m for m in self.monomials if m != Monomial({}, 0)} + + + def __eq__(self, other) -> bool: + """ + Return True if the other polynomial is the same as + this. + """ + if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): + other_poly = Polynomial([Monomial({}, other)]) + return self.__eq__(other_poly) + elif isinstance(other, Monomial): + return self.__eq__(Polynomial([other])) + elif isinstance(other, Polynomial): + return self.all_monomials() == other.all_monomials() + else: + raise ValueError('Can only compare a polynomial with an int, float, Fraction, Monomial, or another Polynomial.') + + + def subs(self, substitutions: Union[int, float, Fraction, Dict[int, Union[int, float, Fraction]]]) -> Union[int, float, Fraction]: + """ + Get the value after substituting + certain values for the variables + defined in substitutions. + """ + if isinstance(substitutions, int) or isinstance(substitutions, float) or isinstance(substitutions, Fraction): + substitutions = {i: Polynomial._rationalize_if_possible(substitutions) for i in set(self.variables())} + return self.subs(substitutions) + elif not isinstance(substitutions, dict): + raise ValueError('The substitutions should be a dictionary.') + if not self.variables().issubset(set(substitutions.keys())): + raise ValueError('Some variables didn\'t receive their values.') + + ans = 0 + for m in self.all_monomials(): + ans += Polynomial._rationalize_if_possible(m.substitute(substitutions)) + return Polynomial._rationalize_if_possible(ans) + + def __str__(self) -> str: + """ + Get a properly formatted string representation of the polynomial. + """ + sorted_monos = sorted(self.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + return ' + '.join(str(m) for m in sorted_monos if m.coeff != Fraction(0, 1)) + + def poly_long_division(self, other: 'Polynomial') -> tuple['Polynomial', 'Polynomial']: + """ + Perform polynomial long division + Returns (quotient, remainder) + """ + if not isinstance(other, Polynomial): + raise ValueError("Can only divide by another Polynomial.") + + if len(other.all_monomials()) == 0: + raise ValueError("Cannot divide by zero polynomial.") + + quotient = Polynomial([]) + remainder = self.clone() + + divisor_monos = sorted(other.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + divisor_lead = divisor_monos[0] + + while remainder.all_monomials() and max(remainder.variables(), default=-1) >= max(other.variables(), + default=-1): + remainder_monos = sorted(remainder.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + remainder_lead = remainder_monos[0] + + if not all(remainder_lead.variables.get(var, 0) >= divisor_lead.variables.get(var, 0) for var in + divisor_lead.variables): + break + + lead_quotient = remainder_lead / divisor_lead + quotient = quotient + Polynomial([lead_quotient]) # Convert Monomial to Polynomial + + remainder = remainder - ( + Polynomial([lead_quotient]) * other) # Convert Monomial to Polynomial before multiplication + + return quotient, remainder + +dividend = Polynomial([ + Monomial({1: 3}, 4), # 4(a_1)^3 + Monomial({1: 2}, 3), # 3(a_1)^2 + Monomial({1: 1}, -2), # -2(a_1) + Monomial({}, 5) # +5 +]) + +divisor = Polynomial([ + Monomial({1: 1}, 2), # 2(a_1) + Monomial({}, -1) # -1 +]) + +quotient = dividend / divisor +print("Quotient:", quotient) diff --git a/algorithms/maths/power.py b/algorithms/maths/power.py new file mode 100644 index 000000000..70d8587de --- /dev/null +++ b/algorithms/maths/power.py @@ -0,0 +1,48 @@ +""" +Performs exponentiation, similarly to the built-in pow() or ** functions. +Allows also for calculating the exponentiation modulo. +""" +def power(a: int, n: int, mod: int = None): + """ + Iterative version of binary exponentiation + + Calculate a ^ n + if mod is specified, return the result modulo mod + + Time Complexity : O(log(n)) + Space Complexity : O(1) + """ + ans = 1 + while n: + if n & 1: + ans = ans * a + a = a * a + if mod: + ans %= mod + a %= mod + n >>= 1 + return ans + + +def power_recur(a: int, n: int, mod: int = None): + """ + Recursive version of binary exponentiation + + Calculate a ^ n + if mod is specified, return the result modulo mod + + Time Complexity : O(log(n)) + Space Complexity : O(log(n)) + """ + if n == 0: + ans = 1 + elif n == 1: + ans = a + else: + ans = power_recur(a, n // 2, mod) + ans = ans * ans + if n % 2: + ans = ans * a + if mod: + ans %= mod + return ans diff --git a/algorithms/maths/prime_check.py b/algorithms/maths/prime_check.py new file mode 100644 index 000000000..60e4427ab --- /dev/null +++ b/algorithms/maths/prime_check.py @@ -0,0 +1,17 @@ +def prime_check(n): + """Return True if n is a prime number + Else return False. + """ + + if n <= 1: + return False + if n == 2 or n == 3: + return True + if n % 2 == 0 or n % 3 == 0: + return False + j = 5 + while j * j <= n: + if n % j == 0 or n % (j + 2) == 0: + return False + j += 6 + return True diff --git a/math/primes_sieve_of_eratosthenes.py b/algorithms/maths/primes_sieve_of_eratosthenes.py similarity index 59% rename from math/primes_sieve_of_eratosthenes.py rename to algorithms/maths/primes_sieve_of_eratosthenes.py index 34289da64..b0d1d96c5 100644 --- a/math/primes_sieve_of_eratosthenes.py +++ b/algorithms/maths/primes_sieve_of_eratosthenes.py @@ -1,11 +1,12 @@ -''' -Using sieve of Eratosthenes, primes(x) returns list of all primes less than x +""" +Return list of all primes less than n, +Using sieve of Eratosthenes. Modification: We don't need to check all even numbers, we can make the sieve excluding even numbers and adding 2 to the primes list by default. -We are going to make an array of: x / 2 - 1 if number is even, else x / 2 +We are going to make an array of: x / 2 - 1 if number is even, else x / 2 (The -1 with even number it's to exclude the number itself) Because we just need numbers [from 3..x if x is odd] @@ -21,20 +22,24 @@ With this, we have reduced the array size to a half, and complexity it's also a half now. -''' +""" -def primes(x): - assert(x >= 0) +def get_primes(n): + """Return list of all primes less than n, + Using sieve of Eratosthenes. + """ + if n <= 0: + raise ValueError("'n' must be a positive integer.") # If x is even, exclude x from list (-1): - sieve_size = (x//2 - 1) if x % 2 == 0 else (x//2) - sieve = [1 for v in range(sieve_size)] # Sieve - primes = [] # List of Primes - if x >= 2: - primes.append(2) # Add 2 by default - for i in range(0, sieve_size): - if sieve[i] == 1: + sieve_size = (n // 2 - 1) if n % 2 == 0 else (n // 2) + sieve = [True for _ in range(sieve_size)] # Sieve + primes = [] # List of Primes + if n >= 2: + primes.append(2) # 2 is prime by default + for i in range(sieve_size): + if sieve[i]: value_at_i = i*2 + 3 primes.append(value_at_i) for j in range(i, sieve_size, value_at_i): - sieve[j] = 0 + sieve[j] = False return primes diff --git a/algorithms/maths/pythagoras.py b/algorithms/maths/pythagoras.py new file mode 100644 index 000000000..b24b682ac --- /dev/null +++ b/algorithms/maths/pythagoras.py @@ -0,0 +1,20 @@ +""" +Given the lengths of two of the three sides of a right angled triangle, this function returns the +length of the third side. +""" + +def pythagoras(opposite, adjacent, hypotenuse): + """ + Returns length of a third side of a right angled triangle. + Passing "?" will indicate the unknown side. + """ + try: + if opposite == str("?"): + return ("Opposite = " + str(((hypotenuse**2) - (adjacent**2))**0.5)) + if adjacent == str("?"): + return ("Adjacent = " + str(((hypotenuse**2) - (opposite**2))**0.5)) + if hypotenuse == str("?"): + return ("Hypotenuse = " + str(((opposite**2) + (adjacent**2))**0.5)) + return "You already know the answer!" + except: + raise ValueError("invalid argument(s) were given.") diff --git a/algorithms/maths/rabin_miller.py b/algorithms/maths/rabin_miller.py new file mode 100644 index 000000000..08b12c117 --- /dev/null +++ b/algorithms/maths/rabin_miller.py @@ -0,0 +1,51 @@ +""" +Rabin-Miller primality test +returning False implies that n is guaranteed composite +returning True means that n is probably prime +with a 4 ** -k chance of being wrong +""" +import random + + +def is_prime(n, k): + + def pow2_factor(num): + """factor n into a power of 2 times an odd number""" + power = 0 + while num % 2 == 0: + num /= 2 + power += 1 + return power, num + + def valid_witness(a): + """ + returns true if a is a valid 'witness' for n + a valid witness increases chances of n being prime + an invalid witness guarantees n is composite + """ + x = pow(int(a), int(d), int(n)) + + if x == 1 or x == n - 1: + return False + + for _ in range(r - 1): + x = pow(int(x), int(2), int(n)) + + if x == 1: + return True + if x == n - 1: + return False + + return True + + # precondition n >= 5 + if n < 5: + return n == 2 or n == 3 # True for prime + + r, d = pow2_factor(n - 1) + + for _ in range(k): + if valid_witness(random.randrange(2, n - 2)): + return False + + return True diff --git a/algorithms/maths/recursive_binomial_coefficient.py b/algorithms/maths/recursive_binomial_coefficient.py new file mode 100644 index 000000000..a92420050 --- /dev/null +++ b/algorithms/maths/recursive_binomial_coefficient.py @@ -0,0 +1,26 @@ +def recursive_binomial_coefficient(n,k): + """Calculates the binomial coefficient, C(n,k), with n>=k using recursion + Time complexity is O(k), so can calculate fairly quickly for large values of k. + + >>> recursive_binomial_coefficient(5,0) + 1 + + >>> recursive_binomial_coefficient(8,2) + 28 + + >>> recursive_binomial_coefficient(500,300) + 5054949849935535817667719165973249533761635252733275327088189563256013971725761702359997954491403585396607971745777019273390505201262259748208640 + + """ + + if k>n: + raise ValueError('Invalid Inputs, ensure that n >= k') + #function is only defined for n>=k + if k == 0 or n == k: + #C(n,0) = C(n,n) = 1, so this is our base case. + return 1 + if k > n/2: + #C(n,k) = C(n,n-k), so if n/2 is sufficiently small, we can reduce the problem size. + return recursive_binomial_coefficient(n,n-k) + #else, we know C(n,k) = (n/k)C(n-1,k-1), so we can use this to reduce our problem size. + return int((n/k)*recursive_binomial_coefficient(n-1,k-1)) diff --git a/algorithms/maths/rsa.py b/algorithms/maths/rsa.py new file mode 100644 index 000000000..bbf193caa --- /dev/null +++ b/algorithms/maths/rsa.py @@ -0,0 +1,93 @@ +""" +RSA encryption algorithm +a method for encrypting a number that uses seperate encryption and decryption keys +this file only implements the key generation algorithm + +there are three important numbers in RSA called n, e, and d +e is called the encryption exponent +d is called the decryption exponent +n is called the modulus + +these three numbers satisfy +((x ** e) ** d) % n == x % n + +to use this system for encryption, n and e are made publicly available, and d is kept secret +a number x can be encrypted by computing (x ** e) % n +the original number can then be recovered by computing (E ** d) % n, where E is +the encrypted number + +fortunately, python provides a three argument version of pow() that can compute powers modulo +a number very quickly: +(a ** b) % c == pow(a,b,c) +""" + +# sample usage: +# n,e,d = generate_key(16) +# data = 20 +# encrypted = pow(data,e,n) +# decrypted = pow(encrypted,d,n) +# assert decrypted == data + +import random + + +def generate_key(k, seed=None): + """ + the RSA key generating algorithm + k is the number of bits in n + """ + + def modinv(a, m): + """calculate the inverse of a mod m + that is, find b such that (a * b) % m == 1""" + b = 1 + while not (a * b) % m == 1: + b += 1 + return b + + def gen_prime(k, seed=None): + """generate a prime with k bits""" + + def is_prime(num): + if num == 2: + return True + for i in range(2, int(num ** 0.5) + 1): + if num % i == 0: + return False + return True + + random.seed(seed) + while True: + key = random.randrange(int(2 ** (k - 1)), int(2 ** k)) + if is_prime(key): + return key + + # size in bits of p and q need to add up to the size of n + p_size = k / 2 + q_size = k - p_size + + e = gen_prime(k, seed) # in many cases, e is also chosen to be a small constant + + while True: + p = gen_prime(p_size, seed) + if p % e != 1: + break + + while True: + q = gen_prime(q_size, seed) + if q % e != 1: + break + + n = p * q + l = (p - 1) * (q - 1) # calculate totient function + d = modinv(e, l) + + return int(n), int(e), int(d) + + +def encrypt(data, e, n): + return pow(int(data), int(e), int(n)) + + +def decrypt(data, d, n): + return pow(int(data), int(d), int(n)) diff --git a/algorithms/maths/sqrt_precision_factor.py b/algorithms/maths/sqrt_precision_factor.py new file mode 100644 index 000000000..bb47c0945 --- /dev/null +++ b/algorithms/maths/sqrt_precision_factor.py @@ -0,0 +1,19 @@ +""" +Given a positive integer N and a precision factor P, +it produces an output +with a maximum error P from the actual square root of N. + +Example: +Given N = 5 and P = 0.001, can produce output x such that +2.235 < x < 2.237. Actual square root of 5 being 2.236. +""" + + +def square_root(n, epsilon=0.001): + """Return square root of n, with maximum absolute error epsilon""" + guess = n / 2 + + while abs(guess * guess - n) > epsilon: + guess = (guess + (n / guess)) / 2 + + return guess diff --git a/algorithms/maths/summing_digits.py b/algorithms/maths/summing_digits.py new file mode 100644 index 000000000..ec30ffda8 --- /dev/null +++ b/algorithms/maths/summing_digits.py @@ -0,0 +1,34 @@ +""" +Recently, I encountered an interview question whose description was as below: + +The number 89 is the first integer with more than one digit whose digits when raised up to +consecutive powers give the same number. For example, 89 = 8**1 + 9**2 gives the number 89. + +The next number after 89 with this property is 135 = 1**1 + 3**2 + 5**3 = 135. + +Write a function that returns a list of numbers with the above property. The function will +receive range as parameter. +""" + +def sum_dig_pow(low, high): + result = [] + + for number in range(low, high + 1): + exponent = 1 # set to 1 + summation = 0 # set to 1 + number_as_string = str(number) + + tokens = list(map(int, number_as_string)) # parse the string into individual digits + + for k in tokens: + summation = summation + (k ** exponent) + exponent += 1 + + if summation == number: + result.append(number) + return result + + +# Some test cases: +assert sum_dig_pow(1, 10) == [1, 2, 3, 4, 5, 6, 7, 8, 9] +assert sum_dig_pow(1, 100) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 89] diff --git a/algorithms/maths/symmetry_group_cycle_index.py b/algorithms/maths/symmetry_group_cycle_index.py new file mode 100644 index 000000000..01b3e05ee --- /dev/null +++ b/algorithms/maths/symmetry_group_cycle_index.py @@ -0,0 +1,159 @@ +""" +The significance of the cycle index (polynomial) of symmetry group +is deeply rooted in counting the number of configurations +of an object excluding those that are symmetric (in terms of permutations). + +For example, the following problem can be solved as a direct +application of the cycle index polynomial of the symmetry +group. + +Note: I came across this problem as a Google's foo.bar challenge at Level 5 +and solved it using a purely Group Theoretic approach. :) +----- + +Problem: + +Given positive integers +w, h, and s, +compute the number of distinct 2D +grids of dimensions w x h that contain +entries from {0, 1, ..., s-1}. +Note that two grids are defined +to be equivalent if one can be +obtained from the other by +switching rows and columns +some number of times. + +----- + +Approach: + +Compute the cycle index (polynomials) +of S_w, and S_h, i.e. the Symmetry +group on w and h symbols respectively. + +Compute the product of the two +cycle indices while combining two +monomials in such a way that +for any pair of cycles c1, and c2 +in the elements of S_w X S_h, +the resultant monomial contains +terms of the form: +$$ x_{lcm(|c1|, |c2|)}^{gcd(|c1|, |c2|)} $$ + +Return the specialization of +the product of cycle indices +at x_i = s (for all the valid i). + +----- + +Code: + +def solve(w, h, s): + s1 = get_cycle_index_sym(w) + s2 = get_cycle_index_sym(h) + + result = cycle_product_for_two_polynomials(s1, s2, s) + + return str(result) +""" + +from fractions import Fraction +from typing import Dict, Union +from polynomial import ( Monomial, Polynomial ) +from gcd import lcm + + +def cycle_product(m1: Monomial, m2: Monomial) -> Monomial: + """ + Given two monomials (from the + cycle index of a symmetry group), + compute the resultant monomial + in the cartesian product + corresponding to their merging. + """ + assert isinstance(m1, Monomial) and isinstance(m2, Monomial) + A = m1.variables + B = m2.variables + result_variables = dict() + for i in A: + for j in B: + k = lcm(i, j) + g = (i * j) // k + if k in result_variables: + result_variables[k] += A[i] * B[j] * g + else: + result_variables[k] = A[i] * B[j] * g + + return Monomial(result_variables, Fraction(m1.coeff * m2.coeff, 1)) + + +def cycle_product_for_two_polynomials(p1: Polynomial, p2: Polynomial, q: Union[float, int, Fraction]) -> Union[float, int, Fraction]: + """ + Compute the product of + given cycle indices p1, + and p2 and evaluate it at q. + """ + ans = Fraction(0, 1) + for m1 in p1.monomials: + for m2 in p2.monomials: + ans += cycle_product(m1, m2).substitute(q) + + return ans + + +def cycle_index_sym_helper(n: int, memo: Dict[int, Polynomial]) -> Polynomial: + """ + A helper for the dp-style evaluation + of the cycle index. + + The recurrence is given in: + https://en.wikipedia.org/wiki/Cycle_index#Symmetric_group_Sn + + """ + if n in memo: + return memo[n] + ans = Polynomial([Monomial({}, Fraction(0, 1))]) + for t in range(1, n+1): + ans = ans.__add__(Polynomial([Monomial({t: 1}, Fraction(1, 1))]) * cycle_index_sym_helper(n-t, memo)) + ans *= Fraction(1, n) + memo[n] = ans + return memo[n] + + +def get_cycle_index_sym(n: int) -> Polynomial: + """ + Compute the cycle index + of S_n, i.e. the symmetry + group of n symbols. + + """ + if n < 0: + raise ValueError('n should be a non-negative integer.') + + memo = { + 0: Polynomial([ + Monomial({}, Fraction(1, 1)) + ]), + 1: Polynomial([ + Monomial({1: 1}, Fraction(1, 1)) + ]), + 2: Polynomial([ + Monomial({1: 2}, Fraction(1, 2)), + Monomial({2: 1}, Fraction(1, 2)) + ]), + 3: Polynomial([ + Monomial({1: 3}, Fraction(1, 6)), + Monomial({1: 1, 2: 1}, Fraction(1, 2)), + Monomial({3: 1}, Fraction(1, 3)) + ]), + 4: Polynomial([ + Monomial({1: 4}, Fraction(1, 24)), + Monomial({2: 1, 1: 2}, Fraction(1, 4)), + Monomial({3: 1, 1: 1}, Fraction(1, 3)), + Monomial({2: 2}, Fraction(1, 8)), + Monomial({4: 1}, Fraction(1, 4)), + ]) + } + result = cycle_index_sym_helper(n, memo) + return result diff --git a/algorithms/matrix/__init__.py b/algorithms/matrix/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/matrix/bomb_enemy.py b/algorithms/matrix/bomb_enemy.py new file mode 100644 index 000000000..c8412635d --- /dev/null +++ b/algorithms/matrix/bomb_enemy.py @@ -0,0 +1,98 @@ +""" +Given a 2D grid, each cell is either a wall 'W', +an enemy 'E' or empty '0' (the number zero), +return the maximum enemies you can kill using one bomb. +The bomb kills all the enemies in the same row and column from +the planted point until it hits the wall since the wall is too strong +to be destroyed. +Note that you can only put the bomb at an empty cell. + +Example: +For the given grid + +0 E 0 0 +E 0 W E +0 E 0 0 + +return 3. (Placing a bomb at (1,1) kills 3 enemies) +""" + + +def max_killed_enemies(grid): + if not grid: + return 0 + m, n = len(grid), len(grid[0]) + max_killed = 0 + row_e, col_e = 0, [0] * n + # iterates over all cells in the grid + for i in range(m): + for j in range(n): + # makes sure we are next to a wall. + if j == 0 or grid[i][j-1] == 'W': + row_e = row_kills(grid, i, j) + # makes sure we are next to a wall. + if i == 0 or grid[i-1][j] == 'W': + col_e[j] = col_kills(grid, i, j) + # makes sure the cell contains a 0 + if grid[i][j] == '0': + # updates the variable + max_killed = max(max_killed, row_e + col_e[j]) + + return max_killed + + +# calculate killed enemies for row i from column j +def row_kills(grid, i, j): + num = 0 + len_row = len(grid[0]) + while j < len_row and grid[i][j] != 'W': + if grid[i][j] == 'E': + num += 1 + j += 1 + return num + + +# calculate killed enemies for column j from row i +def col_kills(grid, i, j): + num = 0 + len_col = len(grid) + while i < len_col and grid[i][j] != 'W': + if grid[i][j] == 'E': + num += 1 + i += 1 + return num + + +# ----------------- TESTS ------------------------- + +""" + Testsuite for the project +""" + +import unittest + + +class TestBombEnemy(unittest.TestCase): + def test_3x4(self): + grid1 = [["0", "E", "0", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"]] + self.assertEqual(3, max_killed_enemies(grid1)) + + def test_4x4(self): + grid1 = [ + ["0", "E", "0", "E"], + ["E", "E", "E", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"]] + grid2 = [ + ["0", "0", "0", "E"], + ["E", "0", "0", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"]] + self.assertEqual(5, max_killed_enemies(grid1)) + self.assertEqual(3, max_killed_enemies(grid2)) + + +if __name__ == "__main__": + unittest.main() diff --git a/algorithms/matrix/cholesky_matrix_decomposition.py b/algorithms/matrix/cholesky_matrix_decomposition.py new file mode 100644 index 000000000..28ef5ea76 --- /dev/null +++ b/algorithms/matrix/cholesky_matrix_decomposition.py @@ -0,0 +1,51 @@ +""" +Cholesky matrix decomposition is used to find the decomposition of a +Hermitian positive-definite matrix A +into matrix V, so that V * V* = A, where V* denotes the conjugate +transpose of L. +The dimensions of the matrix A must match. + +This method is mainly used for numeric solution of linear equations Ax = b. + +example: +Input matrix A: +[[ 4, 12, -16], + [ 12, 37, -43], + [-16, -43, 98]] + +Result: +[[2.0, 0.0, 0.0], +[6.0, 1.0, 0.0], +[-8.0, 5.0, 3.0]] + +Time complexity of this algorithm is O(n^3), specifically about (n^3)/3 + +""" +import math + + +def cholesky_decomposition(A): + """ + :param A: Hermitian positive-definite matrix of type List[List[float]] + :return: matrix of type List[List[float]] if A can be decomposed, + otherwise None + """ + n = len(A) + for ai in A: + if len(ai) != n: + return None + V = [[0.0] * n for _ in range(n)] + for j in range(n): + sum_diagonal_element = 0 + for k in range(j): + sum_diagonal_element = sum_diagonal_element + math.pow(V[j][k], 2) + sum_diagonal_element = A[j][j] - sum_diagonal_element + if sum_diagonal_element <= 0: + return None + V[j][j] = math.pow(sum_diagonal_element, 0.5) + for i in range(j+1, n): + sum_other_element = 0 + for k in range(j): + sum_other_element += V[i][k]*V[j][k] + V[i][j] = (A[i][j] - sum_other_element)/V[j][j] + return V diff --git a/matrix/copy_transform.py b/algorithms/matrix/copy_transform.py similarity index 99% rename from matrix/copy_transform.py rename to algorithms/matrix/copy_transform.py index 772a81c9c..99bfa462d 100644 --- a/matrix/copy_transform.py +++ b/algorithms/matrix/copy_transform.py @@ -9,6 +9,7 @@ def rotate_clockwise(matrix): new[i].append(elem) return new + def rotate_counterclockwise(matrix): new = [] for row in matrix: @@ -20,6 +21,7 @@ def rotate_counterclockwise(matrix): new[i].append(elem) return new + def top_left_invert(matrix): new = [] for row in matrix: @@ -31,6 +33,7 @@ def top_left_invert(matrix): new[i].append(elem) return new + def bottom_left_invert(matrix): new = [] for row in reversed(matrix): @@ -42,6 +45,7 @@ def bottom_left_invert(matrix): new[i].append(elem) return new + if __name__ == '__main__': def print_matrix(matrix, name): print('{}:\n['.format(name)) diff --git a/matrix/count_paths.py b/algorithms/matrix/count_paths.py similarity index 85% rename from matrix/count_paths.py rename to algorithms/matrix/count_paths.py index f1241e779..7f57c9ef4 100644 --- a/matrix/count_paths.py +++ b/algorithms/matrix/count_paths.py @@ -1,5 +1,3 @@ - - # # Count the number of unique paths from a[0][0] to a[m-1][n-1] # We are allowed to move either right or down from a cell in the matrix. @@ -10,6 +8,8 @@ # matrix. Return count[m-1][n-1] # T(n)- O(mn), S(n)- O(mn) # + + def count_paths(m, n): if m < 1 or n < 1: return -1 @@ -25,14 +25,15 @@ def count_paths(m, n): for j in range(1, n): # Number of ways to reach a[i][j] = number of ways to reach # a[i-1][j] + a[i][j-1] - count[i][j] = count[i-1][j] + count[i][j-1] + count[i][j] = count[i - 1][j] + count[i][j - 1] - print count[m-1][n-1] + print(count[m - 1][n - 1]) def main(): - m, n = map(int, raw_input().split()) + m, n = map(int, input('Enter two positive integers: ').split()) count_paths(m, n) + if __name__ == '__main__': - main() \ No newline at end of file + main() diff --git a/algorithms/matrix/crout_matrix_decomposition.py b/algorithms/matrix/crout_matrix_decomposition.py new file mode 100644 index 000000000..bfb859bb3 --- /dev/null +++ b/algorithms/matrix/crout_matrix_decomposition.py @@ -0,0 +1,48 @@ +""" +Crout matrix decomposition is used to find two matrices that, when multiplied +give our input matrix, so L * U = A. +L stands for lower and L has non-zero elements only on diagonal and below. +U stands for upper and U has non-zero elements only on diagonal and above. + +This can for example be used to solve systems of linear equations. +The last if is used if to avoid dividing by zero. + +Example: +We input the A matrix: +[[1,2,3], +[3,4,5], +[6,7,8]] + +We get: +L = [1.0, 0.0, 0.0] + [3.0, -2.0, 0.0] + [6.0, -5.0, 0.0] +U = [1.0, 2.0, 3.0] + [0.0, 1.0, 2.0] + [0.0, 0.0, 1.0] + +We can check that L * U = A. + +I think the complexity should be O(n^3). +""" + + +def crout_matrix_decomposition(A): + n = len(A) + L = [[0.0] * n for i in range(n)] + U = [[0.0] * n for i in range(n)] + for j in range(n): + U[j][j] = 1.0 + for i in range(j, n): + alpha = float(A[i][j]) + for k in range(j): + alpha -= L[i][k]*U[k][j] + L[i][j] = float(alpha) + for i in range(j+1, n): + tempU = float(A[j][i]) + for k in range(j): + tempU -= float(L[j][k]*U[k][i]) + if int(L[j][j]) == 0: + L[j][j] = float(0.1**40) + U[j][i] = float(tempU/L[j][j]) + return (L, U) diff --git a/algorithms/matrix/matrix_exponentiation.py b/algorithms/matrix/matrix_exponentiation.py new file mode 100644 index 000000000..d9b45ba21 --- /dev/null +++ b/algorithms/matrix/matrix_exponentiation.py @@ -0,0 +1,43 @@ +def multiply(matA: list, matB: list) -> list: + """ + Multiplies two square matrices matA and matB of size n x n + Time Complexity: O(n^3) + """ + n = len(matA) + matC = [[0 for i in range(n)] for j in range(n)] + + for i in range(n): + for j in range(n): + for k in range(n): + matC[i][j] += matA[i][k] * matB[k][j] + + return matC + + +def identity(n: int) -> list: + """ + Returns the Identity matrix of size n x n + Time Complexity: O(n^2) + """ + I = [[0 for i in range(n)] for j in range(n)] + + for i in range(n): + I[i][i] = 1 + + return I + + +def matrix_exponentiation(mat: list, n: int) -> list: + """ + Calculates mat^n by repeated squaring + Time Complexity: O(d^3 log(n)) + d: dimension of the square matrix mat + n: power the matrix is raised to + """ + if n == 0: + return identity(len(mat)) + elif n % 2 == 1: + return multiply(matrix_exponentiation(mat, n - 1), mat) + else: + tmp = matrix_exponentiation(mat, n // 2) + return multiply(tmp, tmp) diff --git a/algorithms/matrix/matrix_inversion.py b/algorithms/matrix/matrix_inversion.py new file mode 100644 index 000000000..8d8102d41 --- /dev/null +++ b/algorithms/matrix/matrix_inversion.py @@ -0,0 +1,124 @@ +""" +Inverts an invertible n x n matrix -- i.e., given an n x n matrix A, returns +an n x n matrix B such that AB = BA = In, the n x n identity matrix. + +For a 2 x 2 matrix, inversion is simple using the cofactor equation. For +larger matrices, this is a four step process: +1. calculate the matrix of minors: create an n x n matrix by considering each +position in the original matrix in turn. Exclude the current row and column +and calculate the determinant of the remaining matrix, then place that value +in the current position's equivalent in the matrix of minors. +2. create the matrix of cofactors: take the matrix of minors and multiply +alternate values by -1 in a checkerboard pattern. +3. adjugate: hold the top left to bottom right diagonal constant, but swap all +other values over it. +4. multiply the adjugated matrix by 1 / the determinant of the original matrix + +This code combines steps 1 and 2 into one method to reduce traversals of the +matrix. + +Possible edge cases: will not work for 0x0 or 1x1 matrix, though these are +trivial to calculate without use of this file. +""" +import fractions + + +def invert_matrix(m): + """invert an n x n matrix""" + # Error conditions + if not array_is_matrix(m): + print("Invalid matrix: array is not a matrix") + return [[-1]] + elif len(m) != len(m[0]): + print("Invalid matrix: matrix is not square") + return [[-2]] + elif len(m) < 2: + print("Invalid matrix: matrix is too small") + return [[-3]] + elif get_determinant(m) == 0: + print("Invalid matrix: matrix is square, but singular (determinant = 0)") + return [[-4]] + + # Calculation + elif len(m) == 2: + # simple case + multiplier = 1 / get_determinant(m) + inverted = [[multiplier] * len(m) for n in range(len(m))] + inverted[0][1] = inverted[0][1] * -1 * m[0][1] + inverted[1][0] = inverted[1][0] * -1 * m[1][0] + inverted[0][0] = multiplier * m[1][1] + inverted[1][1] = multiplier * m[0][0] + return inverted + else: + """some steps combined in helpers to reduce traversals""" + # get matrix of minors w/ "checkerboard" signs + m_of_minors = get_matrix_of_minors(m) + + # calculate determinant (we need to know 1/det) + multiplier = fractions.Fraction(1, get_determinant(m)) + + # adjugate (swap on diagonals) and multiply by 1/det + inverted = transpose_and_multiply(m_of_minors, multiplier) + + return inverted + + +def get_determinant(m): + """recursively calculate the determinant of an n x n matrix, n >= 2""" + if len(m) == 2: + # trivial case + return (m[0][0] * m[1][1]) - (m[0][1] * m[1][0]) + else: + sign = 1 + det = 0 + for i in range(len(m)): + det += sign * m[0][i] * get_determinant(get_minor(m, 0, i)) + sign *= -1 + return det + + +def get_matrix_of_minors(m): + """get the matrix of minors and alternate signs""" + matrix_of_minors = [[0 for i in range(len(m))] for j in range(len(m))] + for row in range(len(m)): + for col in range(len(m[0])): + if (row + col) % 2 == 0: + sign = 1 + else: + sign = -1 + matrix_of_minors[row][col] = sign * get_determinant(get_minor(m, row, col)) + return matrix_of_minors + + +def get_minor(m, row, col): + """ + get the minor of the matrix position m[row][col] + (all values m[r][c] where r != row and c != col) + """ + minors = [] + for i in range(len(m)): + if i != row: + new_row = m[i][:col] + new_row.extend(m[i][col + 1:]) + minors.append(new_row) + return minors + + +def transpose_and_multiply(m, multiplier=1): + """swap values along diagonal, optionally adding multiplier""" + for row in range(len(m)): + for col in range(row + 1): + temp = m[row][col] * multiplier + m[row][col] = m[col][row] * multiplier + m[col][row] = temp + return m + + +def array_is_matrix(m): + if len(m) == 0: + return False + first_col = len(m[0]) + for row in m: + if len(row) != first_col: + return False + return True diff --git a/algorithms/matrix/multiply.py b/algorithms/matrix/multiply.py new file mode 100644 index 000000000..2c1cba8f2 --- /dev/null +++ b/algorithms/matrix/multiply.py @@ -0,0 +1,28 @@ +""" +This algorithm takes two compatible two dimensional matrix +and return their product +Space complexity: O(n^2) +Possible edge case: the number of columns of multiplicand not consistent with +the number of rows of multiplier, will raise exception +""" + + +def multiply(multiplicand: list, multiplier: list) -> list: + """ + :type A: List[List[int]] + :type B: List[List[int]] + :rtype: List[List[int]] + """ + multiplicand_row, multiplicand_col = len( + multiplicand), len(multiplicand[0]) + multiplier_row, multiplier_col = len(multiplier), len(multiplier[0]) + if(multiplicand_col != multiplier_row): + raise Exception( + "Multiplicand matrix not compatible with Multiplier matrix.") + # create a result matrix + result = [[0] * multiplier_col for i in range(multiplicand_row)] + for i in range(multiplicand_row): + for j in range(multiplier_col): + for k in range(len(multiplier)): + result[i][j] += multiplicand[i][k] * multiplier[k][j] + return result diff --git a/matrix/rotate_image.py b/algorithms/matrix/rotate_image.py similarity index 84% rename from matrix/rotate_image.py rename to algorithms/matrix/rotate_image.py index 0a6fb50b8..a8b5e4e77 100644 --- a/matrix/rotate_image.py +++ b/algorithms/matrix/rotate_image.py @@ -14,19 +14,20 @@ # 4 5 6 => 4 5 6 => 8 5 2 # 7 8 9 1 2 3 9 6 3 -def rotate(mat:"List[List[int]]"): +def rotate(mat): if not mat: return mat mat.reverse() for i in range(len(mat)): for j in range(i): mat[i][j], mat[j][i] = mat[j][i], mat[i][j] + return mat if __name__ == "__main__": - mat = [[1,2,3], - [4,5,6], - [7,8,9]] + mat = [[1, 2, 3], + [4, 5, 6], + [7, 8, 9]] print(mat) rotate(mat) print(mat) diff --git a/matrix/search_in_sorted_matrix.py b/algorithms/matrix/search_in_sorted_matrix.py similarity index 83% rename from matrix/search_in_sorted_matrix.py rename to algorithms/matrix/search_in_sorted_matrix.py index ce3711200..54502c33a 100644 --- a/matrix/search_in_sorted_matrix.py +++ b/algorithms/matrix/search_in_sorted_matrix.py @@ -10,13 +10,13 @@ def search_in_a_sorted_matrix(mat, m, n, key): i, j = m-1, 0 while i >= 0 and j < n: if key == mat[i][j]: - print ('Key %s found at row- %s column- %s' % (key, i+1, j+1)) + print('Key %s found at row- %s column- %s' % (key, i+1, j+1)) return if key < mat[i][j]: i -= 1 else: j += 1 - print ('Key %s not found' % (key)) + print('Key %s not found' % (key)) def main(): @@ -27,7 +27,7 @@ def main(): [12, 17, 20] ] key = 13 - print (mat) + print(mat) search_in_a_sorted_matrix(mat, len(mat), len(mat[0]), key) diff --git a/algorithms/matrix/sort_matrix_diagonally.py b/algorithms/matrix/sort_matrix_diagonally.py new file mode 100644 index 000000000..b32c71044 --- /dev/null +++ b/algorithms/matrix/sort_matrix_diagonally.py @@ -0,0 +1,77 @@ +""" +Given a m * n matrix mat of integers, +sort it diagonally in ascending order +from the top-left to the bottom-right +then return the sorted array. + +mat = [ + [3,3,1,1], + [2,2,1,2], + [1,1,1,2] +] + +Should return: +[ + [1,1,1,1], + [1,2,2,2], + [1,2,3,3] +] +""" + +from heapq import heappush, heappop +from typing import List + + +def sort_diagonally(mat: List[List[int]]) -> List[List[int]]: + # If the input is a vector, return the vector + if len(mat) == 1 or len(mat[0]) == 1: + return mat + + # Rows + columns - 1 + # The -1 helps you to not repeat a column + for i in range(len(mat)+len(mat[0])-1): + # Process the rows + if i+1 < len(mat): + # Initialize heap, set row and column + h = [] + row = len(mat)-(i+1) + col = 0 + + # Traverse diagonally, and add the values to the heap + while row < len(mat): + heappush(h, (mat[row][col])) + row += 1 + col += 1 + + # Sort the diagonal + row = len(mat)-(i+1) + col = 0 + while h: + ele = heappop(h) + mat[row][col] = ele + row += 1 + col += 1 + else: + # Process the columns + # Initialize heap, row and column + h = [] + row = 0 + col = i - (len(mat)-1) + + # Traverse Diagonally + while col < len(mat[0]) and row < len(mat): + heappush(h, (mat[row][col])) + row += 1 + col += 1 + + # Sort the diagonal + row = 0 + col = i - (len(mat)-1) + while h: + ele = heappop(h) + mat[row][col] = ele + row += 1 + col += 1 + + # Return the updated matrix + return mat diff --git a/algorithms/matrix/sparse_dot_vector.py b/algorithms/matrix/sparse_dot_vector.py new file mode 100644 index 000000000..0cba0a575 --- /dev/null +++ b/algorithms/matrix/sparse_dot_vector.py @@ -0,0 +1,72 @@ +#! /usr/bin/env python3 + +""" +Suppose we have very large sparse vectors, which contains a lot of +zeros and double . + +find a data structure to store them +get the dot product of them +""" + + +def vector_to_index_value_list(vector): + return [(i, v) for i, v in enumerate(vector) if v != 0.0] + + +def dot_product(iv_list1, iv_list2): + + product = 0 + p1 = len(iv_list1) - 1 + p2 = len(iv_list2) - 1 + + while p1 >= 0 and p2 >= 0: + i1, v1 = iv_list1[p1] + i2, v2 = iv_list2[p2] + + if i1 < i2: + p1 -= 1 + elif i2 < i1: + p2 -= 1 + else: + product += v1 * v2 + p1 -= 1 + p2 -= 1 + + return product + + +def __test_simple(): + print(dot_product(vector_to_index_value_list([1., 2., 3.]), + vector_to_index_value_list([0., 2., 2.]))) + # 10 + + +def __test_time(): + vector_length = 1024 + vector_count = 1024 + nozero_counut = 10 + + def random_vector(): + import random + vector = [0 for _ in range(vector_length)] + for i in random.sample(range(vector_length), nozero_counut): + vector[i] = random.random() + return vector + + vectors = [random_vector() for _ in range(vector_count)] + iv_lists = [vector_to_index_value_list(vector) for vector in vectors] + + import time + + time_start = time.time() + for i in range(vector_count): + for j in range(i): + dot_product(iv_lists[i], iv_lists[j]) + time_end = time.time() + + print(time_end - time_start, 'seconds') + + +if __name__ == '__main__': + __test_simple() + __test_time() diff --git a/algorithms/matrix/sparse_mul.py b/algorithms/matrix/sparse_mul.py new file mode 100644 index 000000000..eeaae0eff --- /dev/null +++ b/algorithms/matrix/sparse_mul.py @@ -0,0 +1,108 @@ +""" +Given two sparse matrices A and B, return the result of AB. + +You may assume that A's column number is equal to B's row number. + +Example: + +A = [ + [ 1, 0, 0], + [-1, 0, 3] +] + +B = [ + [ 7, 0, 0 ], + [ 0, 0, 0 ], + [ 0, 0, 1 ] +] + + + | 1 0 0 | | 7 0 0 | | 7 0 0 | +AB = | -1 0 3 | x | 0 0 0 | = | -7 0 3 | + | 0 0 1 | +""" + + +# Python solution without table (~156ms): +def multiply(self, a, b): + """ + :type A: List[List[int]] + :type B: List[List[int]] + :rtype: List[List[int]] + """ + if a is None or b is None: + return None + m, n, l = len(a), len(b[0]), len(b[0]) + if len(b) != n: + raise Exception("A's column number must be equal to B's row number.") + c = [[0 for _ in range(l)] for _ in range(m)] + for i, row in enumerate(a): + for k, eleA in enumerate(row): + if eleA: + for j, eleB in enumerate(b[k]): + if eleB: + c[i][j] += eleA * eleB + return c + + +# Python solution with only one table for B (~196ms): +def multiply(self, a, b): + """ + :type A: List[List[int]] + :type B: List[List[int]] + :rtype: List[List[int]] + """ + if a is None or b is None: + return None + m, n, l = len(a), len(a[0]), len(b[0]) + if len(b) != n: + raise Exception("A's column number must be equal to B's row number.") + c = [[0 for _ in range(l)] for _ in range(m)] + table_b = {} + for k, row in enumerate(b): + table_b[k] = {} + for j, eleB in enumerate(row): + if eleB: + table_b[k][j] = eleB + for i, row in enumerate(a): + for k, eleA in enumerate(row): + if eleA: + for j, eleB in table_b[k].iteritems(): + c[i][j] += eleA * eleB + return c + + +# Python solution with two tables (~196ms): +def multiply(self, a, b): + """ + :type A: List[List[int]] + :type B: List[List[int]] + :rtype: List[List[int]] + """ + if a is None or b is None: + return None + m, n = len(a), len(b[0]) + if len(b) != n: + raise Exception("A's column number must be equal to B's row number.") + l = len(b[0]) + table_a, table_b = {}, {} + for i, row in enumerate(a): + for j, ele in enumerate(row): + if ele: + if i not in table_a: + table_a[i] = {} + table_a[i][j] = ele + for i, row in enumerate(b): + for j, ele in enumerate(row): + if ele: + if i not in table_b: + table_b[i] = {} + table_b[i][j] = ele + c = [[0 for j in range(l)] for i in range(m)] + for i in table_a: + for k in table_a[i]: + if k not in table_b: + continue + for j in table_b[k]: + c[i][j] += table_a[i][k] * table_b[k][j] + return c diff --git a/matrix/spiral_traversal.py b/algorithms/matrix/spiral_traversal.py similarity index 100% rename from matrix/spiral_traversal.py rename to algorithms/matrix/spiral_traversal.py diff --git a/algorithms/matrix/sudoku_validator.py b/algorithms/matrix/sudoku_validator.py new file mode 100644 index 000000000..257fcce8e --- /dev/null +++ b/algorithms/matrix/sudoku_validator.py @@ -0,0 +1,91 @@ +""" +Write a function validSolution/ValidateSolution/valid_solution() +that accepts a 2D array representing a Sudoku board, and returns true +if it is a valid solution, or false otherwise. The cells of the sudoku +board may also contain 0's, which will represent empty cells. +Boards containing one or more zeroes are considered to be invalid solutions. +The board is always 9 cells by 9 cells, and every cell only contains integers +from 0 to 9. + +(More info at: http://en.wikipedia.org/wiki/Sudoku) +""" + +# Using dict/hash-table +from collections import defaultdict + + +def valid_solution_hashtable(board): + for i in range(len(board)): + dict_row = defaultdict(int) + dict_col = defaultdict(int) + for j in range(len(board[0])): + value_row = board[i][j] + value_col = board[j][i] + if not value_row or value_col == 0: + return False + if value_row in dict_row: + return False + else: + dict_row[value_row] += 1 + + if value_col in dict_col: + return False + else: + dict_col[value_col] += 1 + + for i in range(3): + for j in range(3): + grid_add = 0 + for k in range(3): + for l in range(3): + grid_add += board[i * 3 + k][j * 3 + l] + if grid_add != 45: + return False + return True + + +# Without hash-table/dict +def valid_solution(board): + correct = [1, 2, 3, 4, 5, 6, 7, 8, 9] + # check rows + for row in board: + if sorted(row) != correct: + return False + + # check columns + for column in zip(*board): + if sorted(column) != correct: + return False + + # check regions + for i in range(3): + for j in range(3): + region = [] + for line in board[i*3:(i+1)*3]: + region += line[j*3:(j+1)*3] + + if sorted(region) != correct: + return False + + # if everything correct + return True + + +# Using set +def valid_solution_set(board): + valid = set(range(1, 10)) + + for row in board: + if set(row) != valid: + return False + + for col in [[row[i] for row in board] for i in range(9)]: + if set(col) != valid: + return False + + for x in range(3): + for y in range(3): + if set(sum([row[x*3:(x+1)*3] for row in board[y*3:(y+1)*3]], [])) != valid: + return False + + return True diff --git a/algorithms/matrix/sum_sub_squares.py b/algorithms/matrix/sum_sub_squares.py new file mode 100644 index 000000000..1231547ef --- /dev/null +++ b/algorithms/matrix/sum_sub_squares.py @@ -0,0 +1,23 @@ +# Function to find sum of all +# sub-squares of size k x k in a given +# square matrix of size n x n +def sum_sub_squares(matrix, k): + n = len(matrix) + result = [[0 for i in range(k)] for j in range(k)] + + if k > n: + return + for i in range(n - k + 1): + l = 0 + for j in range(n - k + 1): + sum = 0 + + # Calculate and print sum of current sub-square + for p in range(i, k + i): + for q in range(j, k + j): + sum += matrix[p][q] + + result[i][l] = sum + l += 1 + + return result diff --git a/algorithms/ml/nearest_neighbor.py b/algorithms/ml/nearest_neighbor.py new file mode 100644 index 000000000..d0fabab15 --- /dev/null +++ b/algorithms/ml/nearest_neighbor.py @@ -0,0 +1,41 @@ +import math + +def distance(x,y): + """[summary] + HELPER-FUNCTION + calculates the (eulidean) distance between vector x and y. + + Arguments: + x {[tuple]} -- [vector] + y {[tuple]} -- [vector] + """ + assert len(x) == len(y), "The vector must have same length" + result = () + sum = 0 + for i in range(len(x)): + result += (x[i] -y[i],) + for component in result: + sum += component**2 + return math.sqrt(sum) + + +def nearest_neighbor(x, tSet): + """[summary] + Implements the nearest neighbor algorithm + + Arguments: + x {[tupel]} -- [vector] + tSet {[dict]} -- [training set] + + Returns: + [type] -- [result of the AND-function] + """ + assert isinstance(x, tuple) and isinstance(tSet, dict) + current_key = () + min_d = float('inf') + for key in tSet: + d = distance(x, key) + if d < min_d: + min_d = d + current_key = key + return tSet[current_key] diff --git a/algorithms/queues/__init__.py b/algorithms/queues/__init__.py new file mode 100644 index 000000000..3c4f22ca0 --- /dev/null +++ b/algorithms/queues/__init__.py @@ -0,0 +1,4 @@ +from .queue import * +from .max_sliding_window import * +from .reconstruct_queue import * +from .priority_queue import * diff --git a/algorithms/queues/max_sliding_window.py b/algorithms/queues/max_sliding_window.py new file mode 100644 index 000000000..74db65e11 --- /dev/null +++ b/algorithms/queues/max_sliding_window.py @@ -0,0 +1,34 @@ +""" +Given an array and a number k +Find the max elements of each of its sub-arrays of length k. + +Keep indexes of good candidates in deque d. +The indexes in d are from the current window, they're increasing, +and their corresponding nums are decreasing. +Then the first deque element is the index of the largest window value. + +For each index i: + +1. Pop (from the end) indexes of smaller elements (they'll be useless). +2. Append the current index. +3. Pop (from the front) the index i - k, if it's still in the deque + (it falls out of the window). +4. If our window has reached size k, + append the current window maximum to the output. +""" + +import collections + + +def max_sliding_window(arr, k): + qi = collections.deque() # queue storing indexes of elements + result = [] + for i, n in enumerate(arr): + while qi and arr[qi[-1]] < n: + qi.pop() + qi.append(i) + if qi[0] == i - k: + qi.popleft() + if i >= k - 1: + result.append(arr[qi[0]]) + return result diff --git a/queue/moving_average.py b/algorithms/queues/moving_average.py similarity index 100% rename from queue/moving_average.py rename to algorithms/queues/moving_average.py diff --git a/algorithms/queues/priority_queue.py b/algorithms/queues/priority_queue.py new file mode 100644 index 000000000..c573ac3cc --- /dev/null +++ b/algorithms/queues/priority_queue.py @@ -0,0 +1,55 @@ +""" +Implementation of priority queue using linear array. +Insertion - O(n) +Extract min/max Node - O(1) +""" +import itertools + + +class PriorityQueueNode: + def __init__(self, data, priority): + self.data = data + self.priority = priority + + def __repr__(self): + return "{}: {}".format(self.data, self.priority) + + +class PriorityQueue: + def __init__(self, items=None, priorities=None): + """Create a priority queue with items (list or iterable). + If items is not passed, create empty priority queue.""" + self.priority_queue_list = [] + if items is None: + return + if priorities is None: + priorities = itertools.repeat(None) + for item, priority in zip(items, priorities): + self.push(item, priority=priority) + + def __repr__(self): + return "PriorityQueue({!r})".format(self.priority_queue_list) + + def size(self): + """Return size of the priority queue. + """ + return len(self.priority_queue_list) + + def push(self, item, priority=None): + """Push the item in the priority queue. + if priority is not given, priority is set to the value of item. + """ + priority = item if priority is None else priority + node = PriorityQueueNode(item, priority) + for index, current in enumerate(self.priority_queue_list): + if current.priority < node.priority: + self.priority_queue_list.insert(index, node) + return + # when traversed complete queue + self.priority_queue_list.append(node) + + def pop(self): + """Remove and return the item with the lowest priority. + """ + # remove and return the first node from the queue + return self.priority_queue_list.pop().data diff --git a/algorithms/queues/queue.py b/algorithms/queues/queue.py new file mode 100644 index 000000000..b3ccb4e7f --- /dev/null +++ b/algorithms/queues/queue.py @@ -0,0 +1,143 @@ +""" +Queue Abstract Data Type (ADT) +* Queue() creates a new queue that is empty. + It needs no parameters and returns an empty queue. +* enqueue(item) adds a new item to the rear of the queue. + It needs the item and returns nothing. +* dequeue() removes the front item from the queue. + It needs no parameters and returns the item. The queue is modified. +* isEmpty() tests to see whether the queue is empty. + It needs no parameters and returns a boolean value. +* size() returns the number of items in the queue. + It needs no parameters and returns an integer. +* peek() returns the front element of the queue. +""" +from abc import ABCMeta, abstractmethod + + +class AbstractQueue(metaclass=ABCMeta): + + def __init__(self): + self._size = 0 + + def __len__(self): + return self._size + + def is_empty(self): + return self._size == 0 + + @abstractmethod + def enqueue(self, value): + pass + + @abstractmethod + def dequeue(self): + pass + + @abstractmethod + def peek(self): + pass + + @abstractmethod + def __iter__(self): + pass + + +class ArrayQueue(AbstractQueue): + + def __init__(self, capacity=10): + """ + Initialize python List with capacity of 10 or user given input. + Python List type is a dynamic array, so we have to restrict its + dynamic nature to make it work like a static array. + """ + super().__init__() + self._array = [None] * capacity + self._front = 0 + self._rear = 0 + + def __iter__(self): + probe = self._front + while True: + if probe == self._rear: + return + yield self._array[probe] + probe += 1 + + def enqueue(self, value): + if self._rear == len(self._array): + self._expand() + self._array[self._rear] = value + self._rear += 1 + self._size += 1 + + def dequeue(self): + if self.is_empty(): + raise IndexError("Queue is empty") + value = self._array[self._front] + self._array[self._front] = None + self._front += 1 + self._size -= 1 + return value + + def peek(self): + """returns the front element of queue.""" + if self.is_empty(): + raise IndexError("Queue is empty") + return self._array[self._front] + + def _expand(self): + """expands size of the array. + Time Complexity: O(n) + """ + self._array += [None] * len(self._array) + + +class QueueNode: + def __init__(self, value): + self.value = value + self.next = None + + +class LinkedListQueue(AbstractQueue): + + def __init__(self): + super().__init__() + self._front = None + self._rear = None + + def __iter__(self): + probe = self._front + while True: + if probe is None: + return + yield probe.value + probe = probe.next + + def enqueue(self, value): + node = QueueNode(value) + if self._front is None: + self._front = node + self._rear = node + else: + self._rear.next = node + self._rear = node + self._size += 1 + + def dequeue(self): + if self.is_empty(): + raise IndexError("Queue is empty") + value = self._front.value + if self._front is self._rear: + self._front = None + self._rear = None + else: + self._front = self._front.next + self._size -= 1 + return value + + def peek(self): + """returns the front element of queue.""" + if self.is_empty(): + raise IndexError("Queue is empty") + return self._front.value diff --git a/queue/reconstruct_queue.py b/algorithms/queues/reconstruct_queue.py similarity index 95% rename from queue/reconstruct_queue.py rename to algorithms/queues/reconstruct_queue.py index 56069bc35..b86a67cd0 100644 --- a/queue/reconstruct_queue.py +++ b/algorithms/queues/reconstruct_queue.py @@ -23,7 +23,5 @@ def reconstruct_queue(people): queue = [] people.sort(key=lambda x: (-x[0], x[1])) for h, k in people: - queue.insert(k, (h, k)) + queue.insert(k, [h, k]) return queue - - diff --git a/queue/zigzagiterator.py b/algorithms/queues/zigzagiterator.py similarity index 71% rename from queue/zigzagiterator.py rename to algorithms/queues/zigzagiterator.py index a8b571f94..5b1e50371 100644 --- a/queue/zigzagiterator.py +++ b/algorithms/queues/zigzagiterator.py @@ -5,25 +5,28 @@ def __init__(self, v1, v2): :type v1: List[int] :type v2: List[int] """ - self.queue=[_ for _ in (v1,v2) if _] + self.queue = [_ for _ in (v1, v2) if _] print(self.queue) def next(self): """ :rtype: int """ - v=self.queue.pop(0) - ret=v.pop(0) - if v: self.queue.append(v) + v = self.queue.pop(0) + ret = v.pop(0) + if v: + self.queue.append(v) return ret def has_next(self): """ :rtype: bool """ - if self.queue: return True + if self.queue: + return True return False + l1 = [1, 2] l2 = [3, 4, 5, 6] it = ZigZagIterator(l1, l2) diff --git a/algorithms/search/__init__.py b/algorithms/search/__init__.py new file mode 100644 index 000000000..3f39479bc --- /dev/null +++ b/algorithms/search/__init__.py @@ -0,0 +1,17 @@ +""" +Collection of search algorithms: finding the needle in a haystack. +""" + +from .binary_search import * +from .ternary_search import * +from .first_occurrence import * +from .last_occurrence import * +from .linear_search import * +from .search_insert import * +from .two_sum import * +from .search_range import * +from .find_min_rotate import * +from .search_rotate import * +from .jump_search import * +from .next_greatest_letter import * +from .interpolation_search import * diff --git a/algorithms/search/binary_search.py b/algorithms/search/binary_search.py new file mode 100644 index 000000000..2a7c9bc3e --- /dev/null +++ b/algorithms/search/binary_search.py @@ -0,0 +1,52 @@ +""" +Binary Search + +Find an element in a sorted array (in ascending order). +""" + +# For Binary Search, T(N) = T(N/2) + O(1) // the recurrence relation +# Apply Masters Theorem for computing Run time complexity of recurrence relations: +# T(N) = aT(N/b) + f(N) +# Here, +# a = 1, b = 2 => log (a base b) = 1 +# also, here +# f(N) = n^c log^k(n) // k = 0 & c = log (a base b) +# So, +# T(N) = O(N^c log^(k+1)N) = O(log(N)) + +def binary_search(array, query): + """ + Worst-case Complexity: O(log(n)) + + reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + """ + + low, high = 0, len(array) - 1 + while low <= high: + mid = (high + low) // 2 + val = array[mid] + if val == query: + return mid + + if val < query: + low = mid + 1 + else: + high = mid - 1 + return None + +#In this below function we are passing array, it's first index , last index and value to be searched +def binary_search_recur(array, low, high, val): + """ + Worst-case Complexity: O(log(n)) + + reference: https://en.wikipedia.org/wiki/Binary_search_algorithm + """ +#Here in Logic section first we are checking if low is greater than high which means its an error condition because low index should not move ahead of high index + if low > high: + return -1 + mid = low + (high-low)//2 #This mid will not break integer range + if val < array[mid]: + return binary_search_recur(array, low, mid - 1, val) #Go search in the left subarray + if val > array[mid]: + return binary_search_recur(array, mid + 1, high, val) #Go search in the right subarray + return mid diff --git a/algorithms/search/find_min_rotate.py b/algorithms/search/find_min_rotate.py new file mode 100644 index 000000000..b47fd4e87 --- /dev/null +++ b/algorithms/search/find_min_rotate.py @@ -0,0 +1,33 @@ +""" +Suppose an array sorted in ascending order is rotated at some pivot unknown +to you beforehand. (i.e., 0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2). + +Find the minimum element. The complexity must be O(logN) + +You may assume no duplicate exists in the array. +""" +def find_min_rotate(array): + """ + Finds the minimum element in a sorted array that has been rotated. + """ + low = 0 + high = len(array) - 1 + while low < high: + mid = (low + high) // 2 + if array[mid] > array[high]: + low = mid + 1 + else: + high = mid + + return array[low] + +def find_min_rotate_recur(array, low, high): + """ + Finds the minimum element in a sorted array that has been rotated. + """ + mid = (low + high) // 2 + if mid == low: + return array[low] + if array[mid] > array[high]: + return find_min_rotate_recur(array, mid + 1, high) + return find_min_rotate_recur(array, low, mid) diff --git a/algorithms/search/first_occurrence.py b/algorithms/search/first_occurrence.py new file mode 100644 index 000000000..9d9beaae1 --- /dev/null +++ b/algorithms/search/first_occurrence.py @@ -0,0 +1,23 @@ +""" +Find first occurance of a number in a sorted array (increasing order) +Approach- Binary Search +T(n)- O(log n) +""" +def first_occurrence(array, query): + """ + Returns the index of the first occurance of the given element in an array. + The array has to be sorted in increasing order. + """ + + low, high = 0, len(array) - 1 + while low <= high: + mid = low + (high-low)//2 #Now mid will be ininteger range + #print("lo: ", lo, " hi: ", hi, " mid: ", mid) + if low == high: + break + if array[mid] < query: + low = mid + 1 + else: + high = mid + if array[low] == query: + return low diff --git a/algorithms/search/interpolation_search.py b/algorithms/search/interpolation_search.py new file mode 100644 index 000000000..5b1d00a1a --- /dev/null +++ b/algorithms/search/interpolation_search.py @@ -0,0 +1,61 @@ +""" +Python implementation of the Interpolation Search algorithm. +Given a sorted array in increasing order, interpolation search calculates +the starting point of its search according to the search key. + +FORMULA: start_pos = low + [ (x - arr[low])*(high - low) / (arr[high] - arr[low]) ] + +Doc: https://en.wikipedia.org/wiki/Interpolation_search + +Time Complexity: O(log2(log2 n)) for average cases, O(n) for the worst case. +The algorithm performs best with uniformly distributed arrays. +""" + +from typing import List + + +def interpolation_search(array: List[int], search_key: int) -> int: + """ + :param array: The array to be searched. + :param search_key: The key to be searched in the array. + + :returns: Index of search_key in array if found, else -1. + + Examples: + + >>> interpolation_search([-25, -12, -1, 10, 12, 15, 20, 41, 55], -1) + 2 + >>> interpolation_search([5, 10, 12, 14, 17, 20, 21], 55) + -1 + >>> interpolation_search([5, 10, 12, 14, 17, 20, 21], -5) + -1 + + """ + + # highest and lowest index in array + high = len(array) - 1 + low = 0 + + while (low <= high) and (array[low] <= search_key <= array[high]): + # calculate the search position + pos = low + int(((search_key - array[low]) * + (high - low) / (array[high] - array[low]))) + + # search_key is found + if array[pos] == search_key: + return pos + + # if search_key is larger, search_key is in upper part + if array[pos] < search_key: + low = pos + 1 + + # if search_key is smaller, search_key is in lower part + else: + high = pos - 1 + + return -1 + + +if __name__ == "__main__": + import doctest + doctest.testmod() diff --git a/algorithms/search/jump_search.py b/algorithms/search/jump_search.py new file mode 100644 index 000000000..2ec074938 --- /dev/null +++ b/algorithms/search/jump_search.py @@ -0,0 +1,45 @@ +""" +Jump Search + +Find an element in a sorted array. +""" + +import math + +def jump_search(arr,target): + """ + Worst-case Complexity: O(√n) (root(n)) + All items in list must be sorted like binary search + + Find block that contains target value and search it linearly in that block + It returns a first target value in array + + reference: https://en.wikipedia.org/wiki/Jump_search + """ + + length = len(arr) + block_size = int(math.sqrt(length)) + block_prev = 0 + block= block_size + + # return -1 means that array doesn't contain target value + # find block that contains target value + + if arr[length - 1] < target: + return -1 + while block <= length and arr[block - 1] < target: + block_prev = block + block += block_size + + # find target value in block + + while arr[block_prev] < target : + block_prev += 1 + if block_prev == min(block, length) : + return -1 + + # if there is target value in array, return it + + if arr[block_prev] == target : + return block_prev + return -1 diff --git a/algorithms/search/last_occurrence.py b/algorithms/search/last_occurrence.py new file mode 100644 index 000000000..6374625e6 --- /dev/null +++ b/algorithms/search/last_occurrence.py @@ -0,0 +1,20 @@ +""" +Find last occurance of a number in a sorted array (increasing order) +Approach- Binary Search +T(n)- O(log n) +""" +def last_occurrence(array, query): + """ + Returns the index of the last occurance of the given element in an array. + The array has to be sorted in increasing order. + """ + low, high = 0, len(array) - 1 + while low <= high: + mid = (high + low) // 2 + if (array[mid] == query and mid == len(array)-1) or \ + (array[mid] == query and array[mid+1] > query): + return mid + if array[mid] <= query: + low = mid + 1 + else: + high = mid - 1 diff --git a/algorithms/search/linear_search.py b/algorithms/search/linear_search.py new file mode 100644 index 000000000..d375d77f2 --- /dev/null +++ b/algorithms/search/linear_search.py @@ -0,0 +1,15 @@ +""" +Linear search works in any array. +T(n): O(n) +""" + +def linear_search(array, query): + """ + Find the index of the given element in the array. + There are no restrictions on the order of the elements in the array. + If the element couldn't be found, returns -1. + """ + for i, value in enumerate(array): + if value == query: + return i + return -1 diff --git a/algorithms/search/next_greatest_letter.py b/algorithms/search/next_greatest_letter.py new file mode 100644 index 000000000..26ec8536d --- /dev/null +++ b/algorithms/search/next_greatest_letter.py @@ -0,0 +1,60 @@ +''' +Given a list of sorted characters letters containing only lowercase letters, +and given a target letter target, find the smallest element in the list that +is larger than the given target. + +Letters also wrap around. For example, if the target is target = 'z' and +letters = ['a', 'b'], the answer is 'a'. + +Input: +letters = ["c", "f", "j"] +target = "a" +Output: "c" + +Input: +letters = ["c", "f", "j"] +target = "c" +Output: "f" + +Input: +letters = ["c", "f", "j"] +target = "d" +Output: "f" + +Reference: https://leetcode.com/problems/find-smallest-letter-greater-than-target/description/ +''' + +import bisect + +def next_greatest_letter(letters, target): + """ + Using bisect libarary + """ + index = bisect.bisect(letters, target) + return letters[index % len(letters)] + +def next_greatest_letter_v1(letters, target): + """ + Using binary search: complexity O(logN) + """ + if letters[0] > target: + return letters[0] + if letters[len(letters) - 1] <= target: + return letters[0] + left, right = 0, len(letters) - 1 + while left <= right: + mid = left + (right - left) // 2 + if letters[mid] > target: + right = mid - 1 + else: + left = mid + 1 + return letters[left] + +def next_greatest_letter_v2(letters, target): + """ + Brute force: complexity O(N) + """ + for index in letters: + if index > target: + return index + return letters[0] diff --git a/algorithms/search/search_insert.py b/algorithms/search/search_insert.py new file mode 100644 index 000000000..279e64e40 --- /dev/null +++ b/algorithms/search/search_insert.py @@ -0,0 +1,24 @@ +""" +Helper methods for implementing insertion sort. +""" + +def search_insert(array, val): + """ + Given a sorted array and a target value, return the index if the target is + found. If not, return the index where it would be if it were inserted in order. + + For example: + [1,3,5,6], 5 -> 2 + [1,3,5,6], 2 -> 1 + [1,3,5,6], 7 -> 4 + [1,3,5,6], 0 -> 0 + """ + low = 0 + high = len(array) - 1 + while low <= high: + mid = low + (high - low) // 2 + if val > array[mid]: + low = mid + 1 + else: + high = mid - 1 + return low diff --git a/algorithms/search/search_range.py b/algorithms/search/search_range.py new file mode 100644 index 000000000..f0f2bfba0 --- /dev/null +++ b/algorithms/search/search_range.py @@ -0,0 +1,33 @@ +""" +Given an array of integers nums sorted in ascending order, find the starting +and ending position of a given target value. If the target is not found in the +array, return [-1, -1]. + +For example: +Input: nums = [5,7,7,8,8,8,10], target = 8 +Output: [3,5] +Input: nums = [5,7,7,8,8,8,10], target = 11 +Output: [-1,-1] +""" +def search_range(nums, target): + """ + :type nums: List[int] + :type target: int + :rtype: List[int] + """ + low = 0 + high = len(nums) - 1 + # breaks at low == high + # both pointing to first occurence of target + while low < high: + mid = low + (high - low) // 2 + if target <= nums[mid]: + high = mid + else: + low = mid + 1 + + for j in range(len(nums) - 1, -1, -1): + if nums[j] == target: + return [low, j] + + return [-1, -1] diff --git a/algorithms/search/search_rotate.py b/algorithms/search/search_rotate.py new file mode 100644 index 000000000..fe5474538 --- /dev/null +++ b/algorithms/search/search_rotate.py @@ -0,0 +1,80 @@ +""" +Search in Rotated Sorted Array +Suppose an array sorted in ascending order is rotated at some pivot unknown +to you beforehand. (i.e., [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2]). + +You are given a target value to search. If found in the array return its index, +otherwise return -1. + +Your algorithm's runtime complexity must be in the order of O(log n). +--------------------------------------------------------------------------------- +Explanation algorithm: + +In classic binary search, we compare val with the midpoint to figure out if +val belongs on the low or the high side. The complication here is that the +array is rotated and may have an inflection point. Consider, for example: + +Array1: [10, 15, 20, 0, 5] +Array2: [50, 5, 20, 30, 40] + +Note that both arrays have a midpoint of 20, but 5 appears on the left side of +one and on the right side of the other. Therefore, comparing val with the +midpoint is insufficient. + +However, if we look a bit deeper, we can see that one half of the array must be +ordered normally(increasing order). We can therefore look at the normally ordered +half to determine whether we should search the low or hight side. + +For example, if we are searching for 5 in Array1, we can look at the left element (10) +and middle element (20). Since 10 < 20, the left half must be ordered normally. And, since 5 +is not between those, we know that we must search the right half + +In array2, we can see that since 50 > 20, the right half must be ordered normally. We turn to +the middle 20, and right 40 element to check if 5 would fall between them. The value 5 would not +Therefore, we search the left half. + +There are 2 possible solution: iterative and recursion. +Recursion helps you understand better the above algorithm explanation +""" +def search_rotate(array, val): + """ + Finds the index of the given value in an array that has been sorted in + ascending order and then rotated at some unknown pivot. + """ + low, high = 0, len(array) - 1 + while low <= high: + mid = (low + high) // 2 + if val == array[mid]: + return mid + + if array[low] <= array[mid]: + if array[low] <= val <= array[mid]: + high = mid - 1 + else: + low = mid + 1 + else: + if array[mid] <= val <= array[high]: + low = mid + 1 + else: + high = mid - 1 + + return -1 + +# Recursion technique +def search_rotate_recur(array, low, high, val): + """ + Finds the index of the given value in an array that has been sorted in + ascending order and then rotated at some unknown pivot. + """ + if low >= high: + return -1 + mid = (low + high) // 2 + if val == array[mid]: # found element + return mid + if array[low] <= array[mid]: + if array[low] <= val <= array[mid]: + return search_rotate_recur(array, low, mid - 1, val) # Search left + return search_rotate_recur(array, mid + 1, high, val) # Search right + if array[mid] <= val <= array[high]: + return search_rotate_recur(array, mid + 1, high, val) # Search right + return search_rotate_recur(array, low, mid - 1, val) # Search left diff --git a/algorithms/search/ternary_search.py b/algorithms/search/ternary_search.py new file mode 100644 index 000000000..0d0ee1b66 --- /dev/null +++ b/algorithms/search/ternary_search.py @@ -0,0 +1,42 @@ +""" +Ternary search is a divide and conquer algorithm that can be used to find an element in an array. +It is similar to binary search where we divide the array into two parts but in this algorithm, +we divide the given array into three parts and determine which has the key (searched element). +We can divide the array into three parts by taking mid1 and mid2. +Initially, l and r will be equal to 0 and n-1 respectively, where n is the length of the array. +mid1 = l + (r-l)/3 +mid2 = r – (r-l)/3 + +Note: Array needs to be sorted to perform ternary search on it. +T(N) = O(log3(N)) +log3 = log base 3 +""" +def ternary_search(left, right, key, arr): + """ + Find the given value (key) in an array sorted in ascending order. + Returns the index of the value if found, and -1 otherwise. + If the index is not in the range left..right (ie. left <= index < right) returns -1. + """ + + while right >= left: + mid1 = left + (right-left) // 3 + mid2 = right - (right-left) // 3 + + if key == arr[mid1]: + return mid1 + if key == mid2: + return mid2 + + if key < arr[mid1]: + # key lies between l and mid1 + right = mid1 - 1 + elif key > arr[mid2]: + # key lies between mid2 and r + left = mid2 + 1 + else: + # key lies between mid1 and mid2 + left = mid1 + 1 + right = mid2 - 1 + + # key not found + return -1 diff --git a/algorithms/search/two_sum.py b/algorithms/search/two_sum.py new file mode 100644 index 000000000..e8400fd1c --- /dev/null +++ b/algorithms/search/two_sum.py @@ -0,0 +1,71 @@ +""" +Given an array of integers that is already sorted in ascending order, find two +numbers such that they add up to a specific target number. The function two_sum +should return indices of the two numbers such that they add up to the target, +where index1 must be less than index2. Please note that your returned answers +(both index1 and index2) are not zero-based. +You may assume that each input would have exactly one solution and you +may not use the same element twice. + +Input: numbers = [2, 7, 11, 15], target=9 +Output: index1 = 1, index2 = 2 + +Solution: +two_sum: using binary search +two_sum1: using dictionary as a hash table +two_sum2: using two pointers +""" + +def two_sum(numbers, target): + """ + Given a list of numbers sorted in ascending order, find the indices of two + numbers such that their sum is the given target. + + Using binary search. + """ + for i, number in enumerate(numbers): + second_val = target - number + low, high = i+1, len(numbers)-1 + while low <= high: + mid = low + (high - low) // 2 + if second_val == numbers[mid]: + return [i + 1, mid + 1] + + if second_val > numbers[mid]: + low = mid + 1 + else: + high = mid - 1 + return None + +def two_sum1(numbers, target): + """ + Given a list of numbers, find the indices of two numbers such that their + sum is the given target. + + Using a hash table. + """ + dic = {} + for i, num in enumerate(numbers): + if target - num in dic: + return [dic[target - num] + 1, i + 1] + dic[num] = i + return None + +def two_sum2(numbers, target): + """ + Given a list of numbers sorted in ascending order, find the indices of two + numbers such that their sum is the given target. + + Using a bidirectional linear search. + """ + left = 0 # pointer 1 holds from left of array numbers + right = len(numbers) - 1 # pointer 2 holds from right of array numbers + while left < right: + current_sum = numbers[left] + numbers[right] + if current_sum == target: + return [left + 1, right + 1] + + if current_sum > target: + right = right - 1 + else: + left = left + 1 diff --git a/algorithms/set/__init__.py b/algorithms/set/__init__.py new file mode 100644 index 000000000..534e5de48 --- /dev/null +++ b/algorithms/set/__init__.py @@ -0,0 +1 @@ +from .find_keyboard_row import * diff --git a/algorithms/set/find_keyboard_row.py b/algorithms/set/find_keyboard_row.py new file mode 100644 index 000000000..c15dcdadf --- /dev/null +++ b/algorithms/set/find_keyboard_row.py @@ -0,0 +1,27 @@ +""" +Given a List of words, return the words that can be typed using letters of +alphabet on only one row's of American keyboard. + +For example: +Input: ["Hello", "Alaska", "Dad", "Peace"] +Output: ["Alaska", "Dad"] + +Reference: https://leetcode.com/problems/keyboard-row/description/ +""" + +def find_keyboard_row(words): + """ + :type words: List[str] + :rtype: List[str] + """ + keyboard = [ + set('qwertyuiop'), + set('asdfghjkl'), + set('zxcvbnm'), + ] + result = [] + for word in words: + for key in keyboard: + if set(word.lower()).issubset(key): + result.append(word) + return result diff --git a/algorithms/set/randomized_set.py b/algorithms/set/randomized_set.py new file mode 100644 index 000000000..53f2b5af4 --- /dev/null +++ b/algorithms/set/randomized_set.py @@ -0,0 +1,70 @@ +#! /usr/bin/env python3 + +""" +Design a data structure that supports all following operations +in average O(1) time. + +insert(val): Inserts an item val to the set if not already present. +remove(val): Removes an item val from the set if present. +random_element: Returns a random element from current set of elements. + Each element must have the same probability of being returned. +""" + +import random + + +class RandomizedSet(): + """ + idea: shoot + """ + + def __init__(self): + self.elements = [] + self.index_map = {} # element -> index + + def insert(self, new_one): + if new_one in self.index_map: + return + self.index_map[new_one] = len(self.elements) + self.elements.append(new_one) + + def remove(self, old_one): + if not old_one in self.index_map: + return + index = self.index_map[old_one] + last = self.elements.pop() + self.index_map.pop(old_one) + if index == len(self.elements): + return + self.elements[index] = last + self.index_map[last] = index + + def random_element(self): + return random.choice(self.elements) + + +def __test(): + rset = RandomizedSet() + ground_truth = set() + n = 64 + + for i in range(n): + rset.insert(i) + ground_truth.add(i) + + # Remove a half + for i in random.sample(range(n), n // 2): + rset.remove(i) + ground_truth.remove(i) + + print(len(ground_truth), len(rset.elements), len(rset.index_map)) + for i in ground_truth: + assert(i == rset.elements[rset.index_map[i]]) + + for i in range(n): + print(rset.random_element(), end=' ') + print() + + +if __name__ == "__main__": + __test() diff --git a/set/set_covering.py b/algorithms/set/set_covering.py similarity index 100% rename from set/set_covering.py rename to algorithms/set/set_covering.py diff --git a/algorithms/sort/__init__.py b/algorithms/sort/__init__.py new file mode 100644 index 000000000..fb186c024 --- /dev/null +++ b/algorithms/sort/__init__.py @@ -0,0 +1,21 @@ +from .bitonic_sort import * +from .bogo_sort import * +from .bubble_sort import * +from .comb_sort import * +from .counting_sort import * +from .cycle_sort import * +from .exchange_sort import * +from .heap_sort import * +from .insertion_sort import * +from .merge_sort import * +from .pancake_sort import * +from .pigeonhole_sort import * +from .quick_sort import * +from .selection_sort import * +from .top_sort import * +from .bucket_sort import * +from .shell_sort import * +from .stooge_sort import * +from .radix_sort import * +from .gnome_sort import * +from .cocktail_shaker_sort import * diff --git a/algorithms/sort/bead_sort.py b/algorithms/sort/bead_sort.py new file mode 100644 index 000000000..0d949fa82 --- /dev/null +++ b/algorithms/sort/bead_sort.py @@ -0,0 +1,26 @@ +""" +Bead Sort (also known as Gravity Sort) is a natural sorting algorithm that simulates how beads would settle under gravity on an abacus. It is most useful for sorting positive integers, especially when the range of numbers isn't excessively large. However, it is not a comparison-based sort and is generally impractical for large inputs due to its reliance on physical modeling. +Time Complexity +- Best Case: O(n) if the numbers are already sorted +- Average Case: O(n^2) because each bead needs to be placed and then fall under gravity +- Worst Case: O(n^2) since each bead must "fall" individually +""" + +def bead_sort(arr): + if any(num < 0 for num in arr): + raise ValueError("Bead sort only works with non-negative integers.") + + max_num = max(arr) if arr else 0 + grid = [[0] * len(arr) for _ in range(max_num)] + + # Drop beads (place beads in columns) + for col, num in enumerate(arr): + for row in range(num): + grid[row][col] = 1 + + # Let the beads "fall" (count beads in each row) + for row in grid: + sum_beads = sum(row) + for col in range(len(arr)): + row[col] = 1 if col < sum_beads else 0 + diff --git a/algorithms/sort/bitonic_sort.py b/algorithms/sort/bitonic_sort.py new file mode 100644 index 000000000..f8cad90e1 --- /dev/null +++ b/algorithms/sort/bitonic_sort.py @@ -0,0 +1,43 @@ +def bitonic_sort(arr, reverse=False): + """ + bitonic sort is sorting algorithm to use multiple process, but this code not containing parallel process + It can sort only array that sizes power of 2 + It can sort array in both increasing order and decreasing order by giving argument true(increasing) and false(decreasing) + + Worst-case in parallel: O(log(n)^2) + Worst-case in non-parallel: O(nlog(n)^2) + + reference: https://en.wikipedia.org/wiki/Bitonic_sorter + """ + def compare(arr, reverse): + n = len(arr)//2 + for i in range(n): + if reverse != (arr[i] > arr[i+n]): + arr[i], arr[i+n] = arr[i+n], arr[i] + return arr + + def bitonic_merge(arr, reverse): + n = len(arr) + + if n <= 1: + return arr + + arr = compare(arr, reverse) + left = bitonic_merge(arr[:n // 2], reverse) + right = bitonic_merge(arr[n // 2:], reverse) + return left + right + + #end of function(compare and bitionic_merge) definition + n = len(arr) + if n <= 1: + return arr + # checks if n is power of two + if not (n and (not(n & (n - 1))) ): + raise ValueError("the size of input should be power of two") + + left = bitonic_sort(arr[:n // 2], True) + right = bitonic_sort(arr[n // 2:], False) + + arr = bitonic_merge(left + right, reverse) + + return arr diff --git a/algorithms/sort/bogo_sort.py b/algorithms/sort/bogo_sort.py new file mode 100644 index 000000000..60e1be8f0 --- /dev/null +++ b/algorithms/sort/bogo_sort.py @@ -0,0 +1,32 @@ +import random + +def bogo_sort(arr, simulation=False): + """Bogo Sort + Best Case Complexity: O(n) + Worst Case Complexity: O(∞) + Average Case Complexity: O(n(n-1)!) + """ + + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + + def is_sorted(arr): + #check the array is inorder + i = 0 + arr_len = len(arr) + while i+1 < arr_len: + if arr[i] > arr[i+1]: + return False + i += 1 + + + return True + while not is_sorted(arr): + random.shuffle(arr) + + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + + return arr diff --git a/algorithms/sort/bubble_sort.py b/algorithms/sort/bubble_sort.py new file mode 100644 index 000000000..84f406795 --- /dev/null +++ b/algorithms/sort/bubble_sort.py @@ -0,0 +1,35 @@ +""" + +https://en.wikipedia.org/wiki/Bubble_sort + +Worst-case performance: O(N^2) + +If you call bubble_sort(arr,True), you can see the process of the sort +Default is simulation = False + +""" + + +def bubble_sort(arr, simulation=False): + def swap(i, j): + arr[i], arr[j] = arr[j], arr[i] + + n = len(arr) + swapped = True + + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + x = -1 + while swapped: + swapped = False + x = x + 1 + for i in range(1, n-x): + if arr[i - 1] > arr[i]: + swap(i - 1, i) + swapped = True + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + + return arr diff --git a/algorithms/sort/bucket_sort.py b/algorithms/sort/bucket_sort.py new file mode 100644 index 000000000..d89232ccf --- /dev/null +++ b/algorithms/sort/bucket_sort.py @@ -0,0 +1,28 @@ +def bucket_sort(arr): + ''' Bucket Sort + Complexity: O(n^2) + The complexity is dominated by nextSort + ''' + # The number of buckets and make buckets + num_buckets = len(arr) + buckets = [[] for bucket in range(num_buckets)] + # Assign values into bucket_sort + for value in arr: + index = value * num_buckets // (max(arr) + 1) + buckets[index].append(value) + # Sort + sorted_list = [] + for i in range(num_buckets): + sorted_list.extend(next_sort(buckets[i])) + return sorted_list + +def next_sort(arr): + # We will use insertion sort here. + for i in range(1, len(arr)): + j = i - 1 + key = arr[i] + while arr[j] > key and j >= 0: + arr[j+1] = arr[j] + j = j - 1 + arr[j + 1] = key + return arr diff --git a/algorithms/sort/cocktail_shaker_sort.py b/algorithms/sort/cocktail_shaker_sort.py new file mode 100644 index 000000000..973b824b6 --- /dev/null +++ b/algorithms/sort/cocktail_shaker_sort.py @@ -0,0 +1,30 @@ +def cocktail_shaker_sort(arr): + """ + Cocktail_shaker_sort + Sorting a given array + mutation of bubble sort + + reference: https://en.wikipedia.org/wiki/Cocktail_shaker_sort + + Worst-case performance: O(N^2) + """ + + def swap(i, j): + arr[i], arr[j] = arr[j], arr[i] + + n = len(arr) + swapped = True + while swapped: + swapped = False + for i in range(1, n): + if arr[i - 1] > arr[i]: + swap(i - 1, i) + swapped = True + if swapped == False: + return arr + swapped = False + for i in range(n-1,0,-1): + if arr[i - 1] > arr[i]: + swap(i - 1, i) + swapped = True + return arr diff --git a/sort/comb_sort.py b/algorithms/sort/comb_sort.py similarity index 70% rename from sort/comb_sort.py rename to algorithms/sort/comb_sort.py index b9dc1f67a..efa58fc5e 100644 --- a/sort/comb_sort.py +++ b/algorithms/sort/comb_sort.py @@ -6,11 +6,8 @@ """ -from math import floor - def comb_sort(arr): - def swap(i, j): arr[i], arr[j] = arr[j], arr[i] @@ -19,7 +16,7 @@ def swap(i, j): shrink = 1.3 sorted = False while not sorted: - gap = int(floor(gap/shrink)) + gap = int(gap / shrink) if gap > 1: sorted = False else: @@ -32,10 +29,4 @@ def swap(i, j): swap(i, i + gap) sorted = False i = i + 1 - - -array = [1, 5, 65, 23, 57, 1232, -1, -5, -2, 242, 100, - 4, 423, 2, 564, 9, 0, 10, 43, 64, 32, 1, 999] -print(array) -comb_sort(array) -print(array) + return arr diff --git a/algorithms/sort/counting_sort.py b/algorithms/sort/counting_sort.py new file mode 100644 index 000000000..46688e218 --- /dev/null +++ b/algorithms/sort/counting_sort.py @@ -0,0 +1,36 @@ +def counting_sort(arr): + """ + Counting_sort + Sorting a array which has no element greater than k + Creating a new temp_arr,where temp_arr[i] contain the number of + element less than or equal to i in the arr + Then placing the number i into a correct position in the result_arr + return the result_arr + Complexity: 0(n) + """ + + m = min(arr) + # in case there are negative elements, change the array to all positive element + different = 0 + if m < 0: + # save the change, so that we can convert the array back to all positive number + different = -m + for i in range(len(arr)): + arr[i] += -m + k = max(arr) + temp_arr = [0] * (k + 1) + for i in range(0, len(arr)): + temp_arr[arr[i]] = temp_arr[arr[i]] + 1 + # temp_array[i] contain the times the number i appear in arr + + for i in range(1, k + 1): + temp_arr[i] = temp_arr[i] + temp_arr[i - 1] + # temp_array[i] contain the number of element less than or equal i in arr + + result_arr = arr.copy() + # creating a result_arr an put the element in a correct positon + for i in range(len(arr) - 1, -1, -1): + result_arr[temp_arr[arr[i]] - 1] = arr[i] - different + temp_arr[arr[i]] = temp_arr[arr[i]] - 1 + + return result_arr diff --git a/algorithms/sort/cycle_sort.py b/algorithms/sort/cycle_sort.py new file mode 100644 index 000000000..6e512c924 --- /dev/null +++ b/algorithms/sort/cycle_sort.py @@ -0,0 +1,46 @@ +def cycle_sort(arr): + """ + cycle_sort + This is based on the idea that the permutations to be sorted + can be decomposed into cycles, + and the results can be individually sorted by cycling. + + reference: https://en.wikipedia.org/wiki/Cycle_sort + + Average time complexity : O(N^2) + Worst case time complexity : O(N^2) + """ + len_arr = len(arr) + # Finding cycle to rotate. + for cur in range(len_arr - 1): + item = arr[cur] + + # Finding an indx to put items in. + index = cur + for i in range(cur + 1, len_arr): + if arr[i] < item: + index += 1 + + # Case of there is not a cycle + if index == cur: + continue + + # Putting the item immediately right after the duplicate item or on the right. + while item == arr[index]: + index += 1 + arr[index], item = item, arr[index] + + # Rotating the remaining cycle. + while index != cur: + + # Finding where to put the item. + index = cur + for i in range(cur + 1, len_arr): + if arr[i] < item: + index += 1 + + # After item is duplicated, put it in place or put it there. + while item == arr[index]: + index += 1 + arr[index], item = item, arr[index] + return arr diff --git a/algorithms/sort/exchange_sort.py b/algorithms/sort/exchange_sort.py new file mode 100644 index 000000000..c2d2e7923 --- /dev/null +++ b/algorithms/sort/exchange_sort.py @@ -0,0 +1,11 @@ +def exchange_sort(arr): + """ + Reference : https://en.wikipedia.org/wiki/Sorting_algorithm#Exchange_sort + Complexity : O(n^2) + """ + arr_len = len(arr) + for i in range(arr_len-1): + for j in range(i+1, arr_len): + if(arr[i] > arr[j]): + arr[i], arr[j] = arr[j], arr[i] + return arr diff --git a/algorithms/sort/gnome_sort.py b/algorithms/sort/gnome_sort.py new file mode 100644 index 000000000..aaf38a278 --- /dev/null +++ b/algorithms/sort/gnome_sort.py @@ -0,0 +1,19 @@ +""" + +Gnome Sort +Best case performance is O(n) +Worst case performance is O(n^2) + +""" + + +def gnome_sort(arr): + n = len(arr) + index = 0 + while index < n: + if index == 0 or arr[index] >= arr[index-1]: + index = index + 1 + else: + arr[index], arr[index-1] = arr[index-1], arr[index] + index = index - 1 + return arr diff --git a/algorithms/sort/heap_sort.py b/algorithms/sort/heap_sort.py new file mode 100644 index 000000000..f07d4bf61 --- /dev/null +++ b/algorithms/sort/heap_sort.py @@ -0,0 +1,92 @@ +def max_heap_sort(arr, simulation=False): + """ Heap Sort that uses a max heap to sort an array in ascending order + Complexity: O(n log(n)) + """ + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + + for i in range(len(arr) - 1, 0, -1): + iteration = max_heapify(arr, i, simulation, iteration) + + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + return arr + + +def max_heapify(arr, end, simulation, iteration): + """ Max heapify helper for max_heap_sort + """ + last_parent = (end - 1) // 2 + + # Iterate from last parent to first + for parent in range(last_parent, -1, -1): + current_parent = parent + + # Iterate from current_parent to last_parent + while current_parent <= last_parent: + # Find greatest child of current_parent + child = 2 * current_parent + 1 + if child + 1 <= end and arr[child] < arr[child + 1]: + child = child + 1 + + # Swap if child is greater than parent + if arr[child] > arr[current_parent]: + arr[current_parent], arr[child] = arr[child], arr[current_parent] + current_parent = child + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + # If no swap occurred, no need to keep iterating + else: + break + arr[0], arr[end] = arr[end], arr[0] + return iteration + +def min_heap_sort(arr, simulation=False): + """ Heap Sort that uses a min heap to sort an array in ascending order + Complexity: O(n log(n)) + """ + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + + for i in range(0, len(arr) - 1): + iteration = min_heapify(arr, i, simulation, iteration) + + return arr + + +def min_heapify(arr, start, simulation, iteration): + """ Min heapify helper for min_heap_sort + """ + # Offset last_parent by the start (last_parent calculated as if start index was 0) + # All array accesses need to be offset by start + end = len(arr) - 1 + last_parent = (end - start - 1) // 2 + + # Iterate from last parent to first + for parent in range(last_parent, -1, -1): + current_parent = parent + + # Iterate from current_parent to last_parent + while current_parent <= last_parent: + # Find lesser child of current_parent + child = 2 * current_parent + 1 + if child + 1 <= end - start and arr[child + start] > arr[ + child + 1 + start]: + child = child + 1 + + # Swap if child is less than parent + if arr[child + start] < arr[current_parent + start]: + arr[current_parent + start], arr[child + start] = \ + arr[child + start], arr[current_parent + start] + current_parent = child + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + # If no swap occurred, no need to keep iterating + else: + break + return iteration diff --git a/algorithms/sort/insertion_sort.py b/algorithms/sort/insertion_sort.py new file mode 100644 index 000000000..06c86228d --- /dev/null +++ b/algorithms/sort/insertion_sort.py @@ -0,0 +1,25 @@ +def insertion_sort(arr, simulation=False): + """ Insertion Sort + Complexity: O(n^2) + """ + + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + + for i in range(len(arr)): + cursor = arr[i] + pos = i + + while pos > 0 and arr[pos - 1] > cursor: + # Swap the number down the list + arr[pos] = arr[pos - 1] + pos = pos - 1 + # Break and do the final swap + arr[pos] = cursor + + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + + return arr diff --git a/sort/meeting_rooms.py b/algorithms/sort/meeting_rooms.py similarity index 89% rename from sort/meeting_rooms.py rename to algorithms/sort/meeting_rooms.py index 72ebb7d51..2cb60c69a 100644 --- a/sort/meeting_rooms.py +++ b/algorithms/sort/meeting_rooms.py @@ -16,6 +16,6 @@ def can_attend_meetings(intervals): """ intervals = sorted(intervals, key=lambda x: x.start) for i in range(1, len(intervals)): - if intervals[i].start < intervals[i-1].end: + if intervals[i].start < intervals[i - 1].end: return False return True diff --git a/algorithms/sort/merge_sort.py b/algorithms/sort/merge_sort.py new file mode 100644 index 000000000..e2d7f05b9 --- /dev/null +++ b/algorithms/sort/merge_sort.py @@ -0,0 +1,40 @@ +def merge_sort(arr): + """ Merge Sort + Complexity: O(n log(n)) + """ + # Our recursive base case + if len(arr) <= 1: + return arr + mid = len(arr) // 2 + # Perform merge_sort recursively on both halves + left, right = merge_sort(arr[:mid]), merge_sort(arr[mid:]) + + # Merge each side together + # return merge(left, right, arr.copy()) # changed, no need to copy, mutate inplace. + merge(left,right,arr) + return arr + + +def merge(left, right, merged): + """ Merge helper + Complexity: O(n) + """ + + left_cursor, right_cursor = 0, 0 + while left_cursor < len(left) and right_cursor < len(right): + # Sort each one and place into the result + if left[left_cursor] <= right[right_cursor]: + merged[left_cursor+right_cursor]=left[left_cursor] + left_cursor += 1 + else: + merged[left_cursor + right_cursor] = right[right_cursor] + right_cursor += 1 + # Add the left overs if there's any left to the result + for left_cursor in range(left_cursor, len(left)): + merged[left_cursor + right_cursor] = left[left_cursor] + # Add the left overs if there's any left to the result + for right_cursor in range(right_cursor, len(right)): + merged[left_cursor + right_cursor] = right[right_cursor] + + # Return result + # return merged # do not return anything, as it is replacing inplace. diff --git a/algorithms/sort/pancake_sort.py b/algorithms/sort/pancake_sort.py new file mode 100644 index 000000000..19725c043 --- /dev/null +++ b/algorithms/sort/pancake_sort.py @@ -0,0 +1,25 @@ +def pancake_sort(arr): + """ + Pancake_sort + Sorting a given array + mutation of selection sort + + reference: https://www.geeksforgeeks.org/pancake-sorting/ + + Overall time complexity : O(N^2) + """ + + len_arr = len(arr) + if len_arr <= 1: + return arr + for cur in range(len(arr), 1, -1): + #Finding index of maximum number in arr + index_max = arr.index(max(arr[0:cur])) + if index_max+1 != cur: + #Needs moving + if index_max != 0: + #reverse from 0 to index_max + arr[:index_max+1] = reversed(arr[:index_max+1]) + # Reverse list + arr[:cur] = reversed(arr[:cur]) + return arr diff --git a/algorithms/sort/pigeonhole_sort.py b/algorithms/sort/pigeonhole_sort.py new file mode 100644 index 000000000..0569aa994 --- /dev/null +++ b/algorithms/sort/pigeonhole_sort.py @@ -0,0 +1,28 @@ +""" + +https://en.wikipedia.org/wiki/Pigeonhole_sort + +Time complexity: O(n + Range) where n = number of elements and Range = possible values in the array + +Suitable for lists where the number of elements and key values are mostly the same. + +""" + + +def pigeonhole_sort(arr): + Max = max(arr) + Min = min(arr) + size = Max - Min + 1 + + holes = [0]*size + + for i in arr: + holes[i-Min] += 1 + + i = 0 + for count in range(size): + while holes[count] > 0: + holes[count] -= 1 + arr[i] = count + Min + i += 1 + return arr diff --git a/algorithms/sort/quick_sort.py b/algorithms/sort/quick_sort.py new file mode 100644 index 000000000..10794e7a5 --- /dev/null +++ b/algorithms/sort/quick_sort.py @@ -0,0 +1,32 @@ +def quick_sort(arr, simulation=False): + """ Quick sort + Complexity: best O(n log(n)) avg O(n log(n)), worst O(N^2) + """ + + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + arr, _ = quick_sort_recur(arr, 0, len(arr) - 1, iteration, simulation) + return arr + +def quick_sort_recur(arr, first, last, iteration, simulation): + if first < last: + pos = partition(arr, first, last) + # Start our two recursive calls + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + + _, iteration = quick_sort_recur(arr, first, pos - 1, iteration, simulation) + _, iteration = quick_sort_recur(arr, pos + 1, last, iteration, simulation) + + return arr, iteration + +def partition(arr, first, last): + wall = first + for pos in range(first, last): + if arr[pos] < arr[last]: # last is the pivot + arr[pos], arr[wall] = arr[wall], arr[pos] + wall += 1 + arr[wall], arr[last] = arr[last], arr[wall] + return wall diff --git a/algorithms/sort/radix_sort.py b/algorithms/sort/radix_sort.py new file mode 100644 index 000000000..52457063c --- /dev/null +++ b/algorithms/sort/radix_sort.py @@ -0,0 +1,32 @@ +""" +radix sort +complexity: O(nk + n) . n is the size of input list and k is the digit length of the number +""" +def radix_sort(arr, simulation=False): + position = 1 + max_number = max(arr) + + iteration = 0 + if simulation: + print("iteration", iteration, ":", *arr) + + while position <= max_number: + queue_list = [list() for _ in range(10)] + + for num in arr: + digit_number = num // position % 10 + queue_list[digit_number].append(num) + + index = 0 + for numbers in queue_list: + for num in numbers: + arr[index] = num + index += 1 + + if simulation: + iteration = iteration + 1 + print("iteration", iteration, ":", *arr) + + position *= 10 + return arr + \ No newline at end of file diff --git a/algorithms/sort/selection_sort.py b/algorithms/sort/selection_sort.py new file mode 100644 index 000000000..f6d535225 --- /dev/null +++ b/algorithms/sort/selection_sort.py @@ -0,0 +1,23 @@ +def selection_sort(arr, simulation=False): + """ Selection Sort + Complexity: O(n^2) + """ + iteration = 0 + if simulation: + print("iteration",iteration,":",*arr) + + for i in range(len(arr)): + minimum = i + + for j in range(i + 1, len(arr)): + # "Select" the correct value + if arr[j] < arr[minimum]: + minimum = j + + arr[minimum], arr[i] = arr[i], arr[minimum] + + if simulation: + iteration = iteration + 1 + print("iteration",iteration,":",*arr) + + return arr diff --git a/algorithms/sort/shell_sort.py b/algorithms/sort/shell_sort.py new file mode 100644 index 000000000..61f5f612e --- /dev/null +++ b/algorithms/sort/shell_sort.py @@ -0,0 +1,21 @@ +def shell_sort(arr): + ''' Shell Sort + Complexity: O(n^2) + ''' + n = len(arr) + # Initialize size of the gap + gap = n//2 + + while gap > 0: + y_index = gap + while y_index < len(arr): + y = arr[y_index] + x_index = y_index - gap + while x_index >= 0 and y < arr[x_index]: + arr[x_index + gap] = arr[x_index] + x_index = x_index - gap + arr[x_index + gap] = y + y_index = y_index + 1 + gap = gap//2 + + return arr diff --git a/sort/sort_colors.py b/algorithms/sort/sort_colors.py similarity index 89% rename from sort/sort_colors.py rename to algorithms/sort/sort_colors.py index e85879781..aa44e221e 100644 --- a/sort/sort_colors.py +++ b/algorithms/sort/sort_colors.py @@ -25,6 +25,6 @@ def sort_colors(nums): if __name__ == "__main__": - nums = [0,1,1,1,2,2,2,1,1,1,0,0,0,0,1,1,1,0,0,2,2] + nums = [0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2] sort_colors(nums) print(nums) diff --git a/algorithms/sort/stooge_sort.py b/algorithms/sort/stooge_sort.py new file mode 100644 index 000000000..42f8b3bd4 --- /dev/null +++ b/algorithms/sort/stooge_sort.py @@ -0,0 +1,43 @@ +''' + +Stooge Sort +Time Complexity : O(n2.709) +Reference: https://www.geeksforgeeks.org/stooge-sort/ + +''' + + + +def stoogesort(arr, l, h): + if l >= h: + return + + # If first element is smaller + # than last, swap them + if arr[l]>arr[h]: + t = arr[l] + arr[l] = arr[h] + arr[h] = t + + # If there are more than 2 elements in + # the array + if h-l + 1 > 2: + t = (int)((h-l + 1)/3) + + # Recursively sort first 2 / 3 elements + stoogesort(arr, l, (h-t)) + + # Recursively sort last 2 / 3 elements + stoogesort(arr, l + t, (h)) + + # Recursively sort first 2 / 3 elements + # again to confirm + stoogesort(arr, l, (h-t)) + + +if __name__ == "__main__": + array = [1,3,64,5,7,8] + n = len(array) + stoogesort(array, 0, n-1) + for i in range(0, n): + print(array[i], end = ' ') diff --git a/algorithms/sort/top_sort.py b/algorithms/sort/top_sort.py new file mode 100644 index 000000000..b9188bb28 --- /dev/null +++ b/algorithms/sort/top_sort.py @@ -0,0 +1,66 @@ +GRAY, BLACK = 0, 1 + +def top_sort_recursive(graph): + """ Time complexity is the same as DFS, which is O(V + E) + Space complexity: O(V) + """ + order, enter, state = [], set(graph), {} + + def dfs(node): + state[node] = GRAY + #print(node) + for k in graph.get(node, ()): + sk = state.get(k, None) + if sk == GRAY: + raise ValueError("cycle") + if sk == BLACK: + continue + enter.discard(k) + dfs(k) + order.append(node) + state[node] = BLACK + + while enter: dfs(enter.pop()) + return order + +def top_sort(graph): + """ Time complexity is the same as DFS, which is O(V + E) + Space complexity: O(V) + """ + order, enter, state = [], set(graph), {} + + def is_ready(node): + lst = graph.get(node, ()) + if len(lst) == 0: + return True + for k in lst: + sk = state.get(k, None) + if sk == GRAY: + raise ValueError("cycle") + if sk != BLACK: + return False + return True + + while enter: + node = enter.pop() + stack = [] + while True: + state[node] = GRAY + stack.append(node) + for k in graph.get(node, ()): + sk = state.get(k, None) + if sk == GRAY: + raise ValueError("cycle") + if sk == BLACK: + continue + enter.discard(k) + stack.append(k) + while stack and is_ready(stack[-1]): + node = stack.pop() + order.append(node) + state[node] = BLACK + if len(stack) == 0: + break + node = stack.pop() + + return order diff --git a/sort/wiggle_sort.py b/algorithms/sort/wiggle_sort.py similarity index 73% rename from sort/wiggle_sort.py rename to algorithms/sort/wiggle_sort.py index 2e09584c3..15dc76d4b 100644 --- a/sort/wiggle_sort.py +++ b/algorithms/sort/wiggle_sort.py @@ -1,4 +1,6 @@ - +""" +Given an unsorted array nums, reorder it such that nums[0] < nums[1] > nums[2] < nums[3].... +""" def wiggle_sort(nums): for i in range(len(nums)): if (i % 2 == 1) == (nums[i-1] > nums[i]): diff --git a/algorithms/stack/__init__.py b/algorithms/stack/__init__.py new file mode 100644 index 000000000..4e8d0603f --- /dev/null +++ b/algorithms/stack/__init__.py @@ -0,0 +1,10 @@ +from .stack import * +from .is_consecutive import * +from .is_sorted import * +from .remove_min import * +from .stutter import * +from .switch_pairs import * +from .valid_parenthesis import * +from .simplify_path import * +from .stack import * +from .ordered_stack import * diff --git a/algorithms/stack/is_consecutive.py b/algorithms/stack/is_consecutive.py new file mode 100644 index 000000000..44e3f90f5 --- /dev/null +++ b/algorithms/stack/is_consecutive.py @@ -0,0 +1,60 @@ +""" +Given a stack, a function is_consecutive takes a stack as a parameter and that +returns whether or not the stack contains a sequence of consecutive integers +starting from the bottom of the stack (returning true if it does, returning +false if it does not). + +For example: +bottom [3, 4, 5, 6, 7] top +Then the call of is_consecutive(s) should return true. +bottom [3, 4, 6, 7] top +Then the call of is_consecutive(s) should return false. +bottom [3, 2, 1] top +The function should return false due to reverse order. + +Note: There are 2 solutions: +first_is_consecutive: it uses a single stack as auxiliary storage +second_is_consecutive: it uses a single queue as auxiliary storage +""" +import collections + + +def first_is_consecutive(stack): + storage_stack = [] + for i in range(len(stack)): + first_value = stack.pop() + if len(stack) == 0: # Case odd number of values in stack + return True + second_value = stack.pop() + if first_value - second_value != 1: # Not consecutive + return False + stack.append(second_value) # Backup second value + storage_stack.append(first_value) + + # Back up stack from storage stack + for i in range(len(storage_stack)): + stack.append(storage_stack.pop()) + return True + + +def second_is_consecutive(stack): + q = collections.deque() + for i in range(len(stack)): + first_value = stack.pop() + if len(stack) == 0: # Case odd number of values in stack + return True + second_value = stack.pop() + if first_value - second_value != 1: # Not consecutive + return False + stack.append(second_value) # Backup second value + q.append(first_value) + + # Back up stack from queue + for i in range(len(q)): + stack.append(q.pop()) + for i in range(len(stack)): + q.append(stack.pop()) + for i in range(len(q)): + stack.append(q.pop()) + + return True diff --git a/algorithms/stack/is_sorted.py b/algorithms/stack/is_sorted.py new file mode 100644 index 000000000..b3c3337e5 --- /dev/null +++ b/algorithms/stack/is_sorted.py @@ -0,0 +1,32 @@ +""" +Given a stack, a function is_sorted accepts a stack as a parameter and returns +true if the elements in the stack occur in ascending increasing order from +bottom, and false otherwise. That is, the smallest element should be at bottom + +For example: +bottom [6, 3, 5, 1, 2, 4] top +The function should return false +bottom [1, 2, 3, 4, 5, 6] top +The function should return true +""" + + +def is_sorted(stack): + storage_stack = [] + for i in range(len(stack)): + if len(stack) == 0: + break + first_val = stack.pop() + if len(stack) == 0: + break + second_val = stack.pop() + if first_val < second_val: + return False + storage_stack.append(first_val) + stack.append(second_val) + + # Backup stack + for i in range(len(storage_stack)): + stack.append(storage_stack.pop()) + + return True diff --git a/algorithms/stack/longest_abs_path.py b/algorithms/stack/longest_abs_path.py new file mode 100644 index 000000000..edc4ee8b0 --- /dev/null +++ b/algorithms/stack/longest_abs_path.py @@ -0,0 +1,65 @@ +# def lengthLongestPath(input): +# maxlen = 0 +# pathlen = {0: 0} +# for line in input.splitlines(): +# print("---------------") +# print("line:", line) +# name = line.strip('\t') +# print("name:", name) +# depth = len(line) - len(name) +# print("depth:", depth) +# if '.' in name: +# maxlen = max(maxlen, pathlen[depth] + len(name)) +# else: +# pathlen[depth + 1] = pathlen[depth] + len(name) + 1 +# print("maxlen:", maxlen) +# return maxlen + +# def lengthLongestPath(input): +# paths = input.split("\n") +# level = [0] * 10 +# maxLength = 0 +# for path in paths: +# print("-------------") +# levelIdx = path.rfind("\t") +# print("Path: ", path) +# print("path.rfind(\\t)", path.rfind("\t")) +# print("levelIdx: ", levelIdx) +# print("level: ", level) +# level[levelIdx + 1] = level[levelIdx] + len(path) - levelIdx + 1 +# print("level: ", level) +# if "." in path: +# maxLength = max(maxLength, level[levelIdx+1] - 1) +# print("maxlen: ", maxLength) +# return maxLength + +def length_longest_path(input): + """ + :type input: str + :rtype: int + """ + curr_len, max_len = 0, 0 # running length and max length + stack = [] # keep track of the name length + for s in input.split('\n'): + print("---------") + print(":", s) + depth = s.count('\t') # the depth of current dir or file + print("depth: ", depth) + print("stack: ", stack) + print("curlen: ", curr_len) + while len(stack) > depth: # go back to the correct depth + curr_len -= stack.pop() + stack.append(len(s.strip('\t'))+1) # 1 is the length of '/' + curr_len += stack[-1] # increase current length + print("stack: ", stack) + print("curlen: ", curr_len) + if '.' in s: # update maxlen only when it is a file + max_len = max(max_len, curr_len-1) # -1 is to minus one '/' + return max_len + + +st = "dir\n\tsubdir1\n\t\tfile1.ext\n\t\tsubsubdirectory1\n\tsubdir2\n\t\tsubsubdir2\n\t\t\tfile2.ext" +st2 = "a\n\tb1\n\t\tf1.txt\n\taaaaa\n\t\tf2.txt" +print("path:", st2) + +print("answer:", length_longest_path(st2)) diff --git a/algorithms/stack/ordered_stack.py b/algorithms/stack/ordered_stack.py new file mode 100644 index 000000000..94191d6cf --- /dev/null +++ b/algorithms/stack/ordered_stack.py @@ -0,0 +1,36 @@ +# The stack remains always ordered such that the highest value +# is at the top and the lowest at the bottom + + +class OrderedStack: + def __init__(self): + self.items = [] + + def is_empty(self): + return self.items == [] + + def push_t(self, item): + self.items.append(item) + + # push method to maintain order when pushing new elements + def push(self, item): + temp_stack = OrderedStack() + if self.is_empty() or item > self.peek(): + self.push_t(item) + else: + while item < self.peek() and not self.is_empty(): + temp_stack.push_t(self.pop()) + self.push_t(item) + while not temp_stack.is_empty(): + self.push_t(temp_stack.pop()) + + def pop(self): + if self.is_empty(): + raise IndexError("Stack is empty") + return self.items.pop() + + def peek(self): + return self.items[len(self.items) - 1] + + def size(self): + return len(self.items) diff --git a/algorithms/stack/remove_min.py b/algorithms/stack/remove_min.py new file mode 100644 index 000000000..ce635a4ab --- /dev/null +++ b/algorithms/stack/remove_min.py @@ -0,0 +1,30 @@ +""" +Given a stack, a function remove_min accepts a stack as a parameter +and removes the smallest value from the stack. + +For example: +bottom [2, 8, 3, -6, 7, 3] top +After remove_min(stack): +bottom [2, 8, 3, 7, 3] top + +""" + + +def remove_min(stack): + storage_stack = [] + if len(stack) == 0: # Stack is empty + return stack + # Find the smallest value + min = stack.pop() + stack.append(min) + for i in range(len(stack)): + val = stack.pop() + if val <= min: + min = val + storage_stack.append(val) + # Back up stack and remove min value + for i in range(len(storage_stack)): + val = storage_stack.pop() + if val != min: + stack.append(val) + return stack diff --git a/stack/simplify_path.py b/algorithms/stack/simplify_path.py similarity index 70% rename from stack/simplify_path.py rename to algorithms/stack/simplify_path.py index c6b7c7a5a..09f9de826 100644 --- a/stack/simplify_path.py +++ b/algorithms/stack/simplify_path.py @@ -7,16 +7,16 @@ * Did you consider the case where path = "/../"? In this case, you should return "/". -* Another corner case is the path might contain multiple slashes '/' together, such as "/home//foo/". - In this case, you should ignore redundant slashes and return "/home/foo". +* Another corner case is the path might contain multiple slashes '/' together, + such as "/home//foo/". In this case, you should ignore redundant + slashes and return "/home/foo". """ - def simplify_path(path): """ :type path: str :rtype: str """ - skip = set(['..','.','']) + skip = {'..', '.', ''} stack = [] paths = path.split('/') for tok in paths: @@ -25,8 +25,4 @@ def simplify_path(path): stack.pop() elif tok not in skip: stack.append(tok) - return '/' +'/'.join(stack) - -p = '/my/name/is/..//keon' -print(p) -print(simplify_path(p)) + return '/' + '/'.join(stack) diff --git a/algorithms/stack/stack.py b/algorithms/stack/stack.py new file mode 100644 index 000000000..a79aec490 --- /dev/null +++ b/algorithms/stack/stack.py @@ -0,0 +1,132 @@ +""" +Stack Abstract Data Type (ADT) +Stack() creates a new stack that is empty. + It needs no parameters and returns an empty stack. +push(item) adds a new item to the top of the stack. + It needs the item and returns nothing. +pop() removes the top item from the stack. + It needs no parameters and returns the item. The stack is modified. +peek() returns the top item from the stack but does not remove it. + It needs no parameters. The stack is not modified. +is_empty() tests to see whether the stack is empty. + It needs no parameters and returns a boolean value. +""" +from abc import ABCMeta, abstractmethod + + +class AbstractStack(metaclass=ABCMeta): + """Abstract Class for Stacks.""" + def __init__(self): + self._top = -1 + + def __len__(self): + return self._top + 1 + + def __str__(self): + result = " ".join(map(str, self)) + return 'Top-> ' + result + + def is_empty(self): + return self._top == -1 + + @abstractmethod + def __iter__(self): + pass + + @abstractmethod + def push(self, value): + pass + + @abstractmethod + def pop(self): + pass + + @abstractmethod + def peek(self): + pass + + +class ArrayStack(AbstractStack): + def __init__(self, size=10): + """ + Initialize python List with size of 10 or user given input. + Python List type is a dynamic array, so we have to restrict its + dynamic nature to make it work like a static array. + """ + super().__init__() + self._array = [None] * size + + def __iter__(self): + probe = self._top + while True: + if probe == -1: + return + yield self._array[probe] + probe -= 1 + + def push(self, value): + self._top += 1 + if self._top == len(self._array): + self._expand() + self._array[self._top] = value + + def pop(self): + if self.is_empty(): + raise IndexError("Stack is empty") + value = self._array[self._top] + self._top -= 1 + return value + + def peek(self): + """returns the current top element of the stack.""" + if self.is_empty(): + raise IndexError("Stack is empty") + return self._array[self._top] + + def _expand(self): + """ + expands size of the array. + Time Complexity: O(n) + """ + self._array += [None] * len(self._array) # double the size of the array + + +class StackNode: + """Represents a single stack node.""" + def __init__(self, value): + self.value = value + self.next = None + + +class LinkedListStack(AbstractStack): + + def __init__(self): + super().__init__() + self.head = None + + def __iter__(self): + probe = self.head + while True: + if probe is None: + return + yield probe.value + probe = probe.next + + def push(self, value): + node = StackNode(value) + node.next = self.head + self.head = node + self._top += 1 + + def pop(self): + if self.is_empty(): + raise IndexError("Stack is empty") + value = self.head.value + self.head = self.head.next + self._top -= 1 + return value + + def peek(self): + if self.is_empty(): + raise IndexError("Stack is empty") + return self.head.value diff --git a/algorithms/stack/stutter.py b/algorithms/stack/stutter.py new file mode 100644 index 000000000..ceb6451d4 --- /dev/null +++ b/algorithms/stack/stutter.py @@ -0,0 +1,46 @@ +""" +Given a stack, stutter takes a stack as a parameter and replaces every value +in the stack with two occurrences of that value. + +For example, suppose the stack stores these values: +bottom [3, 7, 1, 14, 9] top +Then the stack should store these values after the method terminates: +bottom [3, 3, 7, 7, 1, 1, 14, 14, 9, 9] top + +Note: There are 2 solutions: +first_stutter: it uses a single stack as auxiliary storage +second_stutter: it uses a single queue as auxiliary storage +""" +import collections + + +def first_stutter(stack): + storage_stack = [] + for i in range(len(stack)): + storage_stack.append(stack.pop()) + for i in range(len(storage_stack)): + val = storage_stack.pop() + stack.append(val) + stack.append(val) + + return stack + + +def second_stutter(stack): + q = collections.deque() + # Put all values into queue from stack + for i in range(len(stack)): + q.append(stack.pop()) + # Put values back into stack from queue + for i in range(len(q)): + stack.append(q.pop()) + # Now, stack is reverse, put all values into queue from stack + for i in range(len(stack)): + q.append(stack.pop()) + # Put 2 times value into stack from queue + for i in range(len(q)): + val = q.pop() + stack.append(val) + stack.append(val) + + return stack diff --git a/algorithms/stack/switch_pairs.py b/algorithms/stack/switch_pairs.py new file mode 100644 index 000000000..d8b22dc08 --- /dev/null +++ b/algorithms/stack/switch_pairs.py @@ -0,0 +1,66 @@ +""" +Given a stack, switch_pairs function takes a stack as a parameter and that +switches successive pairs of numbers starting at the bottom of the stack. + +For example, if the stack initially stores these values: +bottom [3, 8, 17, 9, 1, 10] top +Your function should switch the first pair (3, 8), +the second pair (17, 9), ...: +bottom [8, 3, 9, 17, 10, 1] top + +if there are an odd number of values in the stack, the value at the top of the +stack is not moved: For example: +bottom [3, 8, 17, 9, 1] top +It would again switch pairs of values, but the value at the +top of the stack (1) +would not be moved +bottom [8, 3, 9, 17, 1] top + +Note: There are 2 solutions: +first_switch_pairs: it uses a single stack as auxiliary storage +second_switch_pairs: it uses a single queue as auxiliary storage +""" +import collections + + +def first_switch_pairs(stack): + storage_stack = [] + for i in range(len(stack)): + storage_stack.append(stack.pop()) + for i in range(len(storage_stack)): + if len(storage_stack) == 0: + break + first = storage_stack.pop() + if len(storage_stack) == 0: # case: odd number of values in stack + stack.append(first) + break + second = storage_stack.pop() + stack.append(second) + stack.append(first) + return stack + + +def second_switch_pairs(stack): + q = collections.deque() + # Put all values into queue from stack + for i in range(len(stack)): + q.append(stack.pop()) + # Put values back into stack from queue + for i in range(len(q)): + stack.append(q.pop()) + # Now, stack is reverse, put all values into queue from stack + for i in range(len(stack)): + q.append(stack.pop()) + # Swap pairs by appending the 2nd value before appending 1st value + for i in range(len(q)): + if len(q) == 0: + break + first = q.pop() + if len(q) == 0: # case: odd number of values in stack + stack.append(first) + break + second = q.pop() + stack.append(second) + stack.append(first) + + return stack diff --git a/algorithms/stack/valid_parenthesis.py b/algorithms/stack/valid_parenthesis.py new file mode 100644 index 000000000..8fdb861b5 --- /dev/null +++ b/algorithms/stack/valid_parenthesis.py @@ -0,0 +1,22 @@ +""" +Given a string containing just the characters +'(', ')', '{', '}', '[' and ']', +determine if the input string is valid. + +The brackets must close in the correct order, +"()" and "()[]{}" are all valid but "(]" and "([)]" are not. +""" + + +def is_valid(s: str) -> bool: + stack = [] + dic = {")": "(", + "}": "{", + "]": "["} + for char in s: + if char in dic.values(): + stack.append(char) + elif char in dic: + if not stack or dic[char] != stack.pop(): + return False + return not stack diff --git a/algorithms/streaming/__init__.py b/algorithms/streaming/__init__.py new file mode 100644 index 000000000..3e764d2c3 --- /dev/null +++ b/algorithms/streaming/__init__.py @@ -0,0 +1,2 @@ +from .one_sparse_recovery import * +from .misra_gries import * diff --git a/algorithms/streaming/misra_gries.py b/algorithms/streaming/misra_gries.py new file mode 100644 index 000000000..58fd84b5e --- /dev/null +++ b/algorithms/streaming/misra_gries.py @@ -0,0 +1,60 @@ + +""" +Implementation of the Misra-Gries algorithm. +Given a list of items and a value k, it returns the every item in the list +that appears at least n/k times, where n is the length of the array + +By default, k is set to 2, solving the majority problem. + +For the majority problem, this algorithm only guarantees that if there is +an element that appears more than n/2 times, it will be outputed. If there +is no such element, any arbitrary element is returned by the algorithm. +Therefore, we need to iterate through again at the end. But since we have filtred +out the suspects, the memory complexity is significantly lower than +it would be to create counter for every element in the list. + +For example: +Input misras_gries([1,4,4,4,5,4,4]) +Output {'4':5} +Input misras_gries([0,0,0,1,1,1,1]) +Output {'1':4} +Input misras_gries([0,0,0,0,1,1,1,2,2],3) +Output {'0':4,'1':3} +Input misras_gries([0,0,0,1,1,1] +Output None +""" + +def misras_gries(array,k=2): + """Misra-Gries algorithm + + Keyword arguments: + array -- list of integers + k -- value of k (default 2) + """ + keys = {} + for i in array: + val = str(i) + if val in keys: + keys[val] = keys[val] + 1 + + elif len(keys) < k - 1: + keys[val] = 1 + + else: + for key in list(keys): + keys[key] = keys[key] - 1 + if keys[key] == 0: + del keys[key] + + suspects = keys.keys() + frequencies = {} + for suspect in suspects: + freq = _count_frequency(array,int(suspect)) + if freq >= len(array) / k: + frequencies[suspect] = freq + + return frequencies if len(frequencies) > 0 else None + + +def _count_frequency(array,element): + return array.count(element) diff --git a/algorithms/streaming/one_sparse_recovery.py b/algorithms/streaming/one_sparse_recovery.py new file mode 100644 index 000000000..18a26415e --- /dev/null +++ b/algorithms/streaming/one_sparse_recovery.py @@ -0,0 +1,68 @@ +""" +Non-negative 1-sparse recovery problem. +This algorithm assumes we have a non negative dynamic stream. + +Given a stream of tuples, where each tuple contains a number and a sign (+/-), it check if the +stream is 1-sparse, meaning if the elements in the stream cancel eacheother out in such +a way that ther is only a unique number at the end. + +Examples: +#1 +Input: [(4,'+'), (2,'+'),(2,'-'),(4,'+'),(3,'+'),(3,'-')], +Output: 4 +Comment: Since 2 and 3 gets removed. +#2 +Input: [(2,'+'),(2,'+'),(2,'+'),(2,'+'),(2,'+'),(2,'+'),(2,'+')] +Output: 2 +Comment: No other numbers present +#3 +Input: [(2,'+'),(2,'+'),(2,'+'),(2,'+'),(2,'+'),(2,'+'),(1,'+')] +Output: None +Comment: Not 1-sparse +""" + +def one_sparse(array): + """1-sparse algorithm + + Keyword arguments: + array -- stream of tuples + """ + sum_signs = 0 + bitsum = [0]*32 + sum_values = 0 + for val,sign in array: + if sign == "+": + sum_signs += 1 + sum_values += val + else: + sum_signs -= 1 + sum_values -= val + + _get_bit_sum(bitsum,val,sign) + + if sum_signs > 0 and _check_every_number_in_bitsum(bitsum,sum_signs): + return int(sum_values/sum_signs) + else: + return None + +#Helper function to check that every entry in the list is either 0 or the same as the +#sum of signs +def _check_every_number_in_bitsum(bitsum,sum_signs): + for val in bitsum: + if val != 0 and val != sum_signs : + return False + return True + +# Adds bit representation value to bitsum array +def _get_bit_sum(bitsum,val,sign): + i = 0 + if sign == "+": + while val: + bitsum[i] += val & 1 + i +=1 + val >>=1 + else : + while val: + bitsum[i] -= val & 1 + i +=1 + val >>=1 diff --git a/algorithms/strings/__init__.py b/algorithms/strings/__init__.py new file mode 100644 index 000000000..496b1ebe5 --- /dev/null +++ b/algorithms/strings/__init__.py @@ -0,0 +1,41 @@ +from .add_binary import * +from .breaking_bad import * +from .decode_string import * +from .delete_reoccurring import * +from .domain_extractor import * +from .encode_decode import * +from .group_anagrams import * +from .int_to_roman import * +from .is_palindrome import * +from .is_rotated import * +from .license_number import * +from .make_sentence import * +from .merge_string_checker import * +from .multiply_strings import * +from .one_edit_distance import * +from .rabin_karp import * +from .reverse_string import * +from .reverse_vowel import * +from .reverse_words import * +from .roman_to_int import * +from .strip_url_params import * +from .validate_coordinates import * +from .word_squares import * +from .unique_morse import * +from .judge_circle import * +from .strong_password import * +from .caesar_cipher import * +from .check_pangram import * +from .contain_string import * +from .count_binary_substring import * +from .repeat_string import * +from .text_justification import * +from .min_distance import * +from .longest_common_prefix import * +from .rotate import * +from .first_unique_char import * +from .repeat_substring import * +from .atbash_cipher import * +from .longest_palindromic_substring import * +from .knuth_morris_pratt import * +from .panagram import * \ No newline at end of file diff --git a/string/add_binary.py b/algorithms/strings/add_binary.py similarity index 90% rename from string/add_binary.py rename to algorithms/strings/add_binary.py index 74e94794c..0158a80c8 100644 --- a/string/add_binary.py +++ b/algorithms/strings/add_binary.py @@ -21,6 +21,6 @@ def add_binary(a, b): c += ord(b[j]) - zero j -= 1 s = chr(c % 2 + zero) + s - # c //= 2 for python3 - c /= 2 + c //= 2 + return s diff --git a/algorithms/strings/atbash_cipher.py b/algorithms/strings/atbash_cipher.py new file mode 100644 index 000000000..59bf777db --- /dev/null +++ b/algorithms/strings/atbash_cipher.py @@ -0,0 +1,27 @@ +""" +Atbash cipher is mapping the alphabet to it's reverse. +So if we take "a" as it is the first letter, we change it to the last - z. + +Example: +Attack at dawn --> Zggzxp zg wzdm + +Complexity: O(n) +""" + +def atbash(s): + translated = "" + for i in range(len(s)): + n = ord(s[i]) + + if s[i].isalpha(): + + if s[i].isupper(): + x = n - ord('A') + translated += chr(ord('Z') - x) + + if s[i].islower(): + x = n - ord('a') + translated += chr(ord('z') - x) + else: + translated += s[i] + return translated \ No newline at end of file diff --git a/algorithms/strings/breaking_bad.py b/algorithms/strings/breaking_bad.py new file mode 100644 index 000000000..98baf7cdb --- /dev/null +++ b/algorithms/strings/breaking_bad.py @@ -0,0 +1,95 @@ +""" +Given an api which returns an array of words and an array of symbols, display +the word with their matched symbol surrounded by square brackets. + +If the word string matches more than one symbol, then choose the one with +longest length. (ex. 'Microsoft' matches 'i' and 'cro'): + +Example: +Words array: ['Amazon', 'Microsoft', 'Google'] +Symbols: ['i', 'Am', 'cro', 'Na', 'le', 'abc'] + +Output: +[Am]azon, Mi[cro]soft, Goog[le] + +My solution(Wrong): +(I sorted the symbols array in descending order of length and ran loop over +words array to find a symbol match(using indexOf in javascript) which +worked. But I didn't make it through the interview, I am guessing my solution +was O(n^2) and they expected an efficient algorithm. + +output: +['[Am]azon', 'Mi[cro]soft', 'Goog[le]', 'Amaz[o]n', 'Micr[o]s[o]ft', 'G[o][o]gle'] +""" + +from functools import reduce + + +def match_symbol(words, symbols): + import re + combined = [] + for s in symbols: + for c in words: + r = re.search(s, c) + if r: + combined.append(re.sub(s, "[{}]".format(s), c)) + return combined + +def match_symbol_1(words, symbols): + res = [] + # reversely sort the symbols according to their lengths. + symbols = sorted(symbols, key=lambda _: len(_), reverse=True) + for word in words: + for symbol in symbols: + word_replaced = '' + # once match, append the `word_replaced` to res, process next word + if word.find(symbol) != -1: + word_replaced = word.replace(symbol, '[' + symbol + ']') + res.append(word_replaced) + break + # if this word matches no symbol, append it. + if word_replaced == '': + res.append(word) + return res + +""" +Another approach is to use a Tree for the dictionary (the symbols), and then +match brute force. The complexity will depend on the dictionary; +if all are suffixes of the other, it will be n*m +(where m is the size of the dictionary). For example, in Python: +""" + + +class TreeNode: + def __init__(self): + self.c = dict() + self.sym = None + + +def bracket(words, symbols): + root = TreeNode() + for s in symbols: + t = root + for char in s: + if char not in t.c: + t.c[char] = TreeNode() + t = t.c[char] + t.sym = s + result = dict() + for word in words: + i = 0 + symlist = list() + while i < len(word): + j, t = i, root + while j < len(word) and word[j] in t.c: + t = t.c[word[j]] + if t.sym is not None: + symlist.append((j + 1 - len(t.sym), j + 1, t.sym)) + j += 1 + i += 1 + if len(symlist) > 0: + sym = reduce(lambda x, y: x if x[1] - x[0] >= y[1] - y[0] else y, + symlist) + result[word] = "{}[{}]{}".format(word[:sym[0]], sym[2], + word[sym[1]:]) + return tuple(word if word not in result else result[word] for word in words) diff --git a/algorithms/strings/caesar_cipher.py b/algorithms/strings/caesar_cipher.py new file mode 100644 index 000000000..379f63e0d --- /dev/null +++ b/algorithms/strings/caesar_cipher.py @@ -0,0 +1,19 @@ + +""" +Julius Caesar protected his confidential information by encrypting it using a cipher. +Caesar's cipher shifts each letter by a number of letters. If the shift takes you +past the end of the alphabet, just rotate back to the front of the alphabet. +In the case of a rotation by 3, w, x, y and z would map to z, a, b and c. +Original alphabet: abcdefghijklmnopqrstuvwxyz +Alphabet rotated +3: defghijklmnopqrstuvwxyzabc +""" +def caesar_cipher(s, k): + result = "" + for char in s: + n = ord(char) + if 64 < n < 91: + n = ((n - 65 + k) % 26) + 65 + if 96 < n < 123: + n = ((n - 97 + k) % 26) + 97 + result = result + chr(n) + return result diff --git a/algorithms/strings/check_pangram.py b/algorithms/strings/check_pangram.py new file mode 100644 index 000000000..412425793 --- /dev/null +++ b/algorithms/strings/check_pangram.py @@ -0,0 +1,10 @@ +""" +Algorithm that checks if a given string is a pangram or not +""" + +def check_pangram(input_string): + alphabet = "abcdefghijklmnopqrstuvwxyz" + for ch in alphabet: + if ch not in input_string.lower(): + return False + return True \ No newline at end of file diff --git a/algorithms/strings/contain_string.py b/algorithms/strings/contain_string.py new file mode 100644 index 000000000..67056fed6 --- /dev/null +++ b/algorithms/strings/contain_string.py @@ -0,0 +1,25 @@ +""" +Implement strStr(). + +Return the index of the first occurrence of needle in haystack, or -1 if needle is not part of haystack. + +Example 1: +Input: haystack = "hello", needle = "ll" +Output: 2 + +Example 2: +Input: haystack = "aaaaa", needle = "bba" +Output: -1 +Reference: https://leetcode.com/problems/implement-strstr/description/ +""" +def contain_string(haystack, needle): + if len(needle) == 0: + return 0 + if len(needle) > len(haystack): + return -1 + for i in range(len(haystack)): + if len(haystack) - i < len(needle): + return -1 + if haystack[i:i+len(needle)] == needle: + return i + return -1 diff --git a/algorithms/strings/count_binary_substring.py b/algorithms/strings/count_binary_substring.py new file mode 100644 index 000000000..bd775ee53 --- /dev/null +++ b/algorithms/strings/count_binary_substring.py @@ -0,0 +1,33 @@ +""" +Give a string s, count the number of non-empty (contiguous) substrings that have + the same number of 0's and 1's, and all the 0's and all the 1's in these substrings are grouped consecutively. + +Substrings that occur multiple times are counted the number of times they occur. +Example 1: +Input: "00110011" +Output: 6 +Explanation: There are 6 substrings that have equal number of consecutive 1's and 0's: "0011", "01", "1100", "10", "0011", and "01". + +Notice that some of these substrings repeat and are counted the number of times they occur. + +Also, "00110011" is not a valid substring because all the 0's (and 1's) are not grouped together. + +Example 2: +Input: "10101" +Output: 4 +Explanation: There are 4 substrings: "10", "01", "10", "01" that have equal number of consecutive 1's and 0's. +Reference: https://leetcode.com/problems/count-binary-substrings/description/ +""" +def count_binary_substring(s): + cur = 1 + pre = 0 + count = 0 + for i in range(1, len(s)): + if s[i] != s[i - 1]: + count = count + min(pre, cur) + pre = cur + cur = 1 + else: + cur = cur + 1 + count = count + min(pre, cur) + return count diff --git a/string/decode_string.py b/algorithms/strings/decode_string.py similarity index 91% rename from string/decode_string.py rename to algorithms/strings/decode_string.py index d6a0a7aac..6a2350f6f 100644 --- a/string/decode_string.py +++ b/algorithms/strings/decode_string.py @@ -36,9 +36,3 @@ def decode_string(s): else: cur_string += c return cur_string - -a = "3[a]2[bc]" #"aaabcbc". -b = "3[a2[c]]" #"accaccacc". - -print(decode_string(a)) -print(decode_string(b)) diff --git a/algorithms/strings/delete_reoccurring.py b/algorithms/strings/delete_reoccurring.py new file mode 100644 index 000000000..131a953b9 --- /dev/null +++ b/algorithms/strings/delete_reoccurring.py @@ -0,0 +1,19 @@ +""" +QUESTION: Given a string as your input, delete any reoccurring +character, and return the new string. + +This is a Google warmup interview question that was asked duirng phone screening +at my university. +""" + +# time complexity O(n) +def delete_reoccurring_characters(string): + seen_characters = set() + output_string = '' + for char in string: + if char not in seen_characters: + seen_characters.add(char) + output_string += char + return output_string + + \ No newline at end of file diff --git a/algorithms/strings/domain_extractor.py b/algorithms/strings/domain_extractor.py new file mode 100644 index 000000000..1b9ff2b78 --- /dev/null +++ b/algorithms/strings/domain_extractor.py @@ -0,0 +1,29 @@ +""" +Write a function that when given a URL as a string, parses out just the domain name and returns it as a string. + +Examples: +domain_name("http://github.com/SaadBenn") == "github" +domain_name("http://www.zombie-bites.com") == "zombie-bites" +domain_name("https://www.cnet.com") == "cnet" + +Note: The idea is not to use any built-in libraries such as re (regular expression) or urlparse except .split() built-in function +""" + +# Non pythonic way +def domain_name_1(url): + #grab only the non http(s) part + full_domain_name = url.split('//')[-1] + #grab the actual one depending on the len of the list + actual_domain = full_domain_name.split('.') + + # case when www is in the url + if (len(actual_domain) > 2): + return actual_domain[1] + # case when www is not in the url + return actual_domain[0] + + +# pythonic one liner +def domain_name_2(url): + return url.split("//")[-1].split("www.")[-1].split(".")[0] + diff --git a/algorithms/strings/encode_decode.py b/algorithms/strings/encode_decode.py new file mode 100644 index 000000000..4fbdf8943 --- /dev/null +++ b/algorithms/strings/encode_decode.py @@ -0,0 +1,30 @@ +""" Design an algorithm to encode a list of strings to a string. + The encoded mystring is then sent over the network and is decoded + back to the original list of strings. +""" + +# Implement the encode and decode methods. + +def encode(strs): + """Encodes a list of strings to a single string. + :type strs: List[str] + :rtype: str + """ + res = '' + for string in strs.split(): + res += str(len(string)) + ":" + string + return res + +def decode(s): + """Decodes a single string to a list of strings. + :type s: str + :rtype: List[str] + """ + strs = [] + i = 0 + while i < len(s): + index = s.find(":", i) + size = int(s[i:index]) + strs.append(s[index+1: index+1+size]) + i = index+1+size + return strs \ No newline at end of file diff --git a/algorithms/strings/first_unique_char.py b/algorithms/strings/first_unique_char.py new file mode 100644 index 000000000..44ba05e49 --- /dev/null +++ b/algorithms/strings/first_unique_char.py @@ -0,0 +1,27 @@ +""" +Given a string, find the first non-repeating character in it and return it's +index. If it doesn't exist, return -1. + +For example: +s = "leetcode" +return 0. + +s = "loveleetcode", +return 2. + +Reference: https://leetcode.com/problems/first-unique-character-in-a-string/description/ +""" +def first_unique_char(s): + """ + :type s: str + :rtype: int + """ + if (len(s) == 1): + return 0 + ban = [] + for i in range(len(s)): + if all(s[i] != s[k] for k in range(i + 1, len(s))) == True and s[i] not in ban: + return i + else: + ban.append(s[i]) + return -1 diff --git a/algorithms/strings/fizzbuzz.py b/algorithms/strings/fizzbuzz.py new file mode 100644 index 000000000..c811afa25 --- /dev/null +++ b/algorithms/strings/fizzbuzz.py @@ -0,0 +1,55 @@ +""" +Write a function that returns an array containing the numbers from 1 to N, +where N is the parametered value. N will never be less than 1. + +Replace certain values however if any of the following conditions are met: + +If the value is a multiple of 3: use the value 'Fizz' instead +If the value is a multiple of 5: use the value 'Buzz' instead +If the value is a multiple of 3 & 5: use the value 'FizzBuzz' instead +""" + +""" +There is no fancy algorithm to solve fizz buzz. + +Iterate from 1 through n +Use the mod operator to determine if the current iteration is divisible by: +3 and 5 -> 'FizzBuzz' +3 -> 'Fizz' +5 -> 'Buzz' +else -> string of current iteration +return the results +Complexity: + +Time: O(n) +Space: O(n) +""" + +def fizzbuzz(n): + + # Validate the input + if n < 1: + raise ValueError('n cannot be less than one') + if n is None: + raise TypeError('n cannot be None') + + result = [] + + for i in range(1, n+1): + if i%3 == 0 and i%5 == 0: + result.append('FizzBuzz') + elif i%3 == 0: + result.append('Fizz') + elif i%5 == 0: + result.append('Buzz') + else: + result.append(i) + return result + +# Alternative solution +def fizzbuzz_with_helper_func(n): + return [fb(m) for m in range(1,n+1)] + +def fb(m): + r = (m % 3 == 0) * "Fizz" + (m % 5 == 0) * "Buzz" + return r if r != "" else m diff --git a/algorithms/strings/group_anagrams.py b/algorithms/strings/group_anagrams.py new file mode 100644 index 000000000..d3b9047c2 --- /dev/null +++ b/algorithms/strings/group_anagrams.py @@ -0,0 +1,28 @@ +""" +Given an array of strings, group anagrams together. + +For example, given: ["eat", "tea", "tan", "ate", "nat", "bat"], +Return: + +[ + ["ate", "eat","tea"], + ["nat","tan"], + ["bat"] +] +""" + + +def group_anagrams(strs): + d = {} + ans = [] + k = 0 + for str in strs: + sstr = ''.join(sorted(str)) + if sstr not in d: + d[sstr] = k + k += 1 + ans.append([]) + ans[-1].append(str) + else: + ans[d[sstr]].append(str) + return ans diff --git a/algorithms/strings/int_to_roman.py b/algorithms/strings/int_to_roman.py new file mode 100644 index 000000000..88866eae7 --- /dev/null +++ b/algorithms/strings/int_to_roman.py @@ -0,0 +1,15 @@ +""" +Given an integer, convert it to a roman numeral. +Input is guaranteed to be within the range from 1 to 3999. +""" + +def int_to_roman(num): + """ + :type num: int + :rtype: str + """ + m = ["", "M", "MM", "MMM"]; + c = ["", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"]; + x = ["", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"]; + i = ["", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"]; + return m[num//1000] + c[(num%1000)//100] + x[(num%100)//10] + i[num%10]; diff --git a/algorithms/strings/is_palindrome.py b/algorithms/strings/is_palindrome.py new file mode 100644 index 000000000..11a9e3063 --- /dev/null +++ b/algorithms/strings/is_palindrome.py @@ -0,0 +1,105 @@ +""" +Given a string, determine if it is a palindrome, +considering only alphanumeric characters and ignoring cases. +For example, +"A man, a plan, a canal: Panama" is a palindrome. +"race a car" is not a palindrome. +Note: +Have you consider that the string might be empty? +This is a good question to ask during an interview. +For the purpose of this problem, +we define empty string as valid palindrome. +""" +from string import ascii_letters +from collections import deque + + +def is_palindrome(s): + """ + :type s: str + :rtype: bool + """ + i = 0 + j = len(s)-1 + while i < j: + while not s[i].isalnum(): + i += 1 + while not s[j].isalnum(): + j -= 1 + if s[i].lower() != s[j].lower(): + return False + i, j = i+1, j-1 + return True + +""" +Here is a bunch of other variations of is_palindrome function. + +Variation 1: +Find the reverse of the string and compare it with the original string + +Variation 2: +Loop from the start to length/2 and check the first character and last character +and so on... for instance s[0] compared with s[n-1], s[1] == s[n-2]... + +Variation 3: +Using stack idea. + +Note: We are assuming that we are just checking a one word string. To check if a complete sentence +""" +def remove_punctuation(s): + """ + Remove punctuation, case sensitivity and spaces + """ + return "".join(i.lower() for i in s if i in ascii_letters) + +# Variation 1 +def string_reverse(s): + return s[::-1] + +def is_palindrome_reverse(s): + s = remove_punctuation(s) + + # can also get rid of the string_reverse function and just do this return s == s[::-1] in one line. + if (s == string_reverse(s)): + return True + return False + + +# Variation 2 +def is_palindrome_two_pointer(s): + s = remove_punctuation(s) + + for i in range(0, len(s)//2): + if (s[i] != s[len(s) - i - 1]): + return False + return True + + +# Variation 3 +def is_palindrome_stack(s): + stack = [] + s = remove_punctuation(s) + + for i in range(len(s)//2, len(s)): + stack.append(s[i]) + for i in range(0, len(s)//2): + if s[i] != stack.pop(): + return False + return True + +# Variation 4 (using deque) +def is_palindrome_deque(s): + s = remove_punctuation(s) + deq = deque() + for char in s: + deq.appendleft(char) + + equal = True + + while len(deq) > 1 and equal: + first = deq.pop() + last = deq.popleft() + if first != last : + equal = False + + return equal diff --git a/algorithms/strings/is_rotated.py b/algorithms/strings/is_rotated.py new file mode 100644 index 000000000..a827fb497 --- /dev/null +++ b/algorithms/strings/is_rotated.py @@ -0,0 +1,31 @@ +""" +Given two strings s1 and s2, determine if s2 is a rotated version of s1. +For example, +is_rotated("hello", "llohe") returns True +is_rotated("hello", "helol") returns False + +accepts two strings +returns bool +Reference: https://leetcode.com/problems/rotate-string/description/ +""" + +def is_rotated(s1, s2): + if len(s1) == len(s2): + return s2 in s1 + s1 + else: + return False + +""" +Another solution: brutal force +Complexity: O(N^2) +""" +def is_rotated_v1(s1, s2): + if len(s1) != len(s2): + return False + if len(s1) == 0: + return True + + for c in range(len(s1)): + if all(s1[(c + i) % len(s1)] == s2[i] for i in range(len(s1))): + return True + return False diff --git a/algorithms/strings/judge_circle.py b/algorithms/strings/judge_circle.py new file mode 100644 index 000000000..46468a1ad --- /dev/null +++ b/algorithms/strings/judge_circle.py @@ -0,0 +1,25 @@ +""" +Initially, there is a Robot at position (0, 0). Given a sequence of its moves, +judge if this robot makes a circle, which means it moves back to the original place. + +The move sequence is represented by a string. And each move is represent by a +character. The valid robot moves are R (Right), L (Left), U (Up) and D (down). +The output should be true or false representing whether the robot makes a circle. + +Example 1: +Input: "UD" +Output: true +Example 2: +Input: "LL" +Output: false +""" +def judge_circle(moves): + dict_moves = { + 'U' : 0, + 'D' : 0, + 'R' : 0, + 'L' : 0 + } + for char in moves: + dict_moves[char] = dict_moves[char] + 1 + return dict_moves['L'] == dict_moves['R'] and dict_moves['U'] == dict_moves['D'] diff --git a/algorithms/strings/knuth_morris_pratt.py b/algorithms/strings/knuth_morris_pratt.py new file mode 100644 index 000000000..e1953a218 --- /dev/null +++ b/algorithms/strings/knuth_morris_pratt.py @@ -0,0 +1,44 @@ +from typing import Sequence, List + +def knuth_morris_pratt(text : Sequence, pattern : Sequence) -> List[int]: + """ + Given two strings text and pattern, return the list of start indexes in text that matches with the pattern + using knuth_morris_pratt algorithm. + + Args: + text: Text to search + pattern: Pattern to search in the text + Returns: + List of indices of patterns found + + Example: + >>> knuth_morris_pratt('hello there hero!', 'he') + [0, 7, 12] + + If idx is in the list, text[idx : idx + M] matches with pattern. + Time complexity of the algorithm is O(N+M), with N and M the length of text and pattern, respectively. + """ + n = len(text) + m = len(pattern) + pi = [0 for i in range(m)] + i = 0 + j = 0 + # making pi table + for i in range(1, m): + while j and pattern[i] != pattern[j]: + j = pi[j - 1] + if pattern[i] == pattern[j]: + j += 1 + pi[i] = j + # finding pattern + j = 0 + ret = [] + for i in range(n): + while j and text[i] != pattern[j]: + j = pi[j - 1] + if text[i] == pattern[j]: + j += 1 + if j == m: + ret.append(i - m + 1) + j = pi[j - 1] + return ret diff --git a/algorithms/strings/license_number.py b/algorithms/strings/license_number.py new file mode 100644 index 000000000..6f6d9a42c --- /dev/null +++ b/algorithms/strings/license_number.py @@ -0,0 +1,11 @@ + +def license_number(key, k): + res, alnum = [], [] + for char in key: + if char != "-": + alnum.append(char) + for i, char in enumerate(reversed(alnum)): + res.append(char) + if (i+1) % k == 0 and i != len(alnum)-1: + res.append("-") + return "".join(res[::-1]) diff --git a/algorithms/strings/longest_common_prefix.py b/algorithms/strings/longest_common_prefix.py new file mode 100644 index 000000000..80facc934 --- /dev/null +++ b/algorithms/strings/longest_common_prefix.py @@ -0,0 +1,66 @@ +""" +Write a function to find the longest common prefix string amongst an array of strings. + +If there is no common prefix, return an empty string "". + +Example 1: +Input: ["flower","flow","flight"] +Output: "fl" + +Example 2: +Input: ["dog","racecar","car"] +Output: "" +Explanation: There is no common prefix among the input strings. + +Reference: https://leetcode.com/problems/longest-common-prefix/description/ +""" + +""" +First solution: Horizontal scanning +""" +def common_prefix(s1, s2): + "Return prefix common of 2 strings" + if not s1 or not s2: + return "" + k = 0 + while s1[k] == s2[k]: + k = k + 1 + if k >= len(s1) or k >= len(s2): + return s1[0:k] + return s1[0:k] + +def longest_common_prefix_v1(strs): + if not strs: + return "" + result = strs[0] + for i in range(len(strs)): + result = common_prefix(result, strs[i]) + return result + +""" +Second solution: Vertical scanning +""" +def longest_common_prefix_v2(strs): + if not strs: + return "" + for i in range(len(strs[0])): + for string in strs[1:]: + if i == len(string) or string[i] != strs[0][i]: + return strs[0][0:i] + return strs[0] + +""" +Third solution: Divide and Conquer +""" +def longest_common_prefix_v3(strs): + if not strs: + return "" + return longest_common(strs, 0, len(strs) -1) + +def longest_common(strs, left, right): + if left == right: + return strs[left] + mid = (left + right) // 2 + lcp_left = longest_common(strs, left, mid) + lcp_right = longest_common(strs, mid + 1, right) + return common_prefix(lcp_left, lcp_right) diff --git a/algorithms/strings/longest_palindromic_substring.py b/algorithms/strings/longest_palindromic_substring.py new file mode 100644 index 000000000..ad0c831b9 --- /dev/null +++ b/algorithms/strings/longest_palindromic_substring.py @@ -0,0 +1,44 @@ +''' +Given string s, find the longest palindromic substring. + +Example1: + +* input: "dasdasdasdasdasdadsa" +* output: "asdadsa" + +Example2: + +* input: "acdbbdaa" +* output: "dbbd" + +Manacher's algorithm + +''' + +def longest_palindrome(s): + if len(s) < 2: + return s + + n_str = '#' + '#'.join(s) + '#' + p = [0] * len(n_str) + mx, loc = 0, 0 + index, maxlen = 0, 0 + for i in range(len(n_str)): + if i < mx and 2 * loc - i < len(n_str): + p[i] = min(mx - i, p[2 * loc - i]) + else: + p[i] = 1 + + while p[i] + i < len(n_str) and i - p[i] >= 0 and n_str[ + i - p[i]] == n_str[i + p[i]]: + p[i] += 1 + + if i + p[i] > mx: + mx = i + p[i] + loc = i + + if p[i] > maxlen: + index = i + maxlen = p[i] + s = n_str[index - p[index] + 1:index + p[index]] + return s.replace('#', '') diff --git a/string/make_sentence.py b/algorithms/strings/make_sentence.py similarity index 57% rename from string/make_sentence.py rename to algorithms/strings/make_sentence.py index 0cc2263c3..2b7bcf79f 100644 --- a/string/make_sentence.py +++ b/algorithms/strings/make_sentence.py @@ -14,21 +14,14 @@ count = 0 -def make_sentence(str_piece, dictionarys): + +def make_sentence(str_piece, dictionaries): global count if len(str_piece) == 0: return True for i in range(0, len(str_piece)): prefix, suffix = str_piece[0:i], str_piece[i:] - if ((prefix in dictionarys and suffix in dictionarys) - or (prefix in dictionarys - and make_sentence(suffix, dictionarys))): - count += 1 + if prefix in dictionaries: + if suffix in dictionaries or make_sentence(suffix, dictionaries): + count += 1 return True - - -if __name__ == "__main__": - dictionarys = ["", "app", "let", "t", "apple", "applet"] - word = "applet" - make_sentence(word, dictionarys) - print count \ No newline at end of file diff --git a/algorithms/strings/merge_string_checker.py b/algorithms/strings/merge_string_checker.py new file mode 100644 index 000000000..004226e06 --- /dev/null +++ b/algorithms/strings/merge_string_checker.py @@ -0,0 +1,42 @@ +""" +At a job interview, you are challenged to write an algorithm to check if a +given string, s, can be formed from two other strings, part1 and part2. +The restriction is that the characters in part1 and part2 are in the same +order as in s. The interviewer gives you the following example and tells +you to figure out the rest from the given test cases. +'codewars' is a merge from 'cdw' and 'oears': +s: c o d e w a r s = codewars +part1: c d w = cdw +part2: o e a r s = oears +""" + + +# Recursive Solution +def is_merge_recursive(s, part1, part2): + if not part1: + return s == part2 + if not part2: + return s == part1 + if not s: + return part1 + part2 == '' + if s[0] == part1[0] and is_merge_recursive(s[1:], part1[1:], part2): + return True + if s[0] == part2[0] and is_merge_recursive(s[1:], part1, part2[1:]): + return True + return False + + +# An iterative approach +def is_merge_iterative(s, part1, part2): + tuple_list = [(s, part1, part2)] + while tuple_list: + string, p1, p2 = tuple_list.pop() + if string: + if p1 and string[0] == p1[0]: + tuple_list.append((string[1:], p1[1:], p2)) + if p2 and string[0] == p2[0]: + tuple_list.append((string[1:], p1, p2[1:])) + else: + if not p1 and not p2: + return True + return False diff --git a/algorithms/strings/min_distance.py b/algorithms/strings/min_distance.py new file mode 100644 index 000000000..b63f5db2a --- /dev/null +++ b/algorithms/strings/min_distance.py @@ -0,0 +1,62 @@ +""" +Given two words word1 and word2, find the minimum number of steps required to +make word1 and word2 the same, where in each step you can delete one character +in either string. + +For example: +Input: "sea", "eat" +Output: 2 +Explanation: You need one step to make "sea" to "ea" and another step to make "eat" to "ea". + +Reference: https://leetcode.com/problems/delete-operation-for-two-strings/description/ +""" + +def min_distance(word1, word2): + """ + Finds minimum distance by getting longest common subsequence + + :type word1: str + :type word2: str + :rtype: int + """ + return len(word1) + len(word2) - 2 * lcs(word1, word2, len(word1), len(word2)) + +def lcs(word1, word2, i, j): + """ + The length of longest common subsequence among the two given strings word1 and word2 + """ + if i == 0 or j == 0: + return 0 + if word1[i - 1] == word2[j - 1]: + return 1 + lcs(word1, word2, i - 1, j - 1) + return max(lcs(word1, word2, i - 1, j), lcs(word1, word2, i, j - 1)) + +def min_distance_dp(word1, word2): + """ + Finds minimum distance in a dynamic programming manner + TC: O(length1*length2), SC: O(length1*length2) + + :type word1: str + :type word2: str + :rtype: int + """ + length1, length2 = len(word1)+1, len(word2)+1 + res = [[0 for _ in range(length2)] for _ in range(length1)] + + if length1 == length2: + for i in range(1, length1): + res[i][0], res[0][i] = i, i + else: + for i in range(length1): + res[i][0] = i + for i in range(length2): + res[0][i] = i + + for i in range(1, length1): + for j in range(1, length2): + if word1[i-1] == word2[j-1]: + res[i][j] = res[i-1][j-1] + else: + res[i][j] = min(res[i-1][j], res[i][j-1]) + 1 + + return res[len(word1)][len(word2)] diff --git a/string/multiply_strings.py b/algorithms/strings/multiply_strings.py similarity index 93% rename from string/multiply_strings.py rename to algorithms/strings/multiply_strings.py index 0ddc3abf4..2cb0d2206 100644 --- a/string/multiply_strings.py +++ b/algorithms/strings/multiply_strings.py @@ -12,8 +12,7 @@ """ -def multiply(num1:"str", num2:"str")->"str": - carry = 1 +def multiply(num1: "str", num2: "str") -> "str": interm = [] zero = ord('0') i_pos = 1 diff --git a/string/one_edit_distance.py b/algorithms/strings/one_edit_distance.py similarity index 100% rename from string/one_edit_distance.py rename to algorithms/strings/one_edit_distance.py diff --git a/algorithms/strings/panagram.py b/algorithms/strings/panagram.py new file mode 100644 index 000000000..d34965356 --- /dev/null +++ b/algorithms/strings/panagram.py @@ -0,0 +1,36 @@ +""" +Given a string, check whether it is a panagram or not. + +A panagram is a sentence that uses every letter at least once. + +The most famous example is: "he quick brown fox jumps over the lazy dog. + +Note: +A panagram in one language isn't necessarily a panagram in another. This +module assumes the english language. Hence, the Finnish panagram +'Törkylempijävongahdus' won't pass for a panagram despite being considered +a perfect panagram in its language. However, the Swedish panagram +'Yxmördaren Julia Blomqvist på fäktning i Schweiz' will pass despite +including letters not used in the english alphabet. This is because the +Swedish alphabet only extends the Latin one. +""" + +from string import ascii_lowercase + +def panagram(string): + """ + Returns whether the input string is an English panagram or not. + + Parameters: + string (str): A sentence in the form of a string. + + Returns: + A boolean with the result. + """ + letters = set(ascii_lowercase) + for c in string: + try: + letters.remove(c.lower()) + except: + pass + return len(letters) == 0 \ No newline at end of file diff --git a/string/rabin_karp.py b/algorithms/strings/rabin_karp.py similarity index 87% rename from string/rabin_karp.py rename to algorithms/strings/rabin_karp.py index ca6a18aad..d900a7380 100644 --- a/string/rabin_karp.py +++ b/algorithms/strings/rabin_karp.py @@ -2,25 +2,25 @@ # Rabin Karp Algorithm class RollingHash: - def __init__(self, text, sizeWord): + def __init__(self, text, size_word): self.text = text self.hash = 0 - self.sizeWord = sizeWord + self.size_word = size_word - for i in range(0, sizeWord): + for i in range(0, size_word): #ord maps the character to a number #subtract out the ASCII value of "a" to start the indexing at zero - self.hash += (ord(self.text[i]) - ord("a")+1)*(26**(sizeWord - i -1)) + self.hash += (ord(self.text[i]) - ord("a")+1)*(26**(size_word - i -1)) #start index of current window self.window_start = 0 #end of index window - self.window_end = sizeWord + self.window_end = size_word def move_window(self): if self.window_end <= len(self.text) - 1: #remove left letter from hash value - self.hash -= (ord(self.text[self.window_start]) - ord("a")+1)*26**(self.sizeWord-1) + self.hash -= (ord(self.text[self.window_start]) - ord("a")+1)*26**(self.size_word-1) self.hash *= 26 self.hash += ord(self.text[self.window_end])- ord("a")+1 self.window_start += 1 diff --git a/algorithms/strings/repeat_string.py b/algorithms/strings/repeat_string.py new file mode 100644 index 000000000..cc871f64c --- /dev/null +++ b/algorithms/strings/repeat_string.py @@ -0,0 +1,24 @@ +""" +Given two strings A and B, find the minimum number of times A has to be repeated such that B is a substring of it. If no such solution, return -1. + +For example, with A = "abcd" and B = "cdabcdab". + +Return 3, because by repeating A three times (“abcdabcdabcd”), B is a substring of it; and B is not a substring of A repeated two times ("abcdabcd"). + +Note: +The length of A and B will be between 1 and 10000. + +Reference: https://leetcode.com/problems/repeated-string-match/description/ +""" +def repeat_string(A, B): + count = 1 + tmp = A + max_count = (len(B) / len(A)) + 1 + while not(B in tmp): + tmp = tmp + A + if (count > max_count): + count = -1 + break + count = count + 1 + + return count diff --git a/algorithms/strings/repeat_substring.py b/algorithms/strings/repeat_substring.py new file mode 100644 index 000000000..0f26c2819 --- /dev/null +++ b/algorithms/strings/repeat_substring.py @@ -0,0 +1,25 @@ +""" +Given a non-empty string check if it can be constructed by taking +a substring of it and appending multiple copies of the substring together. + +For example: +Input: "abab" +Output: True +Explanation: It's the substring "ab" twice. + +Input: "aba" +Output: False + +Input: "abcabcabcabc" +Output: True +Explanation: It's the substring "abc" four times. + +Reference: https://leetcode.com/problems/repeated-substring-pattern/description/ +""" +def repeat_substring(s): + """ + :type s: str + :rtype: bool + """ + str = (s + s)[1:-1] + return s in str diff --git a/string/reverse_string.py b/algorithms/strings/reverse_string.py similarity index 81% rename from string/reverse_string.py rename to algorithms/strings/reverse_string.py index dc695e2fe..f472135c7 100644 --- a/string/reverse_string.py +++ b/algorithms/strings/reverse_string.py @@ -4,9 +4,6 @@ def recursive(s): return s return recursive(s[l//2:]) + recursive(s[:l//2]) -s = "hello there" -print(recursive(s)) - def iterative(s): r = list(s) i, j = 0, len(s) - 1 @@ -16,13 +13,9 @@ def iterative(s): j -= 1 return "".join(r) -print(iterative(s)) - def pythonic(s): r = list(reversed(s)) return "".join(r) def ultra_pythonic(s): return s[::-1] - -print(ultra_pythonic(s)) diff --git a/string/reverse_vowel.py b/algorithms/strings/reverse_vowel.py similarity index 85% rename from string/reverse_vowel.py rename to algorithms/strings/reverse_vowel.py index 70111ff34..b9fc6305e 100644 --- a/string/reverse_vowel.py +++ b/algorithms/strings/reverse_vowel.py @@ -11,7 +11,3 @@ def reverse_vowel(s): s[i], s[j] = s[j], s[i] i, j = i + 1, j - 1 return "".join(s) - -test = "hello" -print(test) -print(reverse_vowel(test)) diff --git a/algorithms/strings/reverse_words.py b/algorithms/strings/reverse_words.py new file mode 100644 index 000000000..62467ce8a --- /dev/null +++ b/algorithms/strings/reverse_words.py @@ -0,0 +1,20 @@ + +def reverse(array, i, j): + while i < j: + array[i], array[j] = array[j], array[i] + i += 1 + j -= 1 + + +def reverse_words(string): + arr = string.strip().split() # arr is list of words + n = len(arr) + reverse(arr, 0, n-1) + + return " ".join(arr) + + +if __name__ == "__main__": + test = "I am keon kim and I like pizza" + print(test) + print(reverse_words(test)) diff --git a/string/roman_to_int.py b/algorithms/strings/roman_to_int.py similarity index 100% rename from string/roman_to_int.py rename to algorithms/strings/roman_to_int.py diff --git a/algorithms/strings/rotate.py b/algorithms/strings/rotate.py new file mode 100644 index 000000000..5bfcd1971 --- /dev/null +++ b/algorithms/strings/rotate.py @@ -0,0 +1,23 @@ +""" +Given a strings s and int k, return a string that rotates k times + +k can be any positive integer. + +For example, +rotate("hello", 2) return "llohe" +rotate("hello", 5) return "hello" +rotate("hello", 6) return "elloh" +rotate("hello", 7) return "llohe" +rotate("hello", 102) return "lohel" + +""" +def rotate(s, k): + long_string = s * (k // len(s) + 2) + if k <= len(s): + return long_string[k:k + len(s)] + else: + return long_string[k-len(s):k] + +def rotate_alt(string, k): + k = k % len(string) + return string[k:] + string[:k] diff --git a/algorithms/strings/strip_url_params.py b/algorithms/strings/strip_url_params.py new file mode 100644 index 000000000..364f78091 --- /dev/null +++ b/algorithms/strings/strip_url_params.py @@ -0,0 +1,95 @@ +""" +Write a function that does the following: +Removes any duplicate query string parameters from the url +Removes any query string parameters specified within the 2nd argument (optional array) + +An example: +www.saadbenn.com?a=1&b=2&a=2') // returns 'www.saadbenn.com?a=1&b=2' +""" +from collections import defaultdict +import urllib +import urllib.parse + +# Here is a very non-pythonic grotesque solution +def strip_url_params1(url, params_to_strip=None): + + if not params_to_strip: + params_to_strip = [] + if url: + result = '' # final result to be returned + tokens = url.split('?') + domain = tokens[0] + query_string = tokens[-1] + result += domain + # add the '?' to our result if it is in the url + if len(tokens) > 1: + result += '?' + if not query_string: + return url + else: + # logic for removing duplicate query strings + # build up the list by splitting the query_string using digits + key_value_string = [] + string = '' + for char in query_string: + if char.isdigit(): + key_value_string.append(string + char) + string = '' + else: + string += char + dict = defaultdict(int) + # logic for checking whether we should add the string to our result + for i in key_value_string: + _token = i.split('=') + if _token[0]: + length = len(_token[0]) + if length == 1: + if _token and (not(_token[0] in dict)): + if params_to_strip: + if _token[0] != params_to_strip[0]: + dict[_token[0]] = _token[1] + result = result + _token[0] + '=' + _token[1] + else: + if not _token[0] in dict: + dict[_token[0]] = _token[1] + result = result + _token[0] + '=' + _token[1] + else: + check = _token[0] + letter = check[1] + if _token and (not(letter in dict)): + if params_to_strip: + if letter != params_to_strip[0]: + dict[letter] = _token[1] + result = result + _token[0] + '=' + _token[1] + else: + if not letter in dict: + dict[letter] = _token[1] + result = result + _token[0] + '=' + _token[1] + return result + +# A very friendly pythonic solution (easy to follow) +def strip_url_params2(url, param_to_strip=[]): + if '?' not in url: + return url + + queries = (url.split('?')[1]).split('&') + queries_obj = [query[0] for query in queries] + for i in range(len(queries_obj) - 1, 0, -1): + if queries_obj[i] in param_to_strip or queries_obj[i] in queries_obj[0:i]: + queries.pop(i) + + return url.split('?')[0] + '?' + '&'.join(queries) + + +# Here is my friend's solution using python's builtin libraries +def strip_url_params3(url, strip=None): + if not strip: strip = [] + + parse = urllib.parse.urlparse(url) + query = urllib.parse.parse_qs(parse.query) + + query = {k: v[0] for k, v in query.items() if k not in strip} + query = urllib.parse.urlencode(query) + new = parse._replace(query=query) + + return new.geturl() \ No newline at end of file diff --git a/algorithms/strings/strong_password.py b/algorithms/strings/strong_password.py new file mode 100644 index 000000000..85acd0223 --- /dev/null +++ b/algorithms/strings/strong_password.py @@ -0,0 +1,43 @@ +""" +The signup page required her to input a name and a password. However, the password +must be strong. The website considers a password to be strong if it satisfies the following criteria: + +1) Its length is at least 6. +2) It contains at least one digit. +3) It contains at least one lowercase English character. +4) It contains at least one uppercase English character. +5) It contains at least one special character. The special characters are: !@#$%^&*()-+ +She typed a random string of length in the password field but wasn't sure if it was strong. +Given the string she typed, can you find the minimum number of characters she must add to make her password strong? + +Note: Here's the set of types of characters in a form you can paste in your solution: +numbers = "0123456789" +lower_case = "abcdefghijklmnopqrstuvwxyz" +upper_case = "ABCDEFGHIJKLMNOPQRSTUVWXYZ" +special_characters = "!@#$%^&*()-+" + +Input Format +The first line contains an integer denoting the length of the string. +The second line contains a string consisting of characters, the password +typed by Louise. Each character is either a lowercase/uppercase English alphabet, a digit, or a special character. + +Sample Input 1: strong_password(3,"Ab1") +Output: 3 (Because She can make the password strong by adding characters,for example, $hk, turning the password into Ab1$hk which is strong. +2 characters aren't enough since the length must be at least 6.) + +Sample Output 2: strong_password(11,"#Algorithms") +Output: 1 (Because the password isn't strong, but she can make it strong by adding a single digit.) + +""" +def strong_password(n, password): + count_error = 0 + # Return the minimum number of characters to make the password strong + if any(i.isdigit() for i in password) == False: + count_error = count_error + 1 + if any(i.islower() for i in password) == False: + count_error = count_error + 1 + if any(i.isupper() for i in password) == False: + count_error = count_error + 1 + if any(i in '!@#$%^&*()-+' for i in password) == False: + count_error = count_error + 1 + return max(count_error, 6 - n) diff --git a/algorithms/strings/text_justification.py b/algorithms/strings/text_justification.py new file mode 100644 index 000000000..a14a8ba39 --- /dev/null +++ b/algorithms/strings/text_justification.py @@ -0,0 +1,89 @@ +""" +Given an array of words and a width maxWidth, format the text such that each line +has exactly maxWidth characters and is fully (left and right) justified. + +You should pack your words in a greedy approach; that is, pack as many words as +you can in each line. Pad extra spaces ' ' when necessary so that each line has +exactly maxWidth characters. + +Extra spaces between words should be distributed as evenly as possible. If the +number of spaces on a line do not divide evenly between words, the empty slots +on the left will be assigned more spaces than the slots on the right. + +For the last line of text, it should be left justified and no extra space is +inserted between words. + +Note: +A word is defined as a character sequence consisting of non-space characters only. +Each word's length is guaranteed to be greater than 0 and not exceed maxWidth. +The input array words contains at least one word. + +Example: +Input: +words = ["What","must","be","acknowledgment","shall","be"] +maxWidth = 16 +Output: +[ + "What must be", + "acknowledgment ", + "shall be " +] +""" + + +def text_justification(words, max_width): + ''' + :type words: list + :type max_width: int + :rtype: list + ''' + ret = [] # return value + row_len = 0 # current length of strs in a row + row_words = [] # current words in a row + index = 0 # the index of current word in words + is_first_word = True # is current word the first in a row + while index < len(words): + while row_len <= max_width and index < len(words): + if len(words[index]) > max_width: + raise ValueError("there exists word whose length is larger than max_width") + tmp = row_len + row_words.append(words[index]) + tmp += len(words[index]) + if not is_first_word: + tmp += 1 # except for the first word, each word should have at least a ' ' before it. + if tmp > max_width: + row_words.pop() + break + row_len = tmp + index += 1 + is_first_word = False + # here we have already got a row of str , then we should supplement enough ' ' to make sure the length is max_width. + row = "" + # if the row is the last + if index == len(words): + for word in row_words: + row += (word + ' ') + row = row[:-1] + row += ' ' * (max_width - len(row)) + # not the last row and more than one word + elif len(row_words) != 1: + space_num = max_width - row_len + space_num_of_each_interval = space_num // (len(row_words) - 1) + space_num_rest = space_num - space_num_of_each_interval * (len(row_words) - 1) + for j in range(len(row_words)): + row += row_words[j] + if j != len(row_words) - 1: + row += ' ' * (1 + space_num_of_each_interval) + if space_num_rest > 0: + row += ' ' + space_num_rest -= 1 + # row with only one word + else: + row += row_words[0] + row += ' ' * (max_width - len(row)) + ret.append(row) + # after a row , reset those value + row_len = 0 + row_words = [] + is_first_word = True + return ret diff --git a/algorithms/strings/unique_morse.py b/algorithms/strings/unique_morse.py new file mode 100644 index 000000000..6d8618644 --- /dev/null +++ b/algorithms/strings/unique_morse.py @@ -0,0 +1,94 @@ +""" +International Morse Code defines a standard encoding where each letter is mapped to +a series of dots and dashes, as follows: "a" maps to ".-", "b" maps to "-...", "c" +maps to "-.-.", and so on. + +For convenience, the full table for the 26 letters of the English alphabet is given below: + 'a':".-", + 'b':"-...", + 'c':"-.-.", + 'd': "-..", + 'e':".", + 'f':"..-.", + 'g':"--.", + 'h':"....", + 'i':"..", + 'j':".---", + 'k':"-.-", + 'l':".-..", + 'm':"--", + 'n':"-.", + 'o':"---", + 'p':".--.", + 'q':"--.-", + 'r':".-.", + 's':"...", + 't':"-", + 'u':"..-", + 'v':"...-", + 'w':".--", + 'x':"-..-", + 'y':"-.--", + 'z':"--.." + +Now, given a list of words, each word can be written as a concatenation of the +Morse code of each letter. For example, "cab" can be written as "-.-.-....-", +(which is the concatenation "-.-." + "-..." + ".-"). We'll call such a +concatenation, the transformation of a word. + +Return the number of different transformations among all words we have. +Example: +Input: words = ["gin", "zen", "gig", "msg"] +Output: 2 +Explanation: +The transformation of each word is: +"gin" -> "--...-." +"zen" -> "--...-." +"gig" -> "--...--." +"msg" -> "--...--." + +There are 2 different transformations, "--...-." and "--...--.". +""" + +morse_code = { + 'a':".-", + 'b':"-...", + 'c':"-.-.", + 'd': "-..", + 'e':".", + 'f':"..-.", + 'g':"--.", + 'h':"....", + 'i':"..", + 'j':".---", + 'k':"-.-", + 'l':".-..", + 'm':"--", + 'n':"-.", + 'o':"---", + 'p':".--.", + 'q':"--.-", + 'r':".-.", + 's':"...", + 't':"-", + 'u':"..-", + 'v':"...-", + 'w':".--", + 'x':"-..-", + 'y':"-.--", + 'z':"--.." +} +def convert_morse_word(word): + morse_word = "" + word = word.lower() + for char in word: + morse_word = morse_word + morse_code[char] + return morse_word + +def unique_morse(words): + unique_morse_word = [] + for word in words: + morse_word = convert_morse_word(word) + if morse_word not in unique_morse_word: + unique_morse_word.append(morse_word) + return len(unique_morse_word) diff --git a/algorithms/strings/validate_coordinates.py b/algorithms/strings/validate_coordinates.py new file mode 100644 index 000000000..371214be0 --- /dev/null +++ b/algorithms/strings/validate_coordinates.py @@ -0,0 +1,49 @@ +"""" +Create a function that will validate if given parameters are valid geographical coordinates. +Valid coordinates look like the following: "23.32353342, -32.543534534". The return value should be either true or false. +Latitude (which is first float) can be between 0 and 90, positive or negative. Longitude (which is second float) can be between 0 and 180, positive or negative. +Coordinates can only contain digits, or one of the following symbols (including space after comma) -, . +There should be no space between the minus "-" sign and the digit after it. + +Here are some valid coordinates: +-23, 25 +43.91343345, 143 +4, -3 + +And some invalid ones: +23.234, - 23.4234 +N23.43345, E32.6457 +6.325624, 43.34345.345 +0, 1,2 + +""" +# I'll be adding my attempt as well as my friend's solution (took us ~ 1 hour) + +# my attempt +import re +def is_valid_coordinates_0(coordinates): + for char in coordinates: + if not (char.isdigit() or char in ['-', '.', ',', ' ']): + return False + l = coordinates.split(", ") + if len(l) != 2: + return False + try: + latitude = float(l[0]) + longitude = float(l[1]) + except: + return False + return -90 <= latitude <= 90 and -180 <= longitude <= 180 + +# friends solutions +def is_valid_coordinates_1(coordinates): + try: + lat, lng = [abs(float(c)) for c in coordinates.split(',') if 'e' not in c] + except ValueError: + return False + + return lat <= 90 and lng <= 180 + +# using regular expression +def is_valid_coordinates_regular_expression(coordinates): + return bool(re.match("-?(\d|[1-8]\d|90)\.?\d*, -?(\d|[1-9]\d|1[0-7]\d|180)\.?\d*$", coordinates)) diff --git a/string/word_squares.py b/algorithms/strings/word_squares.py similarity index 95% rename from string/word_squares.py rename to algorithms/strings/word_squares.py index 7d05bb982..6614d212d 100644 --- a/string/word_squares.py +++ b/algorithms/strings/word_squares.py @@ -65,6 +65,3 @@ def build(square): build([word]) return squares -dic =["area","lead","wall","lady","ball"] -print(word_squares(dic)) - diff --git a/algorithms/tree/__init__.py b/algorithms/tree/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/tree/avl/__init__.py b/algorithms/tree/avl/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/algorithms/tree/avl/avl.py b/algorithms/tree/avl/avl.py new file mode 100644 index 000000000..e3cbecb7f --- /dev/null +++ b/algorithms/tree/avl/avl.py @@ -0,0 +1,126 @@ +""" Imports TreeNodes""" +from tree.tree import TreeNode + + +class AvlTree(object): + """ + An avl tree. + """ + + def __init__(self): + # Root node of the tree. + self.node = None + self.height = -1 + self.balance = 0 + + def insert(self, key): + """ + Insert new key into node + """ + # Create new node + node = TreeNode(key) + if not self.node: + self.node = node + self.node.left = AvlTree() + self.node.right = AvlTree() + elif key < self.node.val: + self.node.left.insert(key) + elif key > self.node.val: + self.node.right.insert(key) + self.re_balance() + + def re_balance(self): + """ + Re balance tree. After inserting or deleting a node, + """ + self.update_heights(recursive=False) + self.update_balances(False) + + while self.balance < -1 or self.balance > 1: + if self.balance > 1: + if self.node.left.balance < 0: + self.node.left.rotate_left() + self.update_heights() + self.update_balances() + self.rotate_right() + self.update_heights() + self.update_balances() + + if self.balance < -1: + if self.node.right.balance > 0: + self.node.right.rotate_right() + self.update_heights() + self.update_balances() + self.rotate_left() + self.update_heights() + self.update_balances() + + def update_heights(self, recursive=True): + """ + Update tree height + """ + if self.node: + if recursive: + if self.node.left: + self.node.left.update_heights() + if self.node.right: + self.node.right.update_heights() + + self.height = 1 + max(self.node.left.height, + self.node.right.height) + else: + self.height = -1 + + def update_balances(self, recursive=True): + """ + Calculate tree balance factor + + """ + if self.node: + if recursive: + if self.node.left: + self.node.left.update_balances() + if self.node.right: + self.node.right.update_balances() + + self.balance = self.node.left.height - self.node.right.height + else: + self.balance = 0 + + def rotate_right(self): + """ + Right rotation + """ + new_root = self.node.left.node + new_left_sub = new_root.right.node + old_root = self.node + + self.node = new_root + old_root.left.node = new_left_sub + new_root.right.node = old_root + + def rotate_left(self): + """ + Left rotation + """ + new_root = self.node.right.node + new_left_sub = new_root.left.node + old_root = self.node + + self.node = new_root + old_root.right.node = new_left_sub + new_root.left.node = old_root + + def in_order_traverse(self): + """ + In-order traversal of the tree + """ + result = [] + + if not self.node: + return result + + result.extend(self.node.left.in_order_traverse()) + result.append(self.node.key) + result.extend(self.node.right.in_order_traverse()) + return result diff --git a/algorithms/tree/b_tree.py b/algorithms/tree/b_tree.py new file mode 100644 index 000000000..1e68b432f --- /dev/null +++ b/algorithms/tree/b_tree.py @@ -0,0 +1,251 @@ +""" +B-tree is used to disk operations. Each node (except root) contains +at least t-1 keys (t children) and at most 2*t - 1 keys (2*t children) +where t is the degree of b-tree. It is not a kind of typical bst tree, because +this tree grows up. +B-tree is balanced which means that the difference between height of left +subtree and right subtree is at most 1. + +Complexity + n - number of elements + t - degree of tree + Tree always has height at most logt (n+1)/2 + Algorithm Average Worst case + Space O(n) O(n) + Search O(log n) O(log n) + Insert O(log n) O(log n) + Delete O(log n) O(log n) +""" + + +class Node: + """ Class of Node""" + + def __init__(self): + # self.is_leaf = is_leaf + self.keys = [] + self.children = [] + + def __repr__(self): + return "".format(self.keys) + + @property + def is_leaf(self): + """ Return if it is a leaf""" + return len(self.children) == 0 + + +class BTree: + """ Class of BTree """ + + def __init__(self, t_val=2): + self.min_numbers_of_keys = t_val - 1 + self.max_number_of_keys = 2 * t_val - 1 + + self.root = Node() + + def _split_child(self, parent: Node, child_index: int): + new_right_child = Node() + half_max = self.max_number_of_keys // 2 + child = parent.children[child_index] + middle_key = child.keys[half_max] + new_right_child.keys = child.keys[half_max + 1:] + child.keys = child.keys[:half_max] + # child is left child of parent after splitting + + if not child.is_leaf: + new_right_child.children = child.children[half_max + 1:] + child.children = child.children[:half_max + 1] + + parent.keys.insert(child_index, middle_key) + parent.children.insert(child_index + 1, new_right_child) + + def insert_key(self, key): + """ overflow, tree increases in height """ + if len(self.root.keys) >= self.max_number_of_keys: + new_root = Node() + new_root.children.append(self.root) + self.root = new_root + self._split_child(new_root, 0) + self._insert_to_nonfull_node(self.root, key) + else: + self._insert_to_nonfull_node(self.root, key) + + def _insert_to_nonfull_node(self, node: Node, key): + i = len(node.keys) - 1 + while i >= 0 and node.keys[i] >= key: # find position where insert key + i -= 1 + + if node.is_leaf: + node.keys.insert(i + 1, key) + else: + # overflow + if len(node.children[i + 1].keys) >= self.max_number_of_keys: + self._split_child(node, i + 1) + # decide which child is going to have a new key + if node.keys[i + 1] < key: + i += 1 + + self._insert_to_nonfull_node(node.children[i + 1], key) + + def find(self, key) -> bool: + """ Finds key """ + current_node = self.root + while True: + i = len(current_node.keys) - 1 + while i >= 0 and current_node.keys[i] > key: + i -= 1 + if i >= 0 and current_node.keys[i] == key: + return True + if current_node.is_leaf: + return False + current_node = current_node.children[i + 1] + + def remove_key(self, key): + self._remove_key(self.root, key) + + def _remove_key(self, node: Node, key) -> bool: + try: + key_index = node.keys.index(key) + if node.is_leaf: + node.keys.remove(key) + else: + self._remove_from_nonleaf_node(node, key_index) + return True + + except ValueError: # key not found in node + if node.is_leaf: + print("Key not found.") + return False # key not found + else: + i = 0 + number_of_keys = len(node.keys) + # decide in which subtree may be key + while i < number_of_keys and key > node.keys[i]: + i += 1 + + action_performed = self._repair_tree(node, i) + if action_performed: + return self._remove_key(node, key) + else: + return self._remove_key(node.children[i], key) + + def _repair_tree(self, node: Node, child_index: int) -> bool: + child = node.children[child_index] + # The leaf/node is correct + if self.min_numbers_of_keys < len(child.keys) <= self.max_number_of_keys: + return False + + if child_index > 0 and len(node.children[child_index - 1].keys) > self.min_numbers_of_keys: + self._rotate_right(node, child_index) + return True + + if (child_index < len(node.children) - 1 + and len(node.children[child_index + 1].keys) > self.min_numbers_of_keys): # 0 <-- 1 + self._rotate_left(node, child_index) + return True + + if child_index > 0: + # merge child with brother on the left + self._merge(node, child_index - 1, child_index) + else: + # merge child with brother on the right + self._merge(node, child_index, child_index + 1) + + return True + + def _rotate_left(self, parent_node: Node, child_index: int): + """ + Take key from right brother of the child and transfer to the child + """ + new_child_key = parent_node.keys[child_index] + new_parent_key = parent_node.children[child_index + 1].keys.pop(0) + parent_node.children[child_index].keys.append(new_child_key) + parent_node.keys[child_index] = new_parent_key + + if not parent_node.children[child_index + 1].is_leaf: + ownerless_child = parent_node.children[child_index + + 1].children.pop(0) + # make ownerless_child as a new biggest child (with highest key) + # -> transfer from right subtree to left subtree + parent_node.children[child_index].children.append(ownerless_child) + + def _rotate_right(self, parent_node: Node, child_index: int): + """ + Take key from left brother of the child and transfer to the child + """ + parent_key = parent_node.keys[child_index - 1] + new_parent_key = parent_node.children[child_index - 1].keys.pop() + parent_node.children[child_index].keys.insert(0, parent_key) + parent_node.keys[child_index - 1] = new_parent_key + + if not parent_node.children[child_index - 1].is_leaf: + ownerless_child = parent_node.children[child_index + - 1].children.pop() + # make ownerless_child as a new lowest child (with lowest key) + # -> transfer from left subtree to right subtree + parent_node.children[child_index].children.insert( + 0, ownerless_child) + + def _merge(self, parent_node: Node, to_merge_index: int, transfered_child_index: int): + from_merge_node = parent_node.children.pop(transfered_child_index) + parent_key_to_merge = parent_node.keys.pop(to_merge_index) + to_merge_node = parent_node.children[to_merge_index] + to_merge_node.keys.append(parent_key_to_merge) + to_merge_node.keys.extend(from_merge_node.keys) + + if not to_merge_node.is_leaf: + to_merge_node.children.extend(from_merge_node.children) + + if parent_node == self.root and not parent_node.keys: + self.root = to_merge_node + + def _remove_from_nonleaf_node(self, node: Node, key_index: int): + key = node.keys[key_index] + left_subtree = node.children[key_index] + if len(left_subtree.keys) > self.min_numbers_of_keys: + largest_key = self._find_largest_and_delete_in_left_subtree( + left_subtree) + elif len(node.children[key_index + 1].keys) > self.min_numbers_of_keys: + largest_key = self._find_largest_and_delete_in_right_subtree( + node.children[key_index + 1]) + else: + self._merge(node, key_index, key_index + 1) + return self._remove_key(node, key) + + node.keys[key_index] = largest_key + + def _find_largest_and_delete_in_left_subtree(self, node: Node): + if node.is_leaf: + return node.keys.pop() + else: + ch_index = len(node.children) - 1 + self._repair_tree(node, ch_index) + largest_key_in_subtree = self._find_largest_and_delete_in_left_subtree( + node.children[len(node.children) - 1]) + # self._repair_tree(node, ch_index) + return largest_key_in_subtree + + def _find_largest_and_delete_in_right_subtree(self, node: Node): + if node.is_leaf: + return node.keys.pop(0) + else: + ch_index = 0 + self._repair_tree(node, ch_index) + largest_key_in_subtree = self._find_largest_and_delete_in_right_subtree( + node.children[0]) + # self._repair_tree(node, ch_index) + return largest_key_in_subtree + + def traverse_tree(self): + self._traverse_tree(self.root) + print() + + def _traverse_tree(self, node: Node): + if node.is_leaf: + print(node.keys, end=" ") + else: + for i, key in enumerate(node.keys): + self._traverse_tree(node.children[i]) + print(key, end=" ") + self._traverse_tree(node.children[-1]) diff --git a/tree/bintree2list.py b/algorithms/tree/bin_tree_to_list.py similarity index 51% rename from tree/bintree2list.py rename to algorithms/tree/bin_tree_to_list.py index 091295444..566ef7568 100644 --- a/tree/bintree2list.py +++ b/algorithms/tree/bin_tree_to_list.py @@ -1,49 +1,37 @@ -class Node(): - def __init__(self, val = 0): - self.val = val - self.left = None - self.right = None +from tree.tree import TreeNode -def bintree2list(root): + +def bin_tree_to_list(root): """ type root: root class """ if not root: return root - root = bintree2list_util(root) + root = bin_tree_to_list_util(root) while root.left: root = root.left return root -def bintree2list_util(root): + +def bin_tree_to_list_util(root): if not root: return root if root.left: - left = bintree2list_util(root.left) + left = bin_tree_to_list_util(root.left) while left.right: left = left.right left.right = root root.left = left if root.right: - right = bintree2list_util(root.right) + right = bin_tree_to_list_util(root.right) while right.left: right = right.left right.left = root root.right = right return root + def print_tree(root): while root: print(root.val) root = root.right - -tree = Node(10) -tree.left = Node(12) -tree.right = Node(15) -tree.left.left = Node(25) -tree.left.left.right = Node(100) -tree.left.right = Node(30) -tree.right.left = Node(36) - -head = bintree2list(tree) -print_tree(head) diff --git a/algorithms/tree/binary_tree_paths.py b/algorithms/tree/binary_tree_paths.py new file mode 100644 index 000000000..218064b97 --- /dev/null +++ b/algorithms/tree/binary_tree_paths.py @@ -0,0 +1,15 @@ +def binary_tree_paths(root): + res = [] + if root is None: + return res + dfs(res, root, str(root.val)) + return res + + +def dfs(res, root, cur): + if root.left is None and root.right is None: + res.append(cur) + if root.left: + dfs(res, root.left, cur+'->'+str(root.left.val)) + if root.right: + dfs(res, root.right, cur+'->'+str(root.right.val)) diff --git a/tree/bst/BSTIterator.py b/algorithms/tree/bst/BSTIterator.py similarity index 93% rename from tree/bst/BSTIterator.py rename to algorithms/tree/bst/BSTIterator.py index a19aecd8a..af8a68d77 100644 --- a/tree/bst/BSTIterator.py +++ b/algorithms/tree/bst/BSTIterator.py @@ -10,7 +10,7 @@ def has_next(self): return bool(self.stack) def next(self): - node = stack.pop() + node = self.stack.pop() tmp = node if tmp.right: tmp = tmp.right diff --git a/algorithms/tree/bst/array_to_bst.py b/algorithms/tree/bst/array_to_bst.py new file mode 100644 index 000000000..7ca5cf943 --- /dev/null +++ b/algorithms/tree/bst/array_to_bst.py @@ -0,0 +1,21 @@ +""" +Given an array where elements are sorted in ascending order, +convert it to a height balanced BST. +""" + + +class TreeNode(object): + def __init__(self, x): + self.val = x + self.left = None + self.right = None + + +def array_to_bst(nums): + if not nums: + return None + mid = len(nums)//2 + node = TreeNode(nums[mid]) + node.left = array_to_bst(nums[:mid]) + node.right = array_to_bst(nums[mid+1:]) + return node diff --git a/algorithms/tree/bst/bst.py b/algorithms/tree/bst/bst.py new file mode 100644 index 000000000..de1bddd8c --- /dev/null +++ b/algorithms/tree/bst/bst.py @@ -0,0 +1,139 @@ +""" +Implement Binary Search Tree. It has method: + 1. Insert + 2. Search + 3. Size + 4. Traversal (Preorder, Inorder, Postorder) +""" + +import unittest + +class Node(object): + def __init__(self, data): + self.data = data + self.left = None + self.right = None + +class BST(object): + def __init__(self): + self.root = None + + def get_root(self): + return self.root + + """ + Get the number of elements + Using recursion. Complexity O(logN) + """ + def size(self): + return self.recur_size(self.root) + + def recur_size(self, root): + if root is None: + return 0 + else: + return 1 + self.recur_size(root.left) + self.recur_size(root.right) + + """ + Search data in bst + Using recursion. Complexity O(logN) + """ + def search(self, data): + return self.recur_search(self.root, data) + + def recur_search(self, root, data): + if root is None: + return False + if root.data == data: + return True + elif data > root.data: # Go to right root + return self.recur_search(root.right, data) + else: # Go to left root + return self.recur_search(root.left, data) + + """ + Insert data in bst + Using recursion. Complexity O(logN) + """ + def insert(self, data): + if self.root: + return self.recur_insert(self.root, data) + else: + self.root = Node(data) + return True + + def recur_insert(self, root, data): + if root.data == data: # The data is already there + return False + elif data < root.data: # Go to left root + if root.left: # If left root is a node + return self.recur_insert(root.left, data) + else: # left root is a None + root.left = Node(data) + return True + else: # Go to right root + if root.right: # If right root is a node + return self.recur_insert(root.right, data) + else: + root.right = Node(data) + return True + + """ + Preorder, Postorder, Inorder traversal bst + """ + def preorder(self, root): + if root: + print(str(root.data), end = ' ') + self.preorder(root.left) + self.preorder(root.right) + + def inorder(self, root): + if root: + self.inorder(root.left) + print(str(root.data), end = ' ') + self.inorder(root.right) + + def postorder(self, root): + if root: + self.postorder(root.left) + self.postorder(root.right) + print(str(root.data), end = ' ') + +""" + The tree is created for testing: + + 10 + / \ + 6 15 + / \ / \ + 4 9 12 24 + / / \ + 7 20 30 + / + 18 +""" + +class TestSuite(unittest.TestCase): + def setUp(self): + self.tree = BST() + self.tree.insert(10) + self.tree.insert(15) + self.tree.insert(6) + self.tree.insert(4) + self.tree.insert(9) + self.tree.insert(12) + self.tree.insert(24) + self.tree.insert(7) + self.tree.insert(20) + self.tree.insert(30) + self.tree.insert(18) + + def test_search(self): + self.assertTrue(self.tree.search(24)) + self.assertFalse(self.tree.search(50)) + + def test_size(self): + self.assertEqual(11, self.tree.size()) + +if __name__ == '__main__': + unittest.main() diff --git a/tree/bst/bst_closest_value.py b/algorithms/tree/bst/bst_closest_value.py similarity index 100% rename from tree/bst/bst_closest_value.py rename to algorithms/tree/bst/bst_closest_value.py diff --git a/algorithms/tree/bst/count_left_node.py b/algorithms/tree/bst/count_left_node.py new file mode 100644 index 000000000..aa4155566 --- /dev/null +++ b/algorithms/tree/bst/count_left_node.py @@ -0,0 +1,61 @@ +""" +Write a function count_left_node returns the number of left children in the +tree. For example: the following tree has four left children (the nodes +storing the values 6, 3, 7, and 10): + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + count_left_node = 4 + +""" +import unittest +from bst import Node +from bst import bst + +def count_left_node(root): + if root is None: + return 0 + elif root.left is None: + return count_left_node(root.right) + else: + return 1 + count_left_node(root.left) + count_left_node(root.right) + +""" + The tree is created for testing: + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + count_left_node = 4 + +""" + +class TestSuite(unittest.TestCase): + def setUp(self): + self.tree = bst() + self.tree.insert(9) + self.tree.insert(6) + self.tree.insert(12) + self.tree.insert(3) + self.tree.insert(8) + self.tree.insert(10) + self.tree.insert(15) + self.tree.insert(7) + self.tree.insert(18) + + def test_count_left_node(self): + self.assertEqual(4, count_left_node(self.tree.root)) + +if __name__ == '__main__': + unittest.main() diff --git a/tree/bst/delete_node.py b/algorithms/tree/bst/delete_node.py similarity index 97% rename from tree/bst/delete_node.py rename to algorithms/tree/bst/delete_node.py index 7ee827daa..f86ecbc3d 100644 --- a/tree/bst/delete_node.py +++ b/algorithms/tree/bst/delete_node.py @@ -38,7 +38,7 @@ """ class Solution(object): - def deleteNode(self, root, key): + def delete_node(self, root, key): """ :type root: TreeNode :type key: int diff --git a/algorithms/tree/bst/depth_sum.py b/algorithms/tree/bst/depth_sum.py new file mode 100644 index 000000000..9674e65dd --- /dev/null +++ b/algorithms/tree/bst/depth_sum.py @@ -0,0 +1,66 @@ +""" +Write a function depthSum returns the sum of the values stored +in a binary search tree of integers weighted by the depth of each value. + +For example: + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + depth_sum = 1*9 + 2*(6+12) + 3*(3+8+10+15) + 4*(7+18) + +""" +import unittest +from bst import Node +from bst import bst + +def depth_sum(root, n): + if root: + return recur_depth_sum(root, 1) + +def recur_depth_sum(root, n): + if root is None: + return 0 + elif root.left is None and root.right is None: + return root.data * n + else: + return n * root.data + recur_depth_sum(root.left, n+1) + recur_depth_sum(root.right, n+1) + +""" + The tree is created for testing: + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + depth_sum = 1*9 + 2*(6+12) + 3*(3+8+10+15) + 4*(7+18) + +""" + +class TestSuite(unittest.TestCase): + def setUp(self): + self.tree = bst() + self.tree.insert(9) + self.tree.insert(6) + self.tree.insert(12) + self.tree.insert(3) + self.tree.insert(8) + self.tree.insert(10) + self.tree.insert(15) + self.tree.insert(7) + self.tree.insert(18) + + def test_depth_sum(self): + self.assertEqual(253, depth_sum(self.tree.root, 4)) + +if __name__ == '__main__': + unittest.main() diff --git a/algorithms/tree/bst/height.py b/algorithms/tree/bst/height.py new file mode 100644 index 000000000..c84b0c013 --- /dev/null +++ b/algorithms/tree/bst/height.py @@ -0,0 +1,60 @@ +""" +Write a function height returns the height of a tree. The height is defined to +be the number of levels. The empty tree has height 0, a tree of one node has +height 1, a root node with one or two leaves as children has height 2, and so on +For example: height of tree is 4 + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + height = 4 + +""" +import unittest +from bst import Node +from bst import bst + +def height(root): + if root is None: + return 0 + else: + return 1 + max(height(root.left), height(root.right)) + +""" + The tree is created for testing: + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + count_left_node = 4 + +""" + +class TestSuite(unittest.TestCase): + def setUp(self): + self.tree = bst() + self.tree.insert(9) + self.tree.insert(6) + self.tree.insert(12) + self.tree.insert(3) + self.tree.insert(8) + self.tree.insert(10) + self.tree.insert(15) + self.tree.insert(7) + self.tree.insert(18) + + def test_height(self): + self.assertEqual(4, height(self.tree.root)) + +if __name__ == '__main__': + unittest.main() diff --git a/tree/bst/is_bst.py b/algorithms/tree/bst/is_bst.py similarity index 90% rename from tree/bst/is_bst.py rename to algorithms/tree/bst/is_bst.py index 74ef0a579..ad3adc601 100644 --- a/tree/bst/is_bst.py +++ b/algorithms/tree/bst/is_bst.py @@ -20,17 +20,16 @@ Binary tree [1,2,3], return false. """ - -def is_BST(root): +def is_bst(root): """ :type root: TreeNode :rtype: bool """ - if not root: - return True + stack = [] pre = None - while root and stack: + + while root or stack: while root: stack.append(root) root = root.left @@ -39,4 +38,5 @@ def is_BST(root): return False pre = root root = root.right + return True diff --git a/tree/bst/kth_smallest.py b/algorithms/tree/bst/kth_smallest.py similarity index 93% rename from tree/bst/kth_smallest.py rename to algorithms/tree/bst/kth_smallest.py index c2e511a60..4996791f2 100644 --- a/tree/bst/kth_smallest.py +++ b/algorithms/tree/bst/kth_smallest.py @@ -21,7 +21,7 @@ def kth_smallest(root, k): class Solution(object): - def kthSmallest(self, root, k): + def kth_smallest(self, root, k): """ :type root: TreeNode :type k: int @@ -51,4 +51,4 @@ def helper(self, node, count): n2.left, n2.right = n4, n5 n3.left, n3.right = n6, n7 print(kth_smallest(n1, 2)) - print(Solution().kthSmallest(n1, 2)) + print(Solution().kth_smallest(n1, 2)) diff --git a/tree/bst/lowest_common_ancestor.py b/algorithms/tree/bst/lowest_common_ancestor.py similarity index 100% rename from tree/bst/lowest_common_ancestor.py rename to algorithms/tree/bst/lowest_common_ancestor.py diff --git a/algorithms/tree/bst/num_empty.py b/algorithms/tree/bst/num_empty.py new file mode 100644 index 000000000..36600e905 --- /dev/null +++ b/algorithms/tree/bst/num_empty.py @@ -0,0 +1,67 @@ +""" +Write a function num_empty returns returns the number of empty branches in a +tree. Function should count the total number of empty branches among the nodes +of the tree. A leaf node has two empty branches. In the case, if root is None, +it considered as a 1 empty branch +For example: the following tree has 10 empty branch (* is empty branch) + + 9 __ + / \___ + 6 12 + / \ / \ + 3 8 10 15 + / \ / \ / \ / \ + * * 7 * * * * 18 + / \ / \ + * * * * + + empty_branch = 10 + +""" +import unittest +from bst import Node +from bst import bst + +def num_empty(root): + if root is None: + return 1 + elif root.left is None and root.right: + return 1 + num_empty(root.right) + elif root.right is None and root.left: + return 1 + num_empty(root.left) + else: + return num_empty(root.left) + num_empty(root.right) + +""" + The tree is created for testing: + + 9 + / \ + 6 12 + / \ / \ + 3 8 10 15 + / \ + 7 18 + + num_empty = 10 + +""" + +class TestSuite(unittest.TestCase): + def setUp(self): + self.tree = bst() + self.tree.insert(9) + self.tree.insert(6) + self.tree.insert(12) + self.tree.insert(3) + self.tree.insert(8) + self.tree.insert(10) + self.tree.insert(15) + self.tree.insert(7) + self.tree.insert(18) + + def test_num_empty(self): + self.assertEqual(10, num_empty(self.tree.root)) + +if __name__ == '__main__': + unittest.main() diff --git a/tree/bst/predecessor.py b/algorithms/tree/bst/predecessor.py similarity index 100% rename from tree/bst/predecessor.py rename to algorithms/tree/bst/predecessor.py diff --git a/tree/bst/serialize_deserialize.py b/algorithms/tree/bst/serialize_deserialize.py similarity index 82% rename from tree/bst/serialize_deserialize.py rename to algorithms/tree/bst/serialize_deserialize.py index 602e2222d..20f911220 100644 --- a/tree/bst/serialize_deserialize.py +++ b/algorithms/tree/bst/serialize_deserialize.py @@ -1,5 +1,12 @@ +class TreeNode(object): + def __init__(self, x): + self.val = x + self.left = None + self.right = None + + def serialize(root): def build_string(node): if node: diff --git a/tree/bst/successor.py b/algorithms/tree/bst/successor.py similarity index 100% rename from tree/bst/successor.py rename to algorithms/tree/bst/successor.py diff --git a/tree/bst/unique_bst.py b/algorithms/tree/bst/unique_bst.py similarity index 100% rename from tree/bst/unique_bst.py rename to algorithms/tree/bst/unique_bst.py diff --git a/algorithms/tree/construct_tree_postorder_preorder.py b/algorithms/tree/construct_tree_postorder_preorder.py new file mode 100644 index 000000000..a1bc1688a --- /dev/null +++ b/algorithms/tree/construct_tree_postorder_preorder.py @@ -0,0 +1,111 @@ +""" + Given two arrays representing preorder and postorder traversal of a full + binary tree, construct the binary tree and print the inorder traversal of the + tree. + A full binary tree has either 0 or 2 children. + Algorithm: + 1. Assign the first element of preorder array as root of the tree. + 2. Find the same element in the postorder array and divide the postorder + array into left and right subtree. + 3. Repeat the above steps for all the elements and construct the tree. + Eg: pre[] = {1, 2, 4, 8, 9, 5, 3, 6, 7} + post[] = {8, 9, 4, 5, 2, 6, 7, 3, 1} + Tree: + 1 + / \ + 2 3 + / \ / \ + 4 5 6 7 + / \ + 8 9 + Output: 8 4 9 2 5 1 6 3 7 +""" + +class TreeNode: + + def __init__(self, val, left = None, right = None): + self.val = val + self.left = left + self.right = right + +pre_index = 0 + +def construct_tree_util(pre: list, post: list, low: int, high: int, size: int): + """ + Recursive function that constructs tree from preorder and postorder array. + + preIndex is a global variable that keeps track of the index in preorder + array. + preorder and postorder array are represented are pre[] and post[] respectively. + low and high are the indices for the postorder array. + """ + + global pre_index + + if pre_index == -1: + pre_index = 0 + + + #Base case + if(pre_index >= size or low > high): + return None + + root = TreeNode(pre[pre_index]) + pre_index += 1 + + #If only one element in the subarray return root + if(low == high or pre_index >= size): + return root + + #Find the next element of pre[] in post[] + i = low + while i <= high: + if(pre[pre_index] == post[i]): + break + + i += 1 + + #Use index of element present in postorder to divide postorder array + #to two parts: left subtree and right subtree + if(i <= high): + root.left = construct_tree_util(pre, post, low, i, size) + root.right = construct_tree_util(pre, post, i+1, high, size) + + return root + + +def construct_tree(pre: list, post: list, size: int): + """ + Main Function that will construct the full binary tree from given preorder + and postorder array. + """ + + global pre_index + root = construct_tree_util(pre, post, 0, size-1, size) + + return print_inorder(root) + + + +def print_inorder(root: TreeNode, result = None): + """ + Prints the tree constructed in inorder format + """ + if root is None: + return [] + if result is None: + result = [] + + print_inorder(root.left, result) + result.append(root.val) + print_inorder(root.right, result) + return result + +if __name__ == '__main__': + pre = [1, 2, 4, 5, 3, 6, 7] + post = [4, 5, 2, 6, 7, 3, 1] + size = len(pre) + + result = construct_tree(pre, post, size) + + print(result) diff --git a/tree/deepest_left.py b/algorithms/tree/deepest_left.py similarity index 60% rename from tree/deepest_left.py rename to algorithms/tree/deepest_left.py index 1448bc979..6d3a1c262 100644 --- a/tree/deepest_left.py +++ b/algorithms/tree/deepest_left.py @@ -12,18 +12,15 @@ # 7 # should return 4. +from tree.tree import TreeNode -class Node: - def __init__(self, val = None): - self.left = None - self.right = None - self.val = val class DeepestLeft: def __init__(self): self.depth = 0 self.Node = None + def find_deepest_left(root, is_left, depth, res): if not root: return @@ -33,15 +30,17 @@ def find_deepest_left(root, is_left, depth, res): find_deepest_left(root.left, True, depth + 1, res) find_deepest_left(root.right, False, depth + 1, res) -root = Node(1) -root.left = Node(2) -root.right = Node(3) -root.left.left = Node(4) -root.left.right = Node(5) -root.right.right = Node(6) -root.right.right.right = Node(7) - -res = DeepestLeft() -find_deepest_left(root, True, 1, res) -if res.Node: - print(res.Node.val) + +if __name__ == '__main__': + root = TreeNode(1) + root.left = TreeNode(2) + root.right = TreeNode(3) + root.left.left = TreeNode(4) + root.left.right = TreeNode(5) + root.right.right = TreeNode(6) + root.right.right.right = TreeNode(7) + + res = DeepestLeft() + find_deepest_left(root, True, 1, res) + if res.Node: + print(res.Node.val) diff --git a/algorithms/tree/fenwick_tree/fenwick_tree.py b/algorithms/tree/fenwick_tree/fenwick_tree.py new file mode 100644 index 000000000..67ec5105e --- /dev/null +++ b/algorithms/tree/fenwick_tree/fenwick_tree.py @@ -0,0 +1,77 @@ +""" +Fenwick Tree / Binary Indexed Tree + +Consider we have an array arr[0 . . . n-1]. We would like to +1. Compute the sum of the first i elements. +2. Modify the value of a specified element of the array arr[i] = x where 0 <= i <= n-1. + +A simple solution is to run a loop from 0 to i-1 and calculate the sum of the elements. To update a value, simply do arr[i] = x. +The first operation takes O(n) time and the second operation takes O(1) time. +Another simple solution is to create an extra array and store the sum of the first i-th elements at the i-th index in this new array. +The sum of a given range can now be calculated in O(1) time, but the update operation takes O(n) time now. +This works well if there are a large number of query operations but a very few number of update operations. + + +There are two solutions that can perform both the query and update operations in O(logn) time. +1. Fenwick Tree +2. Segment Tree + +Compared with Segment Tree, Binary Indexed Tree requires less space and is easier to implement. +""" + +class Fenwick_Tree(object): + def __init__(self, freq): + self.arr = freq + self.n = len(freq) + + def get_sum(self, bit_tree, i): + """ + Returns sum of arr[0..index]. This function assumes that the array is preprocessed and partial sums of array elements are stored in bit_tree[]. + """ + + s = 0 + + # index in bit_tree[] is 1 more than the index in arr[] + i = i+1 + + # Traverse ancestors of bit_tree[index] + while i > 0: + + # Add current element of bit_tree to sum + s += bit_tree[i] + + # Move index to parent node in getSum View + i -= i & (-i) + return s + + def update_bit(self, bit_tree, i, v): + """ + Updates a node in Binary Index Tree (bit_tree) at given index in bit_tree. The given value 'val' is added to bit_tree[i] and all of its ancestors in tree. + """ + + # index in bit_ree[] is 1 more than the index in arr[] + i += 1 + + # Traverse all ancestors and add 'val' + while i <= self.n: + + # Add 'val' to current node of bit_tree + bit_tree[i] += v + + # Update index to that of parent in update View + i += i & (-i) + + + def construct(self): + """ + Constructs and returns a Binary Indexed Tree for given array of size n. + """ + + # Create and initialize bit_ree[] as 0 + bit_tree = [0]*(self.n+1) + + # Store the actual values in bit_ree[] using update() + for i in range(self.n): + self.update_bit(bit_tree, i, self.arr[i]) + + return bit_tree diff --git a/tree/invert_tree.py b/algorithms/tree/invert_tree.py similarity index 90% rename from tree/invert_tree.py rename to algorithms/tree/invert_tree.py index 2d70c4f8e..9a6d58eee 100644 --- a/tree/invert_tree.py +++ b/algorithms/tree/invert_tree.py @@ -1,7 +1,7 @@ # invert a binary tree def reverse(root): - if not root: + if root is None: return root.left, root.right = root.right, root.left if root.left: diff --git a/algorithms/tree/is_balanced.py b/algorithms/tree/is_balanced.py new file mode 100644 index 000000000..3910e1b7e --- /dev/null +++ b/algorithms/tree/is_balanced.py @@ -0,0 +1,37 @@ +def is_balanced(root): + return __is_balanced_recursive(root) + + +def __is_balanced_recursive(root): + """ + O(N) solution + """ + return -1 != __get_depth(root) + + +def __get_depth(root): + """ + return 0 if unbalanced else depth + 1 + """ + if root is None: + return 0 + left = __get_depth(root.left) + right = __get_depth(root.right) + if abs(left-right) > 1 or -1 in [left, right]: + return -1 + return 1 + max(left, right) + + +# def is_balanced(root): +# """ +# O(N^2) solution +# """ +# left = max_height(root.left) +# right = max_height(root.right) +# return abs(left-right) <= 1 and is_balanced(root.left) and +# is_balanced(root.right) + +# def max_height(root): +# if root is None: +# return 0 +# return max(max_height(root.left), max_height(root.right)) + 1 diff --git a/algorithms/tree/is_subtree.py b/algorithms/tree/is_subtree.py new file mode 100644 index 000000000..3e267f76e --- /dev/null +++ b/algorithms/tree/is_subtree.py @@ -0,0 +1,71 @@ +""" +Given two binary trees s and t, check if t is a subtree of s. +A subtree of a tree t is a tree consisting of a node in t and +all of its descendants in t. + +Example 1: + +Given s: + + 3 + / \ + 4 5 + / \ + 1 2 + +Given t: + + 4 + / \ + 1 2 +Return true, because t is a subtree of s. + +Example 2: + +Given s: + + 3 + / \ + 4 5 + / \ + 1 2 + / + 0 + +Given t: + + 3 + / + 4 + / \ + 1 2 +Return false, because even though t is part of s, +it does not contain all descendants of t. + +Follow up: +What if one tree is significantly lager than the other? +""" +import collections + + +def is_subtree(big, small): + flag = False + queue = collections.deque() + queue.append(big) + while queue: + node = queue.popleft() + if node.val == small.val: + flag = comp(node, small) + break + else: + queue.append(node.left) + queue.append(node.right) + return flag + + +def comp(p, q): + if p is None and q is None: + return True + if p is not None and q is not None: + return p.val == q.val and comp(p.left,q.left) and comp(p.right, q.right) + return False diff --git a/tree/is_symmetric.py b/algorithms/tree/is_symmetric.py similarity index 77% rename from tree/is_symmetric.py rename to algorithms/tree/is_symmetric.py index 3aff3cfd2..19bcd4526 100644 --- a/tree/is_symmetric.py +++ b/algorithms/tree/is_symmetric.py @@ -21,32 +21,32 @@ # TC: O(b) SC: O(log n) def is_symmetric(root): - if not root: + if root is None: return True return helper(root.left, root.right) def helper(p, q): - if not p and not q: + if p is None and q is None: return True - if not p or not q or q.val != p.val: + if p is not None or q is not None or q.val != p.val: return False return helper(p.left, q.right) and helper(p.right, q.left) def is_symmetric_iterative(root): - if not root: + if root is None: return True stack = [[root.left, root.right]] while stack: left, right = stack.pop() # popleft - if not left and not right: + if left is None and right is None: continue - if not left or not right: + if left is None or right is None: return False if left.val == right.val: stack.append([left.left, right.right]) - stack.append([left.right, right.right]) + stack.append([left.right, right.left]) else: return False return True diff --git a/algorithms/tree/longest_consecutive.py b/algorithms/tree/longest_consecutive.py new file mode 100644 index 000000000..84118010c --- /dev/null +++ b/algorithms/tree/longest_consecutive.py @@ -0,0 +1,49 @@ +""" +Given a binary tree, find the length of the longest consecutive sequence path. + +The path refers to any sequence of nodes from some starting node to any node +in the tree along the parent-child connections. +The longest consecutive path need to be from parent to child +(cannot be the reverse). + +For example, + 1 + \ + 3 + / \ + 2 4 + \ + 5 +Longest consecutive sequence path is 3-4-5, so return 3. + 2 + \ + 3 + / + 2 + / + 1 +""" + + +def longest_consecutive(root): + """ + :type root: TreeNode + :rtype: int + """ + if root is None: + return 0 + max_len = 0 + dfs(root, 0, root.val, max_len) + return max_len + + +def dfs(root, cur, target, max_len): + if root is None: + return + if root.val == target: + cur += 1 + else: + cur = 1 + max_len = max(cur, max_len) + dfs(root.left, cur, root.val+1, max_len) + dfs(root.right, cur, root.val+1, max_len) diff --git a/tree/lowest_common_ancestor.py b/algorithms/tree/lowest_common_ancestor.py similarity index 83% rename from tree/lowest_common_ancestor.py rename to algorithms/tree/lowest_common_ancestor.py index 1702949f5..d0f33ccd1 100644 --- a/tree/lowest_common_ancestor.py +++ b/algorithms/tree/lowest_common_ancestor.py @@ -21,17 +21,17 @@ """ -def LCA(root, p, q): +def lca(root, p, q): """ :type root: TreeNode :type p: TreeNode :type q: TreeNode :rtype: TreeNode """ - if not root or root is p or root is q: + if root is None or root is p or root is q: return root - left = LCA(root.left, p, q) - right = LCA(root.right, p, q) - if left and right: + left = lca(root.left, p, q) + right = lca(root.right, p, q) + if left is not None and right is not None: return root return left if left else right diff --git a/tree/max_height.py b/algorithms/tree/max_height.py similarity index 51% rename from tree/max_height.py rename to algorithms/tree/max_height.py index a88a3fff2..c732ac079 100644 --- a/tree/max_height.py +++ b/algorithms/tree/max_height.py @@ -5,21 +5,18 @@ longest path from the root node down to the farthest leaf node. """ - -class Node(): - def __init__(self, val = 0): - self.val = val - self.left = None - self.right = None - # def max_height(root): - # if not root: - # return 0 - # return max(maxDepth(root.left), maxDepth(root.right)) + 1 +# if not root: +# return 0 +# return max(maxDepth(root.left), maxDepth(root.right)) + 1 # iterative + +from tree import TreeNode + + def max_height(root): - if not root: + if root is None: return 0 height = 0 queue = [root] @@ -28,27 +25,30 @@ def max_height(root): level = [] while queue: node = queue.pop(0) - if node.left: + if node.left is not None: level.append(node.left) - if node.right: + if node.right is not None: level.append(node.right) queue = level return height + def print_tree(root): - if root: + if root is not None: print(root.val) print_tree(root.left) print_tree(root.right) -tree = Node(10) -tree.left = Node(12) -tree.right = Node(15) -tree.left.left = Node(25) -tree.left.left.right = Node(100) -tree.left.right = Node(30) -tree.right.left = Node(36) - -height = max_height(tree) -print_tree(tree) -print("height:", height) + +if __name__ == '__main__': + tree = TreeNode(10) + tree.left = TreeNode(12) + tree.right = TreeNode(15) + tree.left.left = TreeNode(25) + tree.left.left.right = TreeNode(100) + tree.left.right = TreeNode(30) + tree.right.left = TreeNode(36) + + height = max_height(tree) + print_tree(tree) + print("height:", height) diff --git a/algorithms/tree/max_path_sum.py b/algorithms/tree/max_path_sum.py new file mode 100644 index 000000000..7f630fe6b --- /dev/null +++ b/algorithms/tree/max_path_sum.py @@ -0,0 +1,13 @@ +def max_path_sum(root): + maximum = float("-inf") + helper(root, maximum) + return maximum + + +def helper(root, maximum): + if root is None: + return 0 + left = helper(root.left, maximum) + right = helper(root.right, maximum) + maximum = max(maximum, left+right+root.val) + return root.val + maximum diff --git a/tree/min_height.py b/algorithms/tree/min_height.py similarity index 50% rename from tree/min_height.py rename to algorithms/tree/min_height.py index ebb8f75be..7913e2965 100644 --- a/tree/min_height.py +++ b/algorithms/tree/min_height.py @@ -1,25 +1,21 @@ -class Node(): - def __init__(self, val = 0): - self.val = val - self.left = None - self.right = None +from tree import TreeNode -def minDepth(self, root): +def min_depth(self, root): """ :type root: TreeNode :rtype: int """ - if not root: + if root is None: return 0 - if not root.left or not root.right: + if root.left is not None or root.right is not None: return max(self.minDepth(root.left), self.minDepth(root.right))+1 return min(self.minDepth(root.left), self.minDepth(root.right)) + 1 # iterative def min_height(root): - if not root: + if root is None: return 0 height = 0 level = [root] @@ -27,30 +23,32 @@ def min_height(root): height += 1 new_level = [] for node in level: - if not node.left and not node.right: + if node.left is None and node.right is None: return height - if node.left: + if node.left is not None: new_level.append(node.left) - if node.right: + if node.right is not None: new_level.append(node.right) level = new_level return height def print_tree(root): - if root: + if root is not None: print(root.val) print_tree(root.left) print_tree(root.right) -tree = Node(10) -tree.left = Node(12) -tree.right = Node(15) -tree.left.left = Node(25) -tree.left.left.right = Node(100) -tree.left.right = Node(30) -tree.right.left = Node(36) - -height = min_height(tree) -print_tree(tree) -print("height:", height) + +if __name__ == '__main__': + tree = TreeNode(10) + tree.left = TreeNode(12) + tree.right = TreeNode(15) + tree.left.left = TreeNode(25) + tree.left.left.right = TreeNode(100) + tree.left.right = TreeNode(30) + tree.right.left = TreeNode(36) + + height = min_height(tree) + print_tree(tree) + print("height:", height) diff --git a/tree/path_sum.py b/algorithms/tree/path_sum.py similarity index 78% rename from tree/path_sum.py rename to algorithms/tree/path_sum.py index b1001c3a4..aa9ff87e7 100644 --- a/tree/path_sum.py +++ b/algorithms/tree/path_sum.py @@ -21,9 +21,9 @@ def has_path_sum(root, sum): :type sum: int :rtype: bool """ - if not root: + if root is None: return False - if not root.left and not root.right and root.val == sum: + if root.left is None and root.right is None and root.val == sum: return True sum -= root.val return has_path_sum(root.left, sum) or has_path_sum(root.right, sum) @@ -31,33 +31,33 @@ def has_path_sum(root, sum): # DFS with stack def has_path_sum2(root, sum): - if not root: + if root is None: return False stack = [(root, root.val)] while stack: node, val = stack.pop() - if not node.left and not node.right: + if node.left is None and node.right is None: if val == sum: return True - if node.left: + if node.left is not None: stack.append((node.left, val+node.left.val)) - if node.right: + if node.right is not None: stack.append((node.right, val+node.right.val)) return False # BFS with queue def has_path_sum3(root, sum): - if not root: + if root is None: return False queue = [(root, sum-root.val)] while queue: node, val = queue.pop(0) # popleft - if not node.left and not node.right: + if node.left is None and node.right is None: if val == 0: return True - if node.left: + if node.left is not None: queue.append((node.left, val-node.left.val)) - if node.right: + if node.right is not None: queue.append((node.right, val-node.right.val)) return False diff --git a/tree/path_sum2.py b/algorithms/tree/path_sum2.py similarity index 64% rename from tree/path_sum2.py rename to algorithms/tree/path_sum2.py index 22c878038..f7c3e3fcf 100644 --- a/tree/path_sum2.py +++ b/algorithms/tree/path_sum2.py @@ -20,51 +20,52 @@ def path_sum(root, sum): - if not root: + if root is None: return [] res = [] - DFS(root, sum, [], res) + dfs(root, sum, [], res) return res -def DFS(root, sum, ls, res): - if not root.left and not root.right and root.val == sum: + +def dfs(root, sum, ls, res): + if root.left is None and root.right is None and root.val == sum: ls.append(root.val) res.append(ls) - if root.left: - DFS(root.left, sum-root.val, ls+[root.val], res) - if root.right: - DFS(root.right, sum-root.val, ls+[root.val], res) + if root.left is not None: + dfs(root.left, sum-root.val, ls+[root.val], res) + if root.right is not None: + dfs(root.right, sum-root.val, ls+[root.val], res) # DFS with stack def path_sum2(root, s): - if not root: + if root is None: return [] res = [] stack = [(root, [root.val])] while stack: node, ls = stack.pop() - if not node.left and not node.right and sum(ls) == s: + if node.left is None and node.right is None and sum(ls) == s: res.append(ls) - if node.left: + if node.left is not None: stack.append((node.left, ls+[node.left.val])) - if node.right: + if node.right is not None: stack.append((node.right, ls+[node.right.val])) return res # BFS with queue def path_sum3(root, sum): - if not root: + if root is None: return [] res = [] queue = [(root, root.val, [root.val])] while queue: node, val, ls = queue.pop(0) # popleft - if not node.left and not node.right and val == sum: + if node.left is None and node.right is None and val == sum: res.append(ls) - if node.left: + if node.left is not None: queue.append((node.left, val+node.left.val, ls+[node.left.val])) - if node.right: + if node.right is not None: queue.append((node.right, val+node.right.val, ls+[node.right.val])) return res diff --git a/algorithms/tree/pretty_print.py b/algorithms/tree/pretty_print.py new file mode 100644 index 000000000..02fc0f027 --- /dev/null +++ b/algorithms/tree/pretty_print.py @@ -0,0 +1,23 @@ +# a -> Adam -> Book -> 4 +# b -> Bill -> Computer -> 5 +# -> TV -> 6 +# Jill -> Sports -> 1 +# c -> Bill -> Sports -> 3 +# d -> Adam -> Computer -> 3 +# Quin -> Computer -> 3 +# e -> Quin -> Book -> 5 +# -> TV -> 2 +# f -> Adam -> Computer -> 7 + +from __future__ import print_function + + +def tree_print(tree): + for key in tree: + print(key, end=' ') # end=' ' prevents a newline character + tree_element = tree[key] # multiple lookups is expensive, even amortized O(1)! + for subElem in tree_element: + print(" -> ", subElem, end=' ') + if type(subElem) != str: # OP wants indenting after digits + print("\n ") # newline and a space to match indenting + print() # forces a newline diff --git a/algorithms/tree/red_black_tree/red_black_tree.py b/algorithms/tree/red_black_tree/red_black_tree.py new file mode 100644 index 000000000..20b6e7bc3 --- /dev/null +++ b/algorithms/tree/red_black_tree/red_black_tree.py @@ -0,0 +1,292 @@ +""" +Implementation of Red-Black tree. +""" + + +class RBNode: + def __init__(self, val, is_red, parent=None, left=None, right=None): + self.val = val + self.parent = parent + self.left = left + self.right = right + self.color = is_red + + +class RBTree: + def __init__(self): + self.root = None + + def left_rotate(self, node): + # set the node as the left child node of the current node's right node + right_node = node.right + if right_node is None: + return + else: + # right node's left node become the right node of current node + node.right = right_node.left + if right_node.left is not None: + right_node.left.parent = node + right_node.parent = node.parent + # check the parent case + if node.parent is None: + self.root = right_node + elif node is node.parent.left: + node.parent.left = right_node + else: + node.parent.right = right_node + right_node.left = node + node.parent = right_node + + def right_rotate(self, node): + # set the node as the right child node of the current node's left node + left_node = node.left + if left_node is None: + return + else: + # left node's right node become the left node of current node + node.left = left_node.right + if left_node.right is not None: + left_node.right.parent = node + left_node.parent = node.parent + # check the parent case + if node.parent is None: + self.root = left_node + elif node is node.parent.left: + node.parent.left = left_node + else: + node.parent.right = left_node + left_node.right = node + node.parent = left_node + + def insert(self, node): + # the inserted node's color is default is red + root = self.root + insert_node_parent = None + # find the position of inserted node + while root is not None: + insert_node_parent = root + if insert_node_parent.val < node.val: + root = root.right + else: + root = root.left + # set the n ode's parent node + node.parent = insert_node_parent + if insert_node_parent is None: + # case 1 inserted tree is null + self.root = node + elif insert_node_parent.val > node.val: + # case 2 not null and find left or right + insert_node_parent.left = node + else: + insert_node_parent.right = node + node.left = None + node.right = None + node.color = 1 + # fix the tree to + self.fix_insert(node) + + def fix_insert(self, node): + # case 1 the parent is null, then set the inserted node as root and color = 0 + if node.parent is None: + node.color = 0 + self.root = node + return + # case 2 the parent color is black, do nothing + # case 3 the parent color is red + while node.parent and node.parent.color == 1: + if node.parent is node.parent.parent.left: + uncle_node = node.parent.parent.right + if uncle_node and uncle_node.color == 1: + # case 3.1 the uncle node is red + # then set parent and uncle color is black and grandparent is red + # then node => node.parent + node.parent.color = 0 + node.parent.parent.right.color = 0 + node.parent.parent.color = 1 + node = node.parent.parent + continue + elif node is node.parent.right: + # case 3.2 the uncle node is black or null, and the node is right of parent + # then set his parent node is current node + # left rotate the node and continue the next + node = node.parent + self.left_rotate(node) + # case 3.3 the uncle node is black and parent node is left + # then parent node set black and grandparent set red + node.parent.color = 0 + node.parent.parent.color = 1 + self.right_rotate(node.parent.parent) + else: + uncle_node = node.parent.parent.left + if uncle_node and uncle_node.color == 1: + # case 3.1 the uncle node is red + # then set parent and uncle color is black and grandparent is red + # then node => node.parent + node.parent.color = 0 + node.parent.parent.left.color = 0 + node.parent.parent.color = 1 + node = node.parent.parent + continue + elif node is node.parent.left: + # case 3.2 the uncle node is black or null, and the node is right of parent + # then set his parent node is current node + # left rotate the node and continue the next + node = node.parent + self.right_rotate(node) + # case 3.3 the uncle node is black and parent node is left + # then parent node set black and grandparent set red + node.parent.color = 0 + node.parent.parent.color = 1 + self.left_rotate(node.parent.parent) + self.root.color = 0 + + def transplant(self, node_u, node_v): + """ + replace u with v + :param node_u: replaced node + :param node_v: + :return: None + """ + if node_u.parent is None: + self.root = node_v + elif node_u is node_u.parent.left: + node_u.parent.left = node_v + elif node_u is node_u.parent.right: + node_u.parent.right = node_v + # check is node_v is None + if node_v: + node_v.parent = node_u.parent + + def maximum(self, node): + """ + find the max node when node regard as a root node + :param node: + :return: max node + """ + temp_node = node + while temp_node.right is not None: + temp_node = temp_node.right + return temp_node + + def minimum(self, node): + """ + find the minimum node when node regard as a root node + :param node: + :return: minimum node + """ + temp_node = node + while temp_node.left: + temp_node = temp_node.left + return temp_node + + def delete(self, node): + # find the node position + node_color = node.color + if node.left is None: + temp_node = node.right + self.transplant(node, node.right) + elif node.right is None: + temp_node = node.left + self.transplant(node, node.left) + else: + # both child exits ,and find minimum child of right child + node_min = self.minimum(node.right) + node_color = node_min.color + temp_node = node_min.right + ## + if node_min.parent is not node: + self.transplant(node_min, node_min.right) + node_min.right = node.right + node_min.right.parent = node_min + self.transplant(node, node_min) + node_min.left = node.left + node_min.left.parent = node_min + node_min.color = node.color + # when node is black, then need to fix it with 4 cases + if node_color == 0: + self.delete_fixup(temp_node) + + def delete_fixup(self, node): + # 4 cases + while node is not self.root and node.color == 0: + # node is not root and color is black + if node is node.parent.left: + # node is left node + node_brother = node.parent.right + + # case 1: node's red, can not get black node + # set brother is black and parent is red + if node_brother.color == 1: + node_brother.color = 0 + node.parent.color = 1 + self.left_rotate(node.parent) + node_brother = node.parent.right + + # case 2: brother node is black, and its children node is both black + if (node_brother.left is None or node_brother.left.color == 0) and ( + node_brother.right is None or node_brother.right.color == 0): + node_brother.color = 1 + node = node.parent + else: + + # case 3: brother node is black , and its left child node is red and right is black + if node_brother.right is None or node_brother.right.color == 0: + node_brother.color = 1 + node_brother.left.color = 0 + self.right_rotate(node_brother) + node_brother = node.parent.right + + # case 4: brother node is black, and right is red, and left is any color + node_brother.color = node.parent.color + node.parent.color = 0 + node_brother.right.color = 0 + self.left_rotate(node.parent) + node = self.root + else: + node_brother = node.parent.left + if node_brother.color == 1: + node_brother.color = 0 + node.parent.color = 1 + self.left_rotate(node.parent) + node_brother = node.parent.right + if (node_brother.left is None or node_brother.left.color == 0) and ( + node_brother.right is None or node_brother.right.color == 0): + node_brother.color = 1 + node = node.parent + else: + if node_brother.left is None or node_brother.left.color == 0: + node_brother.color = 1 + node_brother.right.color = 0 + self.left_rotate(node_brother) + node_brother = node.parent.left + node_brother.color = node.parent.color + node.parent.color = 0 + node_brother.left.color = 0 + self.right_rotate(node.parent) + node = self.root + node.color = 0 + + def inorder(self): + res = [] + if not self.root: + return res + stack = [] + root = self.root + while root or stack: + while root: + stack.append(root) + root = root.left + root = stack.pop() + res.append({'val': root.val, 'color': root.color}) + root = root.right + return res + + +if __name__ == "__main__": + rb = RBTree() + children = [11, 2, 14, 1, 7, 15, 5, 8, 4] + for child in children: + node = RBNode(child, 1) + print(child) + rb.insert(node) + print(rb.inorder()) diff --git a/tree/same_tree.py b/algorithms/tree/same_tree.py similarity index 62% rename from tree/same_tree.py rename to algorithms/tree/same_tree.py index 9100c4f2e..c2805a87c 100644 --- a/tree/same_tree.py +++ b/algorithms/tree/same_tree.py @@ -7,11 +7,11 @@ """ -def isSameTree(p, q): - if not p and not q: +def is_same_tree(tree_p, tree_q): + if tree_p is None and tree_q is None: return True - if p and q and p.val == q.val: - return isSameTree(p.left, q.left) and isSameTree(p.right, q.right) + if tree_p is not None and tree_q is not None and tree_p.val == tree_q.val: + return is_same_tree(tree_p.left, tree_q.left) and is_same_tree(tree_p.right, tree_q.right) return False # Time Complexity O(min(N,M)) diff --git a/algorithms/tree/segment_tree/iterative_segment_tree.py b/algorithms/tree/segment_tree/iterative_segment_tree.py new file mode 100644 index 000000000..84018edc4 --- /dev/null +++ b/algorithms/tree/segment_tree/iterative_segment_tree.py @@ -0,0 +1,53 @@ +""" +SegmentTree creates a segment tree with a given array and a "commutative" function, +this non-recursive version uses less memory than the recursive version and include: +1. range queries in log(N) time +2. update an element in log(N) time +the function should be commutative and takes 2 values and returns the same type value + +Examples - +mytree = SegmentTree([2, 4, 5, 3, 4],max) +print(mytree.query(2, 4)) +mytree.update(3, 6) +print(mytree.query(0, 3)) ... + +mytree = SegmentTree([4, 5, 2, 3, 4, 43, 3], lambda a, b: a + b) +print(mytree.query(0, 6)) +mytree.update(2, -10) +print(mytree.query(0, 6)) ... + +mytree = SegmentTree([(1, 2), (4, 6), (4, 5)], lambda a, b: (a[0] + b[0], a[1] + b[1])) +print(mytree.query(0, 2)) +mytree.update(2, (-1, 2)) +print(mytree.query(0, 2)) ... +""" + + +class SegmentTree: + def __init__(self, arr, function): + self.tree = [None for _ in range(len(arr))] + arr + self.size = len(arr) + self.fn = function + self.build_tree() + + def build_tree(self): + for i in range(self.size - 1, 0, -1): + self.tree[i] = self.fn(self.tree[i * 2], self.tree[i * 2 + 1]) + + def update(self, p, v): + p += self.size + self.tree[p] = v + while p > 1: + p = p // 2 + self.tree[p] = self.fn(self.tree[p * 2], self.tree[p * 2 + 1]) + + def query(self, l, r): + l, r = l + self.size, r + self.size + res = None + while l <= r: + if l % 2 == 1: + res = self.tree[l] if res is None else self.fn(res, self.tree[l]) + if r % 2 == 0: + res = self.tree[r] if res is None else self.fn(res, self.tree[r]) + l, r = (l + 1) // 2, (r - 1) // 2 + return res diff --git a/tree/Segment_Tree/segment_tree.py b/algorithms/tree/segment_tree/segment_tree.py similarity index 80% rename from tree/Segment_Tree/segment_tree.py rename to algorithms/tree/segment_tree/segment_tree.py index d9f0a6909..94aeba5dd 100644 --- a/tree/Segment_Tree/segment_tree.py +++ b/algorithms/tree/segment_tree/segment_tree.py @@ -3,19 +3,19 @@ allowing queries to be done later in log(N) time function takes 2 values and returns a same type value ''' -class segment_tree: +class SegmentTree: def __init__(self,arr,function): self.segment = [0 for x in range(3*len(arr)+3)] self.arr = arr self.fn = function - self.maketree(0,0,len(arr)-1) + self.make_tree(0,0,len(arr)-1) - def maketree(self,i,l,r): + def make_tree(self,i,l,r): if l==r: self.segment[i] = self.arr[l] elif l self.size[root2]: + root1, root2 = root2, root1 + self.parents[root1] = root2 + self.size[root2] += self.size[root1] + self.count -= 1 + +def num_islands(positions): + """ + Given a list of positions to operate, count the number of islands + after each addLand operation. An island is surrounded by water and is + formed by connecting adjacent lands horizontally or vertically. You may + assume all four edges of the grid are all surrounded by water. + + Given a 3x3 grid, positions = [[0,0], [0,1], [1,2], [2,1]]. + Initially, the 2d grid grid is filled with water. + (Assume 0 represents water and 1 represents land). + + 0 0 0 + 0 0 0 + 0 0 0 + Operation #1: addLand(0, 0) turns the water at grid[0][0] into a land. + + 1 0 0 + 0 0 0 Number of islands = 1 + 0 0 0 + Operation #2: addLand(0, 1) turns the water at grid[0][1] into a land. + + 1 1 0 + 0 0 0 Number of islands = 1 + 0 0 0 + Operation #3: addLand(1, 2) turns the water at grid[1][2] into a land. + + 1 1 0 + 0 0 1 Number of islands = 2 + 0 0 0 + Operation #4: addLand(2, 1) turns the water at grid[2][1] into a land. + + 1 1 0 + 0 0 1 Number of islands = 3 + 0 1 0 + """ + + ans = [] + islands = Union() + for position in map(tuple, positions): + islands.add(position) + for delta in (0, 1), (0, -1), (1, 0), (-1, 0): + adjacent = (position[0] + delta[0], position[1] + delta[1]) + if adjacent in islands.parents: + islands.unite(position, adjacent) + ans += [islands.count] + return ans diff --git a/algorithms/unix/__init__.py b/algorithms/unix/__init__.py new file mode 100644 index 000000000..0d1808da0 --- /dev/null +++ b/algorithms/unix/__init__.py @@ -0,0 +1,4 @@ +from .path.join_with_slash import * +from .path.full_path import * +from .path.split import * +from .path.simplify_path import * diff --git a/algorithms/unix/path/full_path.py b/algorithms/unix/path/full_path.py new file mode 100644 index 000000000..3bf109e12 --- /dev/null +++ b/algorithms/unix/path/full_path.py @@ -0,0 +1,6 @@ +""" +Get a full absolute path a file +""" +import os +def full_path(file): + return os.path.abspath(os.path.expanduser(file)) diff --git a/algorithms/unix/path/join_with_slash.py b/algorithms/unix/path/join_with_slash.py new file mode 100644 index 000000000..beec8d106 --- /dev/null +++ b/algorithms/unix/path/join_with_slash.py @@ -0,0 +1,18 @@ +""" +Both URL and file path joins use slashes as dividers between their parts. +For example: + +path/to/dir + file --> path/to/dir/file +path/to/dir/ + file --> path/to/dir/file +http://algorithms.com/ + part --> http://algorithms.com/part +http://algorithms.com + part --> http://algorithms/part +""" +import os + +def join_with_slash(base, suffix): + # Remove / trailing + base = base.rstrip('/') + # Remove / leading + suffix = suffix.lstrip('/').rstrip() + full_path = "{}/{}".format(base, suffix) + return full_path diff --git a/algorithms/unix/path/simplify_path.py b/algorithms/unix/path/simplify_path.py new file mode 100644 index 000000000..8880fc0c6 --- /dev/null +++ b/algorithms/unix/path/simplify_path.py @@ -0,0 +1,29 @@ +""" +Given an absolute path for a file (Unix-style), simplify it. + +For example, +path = "/home/", => "/home" +path = "/a/./b/../../c/", => "/c" + +Corner Cases: + +Did you consider the case where path = "/../"? +In this case, you should return "/". +Another corner case is the path might contain multiple slashes '/' together, such as "/home//foo/". +In this case, you should ignore redundant slashes and return "/home/foo". + +Reference: https://leetcode.com/problems/simplify-path/description/ +""" + +import os +def simplify_path_v1(path): + return os.path.abspath(path) + +def simplify_path_v2(path): + stack, tokens = [], path.split("/") + for token in tokens: + if token == ".." and stack: + stack.pop() + elif token != ".." and token != "." and token: + stack.append(token) + return "/" + "/".join(stack) diff --git a/algorithms/unix/path/split.py b/algorithms/unix/path/split.py new file mode 100644 index 000000000..168b12057 --- /dev/null +++ b/algorithms/unix/path/split.py @@ -0,0 +1,23 @@ +""" +Splitting a path into 2 parts +Example: +Input: https://algorithms/unix/test.py (for url) +Output: + part[0]: https://algorithms/unix + part[1]: test.py + +Input: algorithms/unix/test.py (for file path) +Output: + part[0]: algorithms/unix + part[1]: test.py +""" +import os + +def split(path): + parts = [] + split_part = path.rpartition('/') + # Takt the origin path without the last part + parts.append(split_part[0]) + # Take the last element of list + parts.append(split_part[2]) + return parts diff --git a/array/circular_counter.py b/array/circular_counter.py deleted file mode 100644 index 1fea4f688..000000000 --- a/array/circular_counter.py +++ /dev/null @@ -1,48 +0,0 @@ -""" -There are people sitting in a circular fashion, -print every third member while removing them, -the next counter starts immediately after the member is removed. -Print till all the members are exhausted. - -For example: -Input: consider 123456789 members sitting in a circular fashion, -Output: 369485271 -""" - -a = ['1','2','3','4','5','6','7','8','9'] - -def josepheus(int_list, skip): - skip = skip - 1 #list starts with 0 index - idx = 0 - len_list = (len(int_list)) - while len_list>0: - idx = (skip+idx)%len_list #hashing to keep changing the index to every 3rd - print(int_list.pop(idx)) - len_list -= 1 - - -josepheus(a,3) - -""" -the reason for hashing is that we have to find the index of the item which needs to be removed. -So for e.g. if you iterate with the initial list of folks with every 3rd item eliminated: - -INPUT -int_list = 123456789 -skip = 3 - -While Iteration: - -int_list = 123456789 -len(int_list) = 9 -skip = 2 # as int_list starts from 0 -idx = (0 + 2) % 9 #here previous index was 0 -so 3rd element which is 3 in this case eliminated -int_list = 12456789 -len(int_list) = 8 -idx = (2 + 2) % 8 #here previous index was 2 -so 3rd element starting from 4th person which is 6 would be deleted. -and so on -The reason why we have to do this way is I am not putting the people who escape at the back of list so ideally in 2 while iteration the list should have been -45678912 and then no hashing needed to be done, which means you can directly remove the third element -""" diff --git a/array/flatten.py b/array/flatten.py deleted file mode 100644 index 8ca86b7cb..000000000 --- a/array/flatten.py +++ /dev/null @@ -1,56 +0,0 @@ -""" -Implement Flatten Arrays. -Given an array that may contain nested arrays, -give a single resultant array. - -function flatten(input){ -} - -Example: - -Input: var input = [2, 1, [3, [4, 5], 6], 7, [8]]; -flatten(input); -Output: [2, 1, 3, 4, 5, 6, 7, 8] -""" - - -def list_flatten(l, a=None): - a = list(a) if isinstance(a, (list, tuple)) else [] - for i in l: - if isinstance(i, (list, tuple)): - a = list_flatten(i, a) - else: - a.append(i) - return a - - -# stack version -# public static List flatten(List l) { -# List main = new ArrayList(); - # Stack> stack = new Stack>(); - # Stack indexes = new Stack(); - # stack.add(l); - # indexes.add(0); - # while (true) { - # if (stack.isEmpty()) - # break; - # int index1 = indexes.pop(); - # l = stack.pop(); - # for (int i = index1; i < l.size(); i++) { - # NestedList n = l.get(i); - # if (n.isInteger()) { - # main.add(n.value); - # } else { - # stack.add(l); - # indexes.add(i+1); - # l = n.list; - # stack.add(l); - # indexes.add(0); - # break; - - # } - # } - # } - - # return main; -# } diff --git a/array/garage.py b/array/garage.py deleted file mode 100644 index 6d99f8d7c..000000000 --- a/array/garage.py +++ /dev/null @@ -1,42 +0,0 @@ -# There is a parking lot with only one empty spot. Given the initial state -# of the parking lot and the final state. Each step we are only allowed to -# move a car -# out of its place and move it into the empty spot. -# The goal is to find out the least movement needed to rearrange -# the parking lot from the initial state to the final state. - -# Say the initial state is an array: - -# [1,2,3,0,4], -# where 1,2,3,4 are different cars, and 0 is the empty spot. - -# And the final state is - -# [0,3,2,1,4]. -# We can swap 1 with 0 in the initial array to get [0,2,3,1,4] and so on. -# Each step swap with 0 only. -# Edited by cyberking-saga - - -def garage(initial, final): - steps = 0 - while initial != final: - zero = initial.index(0) - if zero != final.index(0): - car_to_move = final[zero] - pos = initial.index(car_to_move) - initial[zero], initial[pos] = initial[pos], initial[zero] - else: - for i in range(len(initial)): - if initial[i] != final[i]: - initial[zero], initial[i] = initial[i], initial[zero] - break - steps += 1 - return steps - -if __name__ == "__main__": - initial = [1, 2, 3, 0, 4] - final = [0, 3, 2, 1, 4] - print("initial:", initial) - print("final:", final) - print(garage(initial, final)) diff --git a/array/longest_non_repeat.py b/array/longest_non_repeat.py deleted file mode 100644 index c5f6edb59..000000000 --- a/array/longest_non_repeat.py +++ /dev/null @@ -1,27 +0,0 @@ -# Given a string, find the length of the longest substring -# without repeating characters. - -# Examples: - -# Given "abcabcbb", the answer is "abc", which the length is 3. - -# Given "bbbbb", the answer is "b", with the length of 1. - -# Given "pwwkew", the answer is "wke", with the length of 3. -# Note that the answer must be a substring, -# "pwke" is a subsequence and not a substring. - -def longest_non_repeat(s): - start, maxlen = 0, 0 - used_char = {} - for i, char in enumerate(s): - if char in used_char and start <= used_char[char]: - start = used_char[char] + 1 - else: - maxlen = max(maxlen, i-start+1) - used_char[char] = i - return maxlen - -a = "abcabcdefbb" -print(a) -print(longest_non_repeat(a)) diff --git a/array/merge_intervals.py b/array/merge_intervals.py deleted file mode 100644 index 0d465e2d4..000000000 --- a/array/merge_intervals.py +++ /dev/null @@ -1,40 +0,0 @@ -""" -Given a collection of intervals, merge all overlapping intervals. - -For example, -Given [1,3],[2,6],[8,10],[15,18], -return [1,6],[8,10],[15,18]. -""" - -# Definition for an interval. -class Interval(object): - def __init__(self, s=0, e=0): - self.start = s - self.end = e - -def merge(intervals): - """ - :type intervals: List[Interval] - :rtype: List[Interval] - """ - out = [] - for i in sorted(intervals, key=lambda i: i.start): - if out and i.start <= out[-1].end: - out[-1].end = max(out[-1].end, i.end) - else: - out += i, - return out - -def print_intervals(intervals): - res = [] - for i in intervals: - res.append('['+str(i.start)+','+str(i.end)+']') - print("".join(res)) - -if __name__ == "__main__": - given = [[1,3],[2,6],[8,10],[15,18]] - intervals = [] - for l, r in given: - intervals.append(Interval(l,r)) - print_intervals(intervals) - print_intervals(merge(intervals)) diff --git a/array/missing_ranges.py b/array/missing_ranges.py deleted file mode 100644 index 91fc31ccb..000000000 --- a/array/missing_ranges.py +++ /dev/null @@ -1,27 +0,0 @@ -## find missing ranges between low and high in the given array. -# ex) [3, 5] lo=1 hi=10 => answer: [1->2, 4, 6->10] - -def missing_ranges(nums, lo, hi): - res = [] - start = lo - for num in nums: - if num < start: - continue - if num == start: - start += 1 - continue - res.append(get_range(start, num-1)) - start = num + 1 - if start <= hi: - res.append(get_range(start, hi)) - return res - -def get_range(n1, n2): - if n1 == n2: - return str(n1) - else: - return str(n1) + "->" + str(n2) - -nums = [3, 5, 10, 11, 12, 15, 19] -print("original:", nums) -print("missing range: ", missing_ranges(nums,0,20)) diff --git a/array/plus_one.py b/array/plus_one.py deleted file mode 100644 index 65c93e34d..000000000 --- a/array/plus_one.py +++ /dev/null @@ -1,45 +0,0 @@ -# Given a non-negative number represented as an array of digits, -# plus one to the number. - -# The digits are stored such that the most significant -# digit is at the head of the list. - - -def plusOne(digits): - """ - :type digits: List[int] - :rtype: List[int] - """ - digits[-1] = digits[-1] + 1 - res = [] - ten = 0 - i = len(digits)-1 - while i >= 0 or ten == 1: - sum = 0 - if i >= 0: - sum += digits[i] - if ten: - sum += 1 - res.append(sum % 10) - ten = sum / 10 - i -= 1 - return res[::-1] - - -def plus_one(digits): - n = len(digits) - for i in range(n-1, -1, -1): - if digits[i] < 9: - digits[i] += 1 - return digits - digits[i] = 0 - digits.insert(0, 1) - return digits - - -def plus_1(num_arr): - for idx, digit in reversed(list(enumerate(num_arr))): - num_arr[idx] = (num_arr[idx] + 1) % 10 - if num_arr[idx]: - return num_arr - return [1] + num_arr diff --git a/array/rotate_array.py b/array/rotate_array.py deleted file mode 100644 index ecc3e900a..000000000 --- a/array/rotate_array.py +++ /dev/null @@ -1,52 +0,0 @@ -""" -Rotate an array of n elements to the right by k steps. - -For example, with n = 7 and k = 3, -the array [1,2,3,4,5,6,7] is rotated to [5,6,7,1,2,3,4]. - -Note: -Try to come up as many solutions as you can, -there are at least 3 different ways to solve this problem. -""" - - -# -# Rotate the entire array 'k' times -# T(n)- O(nk) -# -def rotate_one_by_one(nums, k): - """ - :type nums: List[int] - :type k: int - :rtype: void Do not return anything, modify nums in-place instead. - """ - n = len(nums) - for i in range(k): - temp = nums[n-1] - for j in range(n-1, 0, -1): - nums[j] = nums[j-1] - nums[0] = temp - - -# -# Reverse segments of the array, followed by the entire array -# T(n)- O(n) -# -def rotate(nums, k): - """ - :type nums: List[int] - :type k: int - :rtype: void Do not return anything, modify nums in-place instead. - """ - n = len(nums) - k = k % n - reverse(nums, 0, n - k - 1) - reverse(nums, n - k, n - 1) - reverse(nums, 0, n - 1) - - -def reverse(array, a, b): - while a < b: - array[a], array[b] = array[b], array[a] - a += 1 - b -= 1 diff --git a/array/summary_ranges.py b/array/summary_ranges.py deleted file mode 100644 index 3cbe5abf4..000000000 --- a/array/summary_ranges.py +++ /dev/null @@ -1,27 +0,0 @@ -""" -Given a sorted integer array without duplicates, -return the summary of its ranges. - -For example, given [0,1,2,4,5,7], return ["0->2","4->5","7"]. -""" - - -def summary_ranges(nums): - """ - :type nums: List[int] - :rtype: List[str] - """ - res = [] - if len(nums) == 1: - return [str(nums[0])] - i = 0 - while i < len(nums): - num = nums[i] - while i+1 < len(nums) and nums[i+1] - nums[i] == 1: - i += 1 - if nums[i] != num: - res.append(str(num) + "->" + str(nums[i])) - else: - res.append(str(num)) - i += 1 - return res diff --git a/array/three_sum.py b/array/three_sum.py deleted file mode 100644 index 4b5753347..000000000 --- a/array/three_sum.py +++ /dev/null @@ -1,46 +0,0 @@ -""" -Given an array S of n integers, are there elements a, b, c in S -such that a + b + c = 0? -Find all unique triplets in the array which gives the sum of zero. - -Note: The solution set must not contain duplicate triplets. - -For example, given array S = [-1, 0, 1, 2, -1, -4], - -A solution set is: -[ - [-1, 0, 1], - [-1, -1, 2] -] -""" - - -def three_sum(nums:"List[int]")->"List[int]": - res = [] - nums.sort() - for i in range(len(nums)-2): - if i > 0 and nums[i] == nums[i-1]: - continue - l, r = i+1, len(nums)-1 - while l < r: - s = nums[i] + nums[l] + nums[r] - if s > 0: - r -= 1 - elif s < 0: - l += 1 - else: - # found three sum - res.append((nums[i], nums[l], nums[r])) - # remove duplicates - while l < r and nums[l] == nums[l+1]: - l+=1 - while l < r and nums[r] == nums[r-1]: - r -= 1 - l += 1 - r -= 1 - return res - - -if __name__ == "__main__": - x = [-1,0,1,2,-1,-4] - print(three_sum(x)) diff --git a/backtrack/anagram.py b/backtrack/anagram.py deleted file mode 100644 index df3c9dc46..000000000 --- a/backtrack/anagram.py +++ /dev/null @@ -1,44 +0,0 @@ -def all_perms(elements): - if len(elements) <=1: - yield elements - else: - for perm in all_perms(elements[1:]): - for i in range(len(elements)): - yield perm[:i] + elements[0:1] + perm[i:] - -def all_perms(elements): - if len(elements) <=1: - return elements - else: - tmp = [] - for perm in all_perms(elements[1:]): - for i in range(len(elements)): - tmp.append(perm[:i] + elements[0:1] + perm[i:]) - return tmp - -word = "abc" -print(list(all_perms(word))) - -def anagram(s1,s2): - c1 = [0]*26 - c2 = [0]*26 - - for i in range(len(s1)): - pos = ord(s1[i])-ord('a') - c1[pos] = c1[pos] + 1 - - for i in range(len(s2)): - pos = ord(s2[i])-ord('a') - c2[pos] = c2[pos] + 1 - - j = 0 - stillOK = True - while j<26 and stillOK: - if c1[j]==c2[j]: - j = j + 1 - else: - stillOK = False - - return stillOK - -print(anagram('apple','pleap')) diff --git a/backtrack/array_sum_combinations.py b/backtrack/array_sum_combinations.py deleted file mode 100644 index b267083d7..000000000 --- a/backtrack/array_sum_combinations.py +++ /dev/null @@ -1,86 +0,0 @@ -""" -WAP to take one element from each of the array add it to the target sum. Print all those three-element combinations. - -/* -A = [1, 2, 3, 3] -B = [2, 3, 3, 4] -C = [1, 2, 2, 2] -target = 7 -*/ - -Result: -[[1, 2, 4], [1, 3, 3], [1, 3, 3], [1, 3, 3], [1, 3, 3], [1, 4, 2], [2, 2, 3], [2, 2, 3], [2, 3, 2], [2, 3, 2], [3, 2, 2], [3, 2, 2]] -""" - - -A = [1, 2, 3, 3] -B = [2, 3, 3, 4] -C = [1, 2, 2, 2] -target = 7 - -def construct_candidates(constructed_sofar): - global A,B,C - array = A - if 1 == len(constructed_sofar) : - array = B - elif 2 == len(constructed_sofar) : - array = C - return array - - -def over(constructed_sofar): - global target - sum = 0 - to_stop, reached_target = False, False - for elem in constructed_sofar: - sum += elem - if sum >= target or len(constructed_sofar) >= 3 : - to_stop = True - if sum == target and 3 == len(constructed_sofar): - reached_target = True - - return to_stop, reached_target - -def backtrack(constructed_sofar): - to_stop, reached_target = over(constructed_sofar) - if to_stop: - if reached_target : - print constructed_sofar - return - candidates = construct_candidates(constructed_sofar) - for candidate in candidates : - constructed_sofar.append(candidate) - backtrack(constructed_sofar[:]) - constructed_sofar.pop() -backtrack([]) - - -# Complexity: O(n(m+p)) - -# 1. Sort all the arrays - a,b,c. - This will improve average time complexity. -# 2. If c[i] < Sum, then look for Sum - c[i] in array a and b. When pair found, insert c[i], a[j] & b[k] into the result list. This can be done in O(n). -# 3. Keep on doing the above procedure while going through complete c array. - - -import itertools -from functools import partial -A = [1,2,3,3] -B = [2,3,3,4] -C = [1,2,2,2] -S = 7 - -def check_sum(N, *nums): - if sum(x for x in nums) == N: - return (True, nums) - else: - return (False, nums) - -pro = itertools.product(A,B,C) -func = partial(check_sum, S) -sums = list(itertools.starmap(func, pro)) - -res = set() -for s in sums: - if s[0] == True and s[1] not in res: - res.add(s[1]) -print res diff --git a/backtrack/expression_add_operators.py b/backtrack/expression_add_operators.py deleted file mode 100644 index 2e1f45067..000000000 --- a/backtrack/expression_add_operators.py +++ /dev/null @@ -1,53 +0,0 @@ -""" -Given a string that contains only digits 0-9 and a target value, -return all possibilities to add binary operators (not unary) +, -, or * -between the digits so they prevuate to the target value. - -Examples: -"123", 6 -> ["1+2+3", "1*2*3"] -"232", 8 -> ["2*3+2", "2+3*2"] -"105", 5 -> ["1*0+5","10-5"] -"00", 0 -> ["0+0", "0-0", "0*0"] -"3456237490", 9191 -> [] -""" - -def add_operator(num, target): - """ - :type num: str - :type target: int - :rtype: List[str] - """ - res = [] - if not num: return res - helper(res, "", num, target, 0, 0, 0) - return res - -def helper(res, path, num, target, pos, prev, multed): - if pos == len(num): - if (target == prev): - res.append(path) - return - for i in range(pos, len(num)): - if i != pos and num[pos] == '0': # all digits have to be used - break - cur = int(num[pos:i+1]) - if pos == 0: - helper(res, path + str(cur), num, target, i+1, cur, cur) - else: - helper(res, path + "+" + str(cur), num, target, i+1, prev + cur, cur) - helper(res, path + "-" + str(cur), num, target, i+1, prev - cur, -cur) - helper(res, path + "*" + str(cur), num, target, i+1, prev - multed + multed * cur, multed * cur) - - -# "123", 6 -> ["1+2+3", "1*2*3"] -s = "123" -target = 6 -print(add_operator(s, target)) -# "232", 8 -> ["2*3+2", "2+3*2"] -s = "232" -target = 8 -print(add_operator(s, target)) - -s = "123045" -target = 3 -print(add_operator(s, target)) diff --git a/backtrack/general_solution.md b/backtrack/general_solution.md deleted file mode 100644 index 0c0ee0c6f..000000000 --- a/backtrack/general_solution.md +++ /dev/null @@ -1,156 +0,0 @@ -This structure might apply to many other backtracking questions, but here I am just going to demonstrate Subsets, Permutations, and Combination Sum. - -# Subsets : https://leetcode.com/problems/subsets/ - -public List> subsets(int[] nums) { - List> list = new ArrayList<>(); - Arrays.sort(nums); - backtrack(list, new ArrayList<>(), nums, 0); - return list; -} - -private void backtrack(List> list , List tempList, int [] nums, int start){ - list.add(new ArrayList<>(tempList)); - for(int i = start; i < nums.length; i++){ - tempList.add(nums[i]); - backtrack(list, tempList, nums, i + 1); - tempList.remove(tempList.size() - 1); - } -} - -# Subsets II (contains duplicates) : https://leetcode.com/problems/subsets-ii/ - -public List> subsetsWithDup(int[] nums) { - List> list = new ArrayList<>(); - Arrays.sort(nums); - backtrack(list, new ArrayList<>(), nums, 0); - return list; -} - -private void backtrack(List> list, List tempList, int [] nums, int start){ - list.add(new ArrayList<>(tempList)); - for(int i = start; i < nums.length; i++){ - if(i > start && nums[i] == nums[i-1]) continue; // skip duplicates - tempList.add(nums[i]); - backtrack(list, tempList, nums, i + 1); - tempList.remove(tempList.size() - 1); - } -} - -# Permutations : https://leetcode.com/problems/permutations/ - -public List> permute(int[] nums) { - List> list = new ArrayList<>(); - // Arrays.sort(nums); // not necessary - backtrack(list, new ArrayList<>(), nums); - return list; -} - -private void backtrack(List> list, List tempList, int [] nums){ - if(tempList.size() == nums.length){ - list.add(new ArrayList<>(tempList)); - } else{ - for(int i = 0; i < nums.length; i++){ - if(tempList.contains(nums[i])) continue; // element already exists, skip - tempList.add(nums[i]); - backtrack(list, tempList, nums); - tempList.remove(tempList.size() - 1); - } - } -} - -# Permutations II (contains duplicates) : https://leetcode.com/problems/permutations-ii/ - -public List> permuteUnique(int[] nums) { - List> list = new ArrayList<>(); - Arrays.sort(nums); - backtrack(list, new ArrayList<>(), nums, new boolean[nums.length]); - return list; -} - -private void backtrack(List> list, List tempList, int [] nums, boolean [] used){ - if(tempList.size() == nums.length){ - list.add(new ArrayList<>(tempList)); - } else{ - for(int i = 0; i < nums.length; i++){ - if(used[i] || i > 0 && nums[i] == nums[i-1] && !used[i - 1]) continue; - used[i] = true; - tempList.add(nums[i]); - backtrack(list, tempList, nums, used); - used[i] = false; - tempList.remove(tempList.size() - 1); - } - } -} - -# Combination Sum : https://leetcode.com/problems/combination-sum/ - -public List> combinationSum(int[] nums, int target) { - List> list = new ArrayList<>(); - Arrays.sort(nums); - backtrack(list, new ArrayList<>(), nums, target, 0); - return list; -} - -private void backtrack(List> list, List tempList, int [] nums, int remain, int start){ - if(remain < 0) return; - else if(remain == 0) list.add(new ArrayList<>(tempList)); - else{ - for(int i = start; i < nums.length; i++){ - tempList.add(nums[i]); - backtrack(list, tempList, nums, remain - nums[i], i); // not i + 1 because we can reuse same elements - tempList.remove(tempList.size() - 1); - } - } -} -# Combination Sum II (can't reuse same element) : https://leetcode.com/problems/combination-sum-ii/ - -public List> combinationSum2(int[] nums, int target) { - List> list = new ArrayList<>(); - Arrays.sort(nums); - backtrack(list, new ArrayList<>(), nums, target, 0); - return list; - -} - -private void backtrack(List> list, List tempList, int [] nums, int remain, int start){ - if(remain < 0) return; - else if(remain == 0) list.add(new ArrayList<>(tempList)); - else{ - for(int i = start; i < nums.length; i++){ - if(i > start && nums[i] == nums[i-1]) continue; // skip duplicates - tempList.add(nums[i]); - backtrack(list, tempList, nums, remain - nums[i], i + 1); - tempList.remove(tempList.size() - 1); - } - } -} - - -# Palindrome Partitioning : https://leetcode.com/problems/palindrome-partitioning/ - -public List> partition(String s) { - List> list = new ArrayList<>(); - backtrack(list, new ArrayList<>(), s, 0); - return list; -} - -public void backtrack(List> list, List tempList, String s, int start){ - if(start == s.length()) - list.add(new ArrayList<>(tempList)); - else{ - for(int i = start; i < s.length(); i++){ - if(isPalindrome(s, start, i)){ - tempList.add(s.substring(start, i + 1)); - backtrack(list, tempList, s, i + 1); - tempList.remove(tempList.size() - 1); - } - } - } -} - -public boolean isPalindrome(String s, int low, int high){ - while(low < high) - if(s.charAt(low++) != s.charAt(high--)) return false; - return true; -} diff --git a/backtrack/generate_abbreviations.py b/backtrack/generate_abbreviations.py deleted file mode 100644 index 929c33994..000000000 --- a/backtrack/generate_abbreviations.py +++ /dev/null @@ -1,26 +0,0 @@ -""" -given input word, return the list of abbreviations. -ex) -word => [1ord, w1rd, wo1d, w2d, 3d, w3 ... etc] -""" - - -def generate_abbreviations(word): - result = [] - backtrack(result, word, 0, 0, "") - return result - - -def backtrack(result, word, pos, count, cur): - if pos == len(word): - if count > 0: - cur += str(count) - result.append(cur) - return - - if count > 0: # add the current word - backtrack(result, word, pos+1, 0, cur+str(count)+word[pos]) - else: - backtrack(result, word, pos+1, 0, cur+word[pos]) - # skip the current word - backtrack(result, word, pos+1, count+1, cur) diff --git a/backtrack/generate_parenthesis.py b/backtrack/generate_parenthesis.py deleted file mode 100644 index 6dac22c94..000000000 --- a/backtrack/generate_parenthesis.py +++ /dev/null @@ -1,32 +0,0 @@ -""" -Given n pairs of parentheses, write a function to generate -all combinations of well-formed parentheses. - -For example, given n = 3, a solution set is: - -[ - "((()))", - "(()())", - "(())()", - "()(())", - "()()()" -] -""" - -def gen_parenthesis(n:"int")->"List[str]": - res = [] - add_pair(res, "", n, 0) - return res - -def add_pair(res, s, left, right): - if left == 0 and right == 0: - res.append(s) - return - if right > 0: - add_pair(res, s+")", left, right-1) - if left > 0: - add_pair(res, s+"(", left-1, right+1) - - -if __name__=="__main__": - print(gen_parenthesis(3)) diff --git a/backtrack/palindrome_partitioning.py b/backtrack/palindrome_partitioning.py deleted file mode 100644 index 654079010..000000000 --- a/backtrack/palindrome_partitioning.py +++ /dev/null @@ -1,29 +0,0 @@ -# It looks like you need to be looking not for all palindromic substrings, but rather for all the ways you can divide the input string up into palindromic substrings. (There's always at least one way, since one-character substrings are always palindromes.) - -# Here's the way I've done it: - -def palindromic_substrings(s): - if not s: - return [[]] - results = [] - for i in range(len(s), 0, -1): - sub = s[:i] - if sub == sub[::-1]: - for rest in palindromic_substrings(s[i:]): - results.append([sub] + rest) - return results - -# There's two loops. -# The outer loop checks each length of initial substring (in descending length order) to see if it is a palindrome. If so, it recurses on the rest of the string and loops over the returned values, adding the initial substring to each item before adding it to the results. - -# A slightly more Pythonic approach would be to make a recursive generator: - -def palindromic_substrings(s): - if not s: - yield [] - return - for i in range(len(s), 0, -1): - sub = s[:i] - if sub == sub[::-1]: - for rest in palindromic_substrings(s[i:]): - yield [sub] + rest diff --git a/backtrack/pattern_match.py b/backtrack/pattern_match.py deleted file mode 100644 index 532dfb9c2..000000000 --- a/backtrack/pattern_match.py +++ /dev/null @@ -1,52 +0,0 @@ -""" -Given a pattern and a string str, -find if str follows the same pattern. - -Here follow means a full match, such that there is a bijection between -a letter in pattern and a non-empty substring in str. - -Examples: -pattern = "abab", str = "redblueredblue" should return true. -pattern = "aaaa", str = "asdasdasdasd" should return true. -pattern = "aabb", str = "xyzabcxzyabc" should return false. -Notes: -You may assume both pattern and str contains only lowercase letters. -""" - - -def pattern_match(pattern, string): - """ - :type pattern: str - :type string: str - :rtype: bool - """ - return backtrack(pattern, string, {}) - - -def backtrack(pattern, string, dic): - print(dic) - if len(pattern) == 0 and len(string) > 0: - return False - if len(pattern) == len(string) == 0: - return True - for end in range(1, len(string)-len(pattern)+2): - if pattern[0] not in dic and string[:end] not in dic.values(): - dic[pattern[0]] = string[:end] - if backtrack(pattern[1:], string[end:], dic): - return True - del dic[pattern[0]] - elif pattern[0] in dic and dic[pattern[0]] == string[:end]: - if backtrack(pattern[1:], string[end:], dic): - return True - return False - -if __name__ == "__main__": - pattern1 = "abab" - string1 = "redblueredblue" - pattern2 = "aaaa" - string2 = "asdasdasdasd" - pattern3 = "aabb" - string3 = "xyzabcxzyabc" - print(pattern_match(pattern1, string1)) - print(pattern_match(pattern2, string2)) - print(pattern_match(pattern3, string3)) diff --git a/backtrack/permute.py b/backtrack/permute.py deleted file mode 100644 index 397597230..000000000 --- a/backtrack/permute.py +++ /dev/null @@ -1,40 +0,0 @@ -# Given a collection of distinct numbers, return all possible permutations. - -# For example, -# [1,2,3] have the following permutations: -# [ - # [1,2,3], - # [1,3,2], - # [2,1,3], - # [2,3,1], - # [3,1,2], - # [3,2,1] -# ] - -def permute(nums): - perms = [[]] - for n in nums: - new_perms = [] - for perm in perms: - for i in range(len(perm)+1): - new_perms.append(perm[:i] + [n] + perm[i:]) ###insert n - print(i, perm[:i], [n], perm[i:], ">>>>", new_perms) - perms = new_perms - return perms - -# DFS Version -# def permute(nums): - # res = [] - # dfs(res, nums, []) - # return res - -# def dfs(res, nums, path): - # if not nums: - # res.append(path) - # for i in range(len(nums)): - # print(nums[:i]+nums[i+1:]) - # dfs(res, nums[:i]+nums[i+1:], path+[nums[i]]) - -test = [1,2,3] -print(test) -print(permute(test)) diff --git a/backtrack/permute_unique.py b/backtrack/permute_unique.py deleted file mode 100644 index 911d40c76..000000000 --- a/backtrack/permute_unique.py +++ /dev/null @@ -1,24 +0,0 @@ -# Given a collection of numbers that might contain duplicates, -# return all possible unique permutations. - -# For example, -# [1,1,2] have the following unique permutations: -# [ - # [1,1,2], - # [1,2,1], - # [2,1,1] -# ] - -def permute_unique(nums): - perms = [[]] - for n in nums: - new_perms = [] - for l in perms: - for i in range(len(l)+1): - new_perms.append(l[:i]+[n]+l[i:]) - if i= len(nums): - # res.append(cur) - # else: - # backtrack(res, nums, cur+[nums[pos]], pos+1) - # backtrack(res, nums, cur, pos+1) - - -# Iteratively -def subsets2(self, nums): - res = [[]] - for num in sorted(nums): - res += [item+[num] for item in res] - return res - -test = [1,2,3] -print(test) -print(subsets(test)) diff --git a/backtrack/subsets_unique.py b/backtrack/subsets_unique.py deleted file mode 100644 index fac0cb0c2..000000000 --- a/backtrack/subsets_unique.py +++ /dev/null @@ -1,38 +0,0 @@ -# Given a collection of integers that might contain duplicates, nums, -# return all possible subsets. - -# Note: The solution set must not contain duplicate subsets. - -# For example, -# If nums = [1,2,2], a solution is: - -# [ - # [2], - # [1], - # [1,2,2], - # [2,2], - # [1,2], - # [] -# ] - -def subsets_unique(nums): - res = set() - backtrack(res, nums, [], 0) - return list(res) - -def backtrack(res, nums, stack, pos): - if pos == len(nums): - res.add(tuple(stack)) - else: - # take - stack.append(nums[pos]) - backtrack(res, nums, stack, pos+1) - stack.pop() - - # don't take - backtrack(res, nums, stack, pos+1) - - -test = [1,2,2] -print(test) -print(subsets_unique(test)) diff --git a/backtrack/word_search.py b/backtrack/word_search.py deleted file mode 100644 index 989e5b29c..000000000 --- a/backtrack/word_search.py +++ /dev/null @@ -1,111 +0,0 @@ -import unittest -''' -Given a matrix of words and a list of words to search, return a list of words that exists in the board -This is Word Search II on LeetCode - -board = [ - ['o','a','a','n'], - ['e','t','a','e'], - ['i','h','k','r'], - ['i','f','l','v'] - ] - -words = ["oath","pea","eat","rain"] - -''' - -def find_words(board, words): - # make a trie structure that is essentially dictionaries of dictionaries that map each character to a potential next character - trie = {} - for word in words: - curr_trie = trie - for char in word: - if char not in curr_trie: - curr_trie[char] = {} - curr_trie = curr_trie[char] - curr_trie['#'] = '#' - - # result is a set of found words since we do not want repeats - result = set() - used = [[False]*len(board[0]) for _ in range(len(board))] - - for i in range(len(board)): - for j in range(len(board[0])): - backtrack(board, i, j, trie, '', used, result) - return list(result) - -''' -backtrack tries to build each words from the board and return all words found -@param: board, the passed in board of characters -@param: i, the row index -@param: j, the column index -@param: trie, a trie of the passed in words -@param: pre, a buffer of currently build string that differs by recursion stack -@param: used, a replica of the board except in booleans to state whether a character has been used -@param: result, the resulting set that contains all words found - -@return: list of words found -''' - -def backtrack(board, i, j, trie, pre, used, result): - if '#' in trie: - result.add(pre) - - if i < 0 or i >= len(board) or j < 0 or j >= len(board[0]): - return - - if not used[i][j] and board[i][j] in trie: - used[i][j]=True - backtrack(board,i+1,j,trie[board[i][j]],pre+board[i][j], used, result) - backtrack(board,i,j+1,trie[board[i][j]],pre+board[i][j], used, result) - backtrack(board,i-1,j,trie[board[i][j]],pre+board[i][j], used, result) - backtrack(board,i,j-1,trie[board[i][j]],pre+board[i][j], used, result) - used[i][j]=False - -class MyTests(unittest.TestCase): - def test_normal(self): - board = [ - ['o','a','a','n'], - ['e','t','a','e'], - ['i','h','k','r'], - ['i','f','l','v'] - ] - - words = ["oath","pea","eat","rain"] - self.assertEqual(find_words(board, words), ['oath', 'eat']) - - def test_none(self): - board = [ - ['o','a','a','n'], - ['e','t','a','e'], - ['i','h','k','r'], - ['i','f','l','v'] - ] - - words = ["chicken", "nugget", "hello", "world"] - self.assertEqual(find_words(board, words), []) - - def test_empty(self): - board = [] - words = [] - self.assertEqual(find_words(board, words), []) - - def test_uneven(self): - board = [ - ['o','a','a','n'], - ['e','t','a','e'] - ] - words = ["oath","pea","eat","rain"] - self.assertEqual(find_words(board, words), ['eat']) - - def test_repeat(self): - board = [ - ['a','a','a'], - ['a','a','a'], - ['a','a','a'] - ] - words = ["a", "aa", "aaa", "aaaa", "aaaaa"] - self.assertTrue(len(find_words(board, words))==5) - -if __name__=="__main__": - unittest.main() diff --git a/bfs/word_ladder.py b/bfs/word_ladder.py deleted file mode 100644 index baf5d8d4e..000000000 --- a/bfs/word_ladder.py +++ /dev/null @@ -1,62 +0,0 @@ -""" -Given two words (beginWord and endWord), and a dictionary's word list, -find the length of shortest transformation sequence -from beginWord to endWord, such that: - -Only one letter can be changed at a time -Each intermediate word must exist in the word list -For example, - -Given: -beginWord = "hit" -endWord = "cog" -wordList = ["hot","dot","dog","lot","log"] -As one shortest transformation is "hit" -> "hot" -> "dot" -> "dog" -> "cog", -return its length 5. -. -Note: -Return 0 if there is no such transformation sequence. -All words have the same length. -All words contain only lowercase alphabetic characters. -""" -def ladderLength(beginWord, endWord, wordList): - """ - Bidirectional BFS!!! - :type beginWord: str - :type endWord: str - :type wordList: Set[str] - :rtype: int - """ - beginSet = set() - endSet = set() - beginSet.add(beginWord) - endSet.add(endWord) - result = 2 - while len(beginSet) != 0 and len(endSet) != 0: - if len(beginSet) > len(endSet): - beginSet, endSet = endSet, beginSet - nextBeginSet = set() - for word in beginSet: - for ladderWord in wordRange(word): - if ladderWord in endSet: - return result - if ladderWord in wordList: - nextBeginSet.add(ladderWord) - wordList.remove(ladderWord) - beginSet = nextBeginSet - result += 1 - print(beginSet) - print(result) - return 0 - -def wordRange(word): - for ind in range(len(word)): - tempC = word[ind] - for c in [chr(x) for x in range(ord('a'), ord('z')+1)]: - if c != tempC: - yield word[:ind] + c + word[ind+1:] - -beginWord = "hit" -endWord = "cog" -wordList = ["hot","dot","dog","lot","log"] -print(ladderLength(beginWord, endWord, wordList)) diff --git a/bit/count_ones.py b/bit/count_ones.py deleted file mode 100644 index 4eb8c59b4..000000000 --- a/bit/count_ones.py +++ /dev/null @@ -1,25 +0,0 @@ -""" -Write a function that takes an unsigned integer and -returns the number of ’1' bits it has -(also known as the Hamming weight). - -For example, the 32-bit integer ’11' has binary -representation 00000000000000000000000000001011, -so the function should return 3. - -T(n)- O(log n) -""" - - -def count_ones(n): - """ - :type n: int - :rtype: int - """ - if n < 0: - return - counter = 0 - while n: - counter += n & 1 - n >>= 1 - return counter diff --git a/calculator/math_parser.py b/calculator/math_parser.py deleted file mode 100644 index 5c6dedd08..000000000 --- a/calculator/math_parser.py +++ /dev/null @@ -1,120 +0,0 @@ -""" -Contributed by izanbf1803. - -Example: -------------------------------------------------------------------------------------------------- - Code: - | exp = "2452 * (3 * 6.5 + 1) * 6 / 235" - | print("Expression:", exp) - | print("Parsed expression:", mp.parse(exp)) - | print("Evaluation result:", mp.evaluate(exp)) - - Output: - | Expression: 2452 * (3 * 6 + 1) * 6 / 235 - | Parsed expression: ['2452', '*', '(', '3', '*', '6', '+', '1', ')', '*', '6', '/', '235'] - | Evaluation result: 1189.4808510638297 -------------------------------------------------------------------------------------------------- -""" - -from collections import deque -import re - -numeric_value = re.compile('\d+(\.\d+)?') - -__operators__ = "+-/*" -__parenthesis__ = "()" -__priority__ = { - '+': 0, - '-': 0, - '*': 1, - '/': 1, -} - -def is_operator(token): - """ - Check if token it's a operator - - token Char: Token - """ - return token in __operators__ - -def higher_priority(op1, op2): - """ - Check if op1 have higher priority than op2 - - op1 Char: Operation Token 1 - op2 Char: Operation Token 2 - """ - return __priority__[op1] >= __priority__[op2] - -def calc(n2, n1, operator): - """ - Calculate operation result - - n2 Number: Number 2 - n1 Number: Number 1 - operator Char: Operation to calculate - """ - if operator == '-': return n1 - n2 - elif operator == '+': return n1 + n2 - elif operator == '*': return n1 * n2 - elif operator == '/': return n1 / n2 - return 0 - -def apply_operation(op_stack, out_stack): - """ - Apply operation to the first 2 items of the output queue - - op_stack Deque (reference) - out_stack Deque (reference) - """ - out_stack.append(calc(out_stack.pop(), out_stack.pop(), op_stack.pop())) - -def parse(expression): - """ - Return array of parsed tokens in the expression - - expression String: Math expression to parse in infix notation - """ - result = [] - current = "" - for i in expression: - if i.isdigit() or i == '.': - current += i - else: - if len(current) > 0: - result.append(current) - current = "" - if i != ' ': - result.append(i) - if len(current) > 0: - result.append(current) - return result - -def evaluate(expression): - """ - Calculate result of expression - - expression String: The expression - type Type (optional): Number type [int, float] - """ - op_stack = deque() # operator stack - out_stack = deque() # output stack (values) - for token in parse(expression): - if numeric_value.match(token): - out_stack.append(float(token)) - elif token == '(': - op_stack.append(token) - elif token == ')': - while len(op_stack) > 0 and op_stack[-1] != '(': - apply_operation(op_stack, out_stack) - op_stack.pop() # Remove remaining '(' - else: # is_operator(token) - while len(op_stack) > 0 and is_operator(op_stack[-1]) and higher_priority(op_stack[-1], token): - apply_operation(op_stack, out_stack) - op_stack.append(token) - - while len(op_stack) > 0: - apply_operation(op_stack, out_stack) - - return out_stack[-1] \ No newline at end of file diff --git a/dfs/sudoku_solver.py b/dfs/sudoku_solver.py deleted file mode 100644 index a6c1a3208..000000000 --- a/dfs/sudoku_solver.py +++ /dev/null @@ -1,79 +0,0 @@ -""" -It's similar to how human solve Sudoku. - -create a hash table (dictionary) val to store possible values in every location. -Each time, start from the location with fewest possible values, choose one value -from it and then update the board and possible values at other locations. -If this update is valid, keep solving (DFS). If this update is invalid (leaving -zero possible values at some locations) or this value doesn't lead to the -solution, undo the updates and then choose the next value. -Since we calculated val at the beginning and start filling the board from the -location with fewest possible values, the amount of calculation and thus the -runtime can be significantly reduced: - - -The run time is 48-68 ms on LeetCode OJ, which seems to be among the fastest -python solutions here. - - -The PossibleVals function may be further simplified/optimized, but it works just -fine for now. (it would look less lengthy if we are allowed to use numpy array -for the board lol). -""" - -def solveSudoku(self, board): - self.board = board - self.val = self.PossibleVals() - self.Solver() - -def PossibleVals(self): - a = "123456789" - d, val = {}, {} - for i in xrange(9): - for j in xrange(9): - ele = self.board[i][j] - if ele != ".": - d[("r", i)] = d.get(("r", i), []) + [ele] - d[("c", j)] = d.get(("c", j), []) + [ele] - d[(i//3, j//3)] = d.get((i//3, j//3), []) + [ele] - else: - val[(i,j)] = [] - for (i,j) in val.keys(): - inval = d.get(("r",i),[])+d.get(("c",j),[])+d.get((i/3,j/3),[]) - val[(i,j)] = [n for n in a if n not in inval ] - return val - -def Solver(self): - if len(self.val)==0: - return True - kee = min(self.val.keys(), key=lambda x: len(self.val[x])) - nums = self.val[kee] - for n in nums: - update = {kee:self.val[kee]} - if self.ValidOne(n, kee, update): # valid choice - if self.Solver(): # keep solving - return True - self.undo(kee, update) # invalid choice or didn't solve it => undo - return False - -def ValidOne(self, n, kee, update): - self.board[kee[0]][kee[1]] = n - del self.val[kee] - i, j = kee - for ind in self.val.keys(): - if n in self.val[ind]: - if ind[0]==i or ind[1]==j or (ind[0]/3,ind[1]/3)==(i/3,j/3): - update[ind] = n - self.val[ind].remove(n) - if len(self.val[ind])==0: - return False - return True - -def undo(self, kee, update): - self.board[kee[0]][kee[1]]="." - for k in update: - if k not in self.val: - self.val[k]= update[k] - else: - self.val[k].append(update[k]) - return None diff --git a/dfs/walls_and_gates.py b/dfs/walls_and_gates.py deleted file mode 100644 index 252cb7a1e..000000000 --- a/dfs/walls_and_gates.py +++ /dev/null @@ -1,22 +0,0 @@ - - -# fill the empty room with distance to its nearest gate - - -def walls_and_gates(rooms): - for i in range(len(rooms)): - for j in range(len(rooms[0])): - if rooms[i][j] == 0: - DFS(rooms, i, j, 0) - - -def DFS(rooms, i, j, depth): - if (i < 0 or i >= len(rooms)) or (j < 0 or j >= len(rooms[0])): - return # out of bounds - if rooms[i][j] < depth: - return # crossed - rooms[i][j] = depth - DFS(rooms, i+1, j, depth+1) - DFS(rooms, i-1, j, depth+1) - DFS(rooms, i, j+1, depth+1) - DFS(rooms, i, j-1, depth+1) diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 000000000..06f6415a1 --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line. +SPHINXOPTS = +SPHINXBUILD = sphinx-build +SPHINXPROJ = algorithms +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/docs/make.bat b/docs/make.bat new file mode 100644 index 000000000..a515cfe0d --- /dev/null +++ b/docs/make.bat @@ -0,0 +1,36 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build +set SPHINXPROJ=algorithms + +if "%1" == "" goto help + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.http://sphinx-doc.org/ + exit /b 1 +) + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% + +:end +popd diff --git a/docs/requirements.txt b/docs/requirements.txt new file mode 100644 index 000000000..3f4e532f7 --- /dev/null +++ b/docs/requirements.txt @@ -0,0 +1,21 @@ +# Progress bars on iterators +tqdm +sphinx_rtd_theme + +# Downloading data and other files +requests + +# Required for tests only: + +# Style-checking for PEP8 +flake8 + +# Run unit tests +pytest + +# Lets pytest find our code by automatically modifying PYTHONPATH +pytest-pythonpath + +# Coverage statistics +pytest-cov +codecov diff --git a/docs/source/_static/algorithms_logo.png b/docs/source/_static/algorithms_logo.png new file mode 100644 index 000000000..2e8487d9e Binary files /dev/null and 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+ :class: hidden-section + +algorithms.backtrack +==================== diff --git a/docs/source/bfs.rst b/docs/source/bfs.rst new file mode 100644 index 000000000..699b9e925 --- /dev/null +++ b/docs/source/bfs.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.bfs +================= diff --git a/docs/source/bit.rst b/docs/source/bit.rst new file mode 100644 index 000000000..b7aa877c0 --- /dev/null +++ b/docs/source/bit.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.bit +================= diff --git a/docs/source/conf.py b/docs/source/conf.py new file mode 100644 index 000000000..768277d1b --- /dev/null +++ b/docs/source/conf.py @@ -0,0 +1,177 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +# +# algorithms documentation build configuration file, created by +# sphinx-quickstart on Wed Jun 6 01:17:26 2018. +# +# This file is execfile()d with the current directory set to its +# containing dir. +# +# Note that not all possible configuration values are present in this +# autogenerated file. +# +# All configuration values have a default; values that are commented out +# serve to show the default. + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +# import os +# import sys +# sys.path.insert(0, os.path.abspath('.')) +from recommonmark.parser import CommonMarkParser + +# -- General configuration ------------------------------------------------ + +# If your documentation needs a minimal Sphinx version, state it here. +# +# needs_sphinx = '1.0' + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = ['sphinx.ext.autodoc', + 'sphinx.ext.doctest', + 'sphinx.ext.todo', + 'sphinx.ext.coverage', + 'sphinx.ext.mathjax', + 'sphinx.ext.ifconfig', + 'sphinx.ext.viewcode', + 'sphinx.ext.githubpages'] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# The suffix(es) of source filenames. +# You can specify multiple suffix as a list of string: +# +source_parsers = { + '.md': CommonMarkParser +} +source_suffix = ['.rst', '.md'] + +# The master toctree document. +master_doc = 'index' + +# General information about the project. +project = 'algorithms' +copyright = '2018, Algorithms Team & Contributors' +author = 'Algorithms Team & Contributors' + +# The version info for the project you're documenting, acts as replacement for +# |version| and |release|, also used in various other places throughout the +# built documents. +# +# The short X.Y version. +version = '0.1.0' +# The full version, including alpha/beta/rc tags. +release = '0.1.0' + +# The language for content autogenerated by Sphinx. Refer to documentation +# for a list of supported languages. +# +# This is also used if you do content translation via gettext catalogs. +# Usually you set "language" from the command line for these cases. +language = None + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This patterns also effect to html_static_path and html_extra_path +exclude_patterns = [] + +# The name of the Pygments (syntax highlighting) style to use. +pygments_style = 'sphinx' + +# If true, `todo` and `todoList` produce output, else they produce nothing. +todo_include_todos = True + + +# -- Options for HTML output ---------------------------------------------- + +# The theme to use for HTML and HTML Help pages. See the documentation for +# a list of builtin themes. +# +html_theme = 'alabaster' + +# Theme options are theme-specific and customize the look and feel of a theme +# further. For a list of options available for each theme, see the +# documentation. +# +# html_theme_options = {} + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +# Custom sidebar templates, must be a dictionary that maps document names +# to template names. +# +# This is required for the alabaster theme +# refs: http://alabaster.readthedocs.io/en/latest/installation.html#sidebars +html_sidebars = { + '**': [ + 'about.html', + 'searchbox.html', + 'navigation.html', + 'relations.html', # needs 'show_related': True theme option to display + ] +} + + +# -- Options for HTMLHelp output ------------------------------------------ + +# Output file base name for HTML help builder. +htmlhelp_basename = 'algorithmsdoc' + + +# -- Options for LaTeX output --------------------------------------------- + +latex_elements = { + # The paper size ('letterpaper' or 'a4paper'). + # + # 'papersize': 'letterpaper', + + # The font size ('10pt', '11pt' or '12pt'). + # + # 'pointsize': '10pt', + + # Additional stuff for the LaTeX preamble. + # + # 'preamble': '', + + # Latex figure (float) alignment + # + # 'figure_align': 'htbp', +} + +# Grouping the document tree into LaTeX files. List of tuples +# (source start file, target name, title, +# author, documentclass [howto, manual, or own class]). +latex_documents = [ + (master_doc, 'algorithms.tex', 'algorithms Documentation', + 'Algorithms Team \\& Contributors', 'manual'), +] + + +# -- Options for manual page output --------------------------------------- + +# One entry per manual page. List of tuples +# (source start file, name, description, authors, manual section). +man_pages = [ + (master_doc, 'algorithms', 'algorithms Documentation', + [author], 1) +] + + +# -- Options for Texinfo output ------------------------------------------- + +# Grouping the document tree into Texinfo files. List of tuples +# (source start file, target name, title, author, +# dir menu entry, description, category) +texinfo_documents = [ + (master_doc, 'algorithms', 'algorithms Documentation', + author, 'algorithms', 'One line description of project.', + 'Miscellaneous'), +] diff --git a/docs/source/dfs.rst b/docs/source/dfs.rst new file mode 100644 index 000000000..1d2c5b6de --- /dev/null +++ b/docs/source/dfs.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.dfs +================= diff --git a/docs/source/dp.rst b/docs/source/dp.rst new file mode 100644 index 000000000..1cc92081e --- /dev/null +++ b/docs/source/dp.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.dp +================= diff --git a/docs/source/examples.rst b/docs/source/examples.rst new file mode 100644 index 000000000..5d3cbdd76 --- /dev/null +++ b/docs/source/examples.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +Examples +================= diff --git a/docs/source/graph.rst b/docs/source/graph.rst new file mode 100644 index 000000000..925d10524 --- /dev/null +++ b/docs/source/graph.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.graph +================= diff --git a/docs/source/heap.rst b/docs/source/heap.rst new file mode 100644 index 000000000..068578a3e --- /dev/null +++ b/docs/source/heap.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.heap +================= diff --git a/docs/source/index.rst b/docs/source/index.rst new file mode 100644 index 000000000..d751ceea4 --- /dev/null +++ b/docs/source/index.rst @@ -0,0 +1,38 @@ +.. image:: /_static/algorithms_logo.png + :target: https://github.com/keon/algorithms + :scale: 50 % + +The :mod:`algorithms` package consists of +minimal and clean example implementations of data structures and algorithms. + +.. toctree:: + :maxdepth: 2 + :caption: Package Reference + + self + algorithms.arrays + algorithms.backtrack + algorithms.bfs + algorithms.bit + algorithms.dfs + algorithms.dp + algorithms.graph + algorithms.heap + algorithms.linkedlist + algorithms.map + algorithms.maths + algorithms.matrix + algorithms.queues + algorithms.search + algorithms.set + algorithms.sort + algorithms.stack + algorithms.strings + algorithms.tree + examples + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` diff --git a/docs/source/linkedlist.rst b/docs/source/linkedlist.rst new file mode 100644 index 000000000..4a37b37e5 --- /dev/null +++ b/docs/source/linkedlist.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.linkedlist +===================== diff --git a/docs/source/map.rst b/docs/source/map.rst new file mode 100644 index 000000000..31d281f85 --- /dev/null +++ b/docs/source/map.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.map +================= diff --git a/docs/source/maths.rst b/docs/source/maths.rst new file mode 100644 index 000000000..1a45b7957 --- /dev/null +++ b/docs/source/maths.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.maths +================= diff --git a/docs/source/matrix.rst b/docs/source/matrix.rst new file mode 100644 index 000000000..4d06e70a4 --- /dev/null +++ b/docs/source/matrix.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.matrix +================= diff --git a/docs/source/queues.rst b/docs/source/queues.rst new file mode 100644 index 000000000..3ee9e18a7 --- /dev/null +++ b/docs/source/queues.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.queue +================= diff --git a/docs/source/search.rst b/docs/source/search.rst new file mode 100644 index 000000000..091f0bf05 --- /dev/null +++ b/docs/source/search.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.search +================= diff --git a/docs/source/set.rst b/docs/source/set.rst new file mode 100644 index 000000000..80984858b --- /dev/null +++ b/docs/source/set.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.set +================= diff --git a/docs/source/sort.rst b/docs/source/sort.rst new file mode 100644 index 000000000..0b106e37b --- /dev/null +++ b/docs/source/sort.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.sort +================= diff --git a/docs/source/stack.rst b/docs/source/stack.rst new file mode 100644 index 000000000..ad1f76525 --- /dev/null +++ b/docs/source/stack.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.stack +================= diff --git a/docs/source/strings.rst b/docs/source/strings.rst new file mode 100644 index 000000000..708df2a0b --- /dev/null +++ b/docs/source/strings.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.string +================= diff --git a/docs/source/tree.rst b/docs/source/tree.rst new file mode 100644 index 000000000..1dea821b4 --- /dev/null +++ b/docs/source/tree.rst @@ -0,0 +1,5 @@ +.. role:: hidden + :class: hidden-section + +algorithms.tree +================= diff --git a/dp/climbing_stairs.py b/dp/climbing_stairs.py deleted file mode 100644 index 6f5f3b697..000000000 --- a/dp/climbing_stairs.py +++ /dev/null @@ -1,32 +0,0 @@ -""" -You are climbing a stair case. -It takes n steps to reach to the top. - -Each time you can either climb 1 or 2 steps. -In how many distinct ways can you climb to the top? - -Note: Given n will be a positive integer. -""" - - -# O(n) space - -def climb_stairs(n): - """ - :type n: int - :rtype: int - """ - arr = [1, 1] - for i in range(2, n+1): - arr.append(arr[-1] + arr[-2]) - return arr[-1] - - -# the above function can be optimized as: -# O(1) space - -def climb_stairs_optimized(n): - a = b = 1 - for _ in range(n): - a, b = b, a + b - return a diff --git a/dp/combination_sum.py b/dp/combination_sum.py deleted file mode 100644 index 469b02885..000000000 --- a/dp/combination_sum.py +++ /dev/null @@ -1,66 +0,0 @@ -""" -Given an integer array with all positive numbers and no duplicates, -find the number of possible combinations that -add up to a positive integer target. - -Example: - -nums = [1, 2, 3] -target = 4 - -The possible combination ways are: -(1, 1, 1, 1) -(1, 1, 2) -(1, 2, 1) -(1, 3) -(2, 1, 1) -(2, 2) -(3, 1) - -Note that different sequences are counted as different combinations. - -Therefore the output is 7. -Follow up: -What if negative numbers are allowed in the given array? -How does it change the problem? -What limitation we need to add to the question to allow negative numbers? - -""" - -dp = None - - -def helper_topdown(nums, target): - global dp - if dp[target] != -1: - return dp[target] - res = 0 - for i in range(0, len(nums)): - if target >= nums[i]: - res += helper_topdown(nums, target - nums[i]) - dp[target] = res - return res - - -def combination_sum_topdown(nums, target): - global dp - dp = [-1] * (target + 1) - dp[0] = 1 - return helper_topdown(nums, target) - - -# EDIT: The above solution is top-down. How about a bottom-up one? -def combination_sum_bottom_up(nums, target): - comb = [0] * (target + 1) - comb[0] = 1 - for i in range(0, len(comb)): - for j in range(len(nums)): - if i - nums[j] >= 0: - comb[i] += comb[i - nums[j]] - return comb[target] - - -combination_sum_topdown([1, 2, 3], 4) -print dp[4] - -print combination_sum_bottom_up([1, 2, 3], 4) diff --git a/dp/job_scheduling.py b/dp/job_scheduling.py deleted file mode 100644 index b644303e7..000000000 --- a/dp/job_scheduling.py +++ /dev/null @@ -1,62 +0,0 @@ -# Python program for weighted job scheduling using Dynamic -# Programming and Binary Search - -# Class to represent a job -class Job: - def __init__(self, start, finish, profit): - self.start = start - self.finish = finish - self.profit = profit - - -# A Binary Search based function to find the latest job -# (before current job) that doesn't conflict with current -# job. "index" is index of the current job. This function -# returns -1 if all jobs before index conflict with it. -# The array jobs[] is sorted in increasing order of finish -# time. -def binarySearch(job, start_index): - - # Initialize 'lo' and 'hi' for Binary Search - lo = 0 - hi = start_index - 1 - - # Perform binary Search iteratively - while lo <= hi: - mid = (lo + hi) // 2 - if job[mid].finish <= job[start_index].start: - if job[mid + 1].finish <= job[start_index].start: - lo = mid + 1 - else: - return mid - else: - hi = mid - 1 - return -1 - -# The main function that returns the maximum possible -# profit from given array of jobs -def schedule(job): - - # Sort jobs according to finish time - job = sorted(job, key = lambda j: j.finish) - - # Create an array to store solutions of subproblems. table[i] - # stores the profit for jobs till arr[i] (including arr[i]) - n = len(job) - table = [0 for _ in range(n)] - - table[0] = job[0].profit; - - # Fill entries in table[] using recursive property - for i in range(1, n): - - # Find profit including the current job - inclProf = job[i].profit - l = binarySearch(job, i) - if (l != -1): - inclProf += table[l]; - - # Store maximum of including and excluding - table[i] = max(inclProf, table[i - 1]) - - return table[n-1] diff --git a/dp/longest_increasing.py b/dp/longest_increasing.py deleted file mode 100644 index 5f6eb8369..000000000 --- a/dp/longest_increasing.py +++ /dev/null @@ -1,23 +0,0 @@ - - -def longest_increasing_subsequence(sequence): - """ - Dynamic Programming Algorithm for - counting the length of longest increasing subsequence - type sequence: List[int] - """ - length = len(sequence) - counts = [1 for _ in range(length)] - for i in range(1, length): - for j in range(0, i): - if sequence[i] > sequence[j]: - counts[i] = max(counts[i], counts[j] + 1) - print(counts) - return max(counts) - - -sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2] -print("sequence: ", sequence) -print("output: ", longest_increasing_subsequence(sequence)) -print("answer: ", 5) - diff --git a/dp/regex_matching.py b/dp/regex_matching.py deleted file mode 100644 index 19ce37a2c..000000000 --- a/dp/regex_matching.py +++ /dev/null @@ -1,107 +0,0 @@ -""" -Implement regular expression matching with support for '.' and '*'. - -'.' Matches any single character. -'*' Matches zero or more of the preceding element. - -The matching should cover the entire input string (not partial). - -The function prototype should be: -bool isMatch(const char *s, const char *p) - -Some examples: -isMatch("aa","a") → false -isMatch("aa","aa") → true -isMatch("aaa","aa") → false -isMatch("aa", "a*") → true -isMatch("aa", ".*") → true -isMatch("ab", ".*") → true -isMatch("aab", "c*a*b") → true -""" - -class Solution(object): - def isMatch(self, s, p): - m, n = len(s) + 1, len(p) + 1 - matches = [[False] * n for _ in range(m)] - - # Match empty string with empty pattern - matches[0][0] = True - - # Match empty string with .* - for i, element in enumerate(p[1:], 2): - matches[0][i] = matches[0][i - 2] and element == '*' - - for i, ss in enumerate(s, 1): - for j, pp in enumerate(p, 1): - if pp != '*': - # The previous character has matched and the current one - # has to be matched. Two possible matches: the same or . - matches[i][j] = matches[i - 1][j - 1] and \ - (ss == pp or pp == '.') - else: - # Horizontal look up [j - 2]. - # Not use the character before *. - matches[i][j] |= matches[i][j - 2] - - # Vertical look up [i - 1]. - # Use at least one character before *. - # p a b * - # s 1 0 0 0 - # a 0 1 0 1 - # b 0 0 1 1 - # b 0 0 0 ? - if ss == p[j - 2] or p[j - 2] == '.': - matches[i][j] |= matches[i - 1][j] - - return matches[-1][-1] - -class TestSolution(unittest.TestCase): - def test_none_0(self): - s = "" - p = "" - self.assertTrue(Solution().isMatch(s, p)) - - def test_none_1(self): - s = "" - p = "a" - self.assertFalse(Solution().isMatch(s, p)) - - def test_no_symbol_equal(self): - s = "abcd" - p = "abcd" - self.assertTrue(Solution().isMatch(s, p)) - - def test_no_symbol_not_equal_0(self): - s = "abcd" - p = "efgh" - self.assertFalse(Solution().isMatch(s, p)) - - def test_no_symbol_not_equal_1(self): - s = "ab" - p = "abb" - self.assertFalse(Solution().isMatch(s, p)) - - def test_symbol_0(self): - s = "" - p = "a*" - self.assertTrue(Solution().isMatch(s, p)) - - def test_symbol_1(self): - s = "a" - p = "ab*" - self.assertTrue(Solution().isMatch(s, p)) - - def test_symbol_2(self): - # E.g. - # s a b b - # p 1 0 0 0 - # a 0 1 0 0 - # b 0 0 1 0 - # * 0 1 1 1 - s = "abb" - p = "ab*" - self.assertTrue(Solution().isMatch(s, p)) - - -if __name__ == "__main__": - unittest.main() diff --git a/dp/rod_cut.py b/dp/rod_cut.py deleted file mode 100644 index 48312b9c3..000000000 --- a/dp/rod_cut.py +++ /dev/null @@ -1,25 +0,0 @@ -# A Dynamic Programming solution for Rod cutting problem -INT_MIN = -32767 - -# Returns the best obtainable price for a rod of length n and -# price[] as prices of different pieces -def cutRod(price, n): - val = [0 for x in range(n+1)] - val[0] = 0 - - # Build the table val[] in bottom up manner and return - # the last entry from the table - for i in range(1, n+1): - max_val = INT_MIN - for j in range(i): - max_val = max(max_val, price[j] + val[i-j-1]) - val[i] = max_val - - return val[n] - -# Driver program to test above functions -arr = [1, 5, 8, 9, 10, 17, 17, 20] -size = len(arr) -print("Maximum Obtainable Value is " + str(cutRod(arr, size))) - -# This code is contributed by Bhavya Jain diff --git a/graph/Transitive_Closure_DFS.py b/graph/Transitive_Closure_DFS.py deleted file mode 100644 index 8e8e74da4..000000000 --- a/graph/Transitive_Closure_DFS.py +++ /dev/null @@ -1,52 +0,0 @@ -# This class represents a directed graph using adjacency -class Graph: - def __init__(self, vertices): - # No. of vertices - self.V = vertices - - # default dictionary to store graph - self.graph = {} - - # To store transitive closure - self.tc = [[0 for j in range(self.V)] for i in range(self.V)] - - # function to add an edge to graph - def add_edge(self, u, v): - if u in self.graph: - self.graph[u].append(v) - else: - self.graph[u] = [v] - - # A recursive DFS traversal function that finds - # all reachable vertices for s - def dfs_util(self, s, v): - - # Mark reachability from s to v as true. - self.tc[s][v] = 1 - - # Find all the vertices reachable through v - for i in self.graph[v]: - if self.tc[s][i] == 0: - self.dfs_util(s, i) - - # The function to find transitive closure. It uses - # recursive dfs_util() - def transitive_closure(self): - - # Call the recursive helper function to print DFS - # traversal starting from all vertices one by one - for i in range(self.V): - self.dfs_util(i, i) - print(self.tc) - - -g = Graph(4) -g.add_edge(0, 1) -g.add_edge(0, 2) -g.add_edge(1, 2) -g.add_edge(2, 0) -g.add_edge(2, 3) -g.add_edge(3, 3) - -print("Transitive closure matrix is") -g.transitive_closure() diff --git a/graph/clone_graph.py b/graph/clone_graph.py deleted file mode 100644 index d2af1def6..000000000 --- a/graph/clone_graph.py +++ /dev/null @@ -1,93 +0,0 @@ -""" -Clone an undirected graph. Each node in the graph contains a label and a list -of its neighbors. - - -OJ's undirected graph serialization: -Nodes are labeled uniquely. - -We use # as a separator for each node, and , as a separator for node label and -each neighbor of the node. -As an example, consider the serialized graph {0,1,2#1,2#2,2}. - -The graph has a total of three nodes, and therefore contains three parts as -separated by #. - -First node is labeled as 0. Connect node 0 to both nodes 1 and 2. -Second node is labeled as 1. Connect node 1 to node 2. -Third node is labeled as 2. Connect node 2 to node 2 (itself), thus forming a -self-cycle. -Visually, the graph looks like the following: - - 1 - / \ - / \ - 0 --- 2 - / \ - \_/ -""" - - -# Definition for a undirected graph node -# class UndirectedGraphNode: -# def __init__(self, x): -# self.label = x -# self.neighbors = [] - - -# BFS -def cloneGraph1(self, node): - if not node: - return - nodeCopy = UndirectedGraphNode(node.label) - dic = {node: nodeCopy} - queue = collections.deque([node]) - while queue: - node = queue.popleft() - for neighbor in node.neighbors: - if neighbor not in dic: # neighbor is not visited - neighborCopy = UndirectedGraphNode(neighbor.label) - dic[neighbor] = neighborCopy - dic[node].neighbors.append(neighborCopy) - queue.append(neighbor) - else: - dic[node].neighbors.append(dic[neighbor]) - return nodeCopy - -# DFS iteratively -def cloneGraph2(self, node): - if not node: - return - nodeCopy = UndirectedGraphNode(node.label) - dic = {node: nodeCopy} - stack = [node] - while stack: - node = stack.pop() - for neighbor in node.neighbors: - if neighbor not in dic: - neighborCopy = UndirectedGraphNode(neighbor.label) - dic[neighbor] = neighborCopy - dic[node].neighbors.append(neighborCopy) - stack.append(neighbor) - else: - dic[node].neighbors.append(dic[neighbor]) - return nodeCopy - -# DFS recursively -def cloneGraph(self, node): - if not node: - return - nodeCopy = UndirectedGraphNode(node.label) - dic = {node: nodeCopy} - self.dfs(node, dic) - return nodeCopy - -def dfs(self, node, dic): - for neighbor in node.neighbors: - if neighbor not in dic: - neighborCopy = UndirectedGraphNode(neighbor.label) - dic[neighbor] = neighborCopy - dic[node].neighbors.append(neighborCopy) - self.dfs(neighbor, dic) - else: - dic[node].neighbors.append(dic[neighbor]) diff --git a/graph/graph.py b/graph/graph.py deleted file mode 100644 index 7e551f3d6..000000000 --- a/graph/graph.py +++ /dev/null @@ -1,25 +0,0 @@ -class Graph: - def __init__(self, vertices): - # No. of vertices - self.V = vertices - - # default dictionary to store graph - self.graph = {} - - # To store transitive closure - self.tc = [[0 for j in range(self.V)] for i in range(self.V)] - - # function to add an edge to graph - def add_edge(self, u, v): - if u in self.graph: - self.graph[u].append(v) - else: - self.graph[u] = [v] - -g = Graph(4) -g.add_edge(0, 1) -g.add_edge(0, 2) -g.add_edge(1, 2) -g.add_edge(2, 0) -g.add_edge(2, 3) -g.add_edge(3, 3) diff --git a/graph/markov_chain.py b/graph/markov_chain.py deleted file mode 100644 index c588311d2..000000000 --- a/graph/markov_chain.py +++ /dev/null @@ -1,26 +0,0 @@ -import random - -my_chain = { - 'A': {'A': 0.6, - 'E': 0.4}, - 'E': {'A': 0.7, - 'E': 0.3} -} - -def __choose_state(state_map): - choice = random.random() - probability_reached = 0 - for state, probability in state_map.items(): - probability_reached += probability - if probability_reached > choice: - return state - -def next_state(chain, current_state): - next_state_map = chain.get(current_state) - next_state = __choose_state(next_state_map) - return next_state - -def iterating_markov_chain(chain, state): - while True: - state = next_state(chain, state) - yield state diff --git a/graph/minimum_spanning_tree.py b/graph/minimum_spanning_tree.py deleted file mode 100644 index 2f47e39bc..000000000 --- a/graph/minimum_spanning_tree.py +++ /dev/null @@ -1,130 +0,0 @@ -# Minimum spanning tree (MST) is going to use an undirected graph -# -# The disjoint set is represented with an list of integers where -# is the parent of the node at position . -# If = , it's a root, or a head, of a set - - -class Edge: - def __init__(self, u, v, weight): - self.u = u - self.v = v - self.weight = weight - - -class DisjointSet: - def __init__(self, n): - # Args: - # n (int): Number of vertices in the graph - - self.parent = [None] * n # Contains wich node is the parent of the node at poisition - self.size = [1] * n # Contains size of node at index , used to optimize merge - for i in range(n): - self.parent[i] = i # Make all nodes his own parent, creating n sets. - - def mergeSet(self, a, b): - # Args: - # a, b (int): Indexes of nodes whose sets will be merged. - - # Get the set of nodes at position and - # If and are the roots, this will be constant O(1) - a = self.findSet(a) - b = self.findSet(b) - - # Join the shortest node to the longest, minimizing tree size (faster find) - if self.size[a] < self.size[b]: - self.parent[a] = b # Merge set(a) and set(b) - self.size[b] += self.size[a] # Add size of old set(a) to set(b) - else: - self.parent[b] = a # Merge set(b) and set(a) - self.size[a] += self.size[b] # Add size of old set(b) to set(a) - - def findSet(self, a): - if self.parent[a] != a: - # Very important, memoize result of the - # recursion in the list to optimize next - # calls and make this operation practically constant, O(1) - self.parent[a] = self.findSet(self.parent[a]) - - # node it's the set root, so we can return that index - return self.parent[a] - - -def kruskal(n, edges, ds): - # Args: - # n (int): Number of vertices in the graph - # edges (list of Edge): Edges of the graph - # ds (DisjointSet): DisjointSet of the vertices - # Returns: - # int: sum of weights of the minnimum spanning tree - # - # Kruskal algorithm: - # This algorithm will find the optimal graph with less edges and less - # total weight to connect all vertices (MST), the MST will always contain - # n-1 edges because it's the minimum required to connect n vertices. - # - # Procedure: - # Sort the edges (criteria: less weight). - # Only take edges of nodes in different sets. - # If we take a edge, we need to merge the sets to discard these. - # After repeat this until select n-1 edges, we will have the complete MST. - edges.sort(key=lambda edge: edge.weight) - - mst = [] # List of edges taken, minimum spanning tree - - for edge in edges: - set_u = ds.findSet(edge.u) # Set of the node - set_v = ds.findSet(edge.v) # Set of the node - if set_u != set_v: - ds.mergeSet(set_u, set_v) - mst.append(edge) - if len(mst) == n-1: - # If we have selected n-1 edges, all the other - # edges will be discarted, so, we can stop here - break - - return sum([edge.weight for edge in mst]) - - - - -if __name__ == "__main__": - # Test. How input works: - # Input consists of different weighted, connected, undirected graphs. - # line 1: - # integers n, m - # lines 2..m+2: - # edge with the format -> node index u, node index v, integer weight - # - # Samples of input: - # - # 5 6 - # 1 2 3 - # 1 3 8 - # 2 4 5 - # 3 4 2 - # 3 5 4 - # 4 5 6 - # - # 3 3 - # 2 1 20 - # 3 1 20 - # 2 3 100 - # - # Sum of weights of the optimal paths: - # 14, 40 - import sys - for n_m in sys.stdin: - n, m = map(int, n_m.split()) - ds = DisjointSet(m) - edges = [None] * m # Create list of size - - # Read edges from input - for i in range(m): - u, v, weight = map(int, input().split()) - u -= 1 # Convert from 1-indexed to 0-indexed - v -= 1 # Convert from 1-indexed to 0-indexed - edges[i] = Edge(u, v, weight) - - # After finish input and graph creation, use Kruskal algorithm for MST: - print("MST weights sum:", kruskal(n, edges, ds)) \ No newline at end of file diff --git a/graph/traversal.py b/graph/traversal.py deleted file mode 100644 index cbfc65ff4..000000000 --- a/graph/traversal.py +++ /dev/null @@ -1,66 +0,0 @@ -graph = {'A': set(['B', 'C', 'F']), - 'B': set(['A', 'D', 'E']), - 'C': set(['A', 'F']), - 'D': set(['B']), - 'E': set(['B', 'F']), - 'F': set(['A', 'C', 'E'])} - -# dfs and bfs are the ultimately same except that they are visiting nodes in -# different order. To simulate this ordering we would use stack for dfs and -# queue for bfs. -# - -def dfs_traverse(graph, start): - visited, stack = set(), [start] - while stack: - node = stack.pop() - if node not in visited: - visited.add(node) - for nextNode in graph[node]: - if nextNode not in visited: - stack.append(nextNode) - return visited - -# print(dfs_traverse(graph, 'A')) - - -def bfs_traverse(graph, start): - visited, queue = set(), [start] - while queue: - node = queue.pop(0) - if node not in visited: - visited.add(node) - for nextNode in graph[node]: - if nextNode not in visited: - queue.append(nextNode) - return visited - -# print(bfs_traverse(graph, 'A')) - -def dfs_traverse_recursive(graph, start, visited=None): - if visited is None: - visited = set() - visited.add(start) - for nextNode in graph[start]: - if nextNode not in visited: - dfs_traverse_recursive(graph, nextNode, visited) - return visited - -# print(dfs_traverse_recursive(graph, 'A')) - -# def find_path(graph, start, end, visited=[]): - # # basecase - # visitied = visited + [start] - # if start == end: - # return visited - # if start not in graph: - # return None - # for node in graph[start]: - # if node not in visited: - # new_visited = find_path(graph, node, end, visited) - # return new_visited - # return None - -# print(find_path(graph, 'A', 'F')) - - diff --git a/heap/merge_sorted_k_lists.py b/heap/merge_sorted_k_lists.py deleted file mode 100644 index 266b12321..000000000 --- a/heap/merge_sorted_k_lists.py +++ /dev/null @@ -1,63 +0,0 @@ -""" -Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity. -""" - -# Definition for singly-linked list. -# class ListNode(object): -# def __init__(self, x): -# self.val = x -# self.next = None - -from heapq import heappush, heappop, heapreplace, heapify - -def mergeKLists(lists): - dummy = node = ListNode(0) - h = [(n.val, n) for n in lists if n] - heapify(h) - while h: - v, n = h[0] - if n.next is None: - heappop(h) #only change heap size when necessary - else: - heapreplace(h, (n.next.val, n.next)) - node.next = n - node = node.next - - return dummy.next - -from Queue import PriorityQueue - -def merge_k_lists(lists): - dummy = ListNode(None) - curr = dummy - q = PriorityQueue() - for node in lists: - if node: q.put((node.val,node)) - while q.qsize()>0: - curr.next = q.get()[1] - curr=curr.next - if curr.next: q.put((curr.next.val, curr.next)) - return dummy.next - - -""" -I think my code's complexity is also O(nlogk) and not using heap or priority queue, -n means the total elements and k means the size of list. - -The mergeTwoLists functiony in my code comes from the problem Merge Two Sorted Lists -whose complexity obviously is O(n), n is the sum of length of l1 and l2. - -To put it simpler, assume the k is 2^x, So the progress of combination is like a full binary tree, -from bottom to top. So on every level of tree, the combination complexity is n, -beacause every level have all n numbers without repetition. -The level of tree is x, ie logk. So the complexity is O(nlogk). - -for example, 8 ListNode, and the length of every ListNode is x1, x2, -x3, x4, x5, x6, x7, x8, total is n. - -on level 3: x1+x2, x3+x4, x5+x6, x7+x8 sum: n - -on level 2: x1+x2+x3+x4, x5+x6+x7+x8 sum: n - -on level 1: x1+x2+x3+x4+x5+x6+x7+x8 sum: n -""" diff --git a/linkedlist/add_two_numbers.py b/linkedlist/add_two_numbers.py deleted file mode 100644 index 2f6d67513..000000000 --- a/linkedlist/add_two_numbers.py +++ /dev/null @@ -1,53 +0,0 @@ -""" -You are given two non-empty linked lists representing -two non-negative integers. The digits are stored in reverse order -and each of their nodes contain a single digit. -Add the two numbers and return it as a linked list. - -You may assume the two numbers do not contain any leading zero, -except the number 0 itself. - -Input: (2 -> 4 -> 3) + (5 -> 6 -> 4) -Output: 7 -> 0 -> 8 -""" - - -class Node: - def __init__(self, x): - self.val = x - self.next = None - - -def add_two_numbers(left:"Node", right:"Node")->"Node": - head = Node(0) - current = head - sum = 0 - while left or right: - print("adding: ", left.val, right.val) - sum //= 10 - if left: - sum += left.val - left = left.next - if right: - sum += right.val - right = right.next - current.next = Node(sum % 10) - current = current.next - if sum // 10 == 1: - current.next = Node(1) - return head.next - - -if __name__ == "__main__": - left = Node(2) - left.next = Node(4) - left.next.next = Node(3) - - right = Node(5) - right.next = Node(6) - right.next.next = Node(4) - - res = add_two_numbers(left, right) - while res: - print(res.val) - res = res.next diff --git a/linkedlist/delete_node.py b/linkedlist/delete_node.py deleted file mode 100644 index 93e761fef..000000000 --- a/linkedlist/delete_node.py +++ /dev/null @@ -1,13 +0,0 @@ -""" -Write a function to delete a node (except the tail) -in a singly linked list, given only access to that node. - -Supposed the linked list is 1 -> 2 -> 3 -> 4 and -you are given the third node with value 3, -the linked list should become 1 -> 2 -> 4 after calling your function. -""" - - -def delete_node(node): - node.val = node.next.val - node.next = node.next.next diff --git a/linkedlist/first_cyclic_node.py b/linkedlist/first_cyclic_node.py deleted file mode 100644 index 48e66bc9e..000000000 --- a/linkedlist/first_cyclic_node.py +++ /dev/null @@ -1,8 +0,0 @@ -# find the first node of a cycle in the linked list. - -# 1 -> 2 -> 3 -> 4 -> 5 -> 1 => 1 -# A -> B -> C -> D -> E -> C => C - -def firstCyclicNode(): - pass - diff --git a/linkedlist/is_palindrome.py b/linkedlist/is_palindrome.py deleted file mode 100644 index b42b20727..000000000 --- a/linkedlist/is_palindrome.py +++ /dev/null @@ -1,48 +0,0 @@ -def is_palindrome(head): - if not head: - return True - # split the list to two parts - fast, slow = head.next, head - while fast and fast.next: - fast = fast.next.next - slow = slow.next - second = slow.next - slow.next = None # Don't forget here! But forget still works! - # reverse the second part - node = None - while second: - nxt = second.next - second.next = node - node = second - second = nxt - # compare two parts - # second part has the same or one less node - while node: - if node.val != head.val: - return False - node = node.next - head = head.next - return True - -def is_palindrome_stack(head): - if not head or not head.next: - return True - - # 1. Get the midpoint (slow) - slow = fast = cur = head - while fast and fast.next: - fast, slow = fast.next.next, slow.next - - # 2. Push the second half into the stack - stack = [slow.val] - while slow.next: - slow = slow.next - stack.append(slow.val) - - # 3. Comparison - while stack: - if stack.pop() != cur.val: - return False - cur = cur.next - - return True diff --git a/linkedlist/kth_to_last.py b/linkedlist/kth_to_last.py deleted file mode 100644 index 873bdccac..000000000 --- a/linkedlist/kth_to_last.py +++ /dev/null @@ -1,44 +0,0 @@ -class Node(): - def __init__(self, val = None): - self.val = val - self.next = None - -def printKthToLast(head): - """ - Time Complexity: O() - Space Complexity: O() - """ - pass - -def printLinkedList(head): - string = "" - while head.next: - string += head.val + " -> " - head = head.next - string += head.val - print(string) - -# A A B C D C F G - -a1 = Node("A") -a2 = Node("A") -b = Node("B") -c1 = Node("C") -d = Node("D") -c2 = Node("C") -f = Node("F") -g = Node("G") - -a1.next = a2 -a2.next = b -b.next = c1 -c1.next = d -d.next = c2 -c2.next = f -f.next = g - -# removeDups(a1) -# printLinkedList(a1) -# removeDupsWithoutSet(a1) -# printLinkedList(a1) - diff --git a/linkedlist/swap_in_pairs.py b/linkedlist/swap_in_pairs.py deleted file mode 100644 index ef0ed2eda..000000000 --- a/linkedlist/swap_in_pairs.py +++ /dev/null @@ -1,45 +0,0 @@ -""" -Given a linked list, swap every two adjacent nodes -and return its head. - -For example, -Given 1->2->3->4, you should return the list as 2->1->4->3. - -Your algorithm should use only constant space. -You may not modify the values in the list, -only nodes itself can be changed. -""" - - -class Node: - def __init__(self, x=0): - self.val = x - self.next = None - - -def swap_pairs(head:"Node")->"Node": - if not head: - return head - start = Node() - pre = start - pre.next = head - while pre.next and pre.next.next: - a = pre.next - b = pre.next.next - pre.next, a.next, b.next = b, b.next, a - pre = a - return start.next - - -if __name__ == "__main__": - n = Node(1) - n.next = Node(2) - n.next.next = Node(3) - n.next.next.next = Node(4) - res = swap_pairs(n) - - while res: - print(res.val, end=" ") - res = res.next - print("should be 2 1 4 3 ") - diff --git a/math/extended_gcd.py b/math/extended_gcd.py deleted file mode 100644 index 69ecfa301..000000000 --- a/math/extended_gcd.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -extended GCD algorithm -return s,t,g -such that a s + b t = GCD(a, b) -and s and t are coprime -""" - -def extended_gcd(a,b): - old_s, s = 1, 0 - old_t, t = 0, 1 - old_r, r = a, b - - while r != 0: - quotient = old_r / r - - old_r, r = r, old_r - quotient * r - old_s, s = s, old_s - quotient * s - old_t, t = t, old_t - quotient * t - - return old_s, old_t, old_r \ No newline at end of file diff --git a/math/gcd.py b/math/gcd.py deleted file mode 100644 index 9792d8faa..000000000 --- a/math/gcd.py +++ /dev/null @@ -1,13 +0,0 @@ -def gcd(a, b): - """Computes the greatest common divisor of integers a and b using - Euclid's Algorithm. - """ - while True: - if b == 0: - return a - a, b = b, a % b - - -def lcm(a, b): - """Computes the lowest common multiple of integers a and b.""" - return a * b / gcd(a, b) diff --git a/math/nth_digit.py b/math/nth_digit.py deleted file mode 100644 index ea2d6819e..000000000 --- a/math/nth_digit.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -find nth digit -1. find the length of the number where the nth digit is from. -2. find the actual number where the nth digit is from -3. find the nth digit and return -""" - - -def find_nth_digit(n): - len = 1 - count = 9 - start = 1 - while n > len * count: - n -= len * count - len += 1 - count *= 10 - start *= 10 - start += (n-1) / len - s = str(start) - return int(s[(n-1) % len]) \ No newline at end of file diff --git a/math/prime_test.py b/math/prime_test.py deleted file mode 100644 index c3b795e4b..000000000 --- a/math/prime_test.py +++ /dev/null @@ -1,18 +0,0 @@ -''' -prime_test(n) returns a True if n is a prime number else it returns False -''' - - -def prime_test(n): - if n <= 1: - return False - if n==2 or n==3: - return True - if n%2==0 or n%3==0: - return False - j = 5 - while(j*j <= n): - if n%(j)==0 or n%(j+2)==0: - return False - j += 6 - return True \ No newline at end of file diff --git a/math/pythagoras.py b/math/pythagoras.py deleted file mode 100644 index 8effe1349..000000000 --- a/math/pythagoras.py +++ /dev/null @@ -1,16 +0,0 @@ -""" -input two of the three side in right angled triangle and return the third. use "?" to indicate the unknown side. -""" - -def pythagoras(opposite,adjacent,hypotenuse): - try: - if opposite == str("?"): - return ("Opposite = " + str(((hypotenuse**2) - (adjacent**2))**0.5)) - elif adjacent == str("?"): - return ("Adjacent = " + str(((hypotenuse**2) - (opposite**2))**0.5)) - elif hypotenuse == str("?"): - return ("Hypotenuse = " + str(((opposite**2) + (adjacent**2))**0.5)) - else: - return "You already know the answer!" - except: - print ("Error, check your input. You must know 2 of the 3 variables.") diff --git a/math/rabin_miller.py b/math/rabin_miller.py deleted file mode 100644 index b06db5c68..000000000 --- a/math/rabin_miller.py +++ /dev/null @@ -1,45 +0,0 @@ -import random,sys - -# factor n into a power of 2 times an odd number -def pow2_factor(n): - power = 0 - while n % 2 == 0: - n /= 2 - power += 1 - return power, n - -""" -Rabin-Miller primality test -returning False implies that n is guarenteed composite -returning True means that n is probably prime -with a 4 ** -k chance of being wrong -""" -def is_prime(n, k): - r, d = pow2_factor(n - 1) - - """ - returns true if a is a valid 'witness' for n - a valid witness increases chances of n being prime - an invalid witness guarentees n is composite - """ - def valid_witness(a): - x = pow(a, d, n) - - if x == 1 or x == n - 1: - return False - - for _ in range(r - 1): - x = pow(x, 2, n) - - if x == 1: - return True - if x == n - 1: - return False - - return True - - for _ in range(k): - if valid_witness(random.randrange(2, n - 2)): - return False - - return True \ No newline at end of file diff --git a/math/rsa.py b/math/rsa.py deleted file mode 100644 index f3b0f6866..000000000 --- a/math/rsa.py +++ /dev/null @@ -1,80 +0,0 @@ -""" -RSA encryption algorithm -a method for encrypting a number that uses seperate encryption and decryption keys -this file only implements the key generation algorithm - -there are three important numbers in RSA called n, e, and d -e is called the encryption exponent -d is called the decryption exponent -n is called the modulus - -these three numbers satisfy -((x ** e) ** d) % n == x % n - -to use this system for encryption, n and e are made publicly available, and d is kept secret -a number x can be encrypted by computing (x ** e) % n -the original number can then be recovered by computing (E ** d) % n, where E is -the encrypted number - -fortunately, python provides a three argument version of pow() that can compute powers modulo -a number very quickly: -(a ** b) % c == pow(a,b,c) -""" - -import random - -from rabin_miller import * # is_prime -from extended_gcd import * # extended_gcd - -""" -generate a prime with k bits -""" -def genprime(k): - while True: - n = random.randrange(2 ** (k - 1),2 ** k) - if is_prime(n,128): - return n - -""" -calculate the inverse of a mod m -that is, find b such that (a * b) % m == 1 -""" -def modinv(a, m): - x, y, g = extended_gcd(a,m) - return x % m - -""" -the RSA key generating algorithm -k is the number of bits in n -""" -def generate_key(k): - # size in bits of p and q need to add up to the size of n - p_size = k / 2 - q_size = k - p_size - - e = genprime(k) # in many cases, e is also chosen to be a small constant - - while True: - p = genprime(k / 2) - if p % e != 1: - break - - while True: - q = genprime(k - k / 2) - if q % e != 1: - break - - n = p * q - l = (p - 1) * (q - 1) # calculate totient function - d = modinv(e,l) - - return n, e, d - -""" -sample usage: -n,e,d = generate_key(1024) -data = 1337 -encrypted = pow(data,e,n) -decrypted = pow(encrypted,d,n) -assert decrypted == data -""" diff --git a/math/sqrt_precision_factor.py b/math/sqrt_precision_factor.py deleted file mode 100644 index ce4f0cf94..000000000 --- a/math/sqrt_precision_factor.py +++ /dev/null @@ -1,17 +0,0 @@ -""" -Given a positive integer N and a precision factor P, -write a square root function that produce an output -with a maximum error P from the actual square root of N. - -Example: -Given N = 5 and P = 0.001, can produce output O such that -2.235 < O > 2.237. Actual square root of 5 being 2.236. -""" - -def square_root(n,p): - guess = float(n) / 2 - - while abs(guess * guess - n) > p: - guess = (guess + (n / guess)) / 2 - - return guess diff --git a/matrix/bomb_enemy.py b/matrix/bomb_enemy.py deleted file mode 100644 index 0310c1197..000000000 --- a/matrix/bomb_enemy.py +++ /dev/null @@ -1,62 +0,0 @@ -# Given a 2D grid, each cell is either a wall 'W', -# an enemy 'E' or empty '0' (the number zero), -# return the maximum enemies you can kill using one bomb. -# The bomb kills all the enemies in the same row and column from -# the planted point until it hits the wall since the wall is too strong -# to be destroyed. -# Note that you can only put the bomb at an empty cell. - -# Example: -# For the given grid - -# 0 E 0 0 -# E 0 W E -# 0 E 0 0 - -# return 3. (Placing a bomb at (1,1) kills 3 enemies) - -def max_killed_enemies(grid): - if not grid: return 0 - m, n = len(grid), len(grid[0]) - max_killed = 0 - row_e, col_e = 0, [0] * n - for i in range(m): - for j in range(n): - if j == 0 or grid[i][j-1] == 'W': - row_e = row_kills(grid, i, j) - - if i == 0 or grid[i-1][j] == 'W': - col_e[j] = col_kills(grid, i, j) - - if grid[i][j] == '0': - max_killed = max(max_killed, row_e + col_e[j]) - - return max_killed - -# calculate killed enemies for row i from column j -def row_kills(grid, i, j): - num = 0 - while j < len(grid[0]) and grid[i][j] != 'W': - if grid[i][j] == 'E': - num += 1 - j += 1 - return num - -# calculate killed enemies for column j from row i -def col_kills(grid, i, j): - num = 0 - while i < len(grid) and grid[i][j] != 'W': - if grid[i][j] == 'E': - num += 1 - i += 1 - return num - -grid = [ -["0", "E", "0", "E"], -["E", "E", "E", "0"], -["E", "0", "W", "E"], -["0", "E", "0", "0"]] -print(grid) - -print(max_killed_enemies(grid)) - diff --git a/matrix/matrix_rotation.txt b/matrix/matrix_rotation.txt deleted file mode 100644 index c25eb201b..000000000 --- a/matrix/matrix_rotation.txt +++ /dev/null @@ -1,580 +0,0 @@ -I'd like to add a little more detail. -In this answer, key concepts are repeated, the pace is slow and intentionally -repetitive. The solution provided here is not the most syntactically compact, -it is however intended for those who wish to learn what matrix rotation is and -the resulting implementation. - -Firstly, what is a matrix? For the purposes of this answer, a matrix is just -a grid where the width and height are the same. Note, the width and height -of a matrix can be different, but for simplicity, this tutorial considers only -matrices with equal width and height -(and yes, matrices is the plural of matrix). -Example matrices are: 2x2, 3x3 or 5x5. Or, more generally, NxN. -A 2x2 matrix will have 4 squares because 2x2=4. -A 5x5 matrix will have 25 squares because 5x5=25. -Each square is called an element or entry. We’ll represent each element with -a period (.) in the diagrams below: - -2x2 matrix - - . . - . . - -3x3 matrix - - . . . - . . . - . . . - -4x4 matrix - - . . . . - . . . . - . . . . - . . . . - - -So, what does it mean to rotate a matrix? Let’s take a 2x2 matrix and -put some numbers in each element so the rotation can be observed: - - 0 1 - 2 3 - -Rotating this by 90 degrees gives us: - - 2 0 - 3 1 - -We literally turned the whole matrix once to the right just like turning the -steering wheel of a car. It may help to think of “tipping” the matrix onto -its right side. We want to write a function, in Python, that takes a matrix and -rotates in once to the right. The function signature will be: - - def rotate(matrix): - # Algorithm goes here. - -The matrix will be defined using a two-dimensional array: - - matrix = [ - [0,1], - [2,3] - ] - -Therefore the first index position accesses the row. -The second index position accesses the column: - - matrix[row][column] - -We’ll define a utility function to print a matrix. - - def print_matrix(matrix): - for row in matrix: - print row - -One method of rotating a matrix is to do it a layer at a time. -But what is a layer? Think of an onion. Just like the layers of an onion, -as each layer is removed, we move towards the center. -ther analogies is a Matryoshka doll or a game of pass-the-parcel. - -The width and height of a matrix dictate the number of layers in that matrix. -Let’s use different symbols for each layer: - -2x2 matrix has 1 layer - - . . - . . - -3x3 matrix has 2 layers - - . . . - . x . - . . . - -4x4 matrix has 2 layers - - . . . . - . x x . - . x x . - . . . . - -5x5 matrix has 3 layers - - . . . . . - . x x x . - . x O x . - . x x x . - . . . . . - -6x6 matrix has 3 layers - - . . . . . . - . x x x x . - . x O O x . - . x O O x . - . x x x x . - . . . . . . - -7x7 matrix has 4 layers - - . . . . . . . - . x x x x x . - . x O O O x . - . x O - O x . - . x O O O x . - . x x x x x . - . . . . . . . - -You may notice that incrementing the width and height of a matrix by one, -does not always increase the number of layers. -Taking the above matrices and tabulating the layers and dimensions, -we see the number of layers increases once for every two increments of -width and height: - - +-----+--------+ - | NxN | Layers | - +-----+--------+ - | 1x1 | 1 | - | 2x2 | 1 | - | 3x3 | 2 | - | 4x4 | 2 | - | 5x5 | 3 | - | 6x6 | 3 | - | 7x7 | 4 | - +-----+--------+ - -However, not all layers need rotating. -A 1x1 matrix is the same before and after rotation. -The central 1x1 layer is always the same before and -after rotation no matter how large the overall matrix: - - +-----+--------+------------------+ - | NxN | Layers | Rotatable Layers | - +-----+--------+------------------+ - | 1x1 | 1 | 0 | - | 2x2 | 1 | 1 | - | 3x3 | 2 | 1 | - | 4x4 | 2 | 2 | - | 5x5 | 3 | 2 | - | 6x6 | 3 | 3 | - | 7x7 | 4 | 3 | - +-----+--------+------------------+ - -Given NxN matrix, how can we programmatically determine the number of layers -we need to rotate? -If we divide the width or height by two and ignore the remainder -we get the following results. - - +-----+--------+------------------+---------+ - | NxN | Layers | Rotatable Layers | N/2 | - +-----+--------+------------------+---------+ - | 1x1 | 1 | 0 | 1/2 = 0 | - | 2x2 | 1 | 1 | 2/2 = 1 | - | 3x3 | 2 | 1 | 3/2 = 1 | - | 4x4 | 2 | 2 | 4/2 = 2 | - | 5x5 | 2 | 2 | 5/2 = 2 | - | 6x6 | 3 | 3 | 6/2 = 3 | - | 7x7 | 4 | 3 | 7/2 = 3 | - +-----+--------+------------------+---------+ - -Notice how N/2 matches the number of layers that need to be rotated? -Sometimes the number of rotatable layers is one less the total number of -layers in the matrix. -This occurs when the innermost layer is formed of only one element -(i.e. a 1x1 matrix) and therefore need not be rotated. It simply gets ignored. - -We will undoubtedly need this information in our function to -rotate a matrix, so let’s add it now: - - def rotate(matrix): - size = len(matrix) - # Rotatable layers only. - layer_count = size / 2 - -Now we know what layers are and how to determine the number of layers -that actually need rotating, how do we isolate a single layer so we can rotate -it? Firstly, we inspect a matrix from the outermost layer, -inwards, to the innermost layer. -A 5x5 matrix has three layers in total and two layers that need rotating: - - . . . . . - . x x x . - . x O x . - . x x x . - . . . . . - -Let’s look at columns first. The position of the columns defining the -outermost layer, assuming we count from 0, are 0 and 4: - - +--------+-----------+ - | Column | 0 1 2 3 4 | - +--------+-----------+ - | | . . . . . | - | | . x x x . | - | | . x O x . | - | | . x x x . | - | | . . . . . | - +--------+-----------+ - -0 and 4 are also the positions of the rows for the outermost layer. - - +-----+-----------+ - | Row | | - +-----+-----------+ - | 0 | . . . . . | - | 1 | . x x x . | - | 2 | . x O x . | - | 3 | . x x x . | - | 4 | . . . . . | - +-----+-----------+ - -This will always be the case since the width and height are the same. -Therefore we can define the column and row positions of a layer with just -two values (rather than four). - -Moving inwards to the second layer, the position of the columns are 1 and 3. -And, yes, you guessed it, it’s the same for rows. -It’s important to understand we had to both increment and decrement the row -and column positions when moving inwards to the next layer. - - +-----------+---------+---------+---------+ - | Layer | Rows | Columns | Rotate? | - +-----------+---------+---------+---------+ - | Outermost | 0 and 4 | 0 and 4 | Yes | - | Inner | 1 and 3 | 1 and 3 | Yes | - | Innermost | 2 | 2 | No | - +-----------+---------+---------+---------+ - -So, to inspect each layer, we want a loop with both increasing and decreasing -counters that represent moving inwards, starting from the outermost layer. -We’ll call this our ‘layer loop’. - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - - for layer in range(0, layer_count): - first = layer - last = size - first - 1 - print 'Layer %d: first: %d, last: %d'%(layer, first, last) - - # 5x5 matrix - matrix = [ - [0,1,2,3,4], - [5,6,6,8,9], - [10,11,12,13,14], - [15,16,17,18,19], - [20,21,22,23,24] - ] - - rotate(matrix) - -The code above loops through the (row and column) positions of any layers that need rotating. - - first: 0, last: 4 - first: 1, last: 3 - -We now have a loop providing the positions of the rows and columns of each layer. The variables first and last identify the index position of the first and last rows and columns. Referring back to our row and column tables: - - +--------+-----------+ - | Column | 0 1 2 3 4 | - +--------+-----------+ - | | . . . . . | - | | . x x x . | - | | . x O x . | - | | . x x x . | - | | . . . . . | - +--------+-----------+ - - +-----+-----------+ - | Row | | - +-----+-----------+ - | 0 | . . . . . | - | 1 | . x x x . | - | 2 | . x O x . | - | 3 | . x x x . | - | 4 | . . . . . | - +-----+-----------+ - -So we can navigate through the layers of a matrix. Now we need a way of navigating within a layer so we can move elements around that layer. Note, elements never ‘jump’ from one layer to another, but they do move within their respective layers. - -Rotating each element in a layer rotates the entire layer. Rotating all layers in a matrix rotates the entire matrix. This sentence is very important, so please try your best to understand it before moving on. - -Now, we need a way of actually moving elements, i.e. rotate each element, and subsequently the layer, and ultimately the matrix. For simplicity, we’ll revert to a 3x3 matrix - that has one rotatable layer. - - 0 1 2 - 3 4 5 - 6 7 8 - -Our layer loop provides the indexes of the first and last columns, as well as first and last rows: - - +-----+-------+ - | Col | 0 1 2 | - +-----+-------+ - | | 0 1 2 | - | | 3 4 5 | - | | 6 7 8 | - +-----+-------+ - - +-----+-------+ - | Row | | - +-----+-------+ - | 0 | 0 1 2 | - | 1 | 3 4 5 | - | 2 | 6 7 8 | - +-----+-------+ - -Because our matrices are always square, we need just two variables, first and last, since index positions are the same for rows and columns. - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - - # Our layer loop i=0, i=1, i=2 - for layer in range(0, layer_count): - - first = layer - last = size - first - 1 - - # We want to move within a layer here. - -The variables first and last can easily be used to reference the four corners of a matrix. This is because the corners themselves can be defined used various permutations of first and last (with no subtraction, addition or offset of those variables): - - +-----------------+-----------------+-------------+ - | Corner | Position | 3x3 Values | - +-----------------+-----------------+-------------+ - | top left | (first, first) | (0,0) | - | top right | (first, last) | (0,2) | - | bottom right | (last, last) | (2,2) | - | bottom left | (last, first) | (2,0) | - +-----------------+-----------------+-------------+ - -For this reason, we start our rotation at the outer four corners: We’ll rotate those first, let’s highlight them with *. - - * 1 * - 3 4 5 - * 7 * - -We want to swap each *, with the * to the right of it. So let’s go ahead a print out our corners defined using only various permutations of first and last: - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - for layer in range(0, layer_count): - - first = layer - last = size - first - 1 - - top_left = (first, first) - top_right = (first, last) - bottom_right = (last, last) - bottom_left = (last, first) - - print 'top_left: %s'%(top_left,) - print 'top_right: %s'%(top_right,) - print 'bottom_right: %s'%(bottom_right,) - print 'bottom_left: %s'%(bottom_left,) - - matrix = [ - [0, 1, 2], - [3, 4, 5], - [6, 7, 8] - ] - - rotate(matrix) - -Output should be: - - top_left: (0, 0) - top_right: (0, 2) - bottom_right: (2, 2) - bottom_left: (2, 0) - -Now we could quite easily swap each of the corners from within our layer loop: - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - for layer in range(0, layer_count): - - first = layer - last = size - first - 1 - - top_left = matrix[first][first] - top_right = matrix[first][last] - bottom_right = matrix[last][last] - bottom_left = matrix[last][first] - - # bottom_left -> top_left - matrix[first][first] = bottom_left - # top_left -> top_right - matrix[first][last] = top_left - # top_right -> bottom_right - matrix[last][last] = top_right - # bottom_right -> bottom_left - matrix[last][first] = bottom_right - - - print_matrix(matrix) - print '---------' - rotate(matrix) - print_matrix(matrix) - -Matrix before rotating corners: - - [0, 1, 2] - [3, 4, 5] - [6, 7, 8] - -Matrix after rotating corners: - - [6, 1, 0] - [3, 4, 5] - [8, 7, 2] - -Great! We have successfully rotated each corner of the matrix. But, we haven’t rotated the elements in the middle of each layer. Clearly we need a way of iterating within a layer. - -The problem is, the only loop in our function so far (our layer loop), moves to the next layer on each iteration. Since our matrix has only one rotatable layer, the layer loop exits after rotating only the corners. Let’s look at what happens with a larger, 5x5 matrix (where two layers need rotating). The function code has been omitted, but it remains the same as above: - - matrix = [ - [0, 1, 2, 3, 4] - [5, 6, 7, 8, 9] - [10, 11, 12, 13, 14] - [15, 16, 17, 18, 19] - [20, 21, 22, 23, 24] - ] - print_matrix(matrix) - print '--------------------' - rotate(matrix) - print_matrix(matrix) - -The output is: - - [20, 1, 2, 3, 0 ] - [5, 16, 7, 6, 9 ] - [10, 11, 12, 13, 14] - [15, 18, 17, 8, 19] - [24, 21, 22, 23, 4 ] - -It shouldn’t be a surprise that the corners of the outermost layer have been rotated, but, you may also notice the corners of the next layer (inwards) have also been rotated. This makes sense. We’ve written code to navigate through layers and also to rotate the corners of each layer. This feels like progress, but unfortunately we must take a step back. It’s just no use moving onto the next layer until the previous (outer) layer has been fully rotated. That is, until each element in the layer has been rotated. Rotating only the corners won’t do! - -Take a deep breath. We need another loop. A nested loop no less. The new, nested loop, will use the first and last variables, plus an offset to navigate within a layer. We’ll call this new loop our ‘element loop’. The element loop will visit each element along the top row, each element down the right side, each element along the bottom row and each element up the left side. - - - Moving across the top row requires the column index to be - incremented. - - Moving down the right side requires the row index to be - incremented. - - Moving backwards along the bottom requires the column - index to be decremented. - - Moving up the left side requires the row - index to be decremented. - -This sound complex, but it’s made easy because the number of times we increment and decrement to achieve the above remains the same along all four sides of the matrix. For example: - - - Move 1 element across the top row. - - Move 1 element down the right side. - - Move 1 element backwards along the bottom row. - - Move 1 element up the left side. - -This means we can use a single variable, in combination with the first and last variables to move within a layer. It may help to note that moving across the top row and down the right side both require incrementing. While moving backwards along the bottom and up the left side both require decrementing. - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - - # Move through layers (i.e. layer loop). - for layer in range(0, layer_count): - - first = layer - last = size - first - 1 - - # Move within a single layer (i.e. element loop). - for element in range(first, last): - - offset = element - first - - # ‘element’ increments column (across right) - top = (first, element) - # ‘element’ increments row (move down) - right_side = (element, last) - # ‘last-offset’ decrements column (across left) - bottom = (last, last-offset) - # ‘last-offset’ decrements row (move up) - left_side = (last-offset, first) - - print 'top: %s'%(top,) - print 'right_side: %s'%(right_side,) - print 'bottom: %s'%(bottom,) - print 'left_side: %s'%(left_side,) - -Now we simply need to assign the top to the right side, right side to the bottom, bottom to the left side, and left side to the top. Putting this all together we get: - - def rotate(matrix): - size = len(matrix) - layer_count = size / 2 - - for layer in range(0, layer_count): - first = layer - last = size - first - 1 - - for element in range(first, last): - offset = element - first - - top = matrix[first][element] - right_side = matrix[element][last] - bottom = matrix[last][last-offset] - left_side = matrix[last-offset][first] - - matrix[first][element] = left_side - matrix[element][last] = top - matrix[last][last-offset] = right_side - matrix[last-offset][first] = bottom - -Given the matrix: - - 0, 1, 2 - 3, 4, 5 - 6, 7, 8 - -Our rotate function results in: - - 6, 3, 0 - 7, 4, 1 - 8, 5, 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/matrix/sparse_dot_vector.py b/matrix/sparse_dot_vector.py deleted file mode 100644 index 0cfceda7b..000000000 --- a/matrix/sparse_dot_vector.py +++ /dev/null @@ -1,12 +0,0 @@ -""" -Suppose we have very large sparse vectors, which contains a lot of zeros and double . - -find a data structure to store them -get the dot product of them - - -In this case, we first have to store the sparse vector using hash map. -for example [3,0,0,5,6] -> (0,3) (3,5) (4,6) The key is each element's position and the value is the number. - -Then we have two hash tables, and we have to iterate through them to calculate the dot product -""" diff --git a/matrix/sparse_mul.py b/matrix/sparse_mul.py deleted file mode 100644 index f87bcd27d..000000000 --- a/matrix/sparse_mul.py +++ /dev/null @@ -1,99 +0,0 @@ -""" -Given two sparse matrices A and B, return the result of AB. - -You may assume that A's column number is equal to B's row number. - -Example: - -A = [ - [ 1, 0, 0], - [-1, 0, 3] -] - -B = [ - [ 7, 0, 0 ], - [ 0, 0, 0 ], - [ 0, 0, 1 ] -] - - - | 1 0 0 | | 7 0 0 | | 7 0 0 | -AB = | -1 0 3 | x | 0 0 0 | = | -7 0 3 | - | 0 0 1 | -""" - - -# Python solution without table (~156ms): -def multiply(self, A, B): - """ - :type A: List[List[int]] - :type B: List[List[int]] - :rtype: List[List[int]] - """ - if A is None or B is None: return None - m, n, l = len(A), len(A[0]), len(B[0]) - if len(B) != n: - raise Exception("A's column number must be equal to B's row number.") - C = [[0 for _ in range(l)] for _ in range(m)] - for i, row in enumerate(A): - for k, eleA in enumerate(row): - if eleA: - for j, eleB in enumerate(B[k]): - if eleB: C[i][j] += eleA * eleB - return C - - -# Python solution with only one table for B (~196ms): -def multiply(self, A, B): - """ - :type A: List[List[int]] - :type B: List[List[int]] - :rtype: List[List[int]] - """ - if A is None or B is None: return None - m, n, l = len(A), len(A[0]), len(B[0]) - if len(B) != n: - raise Exception("A's column number must be equal to B's row number.") - C = [[0 for _ in range(l)] for _ in range(m)] - tableB = {} - for k, row in enumerate(B): - tableB[k] = {} - for j, eleB in enumerate(row): - if eleB: tableB[k][j] = eleB - for i, row in enumerate(A): - for k, eleA in enumerate(row): - if eleA: - for j, eleB in tableB[k].iteritems(): - C[i][j] += eleA * eleB - return C - -# Python solution with two tables (~196ms): -def multiply(self, A, B): - """ - :type A: List[List[int]] - :type B: List[List[int]] - :rtype: List[List[int]] - """ - if A is None or B is None: return None - m, n = len(A), len(A[0]) - if len(B) != n: - raise Exception("A's column number must be equal to B's row number.") - l = len(B[0]) - table_A, table_B = {}, {} - for i, row in enumerate(A): - for j, ele in enumerate(row): - if ele: - if i not in table_A: table_A[i] = {} - table_A[i][j] = ele - for i, row in enumerate(B): - for j, ele in enumerate(row): - if ele: - if i not in table_B: table_B[i] = {} - table_B[i][j] = ele - C = [[0 for j in range(l)] for i in range(m)] - for i in table_A: - for k in table_A[i]: - if k not in table_B: continue - for j in table_B[k]: - C[i][j] += table_A[i][k] * table_B[k][j] - return C diff --git a/queue/__init__.py b/queue/__init__.py deleted file mode 100644 index 2b5cb8ad8..000000000 --- a/queue/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from .queue import * diff --git a/queue/max_sliding_window.py b/queue/max_sliding_window.py deleted file mode 100644 index 36157e301..000000000 --- a/queue/max_sliding_window.py +++ /dev/null @@ -1,34 +0,0 @@ -import collections - -# Keep indexes of good candidates in deque d. -# The indexes in d are from the current window, they're increasing, -# and their corresponding nums are decreasing. -# Then the first deque element is the index of the largest window value. - -# For each index i: - -# 1. Pop (from the end) indexes of smaller elements (they'll be useless). -# 2. Append the current index. -# 3. Pop (from the front) the index i - k, if it's still in the deque -# (it falls out of the window). -# 4. If our window has reached size k, -# append the current window maximum to the output. - - -def max_sliding_window(nums, k): - d = collections.deque() - out = [] - for i, n in enumerate(nums): - while d and nums[d[-1]] < n: - d.pop() - d += i, - if d[0] == i - k: - d.popleft() - if i >= k - 1: - out += nums[d[0]], - return out - - -array = [1,3,-1,-3,5,3,6,7] - -print(max_sliding_window(array)) diff --git a/queue/queue.py b/queue/queue.py deleted file mode 100644 index 28fc3d865..000000000 --- a/queue/queue.py +++ /dev/null @@ -1,118 +0,0 @@ -# Queue Abstract Data Type (ADT) -# * Queue() creates a new queue that is empty. -# It needs no parameters and returns an empty queue. -# * enqueue(item) adds a new item to the rear of the queue. -# It needs the item and returns nothing. -# * dequeue() removes the front item from the queue. -# It needs no parameters and returns the item. The queue is modified. -# * isEmpty() tests to see whether the queue is empty. -# It needs no parameters and returns a boolean value. -# * size() returns the number of items in the queue. -# It needs no parameters and returns an integer. - -class AbstractQueue: - def __init__(self): - self.top = 0 - - def isEmpty(self): - return self.top == 0 - - def __len__(self): - return self.top - - def __str__(self): - result = '------\n' - for element in self: - result += str(element) + '\n' - return result[:-1] + '\n------' - -class ArrayQueue(AbstractQueue): - def __init__(self, size=10): - """ - Initialize python List with size of 10 or user given input. - Python List type is a dynamic array, so we have to restrict its - dynamic nature to make it work like a static array. - """ - AbstractQueue.__init__(self) - self.array = [None] * size - self.front = 0 - self.rear = 0 - - def enqueue(self, value): - if self.rear == len(self.array): - self.expand() - self.array[self.rear] = value - self.rear += 1 - self.top += 1 - - def dequeue(self): - if self.isEmpty(): - raise IndexError("Queue is empty") - value = self.array[self.front] - self.array[self.front] = None - self.front -= 1 - self.top -= 1 - return value - - def expand(self): - """ - expands size of the array. - Time Complexity: O(n) - """ - new_array = [None] * len(self.array) * 2 # double the size of the array - for i, element in enumerate(self.array): - new_array[i] = element - self.array = new_array - - def __iter__(self): - probe = self.rear - while True: - if probe < 0: - raise StopIteration - yield self.array[probe] - probe -= 1 - -class QueueNode(object): - def __init__(self, value): - self.value = value - self.next = None - -class LinkedListQueue(AbstractQueue): - def __init__(self): - AbstractQueue.__init__(self) - self.front = None - self.rear = None - - def enqueue(self, value): - node = QueueNode(value) - if not self.front: - self.front = node - self.rear = node - else: - self.rear.next = node - self.rear = node - self.top += 1 - - def dequeue(self): - if self.isEmpty(): - raise IndexError("Queue is empty") - value = self.front.value - if self.front is self.rear: - self.front = None - self.rear = None - else: - self.front = self.front.next - self.top -= 1 - return value - - def __iter__(self): - probe = self.rear - while True: - if probe is None: - raise StopIteration - yield probe.value - probe = probe.next - -class HeapPriorityQueue(AbstractQueue): - def __init__(self): - pass diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 000000000..e69de29bb diff --git a/search/binary_search.py b/search/binary_search.py deleted file mode 100644 index 71d24bab4..000000000 --- a/search/binary_search.py +++ /dev/null @@ -1,37 +0,0 @@ -# -# Binary search works for a sorted array. -# Note: The code logic is written for an array sorted in -# increasing order. -# T(n): O(log n) -# - - -def binary_search(array, query): - lo, hi = 0, len(array) - 1 - while lo <= hi: - mid = lo + (hi - lo) // 2 - val = array[mid] - if val == query: - return mid - elif val < query: - lo = mid + 1 - else: - hi = mid - 1 - return None - - -def main(): - array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6] - print(array) - print("-----SEARCH-----") - print("found: ", 5, " in index:", binary_search(array, 5)) - print("-----SEARCH-----") - print("found: ", 6, " in index:", binary_search(array, 6)) - print("-----SEARCH-----") - print("found: ", 7, " in index:", binary_search(array, 7)) - print("-----SEARCH-----") - print("found: ", -1, " in index:", binary_search(array, -1)) - print("-----SEARCH-----") - -if __name__ == "__main__": - main() diff --git a/search/first_occurance.py b/search/first_occurance.py deleted file mode 100644 index 3ac6eb025..000000000 --- a/search/first_occurance.py +++ /dev/null @@ -1,45 +0,0 @@ -# -# Find first occurance of a number in a sorted array (increasing order) -# Approach- Binary Search -# T(n)- O(log n) -# - - -def firstOccurance(array, query): - lo, hi = 0, len(array) - 1 - while lo <= hi: - mid = lo + (hi-lo) // 2 - print("lo: ", lo, " hi: ", hi, " mid: ", mid) - if (mid == 0 and array[mid] == query) or \ - (array[mid] == query and array[mid-1] < query): - return mid - elif array[mid] <= query: - lo = mid + 1 - else: - hi = mid - 1 - - -def main(): - array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6] - print(array) - print("-----SEARCH-----") - query = 3 - print("found first: ", query, " in index:", firstOccurance(array, query)) - print("-----SEARCH-----") - query = 5 - print("found first: ", query, " in index:", firstOccurance(array, query)) - print("-----SEARCH-----") - query = 7 - print("found first: ", query, " in index:", firstOccurance(array, query)) - print("-----SEARCH-----") - query = 1 - print("found first: ", query, " in index:", firstOccurance(array, query)) - print("-----SEARCH-----") - query = -1 - print("found first: ", query, " in index:", firstOccurance(array, query)) - print("-----SEARCH-----") - query = 9 - print("found first: ", query, " in index:", firstOccurance(array, query)) - -if __name__ == "__main__": - main() diff --git a/search/last_occurance.py b/search/last_occurance.py deleted file mode 100644 index 0c2c34095..000000000 --- a/search/last_occurance.py +++ /dev/null @@ -1,47 +0,0 @@ -# -# Find last occurance of a number in a sorted array (increasing order) -# Approach- Binary Search -# T(n)- O(log n) -# - - -def lastOccurance(array, query): - lo, hi = 0, len(array) - 1 - while lo <= hi: - mid = lo + (hi - lo) // 2 - if (array[mid] == query and mid == len(array)-1) or \ - (array[mid] == query and array[mid+1] > query): - return mid - elif (array[mid] <= query): - lo = mid + 1 - else: - hi = mid - 1 - - -def main(): - array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6] - print(array) - print("-----SEARCH-----") - query = 3 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = 5 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = 7 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = 1 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = -1 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = 9 - print("found last: ", query, " in index:", lastOccurance(array, query)) - print("-----SEARCH-----") - query = 6 - print("found last: ", query, " in index:", lastOccurance(array, query)) - -if __name__ == "__main__": - main() diff --git a/set/randomized_set.py b/set/randomized_set.py deleted file mode 100644 index 5f66c90b8..000000000 --- a/set/randomized_set.py +++ /dev/null @@ -1,40 +0,0 @@ -""" -Design a data structure that supports all following operations -in average O(1) time. - -insert(val): Inserts an item val to the set if not already present. -remove(val): Removes an item val from the set if present. -get_random: Returns a random element from current set of elements. - Each element must have the same probability of being returned. -""" - - -class RandomizedSet(): - """ - idea: - shit - """ - def __init__(self): - pass - - def insert(self, val): - pass - - def remove(self, val): - pass - - def get_random(self): - pass - - -if __name__ == "__main__": - rset = RandomizedSet() - rset.insert(1) - rset.insert(2) - rset.insert(3) - - rset.remove(2) - - print(rset.get_random()) - print(rset.get_random()) - print(rset.get_random()) diff --git a/setup.py b/setup.py new file mode 100644 index 000000000..c5bb20141 --- /dev/null +++ b/setup.py @@ -0,0 +1,28 @@ +import io +from setuptools import find_packages, setup + + +def long_description(): + with io.open('README.md', 'r', encoding='utf-8') as f: + readme = f.read() + return readme + + +setup(name='algorithms', + version='0.1.4', + description='Pythonic Data Structures and Algorithms', + long_description=long_description(), + long_description_content_type="text/markdown", + url='https://github.com/keon/algorithms', + author='Algorithms Team & Contributors', + author_email="kwk236@gmail.com", + license='MIT', + packages=find_packages(exclude=('tests', 'tests.*')), + classifiers=[ + 'Programming Language :: Python :: 3', + 'Programming Language :: Python :: 3.4', + 'Programming Language :: Python :: 3.5', + 'Programming Language :: Python :: 3.6', + 'Programming Language :: Python :: 3.7', + ], + zip_safe=False) diff --git a/sort/bubble_sort.py b/sort/bubble_sort.py deleted file mode 100644 index 9b5e23ee9..000000000 --- a/sort/bubble_sort.py +++ /dev/null @@ -1,28 +0,0 @@ -""" - -https://en.wikipedia.org/wiki/Bubble_sort - -Worst-case performance: O(N^2) - -""" - - -def bubble_sort(arr): - - def swap(i, j): - arr[i], arr[j] = arr[j], arr[i] - - n = len(arr) - swapped = True - while swapped: - swapped = False - for i in range(1, n): - if arr[i - 1] > arr[i]: - swap(i - 1, i) - swapped = True - -array = [1, 5, 65, 23, 57, 1232, -1, -5, -2, 242, 100, - 4, 423, 2, 564, 9, 0, 10, 43, 64, 32, 1, 999] -print(array) -bubble_sort(array) -print(array) diff --git a/sort/counting_sort.py b/sort/counting_sort.py deleted file mode 100644 index d43bdffbe..000000000 --- a/sort/counting_sort.py +++ /dev/null @@ -1,46 +0,0 @@ -def counting_sort(arr): - """ - Counting_sort - Sorting a array which has no element greater than k - Creating a new temp_arr,where temp_arr[i] contain the number of - element less than or equal to i in the arr - Then placing the number i into a correct position in the result_arr - return the result_arr - Complexity: 0(n) - """ - - m = min(arr) - #in case there are negative elements, change the array to all positive element - different = 0 - if m < 0: - #save the change, so that we can convert the array back to all positive number - different = -m - for i in range (len(arr)): - arr[i]+= -m - k = max(arr) - temp_arr = [0]*(k+1) - for i in range(0,len(arr)): - temp_arr[arr[i]] = temp_arr[arr[i]]+1 - #temp_array[i] contain the times the number i appear in arr - - for i in range(1, k+1): - temp_arr[i] = temp_arr[i] + temp_arr[i-1] - #temp_array[i] contain the number of element less than or equal i in arr - - result_arr = [0]*len(arr) - #creating a result_arr an put the element in a correct positon - for i in range(len(arr)-1,-1,-1): - result_arr[temp_arr[arr[i]]-1] = arr[i]-different - temp_arr[arr[i]] = temp_arr[arr[i]]-1 - - return result_arr - -if __name__ == "__main__": - positive_array = [1,2,3,4,9,1,2,8,3,5,7,0,9,8,1,7,4,5] - negative_array = [-5,-6,-2,-3,-4,-5,0,-9,-2,-3,-8,-4] - x = counting_sort(positive_array) - y = counting_sort(negative_array) - print(x) - print(y) - - diff --git a/sort/heap_sort.py b/sort/heap_sort.py deleted file mode 100644 index 348964bc7..000000000 --- a/sort/heap_sort.py +++ /dev/null @@ -1,93 +0,0 @@ -def max_heap_sort(arr): - """ Heap Sort that uses a max heap to sort an array in ascending order - Complexity: O(n log(n)) - """ - for i in range(len(arr)-1,0,-1): - max_heapify(arr, i) - - temp = arr[0] - arr[0] = arr[i] - arr[i] = temp - - -def max_heapify(arr, end): - """ Max heapify helper for max_heap_sort - """ - last_parent = int((end-1)/2) - - # Iterate from last parent to first - for parent in range(last_parent,-1,-1): - current_parent = parent - - # Iterate from current_parent to last_parent - while current_parent <= last_parent: - # Find greatest child of current_parent - child = 2*current_parent + 1 - if child + 1 <= end and arr[child] < arr[child+1]: - child = child + 1 - - # Swap if child is greater than parent - if arr[child] > arr[current_parent]: - temp = arr[current_parent] - arr[current_parent] = arr[child] - arr[child] = temp - - current_parent = child - # If no swap occured, no need to keep iterating - else: - break - - -def min_heap_sort(arr): - """ Heap Sort that uses a min heap to sort an array in ascending order - Complexity: O(n log(n)) - """ - for i in range(0, len(arr)-1): - min_heapify(arr, i) - - -def min_heapify(arr, start): - """ Min heapify helper for min_heap_sort - """ - # Offset last_parent by the start (last_parent calculated as if start index was 0) - # All array accesses need to be offet by start - end = len(arr)-1 - last_parent = int((end-start-1)/2) - - # Iterate from last parent to first - for parent in range(last_parent,-1,-1): - current_parent = parent - - # Iterate from current_parent to last_parent - while current_parent <= last_parent: - # Find lesser child of current_parent - child = 2*current_parent + 1 - if child + 1 <= end-start and arr[child+start] > arr[child+1+start]: - child = child + 1 - - # Swap if child is less than parent - if arr[child+start] < arr[current_parent+start]: - temp = arr[current_parent+start] - arr[current_parent+start] = arr[child+start] - arr[child+start] = temp - - current_parent = child - # If no swap occured, no need to keep iterating - else: - break - -if __name__ == '__main__': - import timeit - - array = [1,5,65,23,57,1232,-1,-5,-2,242,100,4,423,2,564,9,0,10,43,64] - print("array:") - print(array) - print("Max Heapify:") - max_heap_sort(array) - print(array) - array = [1,5,65,23,57,1232,-1,-5,-2,242,100,4,423,2,564,9,0,10,43,64] - print("Min Heapify:") - min_heap_sort(array) - print(array) - print("Max Heapify Time:", timeit.timeit('max_heap_sort(array)', setup="from __main__ import max_heap_sort, array",number=10000)) - print("Min Heapify Time:", timeit.timeit('min_heap_sort(array)', setup="from __main__ import min_heap_sort, array",number=10000)) diff --git a/sort/insertion_sort.py b/sort/insertion_sort.py deleted file mode 100644 index 99bd2058c..000000000 --- a/sort/insertion_sort.py +++ /dev/null @@ -1,14 +0,0 @@ -def insertion_sort(arr): - """ Insertion Sort - Complexity: O(n^2) - """ - for i in xrange(len(arr)): - cursor = arr[i] - pos = i - while pos > 0 and arr[pos-1] > cursor: - # Swap the number down the list - arr[pos] = arr[pos-1] - pos = pos-1 - # Break and do the final swap - arr[pos] = cursor - return arr diff --git a/sort/merge_sort.py b/sort/merge_sort.py deleted file mode 100644 index e2f2d2a27..000000000 --- a/sort/merge_sort.py +++ /dev/null @@ -1,40 +0,0 @@ -def merge_sort(arr): - """ Merge Sort - Complexity: O(n log(n)) - """ - # Our recursive base case - if len(arr)<= 1: - return arr - mid = len(arr)/2 - # Perform merge_sort recursively on both halves - left, right = merge_sort(arr[mid:]), merge_sort(arr[:mid]) - - # Merge each side together - return merge(left, right) - -def merge(left, right): - """ Merge helper - Complexity: O(n) - """ - arr = [] - left_cursor, right_cursor = 0,0 - while left_cursor < len(left) and right_cursor < len(right): - # Sort each one and place into the result - if left[left_cursor] <= right[right_cursor]: - arr.append(left[left_cursor]) - left_cursor+=1 - else: - arr.append(right[right_cursor]) - right_cursor+=1 - # Add the left overs if there's any left to the result - for i in range(left_cursor,len(left)): - arr.append(left[i]) - for i in range(right_cursor,len(right)): - arr.append(right[i]) - - # Return result - return arr - -array = [1,5, 7,4,3,2,1,9,0,10,43,64] -print(array) -print(merge_sort(array)) diff --git a/sort/quick_sort.py b/sort/quick_sort.py deleted file mode 100644 index 2fd38e10d..000000000 --- a/sort/quick_sort.py +++ /dev/null @@ -1,25 +0,0 @@ -def quick_sort(arr, first, last): - """ Quicksort - Complexity: best O(n) avg O(n log(n)), worst O(N^2) - """ - if first < last: - pos = partition(arr, first, last) - print(arr[first:pos-1], arr[pos+1:last]) - # Start our two recursive calls - quick_sort(arr, first, pos-1) - quick_sort(arr, pos+1, last) - -def partition(arr, first, last): - wall = first - for pos in range(first, last): - if arr[pos] < arr[last]: # last is the pivot - arr[pos], arr[wall] = arr[wall], arr[pos] - wall += 1 - arr[wall], arr[last] = arr[last], arr[wall] - print(wall) - return wall - -array = [1,5,65,23,57,1232,-1,-5,-2,242,100,4,423,2,564,9,0,10,43,64] -print(array) -quick_sort(array, 0, len(array)-1) -print(array) diff --git a/sort/selection_sort.py b/sort/selection_sort.py deleted file mode 100644 index acb0e30da..000000000 --- a/sort/selection_sort.py +++ /dev/null @@ -1,16 +0,0 @@ - -def selection_sort(arr): - """ Selection Sort - Complexity: O(n^2) - """ - for i in xrange(len(arr)): - minimum = i - for j in xrange(i+1, len(arr)): - # "Select" the correct value - if arr[j] < arr[minimum]: - minimum = j - # Using a pythonic swap - arr[minimum], arr[i] = arr[i], arr[minimum] - return arr - - diff --git a/sort/topsort.py b/sort/topsort.py deleted file mode 100644 index 76cd43c11..000000000 --- a/sort/topsort.py +++ /dev/null @@ -1,58 +0,0 @@ -""" -Given a list of system packages, -some packages cannot be installed until the other packages are installed. -Provide a valid sequence to install all of the packages. - -e.g. -a relies on b -b relies on c - -then a valid sequence is [c, b, a] -""" - -depGraph = { - - "a" : [ "b" ], - "b" : [ "c" ], - "c" : [ 'e'], - 'e' : [ ], - "d" : [ ], - "f" : ["e" , "d"] -} - - -given = [ "b", "c", "a", "d", "e", "f" ] - -def retDeps(visited, start): - queue = [] - out = [] - queue.append(start) - while queue: - newNode = queue.pop(0) - if newNode not in visited: - visited.add(newNode) - for child in depGraph[newNode]: - queue.append(child) - out.append(child) - out.append(start) - return out - - -def retDepGraph(): - visited = set() - out = [] - # visited.add(given[0]) - for pac in given: - if pac in visited: - continue - visited.add(pac) - #out.append(pac) - if pac in depGraph: - # find all children - for child in depGraph[pac]: - if child in visited: - continue - out.extend(retDeps(visited, child)) - out.append(pac) - print(out) -retDepGraph() diff --git a/stack/__init__.py b/stack/__init__.py deleted file mode 100644 index 843a7582a..000000000 --- a/stack/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from .stack import * diff --git a/stack/longest_abs_path.py b/stack/longest_abs_path.py deleted file mode 100644 index f7627f5aa..000000000 --- a/stack/longest_abs_path.py +++ /dev/null @@ -1,65 +0,0 @@ -# def lengthLongestPath(input): - # maxlen = 0 - # pathlen = {0: 0} - # for line in input.splitlines(): - # print("---------------") - # print("line:", line) - # name = line.strip('\t') - # print("name:", name) - # depth = len(line) - len(name) - # print("depth:", depth) - # if '.' in name: - # maxlen = max(maxlen, pathlen[depth] + len(name)) - # else: - # pathlen[depth + 1] = pathlen[depth] + len(name) + 1 - # print("maxlen:", maxlen) - # return maxlen - -# def lengthLongestPath(input): - # paths = input.split("\n") - # level = [0] * 10 - # maxLength = 0 - # for path in paths: - # print("-------------") - # levelIdx = path.rfind("\t") - # print("Path: ", path) - # print("path.rfind(\\t)", path.rfind("\t")) - # print("levelIdx: ", levelIdx) - # print("level: ", level) - # level[levelIdx + 1] = level[levelIdx] + len(path) - levelIdx + 1 - # print("level: ", level) - # if "." in path: - # maxLength = max(maxLength, level[levelIdx+1] - 1) - # print("maxlen: ", maxLength) - # return maxLength - -def length_longest_path(input): - """ - :type input: str - :rtype: int - """ - currlen, maxlen = 0, 0 # running length and max length - stack = [] # keep track of the name length - for s in input.split('\n'): - print("---------") - print(":", s) - depth = s.count('\t') # the depth of current dir or file - print("depth: ", depth) - print("stack: ", stack) - print("curlen: ", currlen) - while len(stack) > depth: # go back to the correct depth - currlen -= stack.pop() - stack.append(len(s.strip('\t'))+1) # 1 is the length of '/' - currlen += stack[-1] # increase current length - print("stack: ", stack) - print("curlen: ", currlen) - if '.' in s: # update maxlen only when it is a file - maxlen = max(maxlen, currlen-1) # -1 is to minus one '/' - return maxlen - -st= "dir\n\tsubdir1\n\t\tfile1.ext\n\t\tsubsubdirectory1\n\tsubdir2\n\t\tsubsubdir2\n\t\t\tfile2.ext" -st2 = "a\n\tb1\n\t\tf1.txt\n\taaaaa\n\t\tf2.txt" -print("path:", st2) - -print("answer:", lengthLongestPath(st2)) - diff --git a/stack/stack.py b/stack/stack.py deleted file mode 100644 index d79936379..000000000 --- a/stack/stack.py +++ /dev/null @@ -1,113 +0,0 @@ -# Stack Abstract Data Type (ADT) -# Stack() creates a new stack that is empty. -# It needs no parameters and returns an empty stack. -# push(item) adds a new item to the top of the stack. -# It needs the item and returns nothing. -# pop() removes the top item from the stack. -# It needs no parameters and returns the item. The stack is modified. -# peek() returns the top item from the stack but does not remove it. -# It needs no parameters. The stack is not modified. -# isEmpty() tests to see whether the stack is empty. -# It needs no parameters and returns a boolean value. -# size() returns the number of items on the stack. -# It needs no parameters and returns an integer. - -class AbstractStack: - def __init__(self): - self.top = 0 - - def isEmpty(self): - return self.top == 0 - - def __len__(self): - return self.top - - def __str__(self): - result = '------\n' - for element in self: - result += str(element) + '\n' - return result[:-1] + '\n------' - -class ArrayStack(AbstractStack): - def __init__(self, size=10): - """ - Initialize python List with size of 10 or user given input. - Python List type is a dynamic array, so we have to restrict its - dynamic nature to make it work like a static array. - """ - AbstractStack.__init__(self) - self.array = [None] * size - - def push(self, value): - if self.top == len(self.array): - self.expand() - self.array[self.top] = value - self.top += 1 - - def pop(self): - if self.isEmpty(): - raise IndexError("stack is empty") - value = self.array[self.top - 1] - self.array[self.top - 1] = None - self.top -= 1 - return value - - def peek(self): - if self.isEmpty(): - raise IndexError("stack is empty") - return self.array[self.top] - - def expand(self): - """ - expands size of the array. - Time Complexity: O(n) - """ - newArray = [None] * len(self.array) * 2 # double the size of the array - for i, element in enumerate(self.array): - newArray[i] = element - self.array = newArray - - def __iter__(self): - probe = self.top - 1 - while True: - if probe < 0: - raise StopIteration - yield self.array[probe] - probe -= 1 - -class StackNode(object): - def __init__(self, value): - self.value = value - self.next = None - -class LinkedListStack(AbstractStack): - def __init__(self): - AbstractStack.__init__(self) - self.head = None - - def push(self, value): - node = StackNode(value) - node.next = self.head - self.head = node - self.top += 1 - - def pop(self): - if self.isEmpty(): - raise IndexError("stack is empty") - value = self.head.value - self.head = self.head.next - self.top -= 1 - return value - - def peek(self): - if self.isEmpty(): - raise IndexError("stack is empty") - return self.head.value - - def __iter__(self): - probe = self.head - while True: - if probe is None: - raise StopIteration - yield probe.value - probe = probe.next diff --git a/stack/valid_parenthesis.py b/stack/valid_parenthesis.py deleted file mode 100644 index 7b89734c3..000000000 --- a/stack/valid_parenthesis.py +++ /dev/null @@ -1,38 +0,0 @@ -""" -Given a string containing just the characters -'(', ')', '{', '}', '[' and ']', -determine if the input string is valid. - -The brackets must close in the correct order, -"()" and "()[]{}" are all valid but "(]" and "([)]" are not. -""" - - -def is_valid(s:"str")->"bool": - stack = [] - dic = { ")":"(", - "}":"{", - "]":"["} - for char in s: - if char in dic.values(): - stack.append(char) - elif char in dic.keys(): - if stack == []: - return False - s = stack.pop() - if dic[char] != s: - return False - return stack == [] - - -if __name__ == "__main__": - paren = "[]" - print(paren, is_valid(paren)) - paren = "[]()[]" - print(paren, is_valid(paren)) - paren = "[[[]]" - print(paren, is_valid(paren)) - paren = "{([])}" - print(paren, is_valid(paren)) - paren = "(}" - print(paren, is_valid(paren)) diff --git a/string/breaking_bad.py b/string/breaking_bad.py deleted file mode 100644 index 3248d9108..000000000 --- a/string/breaking_bad.py +++ /dev/null @@ -1,82 +0,0 @@ -""" -Given an api which returns an array of chemical names and an array of chemical -symbols, display the chemical names with their symbol surrounded by square -brackets: - -Ex: -Chemicals array: ['Amazon', 'Microsoft', 'Google'] -Symbols: ['I', 'Am', 'cro', 'Na', 'le', 'abc'] - -Output: -[Am]azon, Mi[cro]soft, Goog[le] - -If the chemical string matches more than one symbol, then choose the one with -longest length. (ex. 'Microsoft' matches 'i' and 'cro') - -My solution: -(I sorted the symbols array in descending order of length and ran loop over -chemicals array to find a symbol match(using indexOf in javascript) which -worked. But I din't make it through the interview, I am guessing my solution -was O(n2) and they expected an efficient algorithm. -""" - -chemicals = ['Amazon', 'Microsoft', 'Google'] -symbols = ['I', 'Am', 'cro', 'le', 'abc'] - -def match_symbol(chemicals, symbols): - import re - combined = [] - - for s in symbols: - for c in chemicals: - r = re.search(s, c) - if r: - combined.append(re.sub(s, "[{}]".format(s), c)) - - return combined - - -print match_symbol(chemicals, symbols) - -""" -One approach is to use a Trie for the dictionary (the symbols), and then match -brute force. The complexity will depend on the dictionary; -if all are suffixes of the other, it will be n*m -(where m is the size of the dictionary). For example, in Python: -""" - -from functools import reduce - -class TrieNode: - def __init__(self): - self.c = dict() - self.sym = None - -def bracket(words, symbols): - root = TrieNode() - for s in symbols: - t = root - for char in s: - if char not in t.c: - t.c[char] = TrieNode() - t = t.c[char] - t.sym = s - result = dict() - for word in words: - i = 0 - symlist = list() - while i < len(word): - j, t = i, root - while j < len(word) and word[j] in t.c: - t = t.c[word[j]] - if t.sym is not None: - symlist.append((j+1-len(t.sym), j+1, t.sym)) - j += 1 - i += 1 - if len(symlist) > 0: - sym = reduce(lambda x, y: x if x[1]-x[0] >= y[1]-y[0] else y, symlist) - result[word] = "{}[{}]{}".format(word[:sym[0]], sym[2], word[sym[1]:]) - return tuple(word if word not in result else result[word] for word in words) - -bracket(['amazon', 'microsoft', 'google'], ['i', 'am', 'cro', 'na', 'le', 'abc']) ->>> ('[am]azon', 'mi[cro]soft', 'goog[le]') diff --git a/string/encode_decode.py b/string/encode_decode.py deleted file mode 100644 index 8fecf3642..000000000 --- a/string/encode_decode.py +++ /dev/null @@ -1,55 +0,0 @@ -# Design an algorithm to encode a list of strings to a string. -# The encoded string is then sent over the network and is decoded -# back to the original list of strings. - -# Machine 1 (sender) has the function: - -# string encode(vector strs) { - # // ... your code - # return encoded_string; -# } -# Machine 2 (receiver) has the function: -# vector decode(string s) { - # //... your code - # return strs; -# } -# So Machine 1 does: - -# string encoded_string = encode(strs); -# and Machine 2 does: - -# vector strs2 = decode(encoded_string); -# strs2 in Machine 2 should be the same as strs in Machine 1. - -# Implement the encode and decode methods. - -def encode(strs): - """Encodes a list of strings to a single string. - :type strs: List[str] - :rtype: str - """ - res = '' - for string in strs.split(): - res += str(len(string)) + ":" + string - return res - -def decode(s): - """Decodes a single string to a list of strings. - :type s: str - :rtype: List[str] - """ - strs = [] - i = 0 - while i < len(s): - index = s.find(":", i) - size = int(s[i:index]) - strs.append(s[index+1: index+1+size]) - i = index+1+size - return strs - -strs = "keon is awesome" -print(strs) -enc = encode(strs) -print(enc) -dec = decode(enc) -print(dec) diff --git a/string/group_anagrams.py b/string/group_anagrams.py deleted file mode 100644 index 1bf3c0a45..000000000 --- a/string/group_anagrams.py +++ /dev/null @@ -1,29 +0,0 @@ -""" -Given an array of strings, group anagrams together. - -For example, given: ["eat", "tea", "tan", "ate", "nat", "bat"], -Return: - -[ - ["ate", "eat","tea"], - ["nat","tan"], - ["bat"] -] -""" - - -class Solution(object): - def groupAnagrams(self, strs): - d = {} - ans = [] - k = 0 - for str in strs: - sstr = ''.join(sorted(str)) - if sstr not in d: - d[sstr] = k - k = k+1 - ans.append([]) - ans[-1].append(str) - else: - ans[d[sstr]].append(str) - return ans diff --git a/string/int_to_roman.py b/string/int_to_roman.py deleted file mode 100644 index dd2563783..000000000 --- a/string/int_to_roman.py +++ /dev/null @@ -1,17 +0,0 @@ -""" -Given an integer, convert it to a roman numeral. -Input is guaranteed to be within the range from 1 to 3999. -""" - -def int_to_roman(num): - """ - :type num: int - :rtype: str - """ - M = ["", "M", "MM", "MMM"]; - C = ["", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"]; - X = ["", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"]; - I = ["", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"]; - return M[num//1000] + C[(num%1000)//100] + X[(num%100)//10] + I[num%10]; - -print(int_to_roman(644)) diff --git a/string/is_palindrome.py b/string/is_palindrome.py deleted file mode 100644 index d9b23b653..000000000 --- a/string/is_palindrome.py +++ /dev/null @@ -1,33 +0,0 @@ -""" -Given a string, determine if it is a palindrome, -considering only alphanumeric characters and ignoring cases. - -For example, -"A man, a plan, a canal: Panama" is a palindrome. -"race a car" is not a palindrome. - -Note: -Have you consider that the string might be empty? -This is a good question to ask during an interview. - -For the purpose of this problem, -we define empty string as valid palindrome. -""" - - -def is_palindrome(s): - """ - :type s: str - :rtype: bool - """ - i = 0 - j = len(s)-1 - while i < j: - while i < j and not s[i].isalnum(): - i += 1 - while i < j and not s[j].isalnum(): - j -= 1 - if s[i].lower() != s[j].lower(): - return False - i, j = i+1, j-1 - return True diff --git a/string/license_number.py b/string/license_number.py deleted file mode 100644 index cbcb2d966..000000000 --- a/string/license_number.py +++ /dev/null @@ -1,19 +0,0 @@ - -def license_number(key, K): - res, alnum = [], [] - for char in key: - if char != "-": - alnum.append(char) - for i, char in enumerate(reversed(alnum)): - res.append(char) - if (i+1) % K == 0 and i != len(alnum)-1: - res.append("-") - return "".join(res[::-1]) - - -print(license_number("a-bc-dfd-df", 1), 1) -print(license_number("a-bc-dfd-df", 2), 2) -print(license_number("a-bc-dfd-df", 3), 3) -print(license_number("a-bc-dfd-df", 4), 4) -print(license_number("a-bc-dfd-df", 5), 5) - diff --git a/string/reverse_words.py b/string/reverse_words.py deleted file mode 100644 index c1a48ace2..000000000 --- a/string/reverse_words.py +++ /dev/null @@ -1,31 +0,0 @@ - -def reverse(array, i, j): - while i < j: - array[i], array[j] = array[j], array[i] - i += 1 - j -= 1 - -def reverse_words(string): - arr = list(string) - n = len(arr) - reverse(arr, 0, n-1) - - start = None - for i in range(n): - if arr[i] == " ": - if start is not None: - reverse(arr, start, i-1) - start = None - elif i == n-1: - if start is not None: - reverse(arr, start, i) - else: - if start is None: - start = i - return "".join(arr) - - -if __name__ == "__main__": - test = "I am keon kim and I like pizza" - print(test) - print(reverse_words(test)) diff --git a/test_requirements.txt b/test_requirements.txt new file mode 100644 index 000000000..f0afad0e9 --- /dev/null +++ b/test_requirements.txt @@ -0,0 +1,7 @@ +flake8 +python-coveralls +coverage +nose +pytest +tox +black diff --git a/tests/test_array.py b/tests/test_array.py new file mode 100644 index 000000000..b73ecb17b --- /dev/null +++ b/tests/test_array.py @@ -0,0 +1,441 @@ +from algorithms.arrays import ( + delete_nth, delete_nth_naive, + flatten_iter, flatten, + garage, + josephus, + longest_non_repeat_v1, longest_non_repeat_v2, + get_longest_non_repeat_v1, get_longest_non_repeat_v2, + Interval, merge_intervals, + missing_ranges, + move_zeros, + plus_one_v1, plus_one_v2, plus_one_v3, + remove_duplicates, + rotate_v1, rotate_v2, rotate_v3, + summarize_ranges, + three_sum, + two_sum, + max_ones_index, + trimmean, + top_1, + limit, + n_sum +) + +import unittest + + +class TestJosephus(unittest.TestCase): + + def test_josephus(self): + + a = ['1', '2', '3', '4', '5', '6', '7', '8', '9'] + josephus_generator = josephus(a, 3) + self.assertEqual(next(josephus_generator), '3') + self.assertEqual(next(josephus_generator), '6') + self.assertEqual(next(josephus_generator), '9') + self.assertEqual(next(josephus_generator), '4') + self.assertEqual(next(josephus_generator), '8') + self.assertEqual(next(josephus_generator), '5') + self.assertEqual(next(josephus_generator), '2') + self.assertEqual(next(josephus_generator), '7') + self.assertEqual(next(josephus_generator), '1') + self.assertRaises(StopIteration, next, josephus_generator) + + +class TestDeleteNth(unittest.TestCase): + + def test_delete_nth_naive(self): + + self.assertListEqual(delete_nth_naive( + [20, 37, 20, 21, 37, 21, 21], n=1), + [20, 37, 21]) + self.assertListEqual(delete_nth_naive( + [1, 1, 3, 3, 7, 2, 2, 2, 2], n=3), + [1, 1, 3, 3, 7, 2, 2, 2]) + self.assertListEqual(delete_nth_naive( + [1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], + n=3), + [1, 2, 3, 1, 1, 2, 2, 3, 3, 4, 5]) + self.assertListEqual(delete_nth_naive([], n=5), + []) + self.assertListEqual(delete_nth_naive( + [1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 3, 1], + n=0), + []) + + def test_delete_nth(self): + + self.assertListEqual(delete_nth([20, 37, 20, 21, 37, 21, 21], n=1), + [20, 37, 21]) + self.assertListEqual(delete_nth([1, 1, 3, 3, 7, 2, 2, 2, 2], n=3), + [1, 1, 3, 3, 7, 2, 2, 2]) + self.assertListEqual(delete_nth([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, + 5, 3, 1], n=3), + [1, 2, 3, 1, 1, 2, 2, 3, 3, 4, 5]) + self.assertListEqual(delete_nth([], n=5), + []) + self.assertListEqual(delete_nth([1, 2, 3, 1, 1, 2, 1, 2, 3, 3, 2, 4, + 5, 3, 1], n=0), + []) + + +class TestFlatten(unittest.TestCase): + + def test_flatten(self): + + nested_list = [2, 1, [3, [4, 5], 6], 7, [8]] + flattened = flatten(nested_list) + self.assertEqual(flattened, [2, 1, 3, 4, 5, 6, 7, 8]) + + nested_list = [[3, [4, 5], 6], 7, [8]] + flattened = flatten(nested_list) + self.assertEqual(flattened, [3, 4, 5, 6, 7, 8]) + + nested_list = [[], [8]] + flattened = flatten(nested_list) + self.assertEqual(flattened, [8]) + + def test_flatten_iter(self): + + nested_list = [2, 1, [3, [4, 5], 6], 7, [8]] + flattened = flatten_iter(nested_list) + self.assertEqual(next(flattened), 2) + self.assertEqual(next(flattened), 1) + self.assertEqual(next(flattened), 3) + self.assertEqual(next(flattened), 4) + self.assertEqual(next(flattened), 5) + self.assertEqual(next(flattened), 6) + self.assertEqual(next(flattened), 7) + self.assertEqual(next(flattened), 8) + self.assertRaises(StopIteration, next, flattened) + + nested_list = [[3, [4, 5], 6], 7, [8]] + flattened = flatten_iter(nested_list) + self.assertEqual(next(flattened), 3) + self.assertEqual(next(flattened), 4) + self.assertEqual(next(flattened), 5) + self.assertEqual(next(flattened), 6) + self.assertEqual(next(flattened), 7) + self.assertEqual(next(flattened), 8) + self.assertRaises(StopIteration, next, flattened) + + nested_list = [[], [8]] + flattened = flatten_iter(nested_list) + self.assertEqual(next(flattened), 8) + self.assertRaises(StopIteration, next, flattened) + + +class TestGarage(unittest.TestCase): + + def test_garage(self): + + initial = [1, 2, 3, 0, 4] + final = [0, 3, 2, 1, 4] + steps, seq = garage(initial, final) + + self.assertEqual(steps, 4) + self.assertListEqual(seq, [[0, 2, 3, 1, 4], + [2, 0, 3, 1, 4], + [2, 3, 0, 1, 4], + [0, 3, 2, 1, 4]]) + + +class TestLongestNonRepeat(unittest.TestCase): + + def test_longest_non_repeat_v1(self): + + string = "abcabcbb" + self.assertEqual(longest_non_repeat_v1(string), 3) + + string = "bbbbb" + self.assertEqual(longest_non_repeat_v1(string), 1) + + string = "pwwkew" + self.assertEqual(longest_non_repeat_v1(string), 3) + + string = "dvdf" + self.assertEqual(longest_non_repeat_v1(string), 3) + + string = "asjrgapa" + self.assertEqual(longest_non_repeat_v1(string), 6) + + def test_longest_non_repeat_v2(self): + + string = "abcabcbb" + self.assertEqual(longest_non_repeat_v2(string), 3) + + string = "bbbbb" + self.assertEqual(longest_non_repeat_v2(string), 1) + + string = "pwwkew" + self.assertEqual(longest_non_repeat_v2(string), 3) + + string = "dvdf" + self.assertEqual(longest_non_repeat_v2(string), 3) + + string = "asjrgapa" + self.assertEqual(longest_non_repeat_v2(string), 6) + + def test_get_longest_non_repeat_v1(self): + string = "abcabcbb" + self.assertEqual(get_longest_non_repeat_v1(string), (3, 'abc')) + + string = "bbbbb" + self.assertEqual(get_longest_non_repeat_v1(string), (1, 'b')) + + string = "pwwkew" + self.assertEqual(get_longest_non_repeat_v1(string), (3, 'wke')) + + string = "dvdf" + self.assertEqual(get_longest_non_repeat_v1(string), (3, 'vdf')) + + string = "asjrgapa" + self.assertEqual(get_longest_non_repeat_v1(string), (6, 'sjrgap')) + + def test_get_longest_non_repeat_v2(self): + string = "abcabcbb" + self.assertEqual(get_longest_non_repeat_v2(string), (3, 'abc')) + + string = "bbbbb" + self.assertEqual(get_longest_non_repeat_v2(string), (1, 'b')) + + string = "pwwkew" + self.assertEqual(get_longest_non_repeat_v2(string), (3, 'wke')) + + string = "dvdf" + self.assertEqual(get_longest_non_repeat_v2(string), (3, 'vdf')) + + string = "asjrgapa" + self.assertEqual(get_longest_non_repeat_v2(string), (6, 'sjrgap')) + + +class TestMaxOnesIndex(unittest.TestCase): + + def test_max_ones_index(self): + + self.assertEqual(9, max_ones_index([1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, + 1, 1])) + self.assertEqual(3, max_ones_index([1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, + 1, 1])) + self.assertEqual(-1, max_ones_index([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, + 1, 1])) + + +class TestMergeInterval(unittest.TestCase): + + def test_merge(self): + interval_list = [[1, 3], [2, 6], [8, 10], [15, 18]] + intervals = [Interval(i[0], i[1]) for i in interval_list] + merged_intervals = Interval.merge(intervals) + self.assertEqual( + merged_intervals, + [Interval(1, 6), Interval(8, 10), Interval(15, 18)] + ) + + def test_merge_intervals(self): + interval_list = [[1, 3], [2, 6], [8, 10], [15, 18]] + merged_intervals = merge_intervals(interval_list) + self.assertEqual( + merged_intervals, + [[1, 6], [8, 10], [15, 18]] + ) + + +class TestMissingRanges(unittest.TestCase): + + def test_missing_ranges(self): + + arr = [3, 5, 10, 11, 12, 15, 19] + + self.assertListEqual(missing_ranges(arr, 0, 20), + [(0, 2), (4, 4), (6, 9), + (13, 14), (16, 18), (20, 20)]) + + self.assertListEqual(missing_ranges(arr, 6, 100), + [(6, 9), (13, 14), (16, 18), (20, 100)]) + + +class TestMoveZeros(unittest.TestCase): + + def test_move_zeros(self): + + self.assertListEqual(move_zeros([False, 1, 0, 1, 2, 0, 1, 3, "a"]), + [False, 1, 1, 2, 1, 3, "a", 0, 0]) + + self.assertListEqual(move_zeros([0, 34, 'rahul', [], None, 0, + True, 0]), + [34, 'rahul', [], None, True, 0, 0, 0]) + + +class TestPlusOne(unittest.TestCase): + + def test_plus_one_v1(self): + + self.assertListEqual(plus_one_v1([0]), [1]) + self.assertListEqual(plus_one_v1([9]), [1, 0]) + self.assertListEqual(plus_one_v1([1, 0, 9]), [1, 1, 0]) + self.assertListEqual(plus_one_v1([9, 9, 8, 0, 0, 9]), + [9, 9, 8, 0, 1, 0]) + self.assertListEqual(plus_one_v1([9, 9, 9, 9]), + [1, 0, 0, 0, 0]) + + def test_plus_one_v2(self): + + self.assertListEqual(plus_one_v2([0]), [1]) + self.assertListEqual(plus_one_v2([9]), [1, 0]) + self.assertListEqual(plus_one_v2([1, 0, 9]), [1, 1, 0]) + self.assertListEqual(plus_one_v2([9, 9, 8, 0, 0, 9]), + [9, 9, 8, 0, 1, 0]) + self.assertListEqual(plus_one_v2([9, 9, 9, 9]), + [1, 0, 0, 0, 0]) + + def test_plus_one_v3(self): + + self.assertListEqual(plus_one_v3([0]), [1]) + self.assertListEqual(plus_one_v3([9]), [1, 0]) + self.assertListEqual(plus_one_v3([1, 0, 9]), [1, 1, 0]) + self.assertListEqual(plus_one_v3([9, 9, 8, 0, 0, 9]), + [9, 9, 8, 0, 1, 0]) + self.assertListEqual(plus_one_v3([9, 9, 9, 9]), + [1, 0, 0, 0, 0]) + +class TestRemoveDuplicate(unittest.TestCase): + + def test_remove_duplicates(self): + self.assertListEqual(remove_duplicates([1,1,1,2,2,2,3,3,4,4,5,6,7,7,7,8,8,9,10,10])) + self.assertListEqual(remove_duplicates(["hey", "hello", "hello", "car", "house", "house"])) + self.assertListEqual(remove_duplicates([True, True, False, True, False, None, None])) + self.assertListEqual(remove_duplicates([1,1,"hello", "hello", True, False, False])) + self.assertListEqual(remove_duplicates([1, "hello", True, False])) + + +class TestRotateArray(unittest.TestCase): + + def test_rotate_v1(self): + + self.assertListEqual(rotate_v1([1, 2, 3, 4, 5, 6, 7], k=3), + [5, 6, 7, 1, 2, 3, 4]) + self.assertListEqual(rotate_v1([1, 2, 3, 4, 5, 6, 7], k=1), + [7, 1, 2, 3, 4, 5, 6]) + self.assertListEqual(rotate_v1([1, 2, 3, 4, 5, 6, 7], k=7), + [1, 2, 3, 4, 5, 6, 7]) + self.assertListEqual(rotate_v1([1, 2], k=111), [2, 1]) + + def test_rotate_v2(self): + + self.assertListEqual(rotate_v2([1, 2, 3, 4, 5, 6, 7], k=3), + [5, 6, 7, 1, 2, 3, 4]) + self.assertListEqual(rotate_v2([1, 2, 3, 4, 5, 6, 7], k=1), + [7, 1, 2, 3, 4, 5, 6]) + self.assertListEqual(rotate_v2([1, 2, 3, 4, 5, 6, 7], k=7), + [1, 2, 3, 4, 5, 6, 7]) + self.assertListEqual(rotate_v2([1, 2], k=111), [2, 1]) + + def test_rotate_v3(self): + + self.assertListEqual(rotate_v3([1, 2, 3, 4, 5, 6, 7], k=3), + [5, 6, 7, 1, 2, 3, 4]) + self.assertListEqual(rotate_v3([1, 2, 3, 4, 5, 6, 7], k=1), + [7, 1, 2, 3, 4, 5, 6]) + self.assertListEqual(rotate_v3([1, 2, 3, 4, 5, 6, 7], k=7), + [1, 2, 3, 4, 5, 6, 7]) + self.assertListEqual(rotate_v3([1, 2], k=111), [2, 1]) + + +class TestSummaryRanges(unittest.TestCase): + + def test_summarize_ranges(self): + + self.assertListEqual(summarize_ranges([0, 1, 2, 4, 5, 7]), + [(0, 2), (4, 5), (7, 7)]) + self.assertListEqual(summarize_ranges([-5, -4, -3, 1, 2, 4, 5, 6]), + [(-5, -3), (1, 2), (4, 6)]) + self.assertListEqual(summarize_ranges([-2, -1, 0, 1, 2]), + [(-2, 2)]) + + +class TestThreeSum(unittest.TestCase): + + def test_three_sum(self): + + self.assertSetEqual(three_sum([-1, 0, 1, 2, -1, -4]), + {(-1, 0, 1), (-1, -1, 2)}) + + self.assertSetEqual(three_sum([-1, 3, 1, 2, -1, -4, -2]), + {(-4, 1, 3), (-2, -1, 3), (-1, -1, 2)}) + + +class TestTwoSum(unittest.TestCase): + + def test_two_sum(self): + + self.assertTupleEqual((0, 2), two_sum([2, 11, 7, 9], target=9)) + self.assertTupleEqual((0, 3), two_sum([-3, 5, 2, 3, 8, -9], target=0)) + + self.assertIsNone(two_sum([-3, 5, 2, 3, 8, -9], target=6)) + + +class TestTrimmean(unittest.TestCase): + + def test_trimmean(self): + + self.assertEqual(trimmean([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 20), 5.5) + self.assertEqual(trimmean([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 20), + 6.0) + + +class TestTop1(unittest.TestCase): + + def test_top_1(self): + self.assertListEqual(top_1([1, 1, 2, 2, 3]), [1, 2]) + self.assertListEqual(top_1([1, 2, 3, 324, 234, 23, 23, 1, 23, 23]), + [23]) + + +class TestLimit(unittest.TestCase): + + def test_limit(self): + self.assertListEqual(limit([1, 2, 3, 4, 5]), [1, 2, 3, 4, 5]) + self.assertListEqual(limit([1, 2, 3, 4, 5], 2, 4), [2, 3, 4]) + self.assertListEqual(limit([1, 2, 3, 4, 5], 2), [2, 3, 4, 5]) + self.assertListEqual(limit([1, 2, 3, 4, 5], None, 4), [1, 2, 3, 4]) + + +class TestNSum(unittest.TestCase): + + def test_n_sum(self): + self.assertEqual(n_sum(2, [-3, 5, 2, 3, 8, -9], 6), []) # noqa: E501 + self.assertEqual(n_sum(3, [-5, -4, -3, -2, -1, 0, 1, 2, 3], 0), + sorted([[-5, 2, 3], [-2, 0, 2], [-4, 1, 3], + [-3, 1, 2], [-1, 0, 1], [-2, -1, 3], + [-3, 0, 3]])) # noqa: E501 + self.assertEqual(n_sum(3, [-1, 0, 1, 2, -1, -4], 0), + sorted([[-1, -1, 2], [-1, 0, 1]])) # noqa: E501 + self.assertEqual(n_sum(4, [1, 0, -1, 0, -2, 2], 0), + sorted([[-2, -1, 1, 2], [-2, 0, 0, 2], + [-1, 0, 0, 1]])) # noqa: E501 + self.assertEqual(n_sum(4, [7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 4, -3, -2], 10), sorted([[-6, 2, 7, 7], [-6, 3, 6, 7], [-6, 4, 5, 7], [-6, 4, 6, 6], [-5, 1, 7, 7], [-5, 2, 6, 7], [-5, 3, 5, 7], [-5, 3, 6, 6], [-5, 4, 4, 7], [-5, 4, 5, 6], [-4, 0, 7, 7], [-4, 1, 6, 7], [-4, 2, 5, 7], [-4, 2, 6, 6], [-4, 3, 4, 7], [-4, 3, 5, 6], [-4, 4, 4, 6], [-3, -1, 7, 7], [-3, 0, 6, 7], [-3, 1, 5, 7], [-3, 1, 6, 6], [-3, 2, 4, 7], [-3, 2, 5, 6], [-3, 3, 4, 6], [-3, 4, 4, 5], [-2, -2, 7, 7], [-2, -1, 6, 7], [-2, 0, 5, 7], [-2, 0, 6, 6], [-2, 1, 4, 7], [-2, 1, 5, 6], [-2, 2, 3, 7], [-2, 2, 4, 6], [-2, 3, 4, 5], [-1, 0, 4, 7], [-1, 0, 5, 6], [-1, 1, 3, 7], [-1, 1, 4, 6], [-1, 2, 3, 6], [-1, 2, 4, 5], [-1, 3, 4, 4], [0, 1, 2, 7], [0, 1, 3, 6], [0, 1, 4, 5], [0, 2, 3, 5], [0, 2, 4, 4], [1, 2, 3, 4]])) # noqa: E501 + + self.assertEqual(n_sum(2, [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], + [-9, 5]], 0, # noqa: E501 + sum_closure=lambda a, b: a[0] + b[0]), # noqa: E501 + [[[-3, 0], [3, 3]], [[-2, 1], [2, 2]]]) # noqa: E501 + self.assertEqual(n_sum(2, [[-3, 0], [-2, 1], [2, 2], [3, 3], [8, 4], + [-9, 5]], [0, 3], # noqa: E501 + sum_closure=lambda a, b: [a[0] + b[0], + a[1] + b[1]], # noqa: E501 + same_closure=lambda a, b: a[0] == b[0] + and a[1] == b[1]), # noqa: E501 + [[[-3, 0], [3, 3]], [[-2, 1], [2, 2]]]) # noqa: E501 + self.assertEqual(n_sum(2, [[-3, 0], [-2, 1], [2, 2], [3, 3], + [8, 4], [-9, 5]], -5, # noqa: E501 + sum_closure=lambda a, b: [a[0] + b[1], + a[1] + b[0]], # noqa: E501 + compare_closure=lambda a, b: -1 if a[0] < b + else 1 if a[0] > b else 0), # noqa: E501 + [[[-9, 5], [8, 4]]]) # noqa: E501 + + +if __name__ == '__main__': + + unittest.main() diff --git a/tests/test_automata.py b/tests/test_automata.py new file mode 100644 index 000000000..dbd766a3f --- /dev/null +++ b/tests/test_automata.py @@ -0,0 +1,48 @@ +from algorithms.automata import DFA + + +import unittest + + +class TestDFA(unittest.TestCase): + def test_DFA(self): + transitions = { + 'a': {'1': 'a', '0': 'b'}, + 'b': {'1': 'b', '0': 'a'} + } + + final = ['a'] + start = 'a' + + self.assertEqual(False, DFA(transitions, start, final, "000111100")) + self.assertEqual(True, DFA(transitions, start, final, "111000011")) + + transitions1 = { + '0': {'0': '1', '1': '0'}, + '1': {'0': '2', '1': '0'}, + '2': {'0': '2', '1': '3'}, + '3': {'0': '3', '1': '3'} + } + + final1 = ['0', '1', '2'] + start1 = '0' + + self.assertEqual(False, DFA(transitions1, start1, final1, "0001111")) + self.assertEqual(True, DFA(transitions1, start1, final1, "01010101")) + + transitions2 = { + '0': {'a': '0', 'b': '1'}, + '1': {'a': '0', 'b': '2'}, + '2': {'a': '3', 'b': '2'}, + '3': {'a': '3', 'b': '3'} + } + + final2 = ['3'] + start2 = '0' + + self.assertEqual(False, DFA(transitions2, start2, final2, "aaabbb")) + self.assertEqual(True, DFA(transitions2, start2, final2, "baabba")) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_backtrack.py b/tests/test_backtrack.py new file mode 100644 index 000000000..516ed6d2d --- /dev/null +++ b/tests/test_backtrack.py @@ -0,0 +1,396 @@ +from algorithms.backtrack import ( + add_operators, + permute_iter, + anagram, + array_sum_combinations, + unique_array_sum_combinations, + combination_sum, + get_factors, + recursive_get_factors, + find_words, + generate_abbreviations, + generate_parenthesis_v1, + generate_parenthesis_v2, + letter_combinations, + palindromic_substrings, + pattern_match, + permute_unique, + permute, + permute_recursive, + subsets_unique, + subsets, + subsets_v2, +) + +import unittest + + +class TestAddOperator(unittest.TestCase): + def test_add_operators(self): + # "123", 6 -> ["1+2+3", "1*2*3"] + s = "123" + target = 6 + self.assertEqual(add_operators(s, target), ["1+2+3", "1*2*3"]) + # "232", 8 -> ["2*3+2", "2+3*2"] + s = "232" + target = 8 + self.assertEqual(add_operators(s, target), ["2+3*2", "2*3+2"]) + + s = "123045" + target = 3 + answer = ['1+2+3*0*4*5', + '1+2+3*0*45', + '1+2-3*0*4*5', + '1+2-3*0*45', + '1-2+3+0-4+5', + '1-2+3-0-4+5', + '1*2+3*0-4+5', + '1*2-3*0-4+5', + '1*23+0-4*5', + '1*23-0-4*5', + '12+3*0-4-5', + '12-3*0-4-5'] + self.assertEqual(add_operators(s, target), answer) + + +class TestPermuteAndAnagram(unittest.TestCase): + + def test_permute(self): + perms = ['abc', 'bac', 'bca', 'acb', 'cab', 'cba'] + self.assertEqual(perms, permute("abc")) + + def test_permute_iter(self): + it = permute_iter("abc") + perms = ['abc', 'bac', 'bca', 'acb', 'cab', 'cba'] + for i in range(len(perms)): + self.assertEqual(perms[i], next(it)) + + def test_angram(self): + self.assertTrue(anagram('apple', 'pleap')) + self.assertFalse(anagram("apple", "cherry")) + + +class TestArrayCombinationSum(unittest.TestCase): + + def test_array_sum_combinations(self): + A = [1, 2, 3, 3] + B = [2, 3, 3, 4] + C = [2, 3, 3, 4] + target = 7 + answer = [[1, 2, 4], [1, 3, 3], [1, 3, 3], [1, 3, 3], + [1, 3, 3], [1, 4, 2], [2, 2, 3], [2, 2, 3], + [2, 3, 2], [2, 3, 2], [3, 2, 2], [3, 2, 2]] + answer.sort() + self.assertListEqual(sorted(array_sum_combinations(A, B, C, target)), + answer) + + def test_unique_array_sum_combinations(self): + A = [1, 2, 3, 3] + B = [2, 3, 3, 4] + C = [2, 3, 3, 4] + target = 7 + answer = [(2, 3, 2), (3, 2, 2), (1, 2, 4), + (1, 4, 2), (2, 2, 3), (1, 3, 3)] + answer.sort() + self.assertListEqual(sorted(unique_array_sum_combinations(A, B, C, + target)), + answer) + + +class TestCombinationSum(unittest.TestCase): + + def check_sum(self, nums, target): + if sum(nums) == target: + return (True, nums) + else: + return (False, nums) + + def test_combination_sum(self): + candidates1 = [2, 3, 6, 7] + target1 = 7 + answer1 = [ + [2, 2, 3], + [7] + ] + self.assertEqual(combination_sum(candidates1, target1), answer1) + + candidates2 = [2, 3, 5] + target2 = 8 + answer2 = [ + [2, 2, 2, 2], + [2, 3, 3], + [3, 5] + ] + self.assertEqual(combination_sum(candidates2, target2), answer2) + + +class TestFactorCombinations(unittest.TestCase): + + def test_get_factors(self): + target1 = 32 + answer1 = [ + [2, 16], + [2, 2, 8], + [2, 2, 2, 4], + [2, 2, 2, 2, 2], + [2, 4, 4], + [4, 8] + ] + self.assertEqual(sorted(get_factors(target1)), sorted(answer1)) + + target2 = 12 + answer2 = [ + [2, 6], + [2, 2, 3], + [3, 4] + ] + self.assertEqual(sorted(get_factors(target2)), sorted(answer2)) + self.assertEqual(sorted(get_factors(1)), []) + self.assertEqual(sorted(get_factors(37)), []) + + def test_recursive_get_factors(self): + target1 = 32 + answer1 = [ + [2, 16], + [2, 2, 8], + [2, 2, 2, 4], + [2, 2, 2, 2, 2], + [2, 4, 4], + [4, 8] + ] + self.assertEqual(sorted(recursive_get_factors(target1)), + sorted(answer1)) + + target2 = 12 + answer2 = [ + [2, 6], + [2, 2, 3], + [3, 4] + ] + self.assertEqual(sorted(recursive_get_factors(target2)), + sorted(answer2)) + self.assertEqual(sorted(recursive_get_factors(1)), []) + self.assertEqual(sorted(recursive_get_factors(37)), []) + + +class TestFindWords(unittest.TestCase): + + def test_normal(self): + board = [ + ['o', 'a', 'a', 'n'], + ['e', 't', 'a', 'e'], + ['i', 'h', 'k', 'r'], + ['i', 'f', 'l', 'v'] + ] + + words = ["oath", "pea", "eat", "rain"] + result = find_words(board, words) + test_result = ['oath', 'eat'] + self.assertEqual(sorted(result),sorted(test_result)) + + def test_none(self): + board = [ + ['o', 'a', 'a', 'n'], + ['e', 't', 'a', 'e'], + ['i', 'h', 'k', 'r'], + ['i', 'f', 'l', 'v'] + ] + + words = ["chicken", "nugget", "hello", "world"] + self.assertEqual(find_words(board, words), []) + + def test_empty(self): + board = [] + words = [] + self.assertEqual(find_words(board, words), []) + + def test_uneven(self): + board = [ + ['o', 'a', 'a', 'n'], + ['e', 't', 'a', 'e'] + ] + words = ["oath", "pea", "eat", "rain"] + self.assertEqual(find_words(board, words), ['eat']) + + def test_repeat(self): + board = [ + ['a', 'a', 'a'], + ['a', 'a', 'a'], + ['a', 'a', 'a'] + ] + words = ["a", "aa", "aaa", "aaaa", "aaaaa"] + self.assertTrue(len(find_words(board, words)) == 5) + + +class TestGenerateAbbreviations(unittest.TestCase): + def test_generate_abbreviations(self): + word1 = "word" + answer1 = ['word', 'wor1', 'wo1d', 'wo2', 'w1rd', 'w1r1', 'w2d', 'w3', + '1ord', '1or1', '1o1d', '1o2', '2rd', '2r1', '3d', '4'] + self.assertEqual(sorted(generate_abbreviations(word1)), + sorted(answer1)) + + word2 = "hello" + answer2 = ['hello', 'hell1', 'hel1o', 'hel2', 'he1lo', 'he1l1', 'he2o', + 'he3', 'h1llo', 'h1ll1', 'h1l1o', 'h1l2', 'h2lo', 'h2l1', + 'h3o', 'h4', '1ello', '1ell1', '1el1o', '1el2', '1e1lo', + '1e1l1', '1e2o', '1e3', '2llo', '2ll1', '2l1o', '2l2', + '3lo', '3l1', '4o', '5'] + self.assertEqual(sorted(generate_abbreviations(word2)), + sorted(answer2)) + + +class TestPatternMatch(unittest.TestCase): + + def test_pattern_match(self): + pattern1 = "abab" + string1 = "redblueredblue" + pattern2 = "aaaa" + string2 = "asdasdasdasd" + pattern3 = "aabb" + string3 = "xyzabcxzyabc" + + self.assertTrue(pattern_match(pattern1, string1)) + self.assertTrue(pattern_match(pattern2, string2)) + self.assertFalse(pattern_match(pattern3, string3)) + + +class TestGenerateParenthesis(unittest.TestCase): + + def test_generate_parenthesis(self): + self.assertEqual(generate_parenthesis_v1(2), ['()()', '(())']) + self.assertEqual(generate_parenthesis_v1(3), ['()()()', '()(())', + '(())()', '(()())', '((()))']) + self.assertEqual(generate_parenthesis_v2(2), ['(())', '()()']) + self.assertEqual(generate_parenthesis_v2(3), ['((()))', '(()())', + '(())()', '()(())', '()()()']) + + +class TestLetterCombinations(unittest.TestCase): + + def test_letter_combinations(self): + digit1 = "23" + answer1 = ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"] + self.assertEqual(sorted(letter_combinations(digit1)), sorted(answer1)) + + digit2 = "34" + answer2 = ['dg', 'dh', 'di', 'eg', 'eh', 'ei', 'fg', 'fh', 'fi'] + self.assertEqual(sorted(letter_combinations(digit2)), sorted(answer2)) + + +class TestPalindromicSubstrings(unittest.TestCase): + + def test_palindromic_substrings(self): + string1 = "abc" + answer1 = [['a', 'b', 'c']] + self.assertEqual(palindromic_substrings(string1), sorted(answer1)) + + string2 = "abcba" + answer2 = [['abcba'], ['a', 'bcb', 'a'], ['a', 'b', 'c', 'b', 'a']] + self.assertEqual(sorted(palindromic_substrings(string2)), + sorted(answer2)) + + string3 = "abcccba" + answer3 = [['abcccba'], ['a', 'bcccb', 'a'], + ['a', 'b', 'ccc', 'b', 'a'], + ['a', 'b', 'cc', 'c', 'b', 'a'], + ['a', 'b', 'c', 'cc', 'b', 'a'], + ['a', 'b', 'c', 'c', 'c', 'b', 'a']] + self.assertEqual(sorted(palindromic_substrings(string3)), + sorted(answer3)) + + +class TestPermuteUnique(unittest.TestCase): + + def test_permute_unique(self): + nums1 = [1, 1, 2] + answer1 = [[2, 1, 1], [1, 2, 1], [1, 1, 2]] + self.assertEqual(sorted(permute_unique(nums1)), sorted(answer1)) + + nums2 = [1, 2, 1, 3] + answer2 = [[3, 1, 2, 1], [1, 3, 2, 1], [1, 2, 3, 1], [1, 2, 1, 3], + [3, 2, 1, 1], [2, 3, 1, 1], [2, 1, 3, 1], [2, 1, 1, 3], + [3, 1, 1, 2], [1, 3, 1, 2], [1, 1, 3, 2], [1, 1, 2, 3]] + self.assertEqual(sorted(permute_unique(nums2)), sorted(answer2)) + + nums3 = [1, 2, 3] + answer3 = [[3, 2, 1], [2, 3, 1], [2, 1, 3], [3, 1, 2], + [1, 3, 2], [1, 2, 3]] + self.assertEqual(sorted(permute_unique(nums3)), sorted(answer3)) + + +class TestPermute(unittest.TestCase): + + def test_permute(self): + nums1 = [1, 2, 3, 4] + answer1 = [[1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 1, 4], [2, 3, 4, 1], + [1, 3, 2, 4], [3, 1, 2, 4], [3, 2, 1, 4], [3, 2, 4, 1], + [1, 3, 4, 2], [3, 1, 4, 2], [3, 4, 1, 2], [3, 4, 2, 1], + [1, 2, 4, 3], [2, 1, 4, 3], [2, 4, 1, 3], [2, 4, 3, 1], + [1, 4, 2, 3], [4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1], + [1, 4, 3, 2], [4, 1, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]] + self.assertEqual(sorted(permute(nums1)), sorted(answer1)) + + nums2 = [1, 2, 3] + answer2 = [[3, 2, 1], [2, 3, 1], [2, 1, 3], [3, 1, 2], + [1, 3, 2], [1, 2, 3]] + self.assertEqual(sorted(permute(nums2)), sorted(answer2)) + + def test_permute_recursive(self): + nums1 = [1, 2, 3, 4] + answer1 = [[1, 2, 3, 4], [2, 1, 3, 4], [2, 3, 1, 4], [2, 3, 4, 1], + [1, 3, 2, 4], [3, 1, 2, 4], [3, 2, 1, 4], [3, 2, 4, 1], + [1, 3, 4, 2], [3, 1, 4, 2], [3, 4, 1, 2], [3, 4, 2, 1], + [1, 2, 4, 3], [2, 1, 4, 3], [2, 4, 1, 3], [2, 4, 3, 1], + [1, 4, 2, 3], [4, 1, 2, 3], [4, 2, 1, 3], [4, 2, 3, 1], + [1, 4, 3, 2], [4, 1, 3, 2], [4, 3, 1, 2], [4, 3, 2, 1]] + self.assertEqual(sorted(permute_recursive(nums1)), sorted(answer1)) + + nums2 = [1, 2, 3] + answer2 = [[3, 2, 1], [2, 3, 1], [2, 1, 3], [3, 1, 2], + [1, 3, 2], [1, 2, 3]] + self.assertEqual(sorted(permute_recursive(nums2)), sorted(answer2)) + + +class TestSubsetsUnique(unittest.TestCase): + + def test_subsets_unique(self): + nums1 = [1, 2, 2] + answer1 = [(1, 2), (1,), (1, 2, 2), (2,), (), (2, 2)] + self.assertEqual(sorted(subsets_unique(nums1)), sorted(answer1)) + + nums2 = [1, 2, 3, 4] + answer2 = [(1, 2), (1, 3), (1, 2, 3, 4), (1,), (2,), (3,), + (1, 4), (1, 2, 3), (4,), (), (2, 3), (1, 2, 4), + (1, 3, 4), (2, 3, 4), (3, 4), (2, 4)] + self.assertEqual(sorted(subsets_unique(nums2)), sorted(answer2)) + + +class TestSubsets(unittest.TestCase): + + def test_subsets(self): + nums1 = [1, 2, 3] + answer1 = [[1, 2, 3], [1, 2], [1, 3], [1], [2, 3], [2], [3], []] + self.assertEqual(sorted(subsets(nums1)), sorted(answer1)) + + nums2 = [1, 2, 3, 4] + answer2 = [[1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], + [1, 3], [1, 4], [1], [2, 3, 4], [2, 3], [2, 4], [2], + [3, 4], [3], [4], []] + self.assertEqual(sorted(subsets(nums2)), sorted(answer2)) + + def test_subsets_v2(self): + nums1 = [1, 2, 3] + answer1 = [[1, 2, 3], [1, 2], [1, 3], [1], [2, 3], [2], [3], []] + self.assertEqual(sorted(subsets_v2(nums1)), sorted(answer1)) + + nums2 = [1, 2, 3, 4] + answer2 = [[1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], + [1, 3], [1, 4], [1], [2, 3, 4], [2, 3], [2, 4], [2], + [3, 4], [3], [4], []] + self.assertEqual(sorted(subsets_v2(nums2)), sorted(answer2)) + + +if __name__ == '__main__': + + unittest.main() diff --git a/tests/test_bfs.py b/tests/test_bfs.py new file mode 100644 index 000000000..f9b22f134 --- /dev/null +++ b/tests/test_bfs.py @@ -0,0 +1,62 @@ +from algorithms.bfs import ( + count_islands, + maze_search, + ladder_length +) + +import unittest + + +class TestCountIslands(unittest.TestCase): + + def test_count_islands(self): + grid_1 = [[1, 1, 1, 1, 0], [1, 1, 0, 1, 0], [1, 1, 0, 0, 0], + [0, 0, 0, 0, 0]] + self.assertEqual(1, count_islands(grid_1)) + grid_2 = [[1, 1, 0, 0, 0], [1, 1, 0, 0, 0], [0, 0, 1, 0, 0], + [0, 0, 0, 1, 1]] + self.assertEqual(3, count_islands(grid_2)) + grid_3 = [[1, 1, 1, 0, 0, 0], [1, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1], + [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 0, 0]] + self.assertEqual(3, count_islands(grid_3)) + grid_4 = [[1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1], + [1, 1, 1, 1, 0, 0]] + self.assertEqual(5, count_islands(grid_4)) + + +class TestMazeSearch(unittest.TestCase): + + def test_maze_search(self): + grid_1 = [[1, 0, 1, 1, 1, 1], [1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 1], + [1, 1, 1, 0, 1, 1]] + self.assertEqual(14, maze_search(grid_1)) + grid_2 = [[1, 0, 0], [0, 1, 1], [0, 1, 1]] + self.assertEqual(-1, maze_search(grid_2)) + + +class TestWordLadder(unittest.TestCase): + + def test_ladder_length(self): + + # hit -> hot -> dot -> dog -> cog + self.assertEqual(5, ladder_length('hit', 'cog', ["hot", "dot", "dog", + "lot", "log"])) + + # pick -> sick -> sink -> sank -> tank == 5 + self.assertEqual(5, ladder_length('pick', 'tank', + ['tock', 'tick', 'sank', 'sink', + 'sick'])) + + # live -> life == 1, no matter what is the word_list. + self.assertEqual(1, ladder_length('live', 'life', ['hoho', 'luck'])) + + # 0 length from ate -> ate + self.assertEqual(0, ladder_length('ate', 'ate', [])) + + # not possible to reach ! + self.assertEqual(-1, ladder_length('rahul', 'coder', ['blahh', + 'blhah'])) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_bit.py b/tests/test_bit.py new file mode 100644 index 000000000..c494a9762 --- /dev/null +++ b/tests/test_bit.py @@ -0,0 +1,274 @@ +from algorithms.bit import ( + add_bitwise_operator, + count_ones_iter, count_ones_recur, + count_flips_to_convert, + find_missing_number, find_missing_number2, + flip_bit_longest_seq, + is_power_of_two, + reverse_bits, + single_number, + single_number2, + single_number3, + subsets, + get_bit, set_bit, clear_bit, update_bit, + int_to_bytes_big_endian, int_to_bytes_little_endian, + bytes_big_endian_to_int, bytes_little_endian_to_int, + swap_pair, + find_difference, + has_alternative_bit, has_alternative_bit_fast, + insert_one_bit, insert_mult_bits, + remove_bit, + binary_gap +) + +import unittest +import random + + +class TestSuite(unittest.TestCase): + + def setUp(self): + """Initialize seed.""" + random.seed("test") + + def test_add_bitwise_operator(self): + self.assertEqual(5432 + 97823, add_bitwise_operator(5432, 97823)) + self.assertEqual(0, add_bitwise_operator(0, 0)) + self.assertEqual(10, add_bitwise_operator(10, 0)) + self.assertEqual(10, add_bitwise_operator(0, 10)) + + def test_count_ones_recur(self): + + # 8 -> 1000 + self.assertEqual(1, count_ones_recur(8)) + + # 109 -> 1101101 + self.assertEqual(5, count_ones_recur(109)) + + # 63 -> 111111 + self.assertEqual(6, count_ones_recur(63)) + + # 0 -> 0 + self.assertEqual(0, count_ones_recur(0)) + + def test_count_ones_iter(self): + + # 8 -> 1000 + self.assertEqual(1, count_ones_iter(8)) + + # 109 -> 1101101 + self.assertEqual(5, count_ones_iter(109)) + + # 63 -> 111111 + self.assertEqual(6, count_ones_iter(63)) + + # 0 -> 0 + self.assertEqual(0, count_ones_iter(0)) + + def test_count_flips_to_convert(self): + # 29: 11101 and 15: 01111 + self.assertEqual(2, count_flips_to_convert(29, 15)) + # 45: 0000101101 and 987: 1111011011 + self.assertEqual(8, count_flips_to_convert(45, 987)) + # 34: 100010 + self.assertEqual(0, count_flips_to_convert(34, 34)) + # 34: 100010 and 53: 110101 + self.assertEqual(4, count_flips_to_convert(34, 53)) + + def test_find_missing_number(self): + + self.assertEqual(7, find_missing_number([4, 1, 3, 0, 6, 5, 2])) + self.assertEqual(0, find_missing_number([1])) + self.assertEqual(1, find_missing_number([0])) + + nums = [i for i in range(100000) if i != 12345] + random.shuffle(nums) + self.assertEqual(12345, find_missing_number(nums)) + + def test_find_missing_number2(self): + + self.assertEqual(7, find_missing_number2([4, 1, 3, 0, 6, 5, 2])) + self.assertEqual(0, find_missing_number2([1])) + self.assertEqual(1, find_missing_number2([0])) + + nums = [i for i in range(100000) if i != 12345] + random.shuffle(nums) + self.assertEqual(12345, find_missing_number2(nums)) + + def test_flip_bit_longest_seq(self): + # 1775: 11011101111 + self.assertEqual(8, flip_bit_longest_seq(1775)) + # 5: 101 + self.assertEqual(3, flip_bit_longest_seq(5)) + # 71: 1000111 + self.assertEqual(4, flip_bit_longest_seq(71)) + # 0: 0 + self.assertEqual(1, flip_bit_longest_seq(0)) + + def test_is_power_of_two(self): + + self.assertTrue(is_power_of_two(64)) + self.assertFalse(is_power_of_two(91)) + self.assertTrue(is_power_of_two(2**1001)) + self.assertTrue(is_power_of_two(1)) + self.assertFalse(is_power_of_two(0)) + + def test_reverse_bits(self): + + self.assertEqual(43261596, reverse_bits(964176192)) + self.assertEqual(964176192, reverse_bits(43261596)) + self.assertEqual(1, reverse_bits(2147483648)) + + # bin(0) => 00000000000000000000000000000000 + self.assertEqual(0, reverse_bits(0)) + + # bin(2**32 - 1) => 11111111111111111111111111111111 + self.assertEqual(2**32 - 1, reverse_bits(2**32 - 1)) + + def test_single_number(self): + + random.seed('test') + + self.assertEqual(0, single_number([1, 0, 2, 1, 2, 3, 3])) + self.assertEqual(101, single_number([101])) + + single = random.randint(1, 100000) + nums = [random.randint(1, 100000) for _ in range(1000)] + nums *= 2 # nums contains pairs of random integers + nums.append(single) + random.shuffle(nums) + + self.assertEqual(single, single_number(nums)) + + def test_single_number2(self): + + self.assertEqual(3, single_number2([4, 2, 3, 2, 1, 1, 4, 2, 4, 1])) + single = random.randint(1, 100000) + nums = [random.randint(1, 100000) for _ in range(1000)] + nums *= 3 # nums contains triplets of random integers + nums.append(single) + random.shuffle(nums) + self.assertEqual(single, single_number2(nums)) + + def test_single_number3(self): + self.assertEqual(sorted([2, 5]), + sorted(single_number3([2, 1, 5, 6, 6, 1]))) + self.assertEqual(sorted([4, 3]), + sorted(single_number3([9, 9, 4, 3]))) + + def test_subsets(self): + + self.assertSetEqual(subsets([1, 2, 3]), + {(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), + (1, 2, 3)}) + + self.assertSetEqual(subsets([10, 20, 30, 40]), + {(10, 40), (10, 20, 40), (10, 30), + (10, 20, 30, 40), (40,), + (10, 30, 40), (30,), (20, 30), (30, 40), (10,), + (), + (10, 20), (20, 40), (20, 30, 40), (10, 20, 30), + (20,)}) + + def test_get_bit(self): + # 22 = 10110 + self.assertEqual(1, get_bit(22, 2)) + self.assertEqual(0, get_bit(22, 3)) + + def test_set_bit(self): + # 22 = 10110 --> after set bit at 3th position: 30 = 11110 + self.assertEqual(30, set_bit(22, 3)) + + def test_clear_bit(self): + # 22 = 10110 --> after clear bit at 2nd position: 20 = 10010 + self.assertEqual(18, clear_bit(22, 2)) + + def test_update_bit(self): + # 22 = 10110 --> after update bit at 3th position with + # value 1: 30 = 11110 + self.assertEqual(30, update_bit(22, 3, 1)) + # 22 = 10110 --> after update bit at 2nd position with + # value 0: 20 = 10010 + self.assertEqual(18, update_bit(22, 2, 0)) + + def test_int_to_bytes_big_endian(self): + self.assertEqual(b'\x11', int_to_bytes_big_endian(17)) + + def test_int_to_bytes_little_endian(self): + self.assertEqual(b'\x11', int_to_bytes_little_endian(17)) + + def test_bytes_big_endian_to_int(self): + self.assertEqual(17, bytes_big_endian_to_int(b'\x11')) + + def test_bytes_little_endian_to_int(self): + self.assertEqual(17, bytes_little_endian_to_int(b'\x11')) + + def test_swap_pair(self): + # 22: 10110 --> 41: 101001 + self.assertEqual(41, swap_pair(22)) + # 10: 1010 --> 5 : 0101 + self.assertEqual(5, swap_pair(10)) + + def test_find_difference(self): + self.assertEqual('e', find_difference("abcd", "abecd")) + + def test_has_alternative_bit(self): + self.assertTrue(has_alternative_bit(5)) + self.assertFalse(has_alternative_bit(7)) + self.assertFalse(has_alternative_bit(11)) + self.assertTrue(has_alternative_bit(10)) + + def test_has_alternative_bit_fast(self): + self.assertTrue(has_alternative_bit_fast(5)) + self.assertFalse(has_alternative_bit_fast(7)) + self.assertFalse(has_alternative_bit_fast(11)) + self.assertTrue(has_alternative_bit_fast(10)) + + def test_insert_one_bit(self): + """ + Input: num = 10101 (21) + insert_one_bit(num, 1, 2): 101101 (45) + insert_one_bit(num, 0 ,2): 101001 (41) + insert_one_bit(num, 1, 5): 110101 (53) + insert_one_bit(num, 1, 0): 101010 (42) + """ + self.assertEqual(45, insert_one_bit(21, 1, 2)) + self.assertEqual(41, insert_one_bit(21, 0, 2)) + self.assertEqual(53, insert_one_bit(21, 1, 5)) + self.assertEqual(43, insert_one_bit(21, 1, 0)) + + def test_insert_mult_bits(self): + """ + Input: num = 101 (5) + insert_mult_bits(num, 7, 3, 1): 101111 (47) + insert_mult_bits(num, 7, 3, 0): 101111 (47) + insert_mult_bits(num, 7, 3, 3): 111101 (61) + """ + self.assertEqual(47, insert_mult_bits(5, 7, 3, 1)) + self.assertEqual(47, insert_mult_bits(5, 7, 3, 0)) + self.assertEqual(61, insert_mult_bits(5, 7, 3, 3)) + + def test_remove_bit(self): + """ + Input: num = 10101 (21) + remove_bit(num, 2): output = 1001 (9) + remove_bit(num, 4): output = 101 (5) + remove_bit(num, 0): output = 1010 (10) + """ + self.assertEqual(9, remove_bit(21, 2)) + self.assertEqual(5, remove_bit(21, 4)) + self.assertEqual(10, remove_bit(21, 0)) + + def test_binary_gap(self): + # 22 = 10110 + self.assertEqual(2, binary_gap(22)) + # 6 = 110 + self.assertEqual(1, binary_gap(6)) + # 8 = 1000 + self.assertEqual(0, binary_gap(8)) + # 145 = 10010001 + self.assertEqual(4, binary_gap(145)) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_compression.py b/tests/test_compression.py new file mode 100644 index 000000000..503369c4a --- /dev/null +++ b/tests/test_compression.py @@ -0,0 +1,74 @@ +from algorithms.compression.huffman_coding import HuffmanCoding +from algorithms.compression.rle_compression import (decode_rle, encode_rle) +from algorithms.compression.elias import (elias_gamma, elias_delta) + +import unittest + + +class TestHuffmanCoding(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.file_in_name = "huffman_coding_in.txt" + cls.file_out_bin_name = "huffman_coding_out.bin" + cls.file_out_name = "huffman_coding_out.txt" + + def setUp(self): + import random + random.seed(1951) + with open(self.file_in_name, "wb") as file_in: + for i in range(10000): + file_in.write(bytes([random.randrange(0, 256)])) + + def test_huffman_coding(self): + HuffmanCoding.encode_file(self.file_in_name, self.file_out_bin_name) + HuffmanCoding.decode_file(self.file_out_bin_name, self.file_out_name) + + with open(self.file_in_name, "rb") as file_1, open(self.file_out_name, "rb") as file_2: + content_1 = file_1.read() + content_2 = file_2.read() + + self.assertEqual(content_1, content_2) + + def tearDown(self): + import os + os.remove(self.file_in_name) + os.remove(self.file_out_bin_name) + os.remove(self.file_out_name) + + +class TestRLECompression(unittest.TestCase): + + def test_encode_rle(self): + self.assertEqual('12W1B12W3B24W1B14W', + encode_rle('WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWW')) + + def test_decode_rle(self): + self.assertEqual('WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWW', + decode_rle('12W1B12W3B24W1B14W')) + + +class TestEliasCoding(unittest.TestCase): + + def test_elias_gamma(self): + correct_result = ['0', '00', '100', '101', '11000', '11001', '11010', + '11011', '1110000', '1110001', '1110010'] + + result = [] + for i in range(11): + result.append(elias_gamma(i)) + + self.assertEqual(correct_result, result) + + def test_elias_delta(self): + correct_result = ['0', '000', '1000', '1001', '10100', '10101', + '10110', '10111', '11000000', '11000001', '11000010'] + + result = [] + for i in range(11): + result.append(elias_delta(i)) + + self.assertEqual(correct_result, result) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_dfs.py b/tests/test_dfs.py new file mode 100644 index 000000000..3164ab873 --- /dev/null +++ b/tests/test_dfs.py @@ -0,0 +1,80 @@ +from algorithms.dfs import ( + get_factors, get_factors_iterative1, get_factors_iterative2, + num_islands, + pacific_atlantic, + Sudoku, + walls_and_gates, + find_path +) + +import unittest + + +class TestAllFactors(unittest.TestCase): + def test_get_factors(self): + self.assertEqual([[2, 16], [2, 2, 8], [2, 2, 2, 4], [2, 2, 2, 2, 2], + [2, 4, 4], [4, 8]], get_factors(32)) + + def test_get_factors_iterative1(self): + self.assertEqual([[2, 16], [4, 8], [2, 2, 8], [2, 4, 4], [2, 2, 2, 4], + [2, 2, 2, 2, 2]], get_factors_iterative1(32)) + + def test_get_factors_iterative2(self): + self.assertEqual([[2, 2, 2, 2, 2], [2, 2, 2, 4], [2, 2, 8], [2, 4, 4], + [2, 16], [4, 8]], get_factors_iterative2(32)) + + +class TestCountIslands(unittest.TestCase): + def test_num_islands(self): + self.assertEqual(1, num_islands([[1, 1, 1, 1, 0], [1, 1, 0, 1, 0], + [1, 1, 0, 0, 0], [0, 0, 0, 0, 0]])) + self.assertEqual(3, num_islands([[1, 1, 0, 0, 0], [1, 1, 0, 0, 0], + [0, 0, 1, 0, 0], [0, 0, 0, 1, 1]])) + + +class TestPacificAtlantic(unittest.TestCase): + def test_pacific_atlantic(self): + self.assertEqual([[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], + [3, 1], [4, 0]], pacific_atlantic([[1, 2, 2, 3, 5], + [3, 2, 3, 4, 4], + [2, 4, 5, 3, 1], + [6, 7, 1, 4, 5], + [5, 1, 1, 2, 4]])) + + +class TestSudoku(unittest.TestCase): + def test_sudoku_solver(self): + board = [["5", "3", "."], ["6", ".", "."], [".", "9", "8"]] + test_obj = Sudoku(board, 3, 3) + test_obj.solve() + self.assertEqual([['5', '3', '1'], ['6', '1', '2'], + ['1', '9', '8']], test_obj.board) + + +class TestWallsAndGates(unittest.TestCase): + def test_walls_and_gates(self): + rooms = [[float("inf"), -1, 0, float("inf")], + [float("inf"), float("inf"), float("inf"), -1], + [float("inf"), -1, float("inf"), -1], + [0, -1, float("inf"), float("inf")]] + walls_and_gates(rooms) + self.assertEqual([[3, -1, 0, 1], [2, 2, 1, -1], [1, -1, 2, -1], + [0, -1, 3, 4]], rooms) + + +class TestMazeSearch(unittest.TestCase): + def test_maze_search(self): + maze_1 = [[1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, + 1, 0, 1, 1, 1], + [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, + 0, 1, 1, 1, 0, 1]] + self.assertEqual(37, find_path(maze_1)) + maze_2 = [[1, 0, 1, 1, 1, 1], [1, 0, 1, 0, 1, 0], + [1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 1]] + self.assertEqual(14, find_path(maze_2)) + maze_3 = [[1, 0, 0], [0, 1, 1], [0, 1, 1]] + self.assertEqual(-1, find_path(maze_3)) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_dp.py b/tests/test_dp.py new file mode 100644 index 000000000..e92800a11 --- /dev/null +++ b/tests/test_dp.py @@ -0,0 +1,263 @@ +from algorithms.dp import ( + max_profit_naive, max_profit_optimized, + climb_stairs, climb_stairs_optimized, + count, + combination_sum_topdown, combination_sum_bottom_up, + edit_distance, + egg_drop, + fib_recursive, fib_list, fib_iter, + hosoya_testing, + house_robber, + Job, schedule, + Item, get_maximum_value, + longest_increasing_subsequence, + longest_increasing_subsequence_optimized, + longest_increasing_subsequence_optimized2, + int_divide,find_k_factor, + planting_trees, regex_matching +) + + +import unittest + + +class TestBuySellStock(unittest.TestCase): + def test_max_profit_naive(self): + self.assertEqual(max_profit_naive([7, 1, 5, 3, 6, 4]), 5) + self.assertEqual(max_profit_naive([7, 6, 4, 3, 1]), 0) + + def test_max_profit_optimized(self): + self.assertEqual(max_profit_optimized([7, 1, 5, 3, 6, 4]), 5) + self.assertEqual(max_profit_optimized([7, 6, 4, 3, 1]), 0) + + +class TestClimbingStairs(unittest.TestCase): + def test_climb_stairs(self): + self.assertEqual(climb_stairs(2), 2) + self.assertEqual(climb_stairs(10), 89) + + def test_climb_stairs_optimized(self): + self.assertEqual(climb_stairs_optimized(2), 2) + self.assertEqual(climb_stairs_optimized(10), 89) + + +class TestCoinChange(unittest.TestCase): + def test_count(self): + self.assertEqual(count([1, 2, 3], 4), 4) + self.assertEqual(count([2, 5, 3, 6], 10), 5) + + +class TestCombinationSum(unittest.TestCase): + def test_combination_sum_topdown(self): + self.assertEqual(combination_sum_topdown([1, 2, 3], 4), 7) + + def test_combination_sum_bottom_up(self): + self.assertEqual(combination_sum_bottom_up([1, 2, 3], 4), 7) + + +class TestEditDistance(unittest.TestCase): + def test_edit_distance(self): + self.assertEqual(edit_distance('food', 'money'), 4) + self.assertEqual(edit_distance('horse', 'ros'), 3) + + +class TestEggDrop(unittest.TestCase): + def test_egg_drop(self): + self.assertEqual(egg_drop(1, 2), 2) + self.assertEqual(egg_drop(2, 6), 3) + self.assertEqual(egg_drop(3, 14), 4) + + +class TestFib(unittest.TestCase): + def test_fib_recursive(self): + self.assertEqual(fib_recursive(10), 55) + self.assertEqual(fib_recursive(30), 832040) + + def test_fib_list(self): + self.assertEqual(fib_list(10), 55) + self.assertEqual(fib_list(30), 832040) + + def test_fib_iter(self): + self.assertEqual(fib_iter(10), 55) + self.assertEqual(fib_iter(30), 832040) + + +class TestHosoyaTriangle(unittest.TestCase): + """[summary] + Test for the file hosoya_triangle + + Arguments: + unittest {[type]} -- [description] + """ + + def test_hosoya(self): + self.assertEqual([1], hosoya_testing(1)) + self.assertEqual([1, + 1, 1, + 2, 1, 2, + 3, 2, 2, 3, + 5, 3, 4, 3, 5, + 8, 5, 6, 6, 5, 8], + hosoya_testing(6)) + self.assertEqual([1, + 1, 1, + 2, 1, 2, + 3, 2, 2, 3, + 5, 3, 4, 3, 5, + 8, 5, 6, 6, 5, 8, + 13, 8, 10, 9, 10, 8, 13, + 21, 13, 16, 15, 15, 16, 13, 21, + 34, 21, 26, 24, 25, 24, 26, 21, 34, + 55, 34, 42, 39, 40, 40, 39, 42, 34, 55], + hosoya_testing(10)) + + +class TestHouseRobber(unittest.TestCase): + def test_house_robber(self): + self.assertEqual(44, house_robber([1, 2, 16, 3, 15, 3, 12, 1])) + + +class TestJobScheduling(unittest.TestCase): + def test_job_scheduling(self): + job1, job2 = Job(1, 3, 2), Job(2, 3, 4) + self.assertEqual(4, schedule([job1, job2])) + + +class TestKnapsack(unittest.TestCase): + def test_get_maximum_value(self): + item1, item2, item3 = Item(60, 10), Item(100, 20), Item(120, 30) + self.assertEqual(220, get_maximum_value([item1, item2, item3], 50)) + + item1, item2, item3, item4 = Item(60, 5), Item(50, 3), Item(70, 4), Item(30, 2) + self.assertEqual(80, get_maximum_value([item1, item2, item3, item4], + 5)) + + +class TestLongestIncreasingSubsequence(unittest.TestCase): + def test_longest_increasing_subsequence(self): + sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2] + self.assertEqual(5, longest_increasing_subsequence(sequence)) + + +class TestLongestIncreasingSubsequenceOptimized(unittest.TestCase): + def test_longest_increasing_subsequence_optimized(self): + sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2] + self.assertEqual(5, longest_increasing_subsequence(sequence)) + + +class TestLongestIncreasingSubsequenceOptimized2(unittest.TestCase): + def test_longest_increasing_subsequence_optimized2(self): + sequence = [1, 101, 10, 2, 3, 100, 4, 6, 2] + self.assertEqual(5, longest_increasing_subsequence(sequence)) + + +class TestIntDivide(unittest.TestCase): + def test_int_divide(self): + self.assertEqual(5, int_divide(4)) + self.assertEqual(42, int_divide(10)) + self.assertEqual(204226, int_divide(50)) + + +class Test_dp_K_Factor(unittest.TestCase): + def test_kfactor(self): + # Test 1 + n1 = 4 + k1 = 1 + self.assertEqual(find_k_factor(n1, k1), 1) + + # Test 2 + n2 = 7 + k2 = 1 + self.assertEqual(find_k_factor(n2, k2), 70302) + + # Test 3 + n3 = 10 + k3 = 2 + self.assertEqual(find_k_factor(n3, k3), 74357) + + # Test 4 + n4 = 8 + k4 = 2 + self.assertEqual(find_k_factor(n4, k4), 53) + + # Test 5 + n5 = 9 + k5 = 1 + self.assertEqual(find_k_factor(n5, k5), 71284044) + + +class TestPlantingTrees(unittest.TestCase): + def test_simple(self): + # arrange + trees = [0, 1, 10, 10] + L = 10 + W = 1 + + # act + res = planting_trees(trees, L, W) + + # assert + self.assertEqual(res, 2.414213562373095) + + def test_simple2(self): + # arrange + trees = [0, 3, 5, 5, 6, 9] + L = 10 + W = 1 + + # act + res = planting_trees(trees, L, W) + + # assert + self.assertEqual(res, 9.28538328578604) + +class TestRegexMatching(unittest.TestCase): + def test_none_0(self): + s = "" + p = "" + self.assertTrue(regex_matching.is_match(s, p)) + + def test_none_1(self): + s = "" + p = "a" + self.assertFalse(regex_matching.is_match(s, p)) + + def test_no_symbol_equal(self): + s = "abcd" + p = "abcd" + self.assertTrue(regex_matching.is_match(s, p)) + + def test_no_symbol_not_equal_0(self): + s = "abcd" + p = "efgh" + self.assertFalse(regex_matching.is_match(s, p)) + + def test_no_symbol_not_equal_1(self): + s = "ab" + p = "abb" + self.assertFalse(regex_matching.is_match(s, p)) + + def test_symbol_0(self): + s = "" + p = "a*" + self.assertTrue(regex_matching.is_match(s, p)) + + def test_symbol_1(self): + s = "a" + p = "ab*" + self.assertTrue(regex_matching.is_match(s, p)) + + def test_symbol_2(self): + # E.g. + # s a b b + # p 1 0 0 0 + # a 0 1 0 0 + # b 0 0 1 0 + # * 0 1 1 1 + s = "abb" + p = "ab*" + self.assertTrue(regex_matching.is_match(s, p)) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_graph.py b/tests/test_graph.py new file mode 100644 index 000000000..540d29983 --- /dev/null +++ b/tests/test_graph.py @@ -0,0 +1,368 @@ +from algorithms.graph import Tarjan +from algorithms.graph import check_bipartite +from algorithms.graph.dijkstra import Dijkstra +from algorithms.graph import ford_fulkerson +from algorithms.graph import edmonds_karp +from algorithms.graph import dinic +from algorithms.graph import maximum_flow_bfs +from algorithms.graph import maximum_flow_dfs +from algorithms.graph import all_pairs_shortest_path +from algorithms.graph import bellman_ford +from algorithms.graph import count_connected_number_of_component +from algorithms.graph import prims_minimum_spanning +from algorithms.graph import check_digraph_strongly_connected +from algorithms.graph import cycle_detection +from algorithms.graph import find_path +from algorithms.graph import path_between_two_vertices_in_digraph +from algorithms.graph import strongly_connected_components_kosaraju + +import unittest + + +class TestTarjan(unittest.TestCase): + """ + Test for the file tarjan.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_tarjan_example_1(self): + # Graph from https://en.wikipedia.org/wiki/File:Scc.png + example = { + 'A': ['B'], + 'B': ['C', 'E', 'F'], + 'C': ['D', 'G'], + 'D': ['C', 'H'], + 'E': ['A', 'F'], + 'F': ['G'], + 'G': ['F'], + 'H': ['D', 'G'] + } + + g = Tarjan(example) + self.assertEqual(g.sccs, [['F', 'G'], ['C', 'D', 'H'], + ['A', 'B', 'E']]) + + def test_tarjan_example_2(self): + # Graph from https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm#/media/File:Tarjan%27s_Algorithm_Animation.gif + example = { + 'A': ['E'], + 'B': ['A'], + 'C': ['B', 'D'], + 'D': ['C'], + 'E': ['B'], + 'F': ['B', 'E', 'G'], + 'G': ['F', 'C'], + 'H': ['G', 'H', 'D'] + } + + g = Tarjan(example) + self.assertEqual(g.sccs, [['A', 'B', 'E'], ['C', 'D'], ['F', 'G'], + ['H']]) + + +class TestCheckBipartite(unittest.TestCase): + def test_check_bipartite(self): + adj_list_1 = [[0, 0, 1], [0, 0, 1], [1, 1, 0]] + self.assertEqual(True, check_bipartite(adj_list_1)) + adj_list_2 = [[0, 1, 0, 1], [1, 0, 1, 0], [0, 1, 0, 1], [1, 0, 1, 0]] + self.assertEqual(True, check_bipartite(adj_list_2)) + adj_list_3 = [[0, 1, 0, 0], [1, 0, 1, 1], [0, 1, 0, 1], [0, 1, 1, 0]] + self.assertEqual(False, check_bipartite(adj_list_3)) + + +class TestDijkstra(unittest.TestCase): + def test_dijkstra(self): + g = Dijkstra(9) + g.graph = [[0, 4, 0, 0, 0, 0, 0, 8, 0], + [4, 0, 8, 0, 0, 0, 0, 11, 0], + [0, 8, 0, 7, 0, 4, 0, 0, 2], + [0, 0, 7, 0, 9, 14, 0, 0, 0], + [0, 0, 0, 9, 0, 10, 0, 0, 0], + [0, 0, 4, 14, 10, 0, 2, 0, 0], + [0, 0, 0, 0, 0, 2, 0, 1, 6], + [8, 11, 0, 0, 0, 0, 1, 0, 7], + [0, 0, 2, 0, 0, 0, 6, 7, 0]] + + self.assertEqual(g.dijkstra(0), [0, 4, 12, 19, 21, 11, 9, 8, 14]) + + +class TestMaximumFlow(unittest.TestCase): + """ + Test for the file maximum_flow.py + + Arguments: + unittest {[type]} -- [description] + """ + def test_ford_fulkerson(self): + capacity = [ + [0, 10, 10, 0, 0, 0, 0], + [0, 0, 2, 0, 4, 8, 0], + [0, 0, 0, 0, 0, 9, 0], + [0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 10], + [0, 0, 0, 0, 6, 0, 10], + [0, 0, 0, 0, 0, 0, 0] + ] + self.assertEqual(19, ford_fulkerson(capacity, 0, 6)) + + def test_edmonds_karp(self): + capacity = [ + [0, 10, 10, 0, 0, 0, 0], + [0, 0, 2, 0, 4, 8, 0], + [0, 0, 0, 0, 0, 9, 0], + [0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 10], + [0, 0, 0, 0, 6, 0, 10], + [0, 0, 0, 0, 0, 0, 0] + ] + self.assertEqual(19, edmonds_karp(capacity, 0, 6)) + + def dinic(self): + capacity = [ + [0, 10, 10, 0, 0, 0, 0], + [0, 0, 2, 0, 4, 8, 0], + [0, 0, 0, 0, 0, 9, 0], + [0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 10], + [0, 0, 0, 0, 6, 0, 10], + [0, 0, 0, 0, 0, 0, 0] + ] + self.assertEqual(19, dinic(capacity, 0, 6)) + + +class TestMaximum_Flow_Bfs(unittest.TestCase): + + """ + Test for the file def maximum_flow_bfs.py + Arguments: + unittest {[type]} -- [description] + """ + def test_maximum_flow_bfs(self): + graph = [ + [0, 16, 13, 0, 0, 0], + [0, 0, 10, 12, 0, 0], + [0, 4, 0, 0, 14, 0], + [0, 0, 9, 0, 0, 20], + [0, 0, 0, 7, 0, 4], + [0, 0, 0, 0, 0, 0] + ] + maximum_flow = maximum_flow_bfs(graph) + + self.assertEqual(maximum_flow, 23) + + +class TestMaximum_Flow_Dfs(unittest.TestCase): + + """ + Test for the file def maximum_flow_dfs.py + Arguments: + unittest {[type]} -- [description] + """ + def test_maximum_flow_dfs(self): + graph = [ + [0, 16, 13, 0, 0, 0], + [0, 0, 10, 12, 0, 0], + [0, 4, 0, 0, 14, 0], + [0, 0, 9, 0, 0, 20], + [0, 0, 0, 7, 0, 4], + [0, 0, 0, 0, 0, 0] + ] + maximum_flow = maximum_flow_dfs(graph) + + self.assertEqual(maximum_flow, 23) + + +class TestAll_Pairs_Shortest_Path(unittest.TestCase): + def test_all_pairs_shortest_path(self): + graph = [[0, 0.1, 0.101, 0.142, 0.277], + [0.465, 0, 0.191, 0.192, 0.587], + [0.245, 0.554, 0, 0.333, 0.931], + [1.032, 0.668, 0.656, 0, 0.151], + [0.867, 0.119, 0.352, 0.398, 0]] + result = all_pairs_shortest_path(graph) + + self.assertEqual(result, [ + [0, 0.1, 0.101, 0.142, 0.277], + [0.436, 0, 0.191, 0.192, + 0.34299999999999997], + [0.245, 0.345, 0, 0.333, 0.484], + [0.706, 0.27, 0.46099999999999997, 0, + 0.151], + [0.5549999999999999, 0.119, 0.31, 0.311, + 0], + ]) + + +class TestBellmanFord(unittest.TestCase): + def test_bellman_ford(self): + graph1 = { + 'a': {'b': 6, 'e': 7}, + 'b': {'c': 5, 'd': -4, 'e': 8}, + 'c': {'b': -2}, + 'd': {'a': 2, 'c': 7}, + 'e': {'b': -3} + } + self.assertEqual(True, bellman_ford(graph1, 'a')) + graph2 = { + 'a': {'d': 3, 'e': 4}, + 'b': {'a': 7, 'e': 2}, + 'c': {'a': 12, 'd': 9, 'e': 11}, + 'd': {'c': 5, 'e': 11}, + 'e': {'a': 7, 'b': 5, 'd': 1} + } + self.assertEqual(True, bellman_ford(graph2, 'a')) + + +class TestConnectedComponentInGraph(unittest.TestCase): + """ + Class for testing different cases for connected components in graph + """ + def test_count_connected_components(self): + """ + Test Function that test the different cases of count connected + components + 2----------0 1--------5 3 + | + | + 4 + output = 3 + """ + expected_result = 3 + # adjacency list representation of graph + l = [[2], + [5], + [0,4], + [], + [2], + [1]] + + size = 5 + result = count_connected_number_of_component.count_components(l, size) + self.assertEqual(result, expected_result) + + def test_connected_components_with_empty_graph(self): + + """ + input : + output : 0 + """ + l = [[]] + expected_result = 0 + size = 0 + result = count_connected_number_of_component.count_components(l, size) + self.assertEqual(result, expected_result) + + def test_connected_components_without_edges_graph(self): + """ + input : 0 2 3 4 + output : 4 + """ + l = [[0], [], [2], [3], [4]] + size = 4 + expected_result = 4 + result = count_connected_number_of_component.count_components(l, size) + self.assertEqual(result, expected_result) + + +class PrimsMinimumSpanning(unittest.TestCase): + def test_prim_spanning(self): + graph1 = { + 1: [[3, 2], [8, 3]], + 2: [[3, 1], [5, 4]], + 3: [[8, 1], [2, 4], [4, 5]], + 4: [[5, 2], [2, 3], [6, 5]], + 5: [[4, 3], [6, 4]] + } + self.assertEqual(14, prims_minimum_spanning(graph1)) + graph2 = { + 1: [[7, 2], [6, 4]], + 2: [[7, 1], [9, 4], [6, 3]], + 3: [[8, 4], [6, 2]], + 4: [[6, 1], [9, 2], [8, 3]] + } + self.assertEqual(19, prims_minimum_spanning(graph2)) + +class TestDigraphStronglyConnected(unittest.TestCase): + def test_digraph_strongly_connected(self): + g1 = check_digraph_strongly_connected.Graph(5) + g1.add_edge(0, 1) + g1.add_edge(1, 2) + g1.add_edge(2, 3) + g1.add_edge(3, 0) + g1.add_edge(2, 4) + g1.add_edge(4, 2) + self.assertTrue(g1.is_strongly_connected()) + + g2 = check_digraph_strongly_connected.Graph(4) + g2.add_edge(0, 1) + g2.add_edge(1, 2) + g2.add_edge(2, 3) + self.assertFalse(g2.is_strongly_connected()) + +class TestCycleDetection(unittest.TestCase): + def test_cycle_detection_with_cycle(self): + graph = {'A': ['B', 'C'], + 'B': ['D'], + 'C': ['F'], + 'D': ['E', 'F'], + 'E': ['B'], + 'F': []} + self.assertTrue(cycle_detection.contains_cycle(graph)) + + def test_cycle_detection_with_no_cycle(self): + graph = {'A': ['B', 'C'], + 'B': ['D', 'E'], + 'C': ['F'], + 'D': ['E'], + 'E': [], + 'F': []} + self.assertFalse(cycle_detection.contains_cycle(graph)) + +class TestFindPath(unittest.TestCase): + def test_find_all_paths(self): + graph = {'A': ['B', 'C'], + 'B': ['C', 'D'], + 'C': ['D', 'F'], + 'D': ['C'], + 'E': ['F'], + 'F': ['C']} + + paths = find_path.find_all_path(graph, 'A', 'F') + print(paths) + self.assertEqual(sorted(paths), sorted([ + ['A', 'C', 'F'], + ['A', 'B', 'C', 'F'], + ['A', 'B', 'D', 'C', 'F'], + ])) + +class TestPathBetweenTwoVertices(unittest.TestCase): + def test_node_is_reachable(self): + g = path_between_two_vertices_in_digraph.Graph(4) + g.add_edge(0, 1) + g.add_edge(0, 2) + g.add_edge(1, 2) + g.add_edge(2, 0) + g.add_edge(2, 3) + g.add_edge(3, 3) + + self.assertTrue(g.is_reachable(1, 3)) + self.assertFalse(g.is_reachable(3, 1)) + +class TestStronglyConnectedComponentsKosaraju(unittest.TestCase): + def test_kosaraju_algorithm(self): + V = 6 + adj = [ + [2], + [0], + [3], + [1, 4], + [5], + [4] + ] + + result = strongly_connected_components_kosaraju.Kosaraju().kosaraju(V, adj) + + # Expected result: 2 strongly connected components + self.assertEqual(result, 2) diff --git a/tests/test_greedy.py b/tests/test_greedy.py new file mode 100644 index 000000000..095f2a282 --- /dev/null +++ b/tests/test_greedy.py @@ -0,0 +1,21 @@ +from algorithms.greedy import ( + max_contiguous_subsequence_sum, +) + +import unittest + +class TestMaxContiguousSubsequenceSum(unittest.TestCase): + def test_max_contiguous_subsequence_sum(self): + arr1 = [-2, 3, 8, -1, 4] + arr2 = [-1, 1, 0] + arr3 = [-1, -3, -4] + arr4 = [-2, 3, 8, -12, 8, 4] + + self.assertEqual(max_contiguous_subsequence_sum(arr1), 14) + self.assertEqual(max_contiguous_subsequence_sum(arr2), 1) + self.assertEqual(max_contiguous_subsequence_sum(arr3), -1) + self.assertEqual(max_contiguous_subsequence_sum(arr4), 12) + +if __name__ == '__main__': + + unittest.main() \ No newline at end of file diff --git a/tests/test_heap.py b/tests/test_heap.py new file mode 100644 index 000000000..afae0d93e --- /dev/null +++ b/tests/test_heap.py @@ -0,0 +1,69 @@ +from algorithms.heap import ( + BinaryHeap, + get_skyline, + max_sliding_window, + k_closest +) + +import unittest + + +class TestBinaryHeap(unittest.TestCase): + """ + Test suite for the binary_heap data structures + """ + + def setUp(self): + self.min_heap = BinaryHeap() + self.min_heap.insert(4) + self.min_heap.insert(50) + self.min_heap.insert(7) + self.min_heap.insert(55) + self.min_heap.insert(90) + self.min_heap.insert(87) + + def test_insert(self): + # Before insert 2: [0, 4, 50, 7, 55, 90, 87] + # After insert: [0, 2, 50, 4, 55, 90, 87, 7] + self.min_heap.insert(2) + self.assertEqual([0, 2, 50, 4, 55, 90, 87, 7], + self.min_heap.heap) + self.assertEqual(7, self.min_heap.current_size) + + def test_remove_min(self): + ret = self.min_heap.remove_min() + # Before remove_min : [0, 4, 50, 7, 55, 90, 87] + # After remove_min: [7, 50, 87, 55, 90] + # Test return value + self.assertEqual(4, ret) + self.assertEqual([0, 7, 50, 87, 55, 90], + self.min_heap.heap) + self.assertEqual(5, self.min_heap.current_size) + + +class TestSuite(unittest.TestCase): + def test_get_skyline(self): + buildings = [[2, 9, 10], [3, 7, 15], [5, 12, 12], + [15, 20, 10], [19, 24, 8]] + # Expect output + output = [[2, 10], [3, 15], [7, 12], [12, 0], [15, 10], + [20, 8], [24, 0]] + self.assertEqual(output, get_skyline(buildings)) + + def test_max_sliding_window(self): + nums = [1, 3, -1, -3, 5, 3, 6, 7] + self.assertEqual([3, 3, 5, 5, 6, 7], max_sliding_window(nums, 3)) + + def test_k_closest_points(self): + points = [(1, 0), (2, 3), (5, 2), (1, 1), (2, 8), (10, 2), + (-1, 0), (-2, -2)] + self.assertEqual([(-1, 0), (1, 0)], k_closest(points, 2)) + self.assertEqual([(1, 1), (-1, 0), (1, 0)], k_closest(points, 3)) + self.assertEqual([(-2, -2), (1, 1), (1, 0), + (-1, 0)], k_closest(points, 4)) + self.assertEqual([(10, 2), (2, 8), (5, 2), (-2, -2), (2, 3), + (1, 0), (-1, 0), (1, 1)], k_closest(points, 8)) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_histogram.py b/tests/test_histogram.py new file mode 100644 index 000000000..cd35bd216 --- /dev/null +++ b/tests/test_histogram.py @@ -0,0 +1,17 @@ +from algorithms.distribution.histogram import get_histogram + +import unittest + + +class TestListsInHistogram(unittest.TestCase): + def test_histogram(self): + list_1 = [3, 3, 2, 1] + list_2 = [2, 3, 5, 5, 5, 6, 4, 3, 7] + + self.assertEqual(get_histogram(list_1), {1: 1, 2: 1, 3: 2}) + self.assertEqual(get_histogram(list_2), + {2: 1, 3: 2, 4: 1, 5: 3, 6: 1, 7: 1}) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_iterative_segment_tree.py b/tests/test_iterative_segment_tree.py new file mode 100644 index 000000000..66d222267 --- /dev/null +++ b/tests/test_iterative_segment_tree.py @@ -0,0 +1,99 @@ +from algorithms.tree.segment_tree.iterative_segment_tree import SegmentTree +from functools import reduce + +import unittest + + +def gcd(a, b): + if b == 0: + return a + return gcd(b, a % b) + + +class TestSegmentTree(unittest.TestCase): + """ + Test for the Iterative Segment Tree data structure + """ + + def test_segment_tree_creation(self): + arr = [2, 4, 3, 6, 8, 9, 3] + max_segment_tree = SegmentTree(arr, max) + min_segment_tree = SegmentTree(arr, min) + sum_segment_tree = SegmentTree(arr, lambda a, b: a + b) + gcd_segment_tree = SegmentTree(arr, gcd) + self.assertEqual(max_segment_tree.tree, + [None, 9, 8, 9, 4, 8, 9, 2, 4, 3, 6, 8, 9, 3]) + self.assertEqual(min_segment_tree.tree, + [None, 2, 3, 2, 3, 6, 3, 2, 4, 3, 6, 8, 9, 3]) + self.assertEqual(sum_segment_tree.tree, + [None, 35, 21, 14, 7, 14, 12, 2, 4, 3, 6, 8, 9, 3]) + self.assertEqual(gcd_segment_tree.tree, + [None, 1, 1, 1, 1, 2, 3, 2, 4, 3, 6, 8, 9, 3]) + + def test_max_segment_tree(self): + arr = [-1, 1, 10, 2, 9, -3, 8, 4, 7, 5, 6, 0] + self.__test_all_segments(arr, max) + + def test_min_segment_tree(self): + arr = [1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12] + self.__test_all_segments(arr, min) + + def test_sum_segment_tree(self): + arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, -11, -12] + self.__test_all_segments(arr, lambda a, b: a + b) + + def test_gcd_segment_tree(self): + arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 12, 14] + self.__test_all_segments(arr, gcd) + + def test_max_segment_tree_with_updates(self): + arr = [-1, 1, 10, 2, 9, -3, 8, 4, 7, 5, 6, 0] + updates = {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, + 9: 10, 10: 11, 11: 12} + self.__test_all_segments_with_updates(arr, max, updates) + + def test_min_segment_tree_with_updates(self): + arr = [1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12] + updates = {0: 7, 1: 2, 2: 6, 3: -14, 4: 5, 5: 4, 6: 7, 7: -10, 8: 9, + 9: 10, 10: 12, 11: 1} + self.__test_all_segments_with_updates(arr, min, updates) + + def test_sum_segment_tree_with_updates(self): + arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, -11, -12] + updates = {0: 12, 1: 11, 2: 10, 3: 9, 4: 8, 5: 7, 6: 6, 7: 5, 8: 4, + 9: 3, 10: 2, 11: 1} + self.__test_all_segments_with_updates(arr, lambda a, b: a + b, updates) + + def test_gcd_segment_tree_with_updates(self): + arr = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 12, 14] + updates = {0: 4, 1: 2, 2: 3, 3: 9, 4: 21, 5: 7, 6: 4, 7: 4, 8: 2, + 9: 5, 10: 17, 11: 12, 12: 3} + self.__test_all_segments_with_updates(arr, gcd, updates) + + def __test_all_segments(self, arr, fnc): + """ + Test all possible segments in the tree + :param arr: array to test + :param fnc: function of the segment tpree + """ + segment_tree = SegmentTree(arr, fnc) + self.__test_segments_helper(segment_tree, fnc, arr) + + def __test_all_segments_with_updates(self, arr, fnc, upd): + """ + Test all possible segments in the tree with updates + :param arr: array to test + :param fnc: function of the segment tree + :param upd: updates to test + """ + segment_tree = SegmentTree(arr, fnc) + for index, value in upd.items(): + arr[index] = value + segment_tree.update(index, value) + self.__test_segments_helper(segment_tree, fnc, arr) + + def __test_segments_helper(self, seg_tree, fnc, arr): + for i in range(0, len(arr)): + for j in range(i, len(arr)): + range_value = reduce(fnc, arr[i:j + 1]) + self.assertEqual(seg_tree.query(i, j), range_value) diff --git a/tests/test_linkedlist.py b/tests/test_linkedlist.py new file mode 100644 index 000000000..6b7f1f4fa --- /dev/null +++ b/tests/test_linkedlist.py @@ -0,0 +1,215 @@ +import unittest + +from algorithms.linkedlist import ( + reverse_list, reverse_list_recursive, + is_sorted, + remove_range, + swap_pairs, + rotate_right, + is_cyclic, + merge_two_list, merge_two_list_recur, + is_palindrome, is_palindrome_stack, is_palindrome_dict, + RandomListNode, copy_random_pointer_v1, copy_random_pointer_v2 +) + + +class Node(object): + def __init__(self, x): + self.val = x + self.next = None + + +# Convert from linked list Node to list for testing +def convert(head): + ret = [] + if head: + current = head + while current: + ret.append(current.val) + current = current.next + return ret + + +class TestSuite(unittest.TestCase): + def setUp(self): + # list test for palindrome + self.l = Node('A') + self.l.next = Node('B') + self.l.next.next = Node('C') + self.l.next.next.next = Node('B') + self.l.next.next.next.next = Node('A') + + self.l1 = Node('A') + self.l1.next = Node('B') + self.l1.next.next = Node('C') + self.l1.next.next.next = Node('B') + + def test_reverse_list(self): + head = Node(1) + head.next = Node(2) + head.next.next = Node(3) + head.next.next.next = Node(4) + self.assertEqual([4, 3, 2, 1], convert(reverse_list(head))) + head = Node(1) + head.next = Node(2) + head.next.next = Node(3) + head.next.next.next = Node(4) + self.assertEqual([4, 3, 2, 1], convert(reverse_list_recursive(head))) + + def test_is_sorted(self): + head = Node(-2) + head.next = Node(2) + head.next.next = Node(2) + head.next.next.next = Node(4) + head.next.next.next.next = Node(9) + # head -> -2 -> 2 -> 2 -> 4 -> 9 + self.assertTrue(is_sorted(head)) + head = Node(1) + head.next = Node(2) + head.next.next = Node(8) + head.next.next.next = Node(4) + head.next.next.next.next = Node(6) + # head -> 1 -> 2 -> 8 -> 4 -> 6 + self.assertFalse(is_sorted(head)) + + def test_remove_range(self): + # Test case: middle case. + head = Node(0) + head.next = Node(1) + head.next.next = Node(2) + head.next.next.next = Node(3) + head.next.next.next.next = Node(4) + # Expect output: 0 4 + self.assertEqual([0, 4], convert(remove_range(head, 1, 3))) + + # Test case: taking out the front node + head = Node(0) + head.next = Node(1) + head.next.next = Node(2) + head.next.next.next = Node(3) + head.next.next.next.next = Node(4) + # Expect output: 2 3 4 + self.assertEqual([2, 3, 4], convert(remove_range(head, 0, 1))) + + # Test case: removing all the nodes + head = Node(0) + head.next = Node(1) + head.next.next = Node(2) + head.next.next.next = Node(3) + head.next.next.next.next = Node(4) + self.assertEqual([], convert(remove_range(head, 0, 7))) + + def test_swap_in_pairs(self): + head = Node(1) + head.next = Node(2) + head.next.next = Node(3) + head.next.next.next = Node(4) + # Expect output : 2 --> 1 --> 4 --> 3 + self.assertEqual([2, 1, 4, 3], convert(swap_pairs(head))) + + def test_rotate_right(self): + # Given 1->2->3->4->5->NULL + head = Node(1) + head.next = Node(2) + head.next.next = Node(3) + head.next.next.next = Node(4) + head.next.next.next.next = Node(5) + # K = 2. Expect output: 4->5->1->2->3->NULL. + self.assertEqual([4, 5, 1, 2, 3], convert(rotate_right(head, 2))) + + def test_is_cyclic(self): + # create linked list => A -> B -> C -> D -> E -> C + head = Node('A') + head.next = Node('B') + curr = head.next + cyclic_node = Node('C') + curr.next = cyclic_node + curr = curr.next + curr.next = Node('D') + curr = curr.next + curr.next = Node('E') + curr = curr.next + curr.next = cyclic_node + self.assertTrue(is_cyclic(head)) + + # create linked list 1 -> 2 -> 3 -> 4 + head = Node(1) + curr = head + for i in range(2, 6): + curr.next = Node(i) + curr = curr.next + self.assertFalse(is_cyclic(head)) + + def test_merge_two_list(self): + """ + Input: head1:1->2->4, head2: 1->3->4 + Output: 1->1->2->3->4->4 + """ + head1 = Node(1) + head1.next = Node(2) + head1.next.next = Node(4) + head2 = Node(1) + head2.next = Node(3) + head2.next.next = Node(4) + self.assertEqual([1, 1, 2, 3, 4, 4], + convert(merge_two_list(head1, head2))) + # Test recursive + head1 = Node(1) + head1.next = Node(2) + head1.next.next = Node(4) + head2 = Node(1) + head2.next = Node(3) + head2.next.next = Node(4) + self.assertEqual([1, 1, 2, 3, 4, 4], + convert(merge_two_list_recur(head1, head2))) + + def test_is_palindrome(self): + self.assertTrue(is_palindrome(self.l)) + self.assertFalse(is_palindrome(self.l1)) + + def test_is_palindrome_stack(self): + self.assertTrue(is_palindrome_stack(self.l)) + self.assertFalse(is_palindrome_stack(self.l1)) + + def test_is_palindrome_dict(self): + self.assertTrue(is_palindrome_dict(self.l)) + self.assertFalse(is_palindrome_dict(self.l1)) + + def test_solution_0(self): + self._init_random_list_nodes() + result = copy_random_pointer_v1(self.random_list_node1) + self._assert_is_a_copy(result) + + def test_solution_1(self): + self._init_random_list_nodes() + result = copy_random_pointer_v2(self.random_list_node1) + self._assert_is_a_copy(result) + + def _assert_is_a_copy(self, result): + self.assertEqual(5, result.next.next.next.next.label) + self.assertEqual(4, result.next.next.next.label) + self.assertEqual(3, result.next.next.label) + self.assertEqual(2, result.next.label) + self.assertEqual(1, result.label) + self.assertEqual(3, result.next.next.next.next.random.label) + self.assertIsNone(result.next.next.next.random) + self.assertEqual(2, result.next.next.random.label) + self.assertEqual(5, result.next.random.label) + self.assertEqual(4, result.random.label) + + def _init_random_list_nodes(self): + self.random_list_node1 = RandomListNode(1) + random_list_node2 = RandomListNode(2) + random_list_node3 = RandomListNode(3) + random_list_node4 = RandomListNode(4) + random_list_node5 = RandomListNode(5) + + self.random_list_node1.next, self.random_list_node1.random = random_list_node2, random_list_node4 + random_list_node2.next, random_list_node2.random = random_list_node3, random_list_node5 + random_list_node3.next, random_list_node3.random = random_list_node4, random_list_node2 + random_list_node4.next = random_list_node5 + random_list_node5.random = random_list_node3 + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_map.py b/tests/test_map.py new file mode 100644 index 000000000..a62656d15 --- /dev/null +++ b/tests/test_map.py @@ -0,0 +1,191 @@ +from algorithms.map import ( + HashTable, ResizableHashTable, + SeparateChainingHashTable, + word_pattern, + is_isomorphic, + is_anagram, + longest_palindromic_subsequence, +) + +import unittest + + +class TestHashTable(unittest.TestCase): + def test_one_entry(self): + m = HashTable(10) + m.put(1, '1') + self.assertEqual('1', m.get(1)) + + def test_add_entry_bigger_than_table_size(self): + m = HashTable(10) + m.put(11, '1') + self.assertEqual('1', m.get(11)) + + def test_get_none_if_key_missing_and_hash_collision(self): + m = HashTable(10) + m.put(1, '1') + self.assertEqual(None, m.get(11)) + + def test_two_entries_with_same_hash(self): + m = HashTable(10) + m.put(1, '1') + m.put(11, '11') + self.assertEqual('1', m.get(1)) + self.assertEqual('11', m.get(11)) + + def test_get_on_full_table_does_halts(self): + # and does not search forever + m = HashTable(10) + for i in range(10, 20): + m.put(i, i) + self.assertEqual(None, m.get(1)) + + def test_delete_key(self): + m = HashTable(10) + for i in range(5): + m.put(i, i**2) + m.del_(1) + self.assertEqual(None, m.get(1)) + self.assertEqual(4, m.get(2)) + + def test_delete_key_and_reassign(self): + m = HashTable(10) + m.put(1, 1) + del m[1] + m.put(1, 2) + self.assertEqual(2, m.get(1)) + + def test_assigning_to_full_table_throws_error(self): + m = HashTable(3) + m.put(1, 1) + m.put(2, 2) + m.put(3, 3) + with self.assertRaises(ValueError): + m.put(4, 4) + + def test_len_trivial(self): + m = HashTable(10) + self.assertEqual(0, len(m)) + for i in range(10): + m.put(i, i) + self.assertEqual(i + 1, len(m)) + + def test_len_after_deletions(self): + m = HashTable(10) + m.put(1, 1) + self.assertEqual(1, len(m)) + m.del_(1) + self.assertEqual(0, len(m)) + m.put(11, 42) + self.assertEqual(1, len(m)) + + def test_resizable_hash_table(self): + m = ResizableHashTable() + self.assertEqual(ResizableHashTable.MIN_SIZE, m.size) + for i in range(ResizableHashTable.MIN_SIZE): + m.put(i, 'foo') + self.assertEqual(ResizableHashTable.MIN_SIZE * 2, m.size) + self.assertEqual('foo', m.get(1)) + self.assertEqual('foo', m.get(3)) + self.assertEqual('foo', m.get(ResizableHashTable.MIN_SIZE - 1)) + + def test_fill_up_the_limit(self): + m = HashTable(10) + for i in range(10): + m.put(i, i**2) + for i in range(10): + self.assertEqual(i**2, m.get(i)) + + +class TestSeparateChainingHashTable(unittest.TestCase): + def test_one_entry(self): + m = SeparateChainingHashTable(10) + m.put(1, '1') + self.assertEqual('1', m.get(1)) + + def test_two_entries_with_same_hash(self): + m = SeparateChainingHashTable(10) + m.put(1, '1') + m.put(11, '11') + self.assertEqual('1', m.get(1)) + self.assertEqual('11', m.get(11)) + + def test_len_trivial(self): + m = SeparateChainingHashTable(10) + self.assertEqual(0, len(m)) + for i in range(10): + m.put(i, i) + self.assertEqual(i + 1, len(m)) + + def test_len_after_deletions(self): + m = SeparateChainingHashTable(10) + m.put(1, 1) + self.assertEqual(1, len(m)) + m.del_(1) + self.assertEqual(0, len(m)) + m.put(11, 42) + self.assertEqual(1, len(m)) + + def test_delete_key(self): + m = SeparateChainingHashTable(10) + for i in range(5): + m.put(i, i**2) + m.del_(1) + self.assertEqual(None, m.get(1)) + self.assertEqual(4, m.get(2)) + + def test_delete_key_and_reassign(self): + m = SeparateChainingHashTable(10) + m.put(1, 1) + del m[1] + m.put(1, 2) + self.assertEqual(2, m.get(1)) + + def test_add_entry_bigger_than_table_size(self): + m = SeparateChainingHashTable(10) + m.put(11, '1') + self.assertEqual('1', m.get(11)) + + def test_get_none_if_key_missing_and_hash_collision(self): + m = SeparateChainingHashTable(10) + m.put(1, '1') + self.assertEqual(None, m.get(11)) + + +class TestWordPattern(unittest.TestCase): + def test_word_pattern(self): + self.assertTrue(word_pattern("abba", "dog cat cat dog")) + self.assertFalse(word_pattern("abba", "dog cat cat fish")) + self.assertFalse(word_pattern("abba", "dog dog dog dog")) + self.assertFalse(word_pattern("aaaa", "dog cat cat dog")) + + +class TestIsSomorphic(unittest.TestCase): + def test_is_isomorphic(self): + self.assertTrue(is_isomorphic("egg", "add")) + self.assertFalse(is_isomorphic("foo", "bar")) + self.assertTrue(is_isomorphic("paper", "title")) + + +class TestLongestPalindromicSubsequence(unittest.TestCase): + def test_longest_palindromic_subsequence_is_correct(self): + self.assertEqual(3, longest_palindromic_subsequence('BBABCBCAB')) + self.assertEqual(4, longest_palindromic_subsequence('abbaeae')) + self.assertEqual(7, longest_palindromic_subsequence('babbbababaa')) + self.assertEqual(4, longest_palindromic_subsequence('daccandeeja')) + + def test_longest_palindromic_subsequence_is_incorrect(self): + self.assertNotEqual(4, longest_palindromic_subsequence('BBABCBCAB')) + self.assertNotEqual(5, longest_palindromic_subsequence('abbaeae')) + self.assertNotEqual(2, longest_palindromic_subsequence('babbbababaa')) + self.assertNotEqual(1, longest_palindromic_subsequence('daccandeeja')) + + +class TestIsAnagram(unittest.TestCase): + def test_is_anagram(self): + self.assertTrue(is_anagram("anagram", "nagaram")) + self.assertFalse(is_anagram("rat", "car")) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_maths.py b/tests/test_maths.py new file mode 100644 index 000000000..c4a54af03 --- /dev/null +++ b/tests/test_maths.py @@ -0,0 +1,597 @@ +from algorithms.maths import ( + power, power_recur, + int_to_base, base_to_int, + decimal_to_binary_ip, + euler_totient, + extended_gcd, + factorial, factorial_recur, + gcd, lcm, trailing_zero, gcd_bit, + gen_strobogrammatic, strobogrammatic_in_range, + is_strobogrammatic, is_strobogrammatic2, + modular_inverse, + modular_exponential, + find_next_square, find_next_square2, + prime_check, + get_primes, + pythagoras, + is_prime, + encrypt, decrypt, + combination, combination_memo, + hailstone, + cosine_similarity, + magic_number, + find_order, + find_primitive_root, + num_digits, + diffie_hellman_key_exchange, krishnamurthy_number, + num_perfect_squares, + chinese_remainder_theorem, + fft +) + +import unittest +import pytest + + +class TestPower(unittest.TestCase): + """ + Test for the file power.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_power(self): + self.assertEqual(8, power(2, 3)) + self.assertEqual(1, power(5, 0)) + self.assertEqual(0, power(10, 3, 5)) + self.assertEqual(280380, power(2265, 1664, 465465)) + + def test_power_recur(self): + self.assertEqual(8, power_recur(2, 3)) + self.assertEqual(1, power_recur(5, 0)) + self.assertEqual(0, power_recur(10, 3, 5)) + self.assertEqual(280380, power_recur(2265, 1664, 465465)) + + +class TestBaseConversion(unittest.TestCase): + """ + Test for the file base_conversion.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_int_to_base(self): + self.assertEqual("101", int_to_base(5, 2)) + self.assertEqual("0", int_to_base(0, 2)) + self.assertEqual("FF", int_to_base(255, 16)) + + def test_base_to_int(self): + self.assertEqual(5, base_to_int("101", 2)) + self.assertEqual(0, base_to_int("0", 2)) + self.assertEqual(255, base_to_int("FF", 16)) + + +class TestDecimalToBinaryIP(unittest.TestCase): + """ + Test for the file decimal_to_binary_ip.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_decimal_to_binary_ip(self): + self.assertEqual("00000000.00000000.00000000.00000000", + decimal_to_binary_ip("0.0.0.0")) + self.assertEqual("11111111.11111111.11111111.11111111", + decimal_to_binary_ip("255.255.255.255")) + self.assertEqual("11000000.10101000.00000000.00000001", + decimal_to_binary_ip("192.168.0.1")) + + +class TestEulerTotient(unittest.TestCase): + """[summary] + Test for the file euler_totient.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_euler_totient(self): + self.assertEqual(4, euler_totient(8)) + self.assertEqual(12, euler_totient(21)) + self.assertEqual(311040, euler_totient(674614)) + self.assertEqual(2354352, euler_totient(3435145)) + + +class TestExtendedGcd(unittest.TestCase): + """[summary] + Test for the file extended_gcd.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_extended_gcd(self): + self.assertEqual((0, 1, 2), extended_gcd(8, 2)) + self.assertEqual((0, 1, 17), extended_gcd(13, 17)) + + +class TestGcd(unittest.TestCase): + """[summary] + Test for the file gcd.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_gcd(self): + self.assertEqual(4, gcd(8, 12)) + self.assertEqual(1, gcd(13, 17)) + + def test_gcd_non_integer_input(self): + with pytest.raises(ValueError, + match=r"Input arguments are not integers"): + gcd(1.0, 5) + gcd(5, 6.7) + gcd(33.8649, 6.12312312) + + def test_gcd_zero_input(self): + with pytest.raises(ValueError, + match=r"One or more input arguments equals zero"): + gcd(0, 12) + gcd(12, 0) + gcd(0, 0) + + def test_gcd_negative_input(self): + self.assertEqual(1, gcd(-13, -17)) + self.assertEqual(4, gcd(-8, 12)) + self.assertEqual(8, gcd(24, -16)) + + def test_lcm(self): + self.assertEqual(24, lcm(8, 12)) + self.assertEqual(5767, lcm(73, 79)) + + def test_lcm_negative_numbers(self): + self.assertEqual(24, lcm(-8, -12)) + self.assertEqual(5767, lcm(73, -79)) + self.assertEqual(1, lcm(-1, 1)) + + def test_lcm_zero_input(self): + with pytest.raises(ValueError, + match=r"One or more input arguments equals zero"): + lcm(0, 12) + lcm(12, 0) + lcm(0, 0) + + def test_trailing_zero(self): + self.assertEqual(1, trailing_zero(34)) + self.assertEqual(3, trailing_zero(40)) + + def test_gcd_bit(self): + self.assertEqual(4, gcd_bit(8, 12)) + self.assertEqual(1, gcd(13, 17)) + + +class TestGenerateStroboGrammatic(unittest.TestCase): + """[summary] + Test for the file generate_strobogrammatic.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_gen_strobomatic(self): + self.assertEqual(['88', '11', '96', '69'], gen_strobogrammatic(2)) + + def test_strobogrammatic_in_range(self): + self.assertEqual(4, strobogrammatic_in_range("10", "100")) + + +class TestIsStrobogrammatic(unittest.TestCase): + """[summary] + Test for the file is_strobogrammatic.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_strobogrammatic(self): + self.assertTrue(is_strobogrammatic("69")) + self.assertFalse(is_strobogrammatic("14")) + + def test_is_strobogrammatic2(self): + self.assertTrue(is_strobogrammatic2("69")) + self.assertFalse(is_strobogrammatic2("14")) + + +class TestModularInverse(unittest.TestCase): + """[summary] + Test for the file modular_Exponential.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_modular_inverse(self): + # checks if x * x_inv == 1 (mod m) + self.assertEqual(1, 2 * modular_inverse.modular_inverse(2, 19) % 19) + self.assertEqual(1, 53 * modular_inverse.modular_inverse(53, 91) % 91) + self.assertEqual(1, 2 * modular_inverse.modular_inverse(2, 1000000007) + % 1000000007) + self.assertRaises(ValueError, modular_inverse.modular_inverse, 2, 20) + + +class TestModularExponential(unittest.TestCase): + """[summary] + Test for the file modular_Exponential.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_modular_exponential(self): + self.assertEqual(1, modular_exponential(5, 117, 19)) + self.assertEqual(pow(1243, 65321, 10 ** 9 + 7), + modular_exponential(1243, 65321, 10 ** 9 + 7)) + self.assertEqual(1, modular_exponential(12, 0, 78)) + self.assertRaises(ValueError, modular_exponential, 12, -2, 455) + + +class TestNextPerfectSquare(unittest.TestCase): + """[summary] + Test for the file next_perfect_square.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_find_next_square(self): + self.assertEqual(36, find_next_square(25)) + self.assertEqual(1, find_next_square(0)) + + def test_find_next_square2(self): + self.assertEqual(36, find_next_square2(25)) + self.assertEqual(1, find_next_square2(0)) + + +class TestPrimesSieveOfEratosthenes(unittest.TestCase): + """[summary] + Test for the file primes_sieve_of_eratosthenes.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_primes(self): + self.assertListEqual([2, 3, 5, 7], get_primes(7)) + self.assertRaises(ValueError, get_primes, -42) + + +class TestPrimeTest(unittest.TestCase): + """[summary] + Test for the file prime_test.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_prime_test(self): + """ + checks all prime numbers between 2 up to 100. + Between 2 up to 100 exists 25 prime numbers! + """ + counter = 0 + for i in range(2, 101): + if prime_check(i): + counter += 1 + self.assertEqual(25, counter) + + +class TestPythagoras(unittest.TestCase): + """[summary] + Test for the file pythagoras.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_pythagoras(self): + self.assertEqual("Hypotenuse = 3.605551275463989", + pythagoras(3, 2, "?")) + + +class TestRabinMiller(unittest.TestCase): + """[summary] + Test for the file rabin_miller.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_prime(self): + self.assertTrue(is_prime(7, 2)) + self.assertTrue(is_prime(13, 11)) + self.assertFalse(is_prime(6, 2)) + + +class TestRSA(unittest.TestCase): + """[summary] + Test for the file rsa.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_encrypt_decrypt(self): + self.assertEqual(7, decrypt(encrypt(7, 23, 143), 47, 143)) + + # def test_key_generator(self): # this test takes a while! + # for i in range(100): + # print("step {0}".format(i)) + # n, e, d = generate_key(26) + # data = 2 + # en = encrypt(data, e, n) + # dec = decrypt(en, d, n) + # self.assertEqual(data,dec) + + +class TestCombination(unittest.TestCase): + """[summary] + Test for the file combination.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_combination(self): + self.assertEqual(10, combination(5, 2)) + self.assertEqual(252, combination(10, 5)) + + def test_combination_memo(self): + self.assertEqual(10272278170, combination_memo(50, 10)) + self.assertEqual(847660528, combination_memo(40, 10)) + + +class TestFactorial(unittest.TestCase): + """[summary] + Test for the file factorial.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_factorial(self): + self.assertEqual(1, factorial(0)) + self.assertEqual(120, factorial(5)) + self.assertEqual(3628800, factorial(10)) + self.assertEqual(637816310, factorial(34521, 10 ** 9 + 7)) + self.assertRaises(ValueError, factorial, -42) + self.assertRaises(ValueError, factorial, 42, -1) + + def test_factorial_recur(self): + self.assertEqual(1, factorial_recur(0)) + self.assertEqual(120, factorial_recur(5)) + self.assertEqual(3628800, factorial_recur(10)) + self.assertEqual(637816310, factorial_recur(34521, 10 ** 9 + 7)) + self.assertRaises(ValueError, factorial_recur, -42) + self.assertRaises(ValueError, factorial_recur, 42, -1) + + +class TestHailstone(unittest.TestCase): + """[summary] + Test for the file hailstone.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_hailstone(self): + self.assertEqual([8, 4, 2, 1], hailstone.hailstone(8)) + self.assertEqual([10, 5, 16, 8, 4, 2, 1], hailstone.hailstone(10)) + + +class TestCosineSimilarity(unittest.TestCase): + """[summary] + Test for the file cosine_similarity.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_cosine_similarity(self): + vec_a = [1, 1, 1] + vec_b = [-1, -1, -1] + vec_c = [1, 2, -1] + self.assertAlmostEqual(cosine_similarity(vec_a, vec_a), 1) + self.assertAlmostEqual(cosine_similarity(vec_a, vec_b), -1) + self.assertAlmostEqual(cosine_similarity(vec_a, vec_c), 0.4714045208) + + +class TestFindPrimitiveRoot(unittest.TestCase): + """[summary] + Test for the file find_primitive_root_simple.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_find_primitive_root_simple(self): + self.assertListEqual([0], find_primitive_root(1)) + self.assertListEqual([2, 3], find_primitive_root(5)) + self.assertListEqual([], find_primitive_root(24)) + self.assertListEqual([2, 5, 13, 15, 17, 18, 19, 20, 22, 24, 32, 35], + find_primitive_root(37)) + + +class TestFindOrder(unittest.TestCase): + """[summary] + Test for the file find_order_simple.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_find_order_simple(self): + self.assertEqual(1, find_order(1, 1)) + self.assertEqual(6, find_order(3, 7)) + self.assertEqual(-1, find_order(128, 256)) + self.assertEqual(352, find_order(3, 353)) + + +class TestKrishnamurthyNumber(unittest.TestCase): + """[summary] + Test for the file krishnamurthy_number.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_krishnamurthy_number(self): + self.assertFalse(krishnamurthy_number(0)) + self.assertTrue(krishnamurthy_number(2)) + self.assertTrue(krishnamurthy_number(1)) + self.assertTrue(krishnamurthy_number(145)) + self.assertTrue(krishnamurthy_number(40585)) + + +class TestMagicNumber(unittest.TestCase): + """[summary] + Test for the file find_order_simple.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_magic_number(self): + self.assertTrue(magic_number(50113)) + self.assertTrue(magic_number(1234)) + self.assertTrue(magic_number(100)) + self.assertTrue(magic_number(199)) + self.assertFalse(magic_number(2000)) + self.assertFalse(magic_number(500000)) + + +class TestDiffieHellmanKeyExchange(unittest.TestCase): + """[summary] + Test for the file diffie_hellman_key_exchange.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_find_order_simple(self): + self.assertFalse(diffie_hellman_key_exchange(3, 6)) + self.assertTrue(diffie_hellman_key_exchange(3, 353)) + self.assertFalse(diffie_hellman_key_exchange(5, 211)) + self.assertTrue(diffie_hellman_key_exchange(11, 971)) + + +class TestNumberOfDigits(unittest.TestCase): + """[summary] + Test for the file num_digits.py + + Arguments: + unittest {[type]} -- [description] + """ + def test_num_digits(self): + self.assertEqual(2, num_digits(12)) + self.assertEqual(5, num_digits(99999)) + self.assertEqual(1, num_digits(8)) + self.assertEqual(1, num_digits(0)) + self.assertEqual(1, num_digits(-5)) + self.assertEqual(3, num_digits(-254)) + + + +class TestNumberOfPerfectSquares(unittest.TestCase): + """[summary] + Test for the file num_perfect_squares.py + + Arguments: + unittest {[type]} -- [description] + """ + def test_num_perfect_squares(self): + self.assertEqual(4,num_perfect_squares(31)) + self.assertEqual(3,num_perfect_squares(12)) + self.assertEqual(2,num_perfect_squares(13)) + self.assertEqual(2,num_perfect_squares(10)) + self.assertEqual(4,num_perfect_squares(1500)) + self.assertEqual(2,num_perfect_squares(1548524521)) + self.assertEqual(3,num_perfect_squares(9999999993)) + self.assertEqual(1,num_perfect_squares(9)) + + +class TestChineseRemainderSolver(unittest.TestCase): + def test_k_three(self): + # Example which should give the answer 143 + # which is the smallest possible x that + # solves the system of equations + num = [3, 7, 10] + rem = [2, 3, 3] + self.assertEqual(chinese_remainder_theorem. + solve_chinese_remainder(num, rem), 143) + + def test_k_five(self): + # Example which should give the answer 3383 + # which is the smallest possible x that + # solves the system of equations + num = [3, 5, 7, 11, 26] + rem = [2, 3, 2, 6, 3] + self.assertEqual(chinese_remainder_theorem. + solve_chinese_remainder(num, rem), 3383) + + def test_exception_non_coprime(self): + # There should be an exception when all + # numbers in num are not pairwise coprime + num = [3, 7, 10, 14] + rem = [2, 3, 3, 1] + with self.assertRaises(Exception): + chinese_remainder_theorem.solve_chinese_remainder(num, rem) + + def test_empty_lists(self): + num = [] + rem = [] + with self.assertRaises(Exception): + chinese_remainder_theorem.solve_chinese_remainder(num, rem) + + +class TestFFT(unittest.TestCase): + """[summary] + Test for the file fft.py + + Arguments: + unittest {[type]} -- [description] + """ + def test_real_numbers(self): + x = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0] + y = [4.000, 2.613, 0.000, 1.082, 0.000, 1.082, 0.000, 2.613] + # abs(complex) returns the magnitude + result = [float("%.3f" % abs(f)) for f in fft.fft(x)] + self.assertEqual(result, y) + + def test_all_zero(self): + x = [0.0, 0.0, 0.0, 0.0] + y = [0.0, 0.0, 0.0, 0.0] + result = [float("%.1f" % abs(f)) for f in fft.fft(x)] + self.assertEqual(result, y) + + def test_all_ones(self): + x = [1.0, 1.0, 1.0, 1.0] + y = [4.0, 0.0, 0.0, 0.0] + result = [float("%.1f" % abs(f)) for f in fft.fft(x)] + self.assertEqual(result, y) + + def test_complex_numbers(self): + x = [2.0+2j, 1.0+3j, 3.0+1j, 2.0+2j] + real = [8.0, 0.0, 2.0, -2.0] + imag = [8.0, 2.0, -2.0, 0.0] + realResult = [float("%.1f" % f.real) for f in fft.fft(x)] + imagResult = [float("%.1f" % f.imag) for f in fft.fft(x)] + self.assertEqual(real, realResult) + self.assertEqual(imag, imagResult) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_matrix.py b/tests/test_matrix.py new file mode 100644 index 000000000..262fdbe62 --- /dev/null +++ b/tests/test_matrix.py @@ -0,0 +1,391 @@ +from algorithms.matrix import ( + bomb_enemy, + copy_transform, + crout_matrix_decomposition, + cholesky_matrix_decomposition, + matrix_exponentiation, + matrix_inversion, + multiply, + rotate_image, + sparse_dot_vector, + spiral_traversal, + sudoku_validator, + sum_sub_squares, + sort_matrix_diagonally +) +import unittest + + +class TestBombEnemy(unittest.TestCase): + def test_3x4(self): + grid1 = [ + ["0", "E", "0", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"] + ] + self.assertEqual(3, bomb_enemy.max_killed_enemies(grid1)) + + grid1 = [ + ["0", "E", "0", "E"], + ["E", "E", "E", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"] + ] + grid2 = [ + ["0", "0", "0", "E"], + ["E", "0", "0", "0"], + ["E", "0", "W", "E"], + ["0", "E", "0", "0"] + ] + self.assertEqual(5, bomb_enemy.max_killed_enemies(grid1)) + self.assertEqual(3, bomb_enemy.max_killed_enemies(grid2)) + + +class TestCopyTransform(unittest.TestCase): + """[summary] + Test for the file copy_transform.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_copy_transform(self): + self.assertEqual(copy_transform.rotate_clockwise( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), + [[7, 4, 1], [8, 5, 2], [9, 6, 3]]) + + self.assertEqual(copy_transform.rotate_counterclockwise( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), + [[3, 6, 9], [2, 5, 8], [1, 4, 7]]) + + self.assertEqual(copy_transform.top_left_invert( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), + [[1, 4, 7], [2, 5, 8], [3, 6, 9]]) + + self.assertEqual(copy_transform.bottom_left_invert( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), + [[9, 6, 3], [8, 5, 2], [7, 4, 1]]) + + +class TestCroutMatrixDecomposition(unittest.TestCase): + """[summary] + Test for the file crout_matrix_decomposition.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_crout_matrix_decomposition(self): + self.assertEqual(([[9.0, 0.0], [7.0, 0.0]], + [[1.0, 1.0], [0.0, 1.0]]), + crout_matrix_decomposition.crout_matrix_decomposition( + [[9, 9], [7, 7]])) + + self.assertEqual(([[1.0, 0.0, 0.0], + [3.0, -2.0, 0.0], + [6.0, -5.0, 0.0]], + [[1.0, 2.0, 3.0], + [0.0, 1.0, 2.0], + [0.0, 0.0, 1.0]]), + crout_matrix_decomposition.crout_matrix_decomposition( + [[1, 2, 3], [3, 4, 5], [6, 7, 8]])) + + self.assertEqual(([[2.0, 0, 0, 0], + [4.0, -1.0, 0, 0], + [6.0, -2.0, 2.0, 0], + [8.0, -3.0, 3.0, 0.0]], + [[1.0, 0.5, 1.5, 0.5], + [0, 1.0, 2.0, 1.0], + [0, 0, 1.0, 0.0], + [0, 0, 0, 1.0]]), + crout_matrix_decomposition.crout_matrix_decomposition( + [[2, 1, 3, 1], [4, 1, 4, 1], [6, 1, 7, 1], + [8, 1, 9, 1]])) + + +class TestCholeskyMatrixDecomposition(unittest.TestCase): + """[summary] + Test for the file cholesky_matrix_decomposition.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_cholesky_matrix_decomposition(self): + self.assertEqual([[2.0, 0.0, 0.0], + [6.0, 1.0, 0.0], + [-8.0, 5.0, 3.0]], + cholesky_matrix_decomposition.cholesky_decomposition( + [[4, 12, -16], [12, 37, -43], [-16, -43, 98]])) + + self.assertEqual(None, + cholesky_matrix_decomposition.cholesky_decomposition( + [[4, 12, -8], [12, 4, -43], [-16, -1, 32]])) + + self.assertEqual(None, + cholesky_matrix_decomposition.cholesky_decomposition( + [[4, 12, -16], [12, 37, -43], [-16, -43, 98], + [1, 2, 3]])) + + # example taken from https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/04LinearAlgebra/cholesky/ + self.assertEqual([[2.23606797749979, 0.0, 0.0, 0.0], + [0.5366563145999494, 2.389979079406345, 0.0, 0.0], + [0.13416407864998736, -0.19749126846635062, + 2.818332343581848, 0.0], + [-0.2683281572999747, 0.43682390737048743, + 0.64657701271919, 3.052723872310221]], + cholesky_matrix_decomposition.cholesky_decomposition( + [[5, 1.2, 0.3, -0.6], [1.2, 6, -0.4, 0.9], + [0.3, -0.4, 8, 1.7], [-0.6, 0.9, 1.7, 10]])) + + +class TestInversion(unittest.TestCase): + """[summary] + Test for the file matrix_inversion.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_inversion(self): + from fractions import Fraction + + m1 = [[1, 1], [1, 2]] + self.assertEqual(matrix_inversion.invert_matrix(m1), + [[2, -1], [-1, 1]]) + + m2 = [[1, 2], [3, 4, 5]] + self.assertEqual(matrix_inversion.invert_matrix(m2), [[-1]]) + + m3 = [[1, 1, 1, 1], [2, 2, 2, 2]] + self.assertEqual(matrix_inversion.invert_matrix(m3), [[-2]]) + + m4 = [[1]] + self.assertEqual(matrix_inversion.invert_matrix(m4), [[-3]]) + + m5 = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] + self.assertEqual(matrix_inversion.invert_matrix(m5), [[-4]]) + + m6 = [[3, 5, 1], [2, 5, 0], [1, 9, 8]] + self.assertEqual(matrix_inversion.invert_matrix(m6), + [[Fraction(40, 53), + Fraction(-31, 53), + Fraction(-5, 53)], + [Fraction(-16, 53), + Fraction(23, 53), + Fraction(2, 53)], + [Fraction(13, 53), + Fraction(-22, 53), + Fraction(5, 53)]]) + + +class TestMatrixExponentiation(unittest.TestCase): + """[summary] + Test for the file matrix_exponentiation.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_matrix_exponentiation(self): + mat = [[1, 0, 2], [2, 1, 0], [0, 2, 1]] + + self.assertEqual(matrix_exponentiation.matrix_exponentiation(mat, 0), + [[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + + self.assertEqual(matrix_exponentiation.matrix_exponentiation(mat, 1), + [[1, 0, 2], [2, 1, 0], [0, 2, 1]]) + + self.assertEqual(matrix_exponentiation.matrix_exponentiation(mat, 2), + [[1, 4, 4], [4, 1, 4], [4, 4, 1]]) + + self.assertEqual(matrix_exponentiation.matrix_exponentiation(mat, 5), + [[81, 72, 90], [90, 81, 72], [72, 90, 81]]) + + +class TestMultiply(unittest.TestCase): + """[summary] + Test for the file multiply.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_multiply(self): + self.assertEqual(multiply.multiply( + [[1, 2, 3], [2, 1, 1]], [[1], [2], [3]]), [[14], [7]]) + + +class TestRotateImage(unittest.TestCase): + """[summary] + Test for the file rotate_image.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_rotate_image(self): + self.assertEqual(rotate_image.rotate( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), + [[7, 4, 1], [8, 5, 2], [9, 6, 3]]) + + +class TestSparseDotVector(unittest.TestCase): + """[summary] + Test for the file sparse_dot_vector.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_sparse_dot_vector(self): + self.assertEqual(sparse_dot_vector. + dot_product(sparse_dot_vector. + vector_to_index_value_list([1., 2., 3.]), + sparse_dot_vector. + vector_to_index_value_list([0., 2., 2.])), + 10) + + +class TestSpiralTraversal(unittest.TestCase): + """[summary] + Test for the file spiral_traversal.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_spiral_traversal(self): + self.assertEqual(spiral_traversal.spiral_traversal( + [[1, 2, 3], [4, 5, 6], [7, 8, 9]]), [1, 2, 3, 6, 9, 8, 7, 4, 5]) + + +class TestSudokuValidator(unittest.TestCase): + """[summary] + Test for the file sudoku_validator.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_sudoku_validator(self): + self.assertTrue( + sudoku_validator.valid_solution( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 5, 3, 4, 8], + [1, 9, 8, 3, 4, 2, 5, 6, 7], + [8, 5, 9, 7, 6, 1, 4, 2, 3], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 6, 1, 5, 3, 7, 2, 8, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 4, 5, 2, 8, 6, 1, 7, 9] + ])) + + self.assertTrue( + sudoku_validator.valid_solution_hashtable( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 5, 3, 4, 8], + [1, 9, 8, 3, 4, 2, 5, 6, 7], + [8, 5, 9, 7, 6, 1, 4, 2, 3], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 6, 1, 5, 3, 7, 2, 8, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 4, 5, 2, 8, 6, 1, 7, 9] + ])) + + self.assertTrue( + sudoku_validator.valid_solution_set( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 5, 3, 4, 8], + [1, 9, 8, 3, 4, 2, 5, 6, 7], + [8, 5, 9, 7, 6, 1, 4, 2, 3], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 6, 1, 5, 3, 7, 2, 8, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 4, 5, 2, 8, 6, 1, 7, 9] + ])) + + self.assertFalse( + sudoku_validator.valid_solution( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 0, 3, 4, 9], + [1, 0, 0, 3, 4, 2, 5, 6, 0], + [8, 5, 9, 7, 6, 1, 0, 2, 0], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 0, 1, 5, 3, 7, 2, 1, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 0, 0, 4, 8, 1, 1, 7, 9] + ])) + + self.assertFalse( + sudoku_validator.valid_solution_hashtable( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 0, 3, 4, 9], + [1, 0, 0, 3, 4, 2, 5, 6, 0], + [8, 5, 9, 7, 6, 1, 0, 2, 0], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 0, 1, 5, 3, 7, 2, 1, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 0, 0, 4, 8, 1, 1, 7, 9] + ])) + + self.assertFalse( + sudoku_validator.valid_solution_set( + [ + [5, 3, 4, 6, 7, 8, 9, 1, 2], + [6, 7, 2, 1, 9, 0, 3, 4, 9], + [1, 0, 0, 3, 4, 2, 5, 6, 0], + [8, 5, 9, 7, 6, 1, 0, 2, 0], + [4, 2, 6, 8, 5, 3, 7, 9, 1], + [7, 1, 3, 9, 2, 4, 8, 5, 6], + [9, 0, 1, 5, 3, 7, 2, 1, 4], + [2, 8, 7, 4, 1, 9, 6, 3, 5], + [3, 0, 0, 4, 8, 1, 1, 7, 9] + ])) + + +class TestSumSubSquares(unittest.TestCase): + """[summary] + Test for the file sum_sub_squares.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_sum_sub_squares(self): + mat = [[1, 1, 1, 1, 1], + [2, 2, 2, 2, 2], + [3, 3, 3, 3, 3], + [4, 4, 4, 4, 4], + [5, 5, 5, 5, 5]] + self.assertEqual(sum_sub_squares.sum_sub_squares(mat, 3), + [[18, 18, 18], [27, 27, 27], [36, 36, 36]]) + + +class TestSortMatrixDiagonally(unittest.TestCase): + def test_sort_diagonally(self): + mat = [ + [3, 3, 1, 1], + [2, 2, 1, 2], + [1, 1, 1, 2] + ] + + self.assertEqual(sort_matrix_diagonally.sort_diagonally(mat), [ + [1, 1, 1, 1], + [1, 2, 2, 2], + [1, 2, 3, 3] + ]) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_ml.py b/tests/test_ml.py new file mode 100644 index 000000000..1622ae1a8 --- /dev/null +++ b/tests/test_ml.py @@ -0,0 +1,40 @@ +from algorithms.ml.nearest_neighbor import ( + distance, + nearest_neighbor +) + +import unittest + + +class TestML(unittest.TestCase): + def setUp(self): + # train set for the AND-function + self.trainSetAND = {(0, 0): 0, (0, 1): 0, (1, 0): 0, (1, 1): 1} + + # train set for light or dark colors + self.trainSetLight = {(11, 98, 237): 'L', (3, 39, 96): 'D', + (242, 226, 12): 'L', (99, 93, 4): 'D', + (232, 62, 32): 'L', (119, 28, 11): 'D', + (25, 214, 47): 'L', (89, 136, 247): 'L', + (21, 34, 63): 'D', (237, 99, 120): 'L', + (73, 33, 39): 'D'} + + def test_nearest_neighbor(self): + # AND-function + self.assertEqual(nearest_neighbor((1, 1), self.trainSetAND), 1) + self.assertEqual(nearest_neighbor((0, 1), self.trainSetAND), 0) + + # dark/light color test + self.assertEqual(nearest_neighbor((31, 242, 164), + self.trainSetLight), 'L') + self.assertEqual(nearest_neighbor((13, 94, 64), + self.trainSetLight), 'D') + self.assertEqual(nearest_neighbor((230, 52, 239), + self.trainSetLight), 'L') + + def test_distance(self): + self.assertAlmostEqual(distance((1, 2, 3), (1, 0, -1)), 4.47, 2) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_monomial.py b/tests/test_monomial.py new file mode 100644 index 000000000..31e56f79b --- /dev/null +++ b/tests/test_monomial.py @@ -0,0 +1,220 @@ +from algorithms.maths.polynomial import Monomial +from fractions import Fraction +import math + + +import unittest + + +class TestSuite(unittest.TestCase): + + def setUp(self): + self.m1 = Monomial({}) + self.m2 = Monomial({1: 1}, 2) + self.m3 = Monomial({1: 2, 2: -1}, 1.5) + self.m4 = Monomial({1: 1, 2: 2, 3: -2}, 3) + self.m5 = Monomial({2: 1, 3: 0}, Fraction(2, 3)) + self.m6 = Monomial({1: 0, 2: 0, 3: 0}, -2.27) + self.m7 = Monomial({1: 2, 7: 2}, -math.pi) + self.m8 = Monomial({150: 5, 170: 2, 10000: 3}, 0) + self.m9 = 2 + self.m10 = math.pi + self.m11 = Fraction(3, 8) + self.m12 = 0 + self.m13 = Monomial({1: 1}, -2) + self.m14 = Monomial({1: 2}, 3) + self.m15 = Monomial({1: 1}, 3) + self.m16 = Monomial({1: 2, 7: 2}, math.pi) + self.m17 = Monomial({1: -1}) + + def test_monomial_addition(self): + + # Monomials with different underlying variables or + # even different power of those variables must not be added! + self.assertRaises(ValueError, lambda x, y: x + y, self.m1, self.m2) + self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m3) + self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m14) + + # Additive inverses of each other should produce the zero monomial. + self.assertEqual(self.m13 + self.m2, self.m1) + + # Zero monomial + Zero monomial = Zero monomial + self.assertEqual(self.m1 + self.m1, self.m1) + + # Coefficient float. + self.assertEqual(self.m7 + self.m7, Monomial({1: 2, 7: 2}, + -2 * math.pi)) + + # Coefficient 0 so should equal the zero monomial. + self.assertEqual(self.m8, self.m1) + + # The constant term cannot be added to any monomial + # that has any variables. + self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m9) + + # Any literal cannot be added to a Monomial. However, a monomial + # can be added to any int, float, Fraction, or Monomial. + + # So 2 + Monomial is raises TypeError but Monomial + 2 may work fine! + self.assertRaises(TypeError, lambda x, y: x + y, self.m9, self.m2) + + # Any constant added to a zero monomial produces + # a monomial. + self.assertEqual(self.m1 + self.m9, Monomial({}, 2)) + self.assertEqual(self.m1 + self.m12, Monomial({}, 0)) + + return + + def test_monomial_subtraction(self): + + # Monomials with different underlying variables or + # even different power of those variables must not be subtracted! + self.assertRaises(ValueError, lambda x, y: x - y, self.m1, self.m2) + self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m3) + self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m14) + + # Additive inverses of each other should produce the zero monomial. + self.assertEqual(self.m2 - self.m2, self.m1) + self.assertEqual(self.m2 - self.m2, Monomial({}, 0)) + + # Zero monomial - Zero monomial = Zero monomial + self.assertEqual(self.m1 - self.m1, self.m1) + + # Coefficient int. + self.assertEqual(self.m2 - self.m15, Monomial({1: 1}, -1)) + + # Coefficient float. + self.assertEqual(self.m16 - self.m7, Monomial({1: 2, 7: 2}, + 2 * math.pi)) + + # The constant term cannot be added to any monomial + # that has any variables. + self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m9) + + # Any literal cannot be added to a Monomial. However, a monomial + # can be added to any int, float, Fraction, or Monomial. + + # So 2 + Monomial is raises TypeError but Monomial + 2 may work fine! + self.assertRaises(TypeError, lambda x, y: x - y, self.m9, self.m2) + + # Any constant added to a zero monomial produces + # a monomial. + self.assertEqual(self.m1 - self.m9, Monomial({}, -2)) + self.assertEqual(self.m1 - self.m12, Monomial({}, 0)) + + return + + def test_monomial_multiplication(self): + + # Usual multiplication. + # The positive and negative powers of the same variable + # should cancel out. + self.assertEqual(self.m2 * self.m13, Monomial({1: 2}, -4)) + self.assertEqual(self.m2 * self.m17, Monomial({}, 2)) + + # A coefficient of zero should make the product zero. + # Zero monomial * any int, float, Fraction, or Monomial = Zero monomial + self.assertEqual(self.m8 * self.m5, self.m1) + self.assertEqual(self.m1 * self.m2, self.m1) + + # Test usual float multiplication. + self.assertEqual(self.m7 * self.m3, Monomial({1: 4, 2: -1, 7: 2}, + -1.5*math.pi)) + + return + + def test_monomial_inverse(self): + + # The Zero monomial is not invertible. + self.assertRaises(ValueError, lambda x: x.inverse(), self.m1) + self.assertRaises(ValueError, lambda x: x.inverse(), self.m8) + self.assertRaises(ValueError, lambda x: x.inverse(), + Monomial({}, self.m12)) + + # Check some inverses. + self.assertEqual(self.m7.inverse(), Monomial({1: -2, 7: -2}, -1 / math.pi)) + + # Doesn't matter if the coefficient is Fraction or float. + # Both should be treated as same. + self.assertEqual(self.m5.inverse(), Monomial({2: -1}, Fraction(3, 2))) + self.assertEqual(self.m5.inverse(), Monomial({2: -1}, 1.5)) + + # Should work fine without variables too! + self.assertTrue(self.m6.inverse(), Monomial({}, Fraction(-100, 227))) + self.assertEqual(self.m6.inverse(), Monomial({}, -1/2.27)) + return + + def test_monomial_division(self): + # Any monomial divided by the Zero Monomial should raise a ValueError. + self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), + self.m2, self.m1) + self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), + self.m2, self.m8) + self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), + self.m2, self.m12) + + # Test some usual cases. + self.assertEqual(self.m7 / self.m3, Monomial({2: 1, 7: 2}, + -2 * math.pi / 3)) + self.assertEqual(self.m14 / self.m13, Monomial({1: 1}) * Fraction(-3, 2)) + + return + + def test_monomial_substitution(self): + # Test with int. + self.assertAlmostEqual(self.m7.substitute(2), -16 * math.pi, delta=1e-9) + # Test with float. + self.assertAlmostEqual(self.m7.substitute(1.5), (1.5 ** 4) * -math.pi, + delta=1e-9) + # Test with Fraction. + self.assertAlmostEqual(self.m7.substitute(Fraction(-1, 2)), + (Fraction(-1, 2) ** 4)*-math.pi, delta=1e-9) + # Test with a complete substitution map. + self.assertAlmostEqual(self.m7.substitute({1: 3, 7: 0}), + (3 ** 2) * (0 ** 2) * -math.pi, delta=1e-9) + # Test with a more than complete substitution map. + self.assertAlmostEqual(self.m7.substitute({1: 3, 7: 0, 2: 2}), + (3 ** 2) * (0 ** 2) * -math.pi, delta=1e-9) + + # Should raise a ValueError if not enough variables are supplied! + self.assertRaises(ValueError, lambda x, y: x.substitute(y), self.m7, + {1: 3, 2: 2}) + self.assertRaises(ValueError, lambda x, y: x.substitute(y), self.m7, + {2: 2}) + + # The zero monomial always gives zero upon substitution. + self.assertEqual(self.m8.substitute(2), 0) + self.assertEqual(self.m8.substitute({1231: 2, 1: 2}), 0) + + return + + def test_monomial_all_variables(self): + + # Any variable with zero power should not exist in the set + # of variables. + self.assertEqual(self.m5.all_variables(), {2}) + self.assertEqual(self.m6.all_variables(), set()) + + # The zero monomial should output empty set. + self.assertEqual(self.m8.all_variables(), set()) + + return + + def test_monomial_clone(self): + + # A monomial should produce its copy + # with same underlying variable dictionary + # and same coefficient. + self.assertEqual(self.m3, self.m3.clone()) + + # The zero monomial is identified and + # always clones to itself. + self.assertEqual(self.m1, self.m8.clone()) + self.assertEqual(self.m1, self.m1.clone()) + self.assertEqual(self.m8, self.m1.clone()) + self.assertEqual(self.m8, self.m8.clone()) + return + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_polynomial.py b/tests/test_polynomial.py new file mode 100644 index 000000000..ab5674017 --- /dev/null +++ b/tests/test_polynomial.py @@ -0,0 +1,201 @@ +from algorithms.maths.polynomial import ( + Polynomial, + Monomial +) +from fractions import Fraction +import math + + +import unittest + +class TestSuite(unittest.TestCase): + + def setUp(self): + self.p0 = Polynomial([ + Monomial({}) + ]) + self.p1 = Polynomial([ + Monomial({}), Monomial({}) + ]) + self.p2 = Polynomial([ + Monomial({1: 1}, 2) + ]) + self.p3 = Polynomial([ + Monomial({1: 1}, 2), + Monomial({1: 2, 2: -1}, 1.5) + ]) + self.p4 = Polynomial([ + Monomial({2: 1, 3: 0}, Fraction(2, 3)), + Monomial({1: -1, 3: 2}, math.pi), + Monomial({1: -1, 3: 2}, 1) + ]) + self.p5 = Polynomial([ + Monomial({150: 5, 170: 2, 10000:3}, 0), + Monomial({1: -1, 3: 2}, 1), + ]) + self.p6 = Polynomial([ + 2, + -3, + Fraction(1, 7), + 2**math.pi, + Monomial({2: 3, 3: 1}, 1.25) + ]) + self.p7 = Polynomial([ + Monomial({1: 1}, -2), + Monomial({1: 2, 2: -1}, -1.5) + ]) + + self.m1 = Monomial({1: 2, 2: 3}, -1) + + return + + def test_polynomial_addition(self): + + # The zero polynomials should add up to + # itselves only. + self.assertEqual(self.p0 + self.p1, self.p0) + self.assertEqual(self.p0 + self.p1, self.p1) + + # Additive inverses should add up to the + # zero polynomial. + self.assertEqual(self.p3 + self.p7, self.p0) + self.assertEqual(self.p3 + self.p7, self.p1) + + # Like terms should combine. + # The order of monomials should not matter. + self.assertEqual(self.p2 + self.p3, Polynomial([ + Monomial({1: 1}, 4), + Monomial({1: 2, 2: -1}, 1.5) + ])) + self.assertEqual(self.p2 + self.p3, Polynomial([ + Monomial({1: 2, 2: -1}, 1.5), + Monomial({1: 1}, 4), + ])) + + # Another typical computation. + self.assertEqual(self.p5 + self.p6, Polynomial([ + Monomial({}, 7.96783496993343), + Monomial({2: 3, 3: 1}, 1.25), + Monomial({1: -1, 3: 2}) + ])) + + return + + def test_polynomial_subtraction(self): + + self.assertEqual(self.p3 - self.p2, Polynomial([ + Monomial({1: 2, 2: -1}, 1.5) + ])) + + self.assertEqual(self.p3 - self.p3, Polynomial([])) + + self.assertEqual(self.p2 - self.p3, Polynomial([ + Monomial({1: 2, 2: -1}, -1.5) + ])) + + pass + + def test_polynomial_multiplication(self): + self.assertEqual(self.p0 * self.p2, Polynomial([])) + self.assertEqual(self.p1 * self.p2, Polynomial([])) + + self.assertEqual(self.p2 * self.p3, Polynomial([ + Monomial({1: 2}, 4), + Monomial({1: 3, 2: -1}, Fraction(3, 1)) + ])) + return + + def test_polynomial_variables(self): + # The zero polynomial has no variables. + + self.assertEqual(self.p0.variables(), set()) + self.assertEqual(self.p1.variables(), set()) + + # The total variables are the union of the variables + # from the monomials. + self.assertEqual(self.p4.variables(), {1, 2, 3}) + + # The monomials with coefficient 0 should be dropped. + self.assertEqual(self.p5.variables(), {1, 3}) + return + + def test_polynomial_subs(self): + # Anything substitued in the zero polynomial + # should evaluate to 0. + self.assertEqual(self.p1.subs(2), 0) + self.assertEqual(self.p0.subs(-101231), 0) + + # Should raise a ValueError if not enough variables are supplied. + self.assertRaises(ValueError, lambda x, y: x.subs(y), self.p4, {1: 3, 2: 2}) + self.assertRaises(ValueError, lambda x, y: x.subs(y), self.p4, {}) + + # Should work fine if a complete subsitution map is provided. + self.assertAlmostEqual(self.p4.subs({1: 1, 2: 1, 3: 1}), (1 + math.pi + Fraction(2, 3)), delta=1e-9) + # Should work fine if more than enough substitutions are provided. + self.assertAlmostEqual(self.p4.subs({1: 1, 2: 1, 3: 1, 4: 1}), (1 + math.pi + Fraction(2, 3)), delta=1e-9) + return + + def test_polynomial_clone(self): + + # The zero polynomial always clones to itself. + self.assertEqual(self.p0.clone(), self.p0) + self.assertEqual(self.p1.clone(), self.p0) + self.assertEqual(self.p0.clone(), self.p1) + self.assertEqual(self.p1.clone(), self.p1) + + # The polynomial should clone nicely. + self.assertEqual(self.p4.clone(), self.p4) + + # The monomial with a zero coefficient should be dropped + # in the clone. + self.assertEqual(self.p5.clone(), Polynomial([ + Monomial({1: -1, 3: 2}, 1) + ])) + return + + def test_polynomial_long_division(self): + """ + Test polynomial long division + """ + + # Dividend: 4a_1^3 + 3a_1^2 - 2a_1 + 5 + dividend = Polynomial([ + Monomial({1: 3}, 4), # 4(a_1)^3 + Monomial({1: 2}, 3), # 3(a_1)^2 + Monomial({1: 1}, -2), # -2(a_1) + Monomial({}, 5) # +5 + ]) + + # Divisor: 2a_1 - 1 + divisor = Polynomial([ + Monomial({1: 1}, 2), # 2(a_1) + Monomial({}, -1) # -1 + ]) + + # Expected Quotient: 2a_1^2 + (5/2)a_1 + 1/4 + expected_quotient = Polynomial([ + Monomial({1: 2}, 2), # 2(a_1)^2 + Monomial({1: 1}, Fraction(5, 2)), # (5/2)(a_1) + Monomial({}, Fraction(1, 4)) # +1/4 + ]) + + # Expected Remainder: 21/4 + expected_remainder = Polynomial([ + Monomial({}, Fraction(21, 4)) # 21/4 + ]) + + quotient_long_div, remainder_long_div = dividend.poly_long_division(divisor) + + quotient_truediv = dividend / divisor # Calls __truediv__, which returns only the quotient + + # Check if quotient from poly_long_division matches expected + self.assertEqual(quotient_long_div, expected_quotient) + + # Check if remainder from poly_long_division matches expected + self.assertEqual(remainder_long_div, expected_remainder) + + # Check if quotient from __truediv__ matches quotient from poly_long_division + self.assertEqual(quotient_truediv, quotient_long_div) + + return + diff --git a/tests/test_queues.py b/tests/test_queues.py new file mode 100644 index 000000000..5a2f4c89d --- /dev/null +++ b/tests/test_queues.py @@ -0,0 +1,110 @@ +import unittest + +from algorithms.queues import ( + ArrayQueue, LinkedListQueue, + max_sliding_window, + reconstruct_queue, + PriorityQueue +) + + +class TestQueue(unittest.TestCase): + """ + Test suite for the Queue data structures. + """ + + def test_ArrayQueue(self): + queue = ArrayQueue() + queue.enqueue(1) + queue.enqueue(2) + queue.enqueue(3) + + # test __iter__() + it = iter(queue) + self.assertEqual(1, next(it)) + self.assertEqual(2, next(it)) + self.assertEqual(3, next(it)) + self.assertRaises(StopIteration, next, it) + + # test __len__() + self.assertEqual(3, len(queue)) + + # test is_empty() + self.assertFalse(queue.is_empty()) + + # test peek() + self.assertEqual(1, queue.peek()) + + # test dequeue() + self.assertEqual(1, queue.dequeue()) + self.assertEqual(2, queue.dequeue()) + self.assertEqual(3, queue.dequeue()) + + self.assertTrue(queue.is_empty()) + + def test_LinkedListQueue(self): + queue = LinkedListQueue() + queue.enqueue(1) + queue.enqueue(2) + queue.enqueue(3) + + # test __iter__() + it = iter(queue) + self.assertEqual(1, next(it)) + self.assertEqual(2, next(it)) + self.assertEqual(3, next(it)) + self.assertRaises(StopIteration, next, it) + + # test __len__() + self.assertEqual(3, len(queue)) + + # test is_empty() + self.assertFalse(queue.is_empty()) + + # test peek() + self.assertEqual(1, queue.peek()) + + # test dequeue() + self.assertEqual(1, queue.dequeue()) + self.assertEqual(2, queue.dequeue()) + self.assertEqual(3, queue.dequeue()) + + self.assertTrue(queue.is_empty()) + + +class TestSuite(unittest.TestCase): + def test_max_sliding_window(self): + array = [1, 3, -1, -3, 5, 3, 6, 7] + self.assertEqual(max_sliding_window(array, k=5), [5, 5, 6, 7]) + self.assertEqual(max_sliding_window(array, k=3), [3, 3, 5, 5, 6, 7]) + self.assertEqual(max_sliding_window(array, k=7), [6, 7]) + + array = [8, 5, 10, 7, 9, 4, 15, 12, 90, 13] + self.assertEqual(max_sliding_window(array, k=4), + [10, 10, 10, 15, 15, 90, 90]) + self.assertEqual(max_sliding_window(array, k=7), [15, 15, 90, 90]) + self.assertEqual(max_sliding_window(array, k=2), + [8, 10, 10, 9, 9, 15, 15, 90, 90]) + + def test_reconstruct_queue(self): + self.assertEqual([[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]], + reconstruct_queue([[7, 0], [4, 4], [7, 1], [5, 0], + [6, 1], [5, 2]])) + + +class TestPriorityQueue(unittest.TestCase): + """Test suite for the PriorityQueue data structures. + """ + + def test_PriorityQueue(self): + queue = PriorityQueue([3, 4, 1, 6]) + self.assertEqual(4, queue.size()) + self.assertEqual(1, queue.pop()) + self.assertEqual(3, queue.size()) + queue.push(2) + self.assertEqual(4, queue.size()) + self.assertEqual(2, queue.pop()) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_search.py b/tests/test_search.py new file mode 100644 index 000000000..f515cfcb9 --- /dev/null +++ b/tests/test_search.py @@ -0,0 +1,153 @@ +from algorithms.search import ( + binary_search, binary_search_recur, + ternary_search, + first_occurrence, + last_occurrence, + linear_search, + search_insert, + two_sum, two_sum1, two_sum2, + search_range, + find_min_rotate, find_min_rotate_recur, + search_rotate, search_rotate_recur, + jump_search, + next_greatest_letter, next_greatest_letter_v1, next_greatest_letter_v2, + interpolation_search +) + +import unittest + + +class TestSuite(unittest.TestCase): + + def test_first_occurrence(self): + def helper(array, query): + idx = array.index(query) if query in array else None + return idx + array = [1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6] + self.assertEqual(first_occurrence(array, 1), helper(array, 1)) + self.assertEqual(first_occurrence(array, 3), helper(array, 3)) + self.assertEqual(first_occurrence(array, 5), helper(array, 5)) + self.assertEqual(first_occurrence(array, 6), helper(array, 6)) + self.assertEqual(first_occurrence(array, 7), helper(array, 7)) + self.assertEqual(first_occurrence(array, -1), helper(array, -1)) + + def test_binary_search(self): + array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6] + self.assertEqual(10, binary_search(array, 5)) + self.assertEqual(11, binary_search(array, 6)) + self.assertEqual(None, binary_search(array, 7)) + self.assertEqual(None, binary_search(array, -1)) + # Test binary_search_recur + self.assertEqual(10, binary_search_recur(array, 0, 11, 5)) + self.assertEqual(11, binary_search_recur(array, 0, 11, 6)) + self.assertEqual(-1, binary_search_recur(array, 0, 11, 7)) + self.assertEqual(-1, binary_search_recur(array, 0, 11, -1)) + + def test_ternary_search(self): + array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6] + self.assertEqual(10, ternary_search(0, 11, 5, array)) + self.assertEqual(3, ternary_search(0, 10, 3, array)) + self.assertEqual(-1, ternary_search(0, 10, 5, array)) + self.assertEqual(-1, ternary_search(0, 11, 7, array)) + self.assertEqual(-1, ternary_search(0, 11, -1, array)) + + def test_last_occurrence(self): + array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6] + self.assertEqual(5, last_occurrence(array, 3)) + self.assertEqual(10, last_occurrence(array, 5)) + self.assertEqual(None, last_occurrence(array, 7)) + self.assertEqual(0, last_occurrence(array, 1)) + self.assertEqual(13, last_occurrence(array, 6)) + + def test_linear_search(self): + array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6] + self.assertEqual(6, linear_search(array, 4)) + self.assertEqual(10, linear_search(array, 5)) + self.assertEqual(-1, linear_search(array, 7)) + self.assertEqual(-1, linear_search(array, -1)) + + def test_search_insert(self): + array = [1, 3, 5, 6] + self.assertEqual(2, search_insert(array, 5)) + self.assertEqual(1, search_insert(array, 2)) + self.assertEqual(4, search_insert(array, 7)) + self.assertEqual(0, search_insert(array, 0)) + + def test_two_sum(self): + array = [2, 7, 11, 15] + # test two_sum + self.assertEqual([1, 2], two_sum(array, 9)) + self.assertEqual([2, 4], two_sum(array, 22)) + # test two_sum1 + self.assertEqual([1, 2], two_sum1(array, 9)) + self.assertEqual([2, 4], two_sum1(array, 22)) + # test two_sum2 + self.assertEqual([1, 2], two_sum2(array, 9)) + self.assertEqual([2, 4], two_sum2(array, 22)) + + def test_search_range(self): + array = [5, 7, 7, 8, 8, 8, 10] + self.assertEqual([3, 5], search_range(array, 8)) + self.assertEqual([1, 2], search_range(array, 7)) + self.assertEqual([-1, -1], search_range(array, 11)) + + array = [5, 7, 7, 7, 7, 8, 8, 8, 8, 10] + self.assertEqual([5, 8], search_range(array, 8)) + self.assertEqual([1, 4], search_range(array, 7)) + self.assertEqual([-1, -1], search_range(array, 11)) + + def test_find_min_rotate(self): + array = [4, 5, 6, 7, 0, 1, 2] + self.assertEqual(0, find_min_rotate(array)) + array = [10, 20, -1, 0, 1, 2, 3, 4, 5] + self.assertEqual(-1, find_min_rotate(array)) + # Test find min using recursion + array = [4, 5, 6, 7, 0, 1, 2] + self.assertEqual(0, find_min_rotate_recur(array, 0, 6)) + array = [10, 20, -1, 0, 1, 2, 3, 4, 5] + self.assertEqual(-1, find_min_rotate_recur(array, 0, 8)) + + def test_search_rotate(self): + array = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14] + self.assertEqual(8, search_rotate(array, 5)) + self.assertEqual(-1, search_rotate(array, 9)) + self.assertEqual(8, search_rotate_recur(array, 0, 11, 5)) + self.assertEqual(-1, search_rotate_recur(array, 0, 11, 9)) + + def test_jump_search(self): + array = [1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6] + self.assertEqual(10, jump_search(array, 5)) + self.assertEqual(2, jump_search(array, 3)) + self.assertEqual(-1, jump_search(array, 7)) + self.assertEqual(-1, jump_search(array, -1)) + + def test_next_greatest_letter(self): + letters = ["c", "f", "j"] + target = "a" + self.assertEqual("c", next_greatest_letter(letters, target)) + self.assertEqual("c", next_greatest_letter_v1(letters, target)) + self.assertEqual("c", next_greatest_letter_v2(letters, target)) + letters = ["c", "f", "j"] + target = "d" + self.assertEqual("f", next_greatest_letter(letters, target)) + self.assertEqual("f", next_greatest_letter_v1(letters, target)) + self.assertEqual("f", next_greatest_letter_v2(letters, target)) + letters = ["c", "f", "j"] + target = "j" + self.assertEqual("c", next_greatest_letter(letters, target)) + self.assertEqual("c", next_greatest_letter_v1(letters, target)) + self.assertEqual("c", next_greatest_letter_v2(letters, target)) + + def test_interpolation_search(self): + array = [0, 3, 5, 5, 9, 12, 12, 15, 16, 19, 20] + self.assertEqual(1, interpolation_search(array, 3)) + self.assertEqual(2, interpolation_search(array, 5)) + self.assertEqual(6, interpolation_search(array, 12)) + self.assertEqual(-1, interpolation_search(array, 22)) + self.assertEqual(-1, interpolation_search(array, -10)) + self.assertEqual(10, interpolation_search(array, 20)) + + +if __name__ == '__main__': + + unittest.main() diff --git a/tests/test_set.py b/tests/test_set.py new file mode 100644 index 000000000..e2985c942 --- /dev/null +++ b/tests/test_set.py @@ -0,0 +1,12 @@ +from algorithms.set import ( + find_keyboard_row +) + +import unittest + + +class TestFindKeyboardRow(unittest.TestCase): + def test_find_keyboard_row(self): + self.assertEqual(["Alaska", "Dad"], + find_keyboard_row(["Hello", "Alaska", + "Dad", "Peace"])) diff --git a/tests/test_sort.py b/tests/test_sort.py new file mode 100644 index 000000000..c80290fdf --- /dev/null +++ b/tests/test_sort.py @@ -0,0 +1,130 @@ +from algorithms.sort import ( + bitonic_sort, + bogo_sort, + bubble_sort, + comb_sort, + counting_sort, + cycle_sort, + exchange_sort, + max_heap_sort, min_heap_sort, + merge_sort, + pancake_sort, + pigeonhole_sort, + quick_sort, + selection_sort, + bucket_sort, + shell_sort, + radix_sort, + gnome_sort, + cocktail_shaker_sort, + top_sort, top_sort_recursive +) + +import unittest + + +def is_sorted(array): + """ + Helper function to check if the given array is sorted. + :param array: Array to check if sorted + :return: True if sorted in ascending order, else False + """ + for i in range(len(array) - 1): + if array[i] > array[i + 1]: + return False + + return True + + +class TestSuite(unittest.TestCase): + def test_bogo_sort(self): + self.assertTrue(is_sorted(bogo_sort([1, 23, 5]))) + + def test_bitonic_sort(self): + self.assertTrue(is_sorted(bitonic_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_bubble_sort(self): + self.assertTrue(is_sorted(bubble_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_comb_sort(self): + self.assertTrue(is_sorted(comb_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_counting_sort(self): + self.assertTrue(is_sorted(counting_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_cycle_sort(self): + self.assertTrue(is_sorted(cycle_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_exchange_sort(self): + self.assertTrue(is_sorted(exchange_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_heap_sort(self): + self.assertTrue(is_sorted(max_heap_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + self.assertTrue(is_sorted(min_heap_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_insertion_sort(self): + self.assertTrue(is_sorted(bitonic_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_merge_sort(self): + self.assertTrue(is_sorted(merge_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_pancake_sort(self): + self.assertTrue(is_sorted(pancake_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_pigeonhole_sort(self): + self.assertTrue(is_sorted(pigeonhole_sort([1, 5, 65, 23, 57, 1232]))) + + def test_quick_sort(self): + self.assertTrue(is_sorted(quick_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_selection_sort(self): + self.assertTrue(is_sorted(selection_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + def test_bucket_sort(self): + self.assertTrue(is_sorted(bucket_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_shell_sort(self): + self.assertTrue(is_sorted(shell_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_radix_sort(self): + self.assertTrue(is_sorted(radix_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_gnome_sort(self): + self.assertTrue(is_sorted(gnome_sort([1, 3, 2, 5, 65, 23, 57, 1232]))) + + def test_cocktail_shaker_sort(self): + self.assertTrue(is_sorted(cocktail_shaker_sort([1, 3, 2, 5, 65, + 23, 57, 1232]))) + + +class TestTopSort(unittest.TestCase): + def setUp(self): + self.depGraph = { + "a": ["b"], + "b": ["c"], + "c": ['e'], + 'e': ['g'], + "d": [], + "f": ["e", "d"], + "g": [] + } + + def test_topsort(self): + res = top_sort_recursive(self.depGraph) + # print(res) + self.assertTrue(res.index('g') < res.index('e')) + res = top_sort(self.depGraph) + self.assertTrue(res.index('g') < res.index('e')) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_stack.py b/tests/test_stack.py new file mode 100644 index 000000000..93b389737 --- /dev/null +++ b/tests/test_stack.py @@ -0,0 +1,154 @@ +from algorithms.stack import ( + first_is_consecutive, second_is_consecutive, + is_sorted, + remove_min, + first_stutter, second_stutter, + first_switch_pairs, second_switch_pairs, + is_valid, + simplify_path, + ArrayStack, LinkedListStack, + OrderedStack +) + +import unittest + + +class TestSuite(unittest.TestCase): + def test_is_consecutive(self): + self.assertTrue(first_is_consecutive([3, 4, 5, 6, 7])) + self.assertFalse(first_is_consecutive([3, 4, 6, 7])) + self.assertFalse(first_is_consecutive([3, 2, 1])) + + self.assertTrue(second_is_consecutive([3, 4, 5, 6, 7])) + self.assertFalse(second_is_consecutive([3, 4, 6, 7])) + self.assertFalse(second_is_consecutive([3, 2, 1])) + + def test_is_sorted(self): + # Test case: bottom [6, 3, 5, 1, 2, 4] top + self.assertFalse(is_sorted([6, 3, 5, 1, 2, 4])) + self.assertTrue(is_sorted([1, 2, 3, 4, 5, 6])) + self.assertFalse(is_sorted([3, 4, 7, 8, 5, 6])) + + def test_remove_min(self): + # Test case: bottom [2, 8, 3, -6, 7, 3] top + self.assertEqual([2, 8, 3, 7, 3], remove_min([2, 8, 3, -6, 7, 3])) + # Test case: 2 smallest value [2, 8, 3, 7, 3] + self.assertEqual([4, 8, 7], remove_min([4, 8, 3, 7, 3])) + + def test_stutter(self): + # Test case: bottom [3, 7, 1, 14, 9] top + self.assertEqual([3, 3, 7, 7, 1, 1, 14, 14, 9, 9], + first_stutter([3, 7, 1, 14, 9])) + self.assertEqual([3, 3, 7, 7, 1, 1, 14, 14, 9, 9], + second_stutter([3, 7, 1, 14, 9])) + + def test_switch_pairs(self): + # Test case: even number of values in stack + # bottom [3, 8, 17, 9, 1, 10] top + self.assertEqual([8, 3, 9, 17, 10, 1], + first_switch_pairs([3, 8, 17, 9, 1, 10])) + self.assertEqual([8, 3, 9, 17, 10, 1], + second_switch_pairs([3, 8, 17, 9, 1, 10])) + # Test case: odd number of values in stack + # bottom [3, 8, 17, 9, 1] top + self.assertEqual([8, 3, 9, 17, 1], + first_switch_pairs([3, 8, 17, 9, 1])) + self.assertEqual([8, 3, 9, 17, 1], + second_switch_pairs([3, 8, 17, 9, 1])) + + def test_is_valid_parenthesis(self): + + self.assertTrue(is_valid("[]")) + self.assertTrue(is_valid("[]()[]")) + self.assertFalse(is_valid("[[[]]")) + self.assertTrue(is_valid("{([])}")) + self.assertFalse(is_valid("(}")) + + def test_simplify_path(self): + p = '/my/name/is/..//keon' + self.assertEqual('/my/name/keon', simplify_path(p)) + + +class TestStack(unittest.TestCase): + def test_ArrayStack(self): + stack = ArrayStack() + stack.push(1) + stack.push(2) + stack.push(3) + + # test __iter__() + it = iter(stack) + self.assertEqual(3, next(it)) + self.assertEqual(2, next(it)) + self.assertEqual(1, next(it)) + self.assertRaises(StopIteration, next, it) + + # test __len__() + self.assertEqual(3, len(stack)) + + # test __str__() + self.assertEqual(str(stack), "Top-> 3 2 1") + + # test is_empty() + self.assertFalse(stack.is_empty()) + + # test peek() + self.assertEqual(3, stack.peek()) + + # test pop() + self.assertEqual(3, stack.pop()) + self.assertEqual(2, stack.pop()) + self.assertEqual(1, stack.pop()) + + self.assertTrue(stack.is_empty()) + + def test_LinkedListStack(self): + stack = LinkedListStack() + + stack.push(1) + stack.push(2) + stack.push(3) + + # test __iter__() + it = iter(stack) + self.assertEqual(3, next(it)) + self.assertEqual(2, next(it)) + self.assertEqual(1, next(it)) + self.assertRaises(StopIteration, next, it) + + # test __len__() + self.assertEqual(3, len(stack)) + + # test __str__() + self.assertEqual(str(stack), "Top-> 3 2 1") + + # test is_empty() + self.assertFalse(stack.is_empty()) + + # test peek() + self.assertEqual(3, stack.peek()) + + # test pop() + self.assertEqual(3, stack.pop()) + self.assertEqual(2, stack.pop()) + self.assertEqual(1, stack.pop()) + + self.assertTrue(stack.is_empty()) + + +class TestOrderedStack(unittest.TestCase): + def test_OrderedStack(self): + stack = OrderedStack() + self.assertTrue(stack.is_empty()) + stack.push(1) + stack.push(4) + stack.push(3) + stack.push(6) + "bottom - > 1 3 4 6 " + self.assertEqual(6, stack.pop()) + self.assertEqual(4, stack.peek()) + self.assertEqual(3, stack.size()) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_streaming.py b/tests/test_streaming.py new file mode 100644 index 000000000..2f59827ef --- /dev/null +++ b/tests/test_streaming.py @@ -0,0 +1,41 @@ +from algorithms.streaming.misra_gries import ( + misras_gries, +) +from algorithms.streaming import ( + one_sparse +) +import unittest + + +class TestMisraGreis(unittest.TestCase): + def test_misra_correct(self): + self.assertEqual({'4': 5}, misras_gries([1, 4, 4, 4, 5, 4, 4])) + self.assertEqual({'1': 4}, misras_gries([0, 0, 0, 1, 1, 1, 1])) + self.assertEqual({'0': 4, '1': 3}, misras_gries([0, 0, 0, 0, 1, 1, + 1, 2, 2], 3)) + + def test_misra_incorrect(self): + self.assertEqual(None, misras_gries([1, 2, 5, 4, 5, 4, 4, 5, 4, 4, 5])) + self.assertEqual(None, misras_gries([0, 0, 0, 2, 1, 1, 1])) + self.assertEqual(None, misras_gries([0, 0, 0, 1, 1, 1])) + + +class TestOneSparse(unittest.TestCase): + def test_one_sparse_correct(self): + self.assertEqual(4, one_sparse([(4, '+'), (2, '+'), (2, '-'), + (4, '+'), (3, '+'), (3, '-')])) + self.assertEqual(2, one_sparse([(2, '+'), (2, '+'), (2, '+'), + (2, '+'), (2, '+'), (2, '+'), + (2, '+')])) + + def test_one_sparse_incorrect(self): + self.assertEqual(None, one_sparse([(2, '+'), (2, '+'), (2, '+'), + (2, '+'), (2, '+'), (2, '+'), + (1, '+')])) # Two values remaining + self.assertEqual(None, one_sparse([(2, '+'), (2, '+'), + (2, '+'), (2, '+'), + (2, '-'), (2, '-'), (2, '-'), + (2, '-')])) # No values remaining + # Bitsum sum of sign is inccorect + self.assertEqual(None, one_sparse([(2, '+'), (2, '+'), + (4, '+'), (4, '+')])) diff --git a/tests/test_strings.py b/tests/test_strings.py new file mode 100644 index 000000000..e7a68302a --- /dev/null +++ b/tests/test_strings.py @@ -0,0 +1,732 @@ +from algorithms.strings import ( + add_binary, + match_symbol, match_symbol_1, bracket, + decode_string, + delete_reoccurring_characters, + domain_name_1, domain_name_2, + encode, decode, + group_anagrams, + int_to_roman, + is_palindrome, is_palindrome_reverse, + is_palindrome_two_pointer, is_palindrome_stack, is_palindrome_deque, + is_rotated, is_rotated_v1, + license_number, + make_sentence, + is_merge_recursive, is_merge_iterative, + multiply, + is_one_edit, is_one_edit2, + rabin_karp, + ultra_pythonic, iterative, recursive, pythonic, + reverse_vowel, + reverse_words, + roman_to_int, + is_valid_coordinates_0, + word_squares, + convert_morse_word, unique_morse, + judge_circle, + strong_password, + caesar_cipher, + check_pangram, + contain_string, + count_binary_substring, + repeat_string, + text_justification, + min_distance, + min_distance_dp, + longest_common_prefix_v1, longest_common_prefix_v2, + longest_common_prefix_v3, + rotate, rotate_alt, + first_unique_char, + repeat_substring, + atbash, + longest_palindrome, + knuth_morris_pratt, + panagram, + fizzbuzz +) + +import unittest + + +class TestAddBinary(unittest.TestCase): + """[summary] + Test for the file add_binary.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_add_binary(self): + self.assertEqual("100", add_binary("11", "1")) + self.assertEqual("101", add_binary("100", "1")) + self.assertEqual("10", add_binary("1", "1")) + + +class TestBreakingBad(unittest.TestCase): + """[summary] + Test for the file breaking_bad.py + + Arguments: + unittest {[type]} -- [description] + """ + + def setUp(self): + self.words = ['Amazon', 'Microsoft', 'Google'] + self.symbols = ['i', 'Am', 'cro', 'le', 'abc'] + self.result = ['M[i]crosoft', '[Am]azon', 'Mi[cro]soft', 'Goog[le]'] + + def test_match_symbol(self): + self.assertEqual(self.result, match_symbol(self.words, self.symbols)) + + def test_match_symbol_1(self): + self.assertEqual(['[Am]azon', 'Mi[cro]soft', 'Goog[le]'], + match_symbol_1(self.words, self.symbols)) + + def test_bracket(self): + self.assertEqual(('[Am]azon', 'Mi[cro]soft', 'Goog[le]'), + bracket(self.words, self.symbols)) + self.assertEqual(('Amazon', 'Microsoft', 'Google'), + bracket(self.words, ['thisshouldnotmatch'])) + self.assertEqual(('Amazon', 'M[i]crosoft', 'Google'), + bracket(self.words, ['i', 'i'])) + + +class TestDecodeString(unittest.TestCase): + """[summary] + Test for the file decode_string.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_decode_string(self): + self.assertEqual("aaabcbc", decode_string("3[a]2[bc]")) + self.assertEqual("accaccacc", decode_string("3[a2[c]]")) + + +class TestDeleteReoccurring(unittest.TestCase): + """[summary] + Test for the file delete_reoccurring.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_delete_reoccurring_characters(self): + self.assertEqual("abc", delete_reoccurring_characters("aaabcccc")) + + +class TestDomainExtractor(unittest.TestCase): + """[summary] + Test for the file domain_extractor.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_valid(self): + self.assertEqual(domain_name_1("https://github.com/SaadBenn"), + "github") + + def test_invalid(self): + self.assertEqual(domain_name_2("http://google.com"), "google") + + +class TestEncodeDecode(unittest.TestCase): + """[summary] + Test for the file encode_decode.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_encode(self): + self.assertEqual("4:keon2:is7:awesome", encode("keon is awesome")) + + def test_decode(self): + self.assertEqual(['keon', 'is', 'awesome'], + decode("4:keon2:is7:awesome")) + + +class TestGroupAnagrams(unittest.TestCase): + """[summary] + Test for the file group_anagrams.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_group_anagrams(self): + self.assertEqual([['eat', 'tea', 'ate'], ['tan', 'nat'], ['bat']], \ + group_anagrams(["eat", "tea", "tan", "ate", "nat", + "bat"])) + + +class TestIntToRoman(unittest.TestCase): + """[summary] + Test for the file int_to_roman.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_int_to_roman(self): + self.assertEqual("DCXLIV", int_to_roman(644)) + self.assertEqual("I", int_to_roman(1)) + self.assertEqual("MMMCMXCIX", int_to_roman(3999)) + + +class TestIsPalindrome(unittest.TestCase): + """[summary] + Test for the file is_palindrome.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_palindrome(self): + # 'Otto' is a old german name. + self.assertTrue(is_palindrome("Otto")) + self.assertFalse(is_palindrome("house")) + + def test_is_palindrome_reverse(self): + # 'Otto' is a old german name. + self.assertTrue(is_palindrome_reverse("Otto")) + self.assertFalse(is_palindrome_reverse("house")) + + def test_is_palindrome_two_pointer(self): + # 'Otto' is a old german name. + self.assertTrue(is_palindrome_two_pointer("Otto")) + self.assertFalse(is_palindrome_two_pointer("house")) + + def test_is_palindrome_stack(self): + # 'Otto' is a old german name. + self.assertTrue(is_palindrome_stack("Otto")) + self.assertFalse(is_palindrome_stack("house")) + + def test_is_palindrome_deque(self): + # 'Otto' is a old german name. + self.assertTrue(is_palindrome_deque("Otto")) + self.assertFalse(is_palindrome_deque("house")) + + +class TestIsRotated(unittest.TestCase): + """[summary] + Test for the file is_rotated.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_rotated(self): + self.assertTrue(is_rotated("hello", "hello")) + self.assertTrue(is_rotated("hello", "llohe")) + self.assertFalse(is_rotated("hello", "helol")) + self.assertFalse(is_rotated("hello", "lloh")) + self.assertTrue(is_rotated("", "")) + + def test_is_rotated_v1(self): + self.assertTrue(is_rotated_v1("hello", "hello")) + self.assertTrue(is_rotated_v1("hello", "llohe")) + self.assertFalse(is_rotated_v1("hello", "helol")) + self.assertFalse(is_rotated_v1("hello", "lloh")) + self.assertTrue(is_rotated_v1("", "")) + + +class TestRotated(unittest.TestCase): + def test_rotate(self): + self.assertEqual("llohe", rotate("hello", 2)) + self.assertEqual("hello", rotate("hello", 5)) + self.assertEqual("elloh", rotate("hello", 6)) + self.assertEqual("llohe", rotate("hello", 7)) + + def test_rotate_alt(self): + self.assertEqual("llohe", rotate_alt("hello", 2)) + self.assertEqual("hello", rotate_alt("hello", 5)) + self.assertEqual("elloh", rotate_alt("hello", 6)) + self.assertEqual("llohe", rotate_alt("hello", 7)) + + +class TestLicenseNumber(unittest.TestCase): + """[summary] + Test for the file license_number.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_license_number(self): + self.assertEqual("a-b-c-d-f-d-d-f", license_number("a-bc-dfd-df", 1)) + self.assertEqual("ab-cd-fd-df", license_number("a-bc-dfd-df", 2)) + self.assertEqual("ab-cdf-ddf", license_number("a-bc-dfd-df", 3)) + self.assertEqual("abcd-fddf", license_number("a-bc-dfd-df", 4)) + self.assertEqual("abc-dfddf", license_number("a-bc-dfd-df", 5)) + + +class TestMakeSentence(unittest.TestCase): + """[summary] + Test for the file make_sentence.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_make_sentence(self): + dictionarys = ["", "app", "let", "t", "apple", "applet"] + word = "applet" + self.assertTrue(make_sentence(word, dictionarys)) + + +class TestMergeStringChecker(unittest.TestCase): + """[summary] + Test for the file merge_string_checker.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_merge_recursive(self): + self.assertTrue(is_merge_recursive("codewars", "cdw", "oears")) + + def test_is_merge_iterative(self): + self.assertTrue(is_merge_iterative("codewars", "cdw", "oears")) + + +class TestMultiplyStrings(unittest.TestCase): + """[summary] + Test for the file multiply_strings.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_multiply(self): + self.assertEqual("23", multiply("1", "23")) + self.assertEqual("529", multiply("23", "23")) + self.assertEqual("0", multiply("0", "23")) + self.assertEqual("1000000", multiply("100", "10000")) + + +class TestOneEditDistance(unittest.TestCase): + """[summary] + Test for the file one_edit_distance.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_is_one_edit(self): + self.assertTrue(is_one_edit("abc", "abd")) + self.assertFalse(is_one_edit("abc", "aed")) + self.assertFalse(is_one_edit("abcd", "abcd")) + + def test_is_one_edit2(self): + self.assertTrue(is_one_edit2("abc", "abd")) + self.assertFalse(is_one_edit2("abc", "aed")) + self.assertFalse(is_one_edit2("abcd", "abcd")) + + +class TestRabinKarp(unittest.TestCase): + """[summary] + Test for the file rabin_karp.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_rabin_karp(self): + self.assertEqual(3, rabin_karp("abc", "zsnabckfkd")) + self.assertEqual(None, rabin_karp("abc", "zsnajkskfkd")) + + +class TestReverseString(unittest.TestCase): + """[summary] + Test for the file reverse_string.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_recursive(self): + self.assertEqual("ereht olleh", recursive("hello there")) + + def test_iterative(self): + self.assertEqual("ereht olleh", iterative("hello there")) + + def test_pythonic(self): + self.assertEqual("ereht olleh", pythonic("hello there")) + + def test_ultra_pythonic(self): + self.assertEqual("ereht olleh", ultra_pythonic("hello there")) + + +class TestReverseVowel(unittest.TestCase): + """[summary] + Test for the file reverse_vowel.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_reverse_vowel(self): + self.assertEqual("holle", reverse_vowel("hello")) + + +class TestReverseWords(unittest.TestCase): + """[summary] + Test for the file reverse_words.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_reverse_words(self): + self.assertEqual("pizza like I and kim keon am I", \ + reverse_words("I am keon kim and I like pizza")) + + +class TestRomanToInt(unittest.TestCase): + """[summary] + Test for the file roman_to_int.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_roman_to_int(self): + self.assertEqual(621, roman_to_int("DCXXI")) + self.assertEqual(1, roman_to_int("I")) + self.assertEqual(3999, roman_to_int("MMMCMXCIX")) + + +# class TestStripUrlParams(unittest.TestCase): +# """[summary] +# Test for the file strip_urls_params.py + +# Arguments: +# unittest {[type]} -- [description] +# """ + +# def test_strip_url_params1(self): +# self.assertEqual(strip_url_params1("www.saadbenn.com?a=1&b=2&a=2"), +# "www.saadbenn.com?a=1&b=2") +# self.assertEqual(strip_url_params1("www.saadbenn.com?a=1&b=2", +# ['b']), "www.saadbenn.com?a=1") +# def test_strip_url_params2(self): +# self.assertEqual(strip_url_params2("www.saadbenn.com?a=1&b=2&a=2"), +# "www.saadbenn.com?a=1&b=2") +# self.assertEqual(strip_url_params2("www.saadbenn.com?a=1&b=2", +# 'b']), "www.saadbenn.com?a=1") +# def test_strip_url_params3(self): +# self.assertEqual(strip_url_params3("www.saadbenn.com?a=1&b=2&a=2"), +# "www.saadbenn.com?a=1&b=2") +# self.assertEqual(strip_url_params3("www.saadbenn.com?a=1&b=2", +# ['b']), "www.saadbenn.com?a=1") + + +class TestValidateCoordinates(unittest.TestCase): + """[summary] + Test for the file validate_coordinates.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_valid(self): + valid_coordinates = ["-23, 25", "4, -3", "90, 180", "-90, -180"] + for coordinate in valid_coordinates: + self.assertTrue(is_valid_coordinates_0(coordinate)) + + def test_invalid(self): + invalid_coordinates = ["23.234, - 23.4234", "99.234, 12.324", + "6.325624, 43.34345.345", "0, 1,2", + "23.245, 1e1"] + for coordinate in invalid_coordinates: + self.assertFalse(is_valid_coordinates_0(coordinate)) + + +class TestWordSquares(unittest.TestCase): + """[summary] + Test for the file word_squares.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_word_squares(self): + self.assertEqual([['wall', 'area', 'lead', 'lady'], ['ball', 'area', + 'lead', 'lady']], \ + word_squares(["area", "lead", "wall", + "lady", "ball"])) + + +class TestUniqueMorse(unittest.TestCase): + def test_convert_morse_word(self): + self.assertEqual("--...-.", convert_morse_word("gin")) + self.assertEqual("--...--.", convert_morse_word("msg")) + + def test_unique_morse(self): + self.assertEqual(2, unique_morse(["gin", "zen", "gig", "msg"])) + + +class TestJudgeCircle(unittest.TestCase): + def test_judge_circle(self): + self.assertTrue(judge_circle("UDLRUD")) + self.assertFalse(judge_circle("LLRU")) + + +class TestStrongPassword(unittest.TestCase): + def test_strong_password(self): + self.assertEqual(3, strong_password(3, "Ab1")) + self.assertEqual(1, strong_password(11, "#Algorithms")) + + +class TestCaesarCipher(unittest.TestCase): + def test_caesar_cipher(self): + self.assertEqual("Lipps_Asvph!", caesar_cipher("Hello_World!", 4)) + self.assertEqual("okffng-Qwvb", caesar_cipher("middle-Outz", 2)) + + +class TestCheckPangram(unittest.TestCase): + def test_check_pangram(self): + self.assertTrue(check_pangram("The quick brown fox jumps over the lazy dog")) + self.assertFalse(check_pangram("The quick brown fox")) + + +class TestContainString(unittest.TestCase): + def test_contain_string(self): + self.assertEqual(-1, contain_string("mississippi", "issipi")) + self.assertEqual(0, contain_string("Hello World", "")) + self.assertEqual(2, contain_string("hello", "ll")) + + +class TestCountBinarySubstring(unittest.TestCase): + def test_count_binary_substring(self): + self.assertEqual(6, count_binary_substring("00110011")) + self.assertEqual(4, count_binary_substring("10101")) + self.assertEqual(3, count_binary_substring("00110")) + + +class TestCountBinarySubstring(unittest.TestCase): + def test_repeat_string(self): + self.assertEqual(3, repeat_string("abcd", "cdabcdab")) + self.assertEqual(4, repeat_string("bb", "bbbbbbb")) + + +class TestTextJustification(unittest.TestCase): + def test_text_justification(self): + self.assertEqual(["This is an", + "example of text", + "justification. "], + text_justification(["This", "is", "an", "example", + "of", "text", + "justification."], 16) + ) + + self.assertEqual(["What must be", + "acknowledgment ", + "shall be "], + text_justification(["What", "must", "be", + "acknowledgment", "shall", + "be"], 16) + ) + + +class TestMinDistance(unittest.TestCase): + def test_min_distance(self): + self.assertEqual(2, min_distance("sea", "eat")) + self.assertEqual(6, min_distance("abAlgocrithmf", "Algorithmmd")) + self.assertEqual(4, min_distance("acbbd", "aabcd")) + +class TestMinDistanceDP(unittest.TestCase): + def test_min_distance(self): + self.assertEqual(2, min_distance_dp("sea", "eat")) + self.assertEqual(6, min_distance_dp("abAlgocrithmf", "Algorithmmd")) + self.assertEqual(4, min_distance("acbbd", "aabcd")) + + +class TestLongestCommonPrefix(unittest.TestCase): + def test_longest_common_prefix(self): + # Test first solution + self.assertEqual("fl", longest_common_prefix_v1(["flower", "flow", + "flight"])) + self.assertEqual("", longest_common_prefix_v1(["dog", "racecar", + "car"])) + # Test second solution + self.assertEqual("fl", longest_common_prefix_v2(["flower", "flow", + "flight"])) + self.assertEqual("", longest_common_prefix_v2(["dog", "racecar", + "car"])) + # Test third solution + self.assertEqual("fl", longest_common_prefix_v3(["flower", "flow", + "flight"])) + self.assertEqual("", longest_common_prefix_v3(["dog", "racecar", + "car"])) + + +class TestFirstUniqueChar(unittest.TestCase): + def test_first_unique_char(self): + self.assertEqual(0, first_unique_char("leetcode")) + self.assertEqual(2, first_unique_char("loveleetcode")) + + +class TestRepeatSubstring(unittest.TestCase): + def test_repeat_substring(self): + self.assertTrue(repeat_substring("abab")) + self.assertFalse(repeat_substring("aba")) + self.assertTrue(repeat_substring("abcabcabcabc")) + + +class TestAtbashCipher(unittest.TestCase): + """[summary] + Test for the file atbash_cipher.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_atbash_cipher(self): + self.assertEqual("zyxwvutsrqponml", atbash("abcdefghijklmno")) + self.assertEqual("KbgslM", atbash("PythoN")) + self.assertEqual("AttaCK at DawN", atbash("ZggzXP zg WzdM")) + self.assertEqual("ZggzXP zg WzdM", atbash("AttaCK at DawN")) + + +class TestLongestPalindromicSubstring(unittest.TestCase): + """[summary] + Test for the file longest_palindromic_substring.py + Arguments: + unittest {[type]} -- [description] + """ + def test_longest_palindromic_substring(self): + self.assertEqual("bb", longest_palindrome("cbbd")) + self.assertEqual("abba", longest_palindrome("abba")) + self.assertEqual("asdadsa", longest_palindrome("dasdasdasdasdasdadsa")) + self.assertEqual("abba", longest_palindrome("cabba")) + + +class TestKnuthMorrisPratt(unittest.TestCase): + """[summary] + Test for the file knuth_morris_pratt.py + + + Arguments: + unittest {[type]} -- [description] + """ + + def test_knuth_morris_pratt(self): + self.assertEqual([0, 1, 2, 3, 4], knuth_morris_pratt("aaaaaaa", "aaa")) + self.assertEqual([0, 4], knuth_morris_pratt("abcdabc", "abc")) + self.assertEqual([], knuth_morris_pratt("aabcdaab", "aba")) + self.assertEqual([0, 4], knuth_morris_pratt([0,0,1,1,0,0,1,0], [0,0])) + + +class TestPanagram(unittest.TestCase): + """[summary] + Test for the file panagram.py + + Arguments: + unittest {[type]} -- [description] + """ + + def test_empty_string(self): + # Arrange + string = "" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(False, res) + + def test_single_word_non_panagram(self): + # Arrange + string = "sentence" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(False, res) + + def test_fox_panagram_no_spaces(self): + # Arrange + string = "thequickbrownfoxjumpsoverthelazydog" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(True, res) + + def test_fox_panagram_mixed_case(self): + # Arrange + string = "theqUiCkbrOwnfOxjUMPSOVErThELAzYDog" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(True, res) + + def test_whitespace_punctuation(self): + # Arrange + string = "\n\t\r,.-_!?" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(False, res) + + def test_fox_panagram(self): + # Arrange + string = "the quick brown fox jumps over the lazy dog" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(True, res) + + def test_swedish_panagram(self): + # Arrange + string = "Yxmördaren Julia Blomqvist på fäktning i Schweiz" + + # Act + res = panagram(string) + + # Assert + self.assertEqual(True, res) + + +class TestFizzbuzz(unittest.TestCase): + """[summary] + Tests for the fizzbuzz method in file fizzbuzz.py + """ + def test_fizzbuzz(self): + # Testing that n < 0 returns a Value Error + self.assertRaises(ValueError, fizzbuzz.fizzbuzz, -2) + + # Testing that a string returns a Type Error. + self.assertRaises(TypeError, fizzbuzz.fizzbuzz, "hello") + + # Testing a base case, n = 3 + result = fizzbuzz.fizzbuzz(3) + expected = [1, 2, "Fizz"] + self.assertEqual(result, expected) + + # Testing a base case, n = 5 + result = fizzbuzz.fizzbuzz(5) + expected = [1, 2, "Fizz", 4, "Buzz"] + self.assertEqual(result, expected) + + # Testing a base case, n = 15 i.e. mod 3 and 5 + result = fizzbuzz.fizzbuzz(15) + expected = [1, 2, "Fizz", 4, "Buzz", "Fizz", 7, 8, "Fizz", "Buzz", 11, + "Fizz", 13, 14, "FizzBuzz"] + self.assertEqual(result, expected) + + +if __name__ == "__main__": + unittest.main() diff --git a/tests/test_tree.py b/tests/test_tree.py new file mode 100644 index 000000000..c9d0f0fd4 --- /dev/null +++ b/tests/test_tree.py @@ -0,0 +1,180 @@ +from algorithms.tree.traversal import ( + preorder, + preorder_rec, + postorder, + postorder_rec, + inorder, + inorder_rec +) +from algorithms.tree.b_tree import BTree + +from algorithms.tree import construct_tree_postorder_preorder as ctpp + +from algorithms.tree.fenwick_tree.fenwick_tree import Fenwick_Tree + +import unittest + + +class Node: + + def __init__(self, val, left=None, right=None): + self.val = val + self.left = left + self.right = right + + +class TestTraversal(unittest.TestCase): + + def test_preorder(self): + tree = create_tree() + self.assertEqual([100, 50, 25, 75, 150, 125, 175], preorder(tree)) + self.assertEqual([100, 50, 25, 75, 150, 125, 175], preorder_rec(tree)) + + def test_postorder(self): + tree = create_tree() + self.assertEqual([25, 75, 50, 125, 175, 150, 100], postorder(tree)) + self.assertEqual([25, 75, 50, 125, 175, 150, 100], postorder_rec(tree)) + + def test_inorder(self): + tree = create_tree() + self.assertEqual([25, 50, 75, 100, 125, 150, 175], inorder(tree)) + self.assertEqual([25, 50, 75, 100, 125, 150, 175], inorder_rec(tree)) + + +def create_tree(): + n1 = Node(100) + n2 = Node(50) + n3 = Node(150) + n4 = Node(25) + n5 = Node(75) + n6 = Node(125) + n7 = Node(175) + n1.left, n1.right = n2, n3 + n2.left, n2.right = n4, n5 + n3.left, n3.right = n6, n7 + return n1 + + +class TestBTree(unittest.TestCase): + + @classmethod + def setUpClass(cls): + import random + random.seed(18719) + cls.random = random + cls.range = 10000 + + def setUp(self): + self.keys_to_insert = [self.random.randrange(-self.range, self.range) + for i in range(self.range)] + + def test_insertion_and_find_even_degree(self): + btree = BTree(4) + for i in self.keys_to_insert: + btree.insert_key(i) + + for i in range(100): + key = self.random.choice(self.keys_to_insert) + self.assertTrue(btree.find(key)) + + def test_insertion_and_find_odd_degree(self): + btree = BTree(3) + for i in self.keys_to_insert: + btree.insert_key(i) + + for i in range(100): + key = self.random.choice(self.keys_to_insert) + self.assertTrue(btree.find(key)) + + def test_deletion_even_degree(self): + btree = BTree(4) + key_list = set(self.keys_to_insert) + for i in key_list: + btree.insert_key(i) + + for key in key_list: + btree.remove_key(key) + self.assertFalse(btree.find(key)) + + self.assertEqual(btree.root.keys, []) + self.assertEqual(btree.root.children, []) + + def test_deletion_odd_degree(self): + btree = BTree(3) + key_list = set(self.keys_to_insert) + for i in key_list: + btree.insert_key(i) + + for key in key_list: + btree.remove_key(key) + self.assertFalse(btree.find(key)) + + self.assertEqual(btree.root.keys, []) + self.assertEqual(btree.root.children, []) + + +class TestConstructTreePreorderPostorder(unittest.TestCase): + def test_construct_tree(self): + + # Test 1 + ctpp.pre_index = 0 + pre1 = [1, 2, 4, 8, 9, 5, 3, 6, 7] + post1 = [8, 9, 4, 5, 2, 6, 7, 3, 1] + size1 = len(pre1) + + self.assertEqual(ctpp.construct_tree(pre1, post1, size1), + [8, 4, 9, 2, 5, 1, 6, 3, 7]) + + # Test 2 + ctpp.pre_index = 0 + pre2 = [1, 2, 4, 5, 3, 6, 7] + post2 = [4, 5, 2, 6, 7, 3, 1] + size2 = len(pre2) + + self.assertEqual(ctpp.construct_tree(pre2, post2, size2), + [4, 2, 5, 1, 6, 3, 7]) + + # Test 3 + ctpp.pre_index = 0 + pre3 = [12, 7, 16, 21, 5, 1, 9] + post3 = [16, 21, 7, 1, 9, 5, 12] + size3 = len(pre3) + + self.assertEqual(ctpp.construct_tree(pre3, post3, size3), + [16, 7, 21, 12, 1, 5, 9]) + + +class TestFenwickTree(unittest.TestCase): + def test_construct_tree_with_update_1(self): + freq = [2, 1, 1, 3, 2, 3, 4, 5, 6, 7, 8, 9] + ft = Fenwick_Tree(freq) + bit_tree = ft.construct() + self.assertEqual(12, ft.get_sum(bit_tree, 5)) + + freq[3] += 6 + ft.update_bit(bit_tree, 3, 6) + self.assertEqual(18, ft.get_sum(bit_tree, 5)) + + def test_construct_tree_with_update_2(self): + freq = [1, 2, 3, 4, 5] + ft = Fenwick_Tree(freq) + bit_tree = ft.construct() + self.assertEqual(10, ft.get_sum(bit_tree, 3)) + + freq[3] -= 5 + ft.update_bit(bit_tree, 3, -5) + self.assertEqual(5, ft.get_sum(bit_tree, 3)) + + def test_construct_tree_with_update_3(self): + freq = [2, 1, 4, 6, -1, 5, -32, 0, 1] + ft = Fenwick_Tree(freq) + bit_tree = ft.construct() + self.assertEqual(12, ft.get_sum(bit_tree, 4)) + + freq[2] += 11 + ft.update_bit(bit_tree, 2, 11) + self.assertEqual(23, ft.get_sum(bit_tree, 4)) + + +if __name__ == '__main__': + unittest.main() diff --git a/tests/test_unix.py b/tests/test_unix.py new file mode 100644 index 000000000..3cafba98f --- /dev/null +++ b/tests/test_unix.py @@ -0,0 +1,48 @@ +from algorithms.unix import ( + join_with_slash, + full_path, + split, + simplify_path_v1, simplify_path_v2 +) +import os +import unittest + + +class TestUnixPath(unittest.TestCase): + def test_join_with_slash(self): + self.assertEqual("path/to/dir/file", + join_with_slash("path/to/dir/", "file")) + self.assertEqual("path/to/dir/file", + join_with_slash("path/to/dir", "file")) + self.assertEqual("http://algorithms/part", + join_with_slash("http://algorithms", "part")) + self.assertEqual("http://algorithms/part", + join_with_slash("http://algorithms/", "part")) + + def test_full_path(self): + file_name = "file_name" + # Test full path relative + expect_path = "{}/{}".format(os.getcwd(), file_name) + self.assertEqual(expect_path, full_path(file_name)) + # Test full path with expanding user + # ~/file_name + expect_path = "{}/{}".format(os.path.expanduser('~'), file_name) + self.assertEqual(expect_path, full_path("~/{}".format(file_name))) + + def test_split(self): + # Test url path + path = "https://algorithms/unix/test.py" + expect_result = split(path) + self.assertEqual("https://algorithms/unix", expect_result[0]) + self.assertEqual("test.py", expect_result[1]) + # Test file path + path = "algorithms/unix/test.py" + expect_result = split(path) + self.assertEqual("algorithms/unix", expect_result[0]) + self.assertEqual("test.py", expect_result[1]) + + def test_simplify_path(self): + self.assertEqual("/", simplify_path_v1("/../")) + self.assertEqual("/home/foo", simplify_path_v1("/home//foo/")) + self.assertEqual("/", simplify_path_v2("/../")) + self.assertEqual("/home/foo", simplify_path_v2("/home//foo/")) diff --git a/tmp/temporary.md b/tmp/temporary.md deleted file mode 100644 index 7f1f3247b..000000000 --- a/tmp/temporary.md +++ /dev/null @@ -1,29 +0,0 @@ -Given input which is a vector of (user name, log-in time, log-out time), -output time series which will have number of users logged in at each given -time slot in the input, output should only contain time slots which are given -in input for example if the input is "September", 1.2, 4.5), -("June", 3.1, 6.7), ("August", 8.9, 10.3) output should contain only -1.2, 3.1, 4.5, 3.1, 6.7, 8.9, 10.3 -Example: /* [ ("September", 1.2, 4.5), ("June", 3.1, 6.7), ("August", 8.9, 10.3) ] => -[(1.2, 1), (3.1, 2), (4.5, 1), (6.7, 0), (8.9, 1), (10.3, 0)] */ - - -• Sweeping line method - § record the time instance and it type: log in, log out - § Sort the time instances. Keep a variable to record the number of logged in users, number - § For a time instance, - □ if it is log-in type, number++, print -else number--, print - - -1. Constant time random access hash implementation - -2. Efficient elevator API - -3. Ransom note - -4. Median of k unsorted arrays - -5. Design of a task scheduler - -6. Custom comparator diff --git a/tox.ini b/tox.ini new file mode 100644 index 000000000..f9182236e --- /dev/null +++ b/tox.ini @@ -0,0 +1,63 @@ +[tox] +envlist = + py35 + py36 + py37 + coverage + +[testenv] +passenv = TRAVIS TRAVIS_* +basepython = + py35: python3.5 + py36: python3.6 + py37: python3.7 +deps = + coverage + coveralls +commands = + coverage run --source=tests,algorithms -m unittest discover tests + coverage report -m + coveralls + +[testenv:py35] +passenv = CI TRAVIS TRAVIS_* +basepython = + python3.5 +deps = + pytest +commands = + python3 -m unittest discover tests + python3 -m pytest tests + +[testenv:py36] +passenv = CI TRAVIS TRAVIS_* +basepython = + python3.6 +deps = + pytest +commands = + python3 -m unittest discover tests + python3 -m pytest tests + +[testenv:py37] +passenv = CI TRAVIS TRAVIS_* +basepython = + python3.7 +deps = + pytest +commands = + python3 -m unittest discover tests + python3 -m pytest tests + +[testenv:coverage] +passenv = CI TRAVIS TRAVIS_* +skip_install = True +basepython = + python3.7 +commands = + coverage run --source=tests,algorithms -m unittest discover tests + coverage report -m + coveralls +deps = + coverage + coveralls diff --git a/tree.md b/tree.md deleted file mode 100644 index 37d6f316b..000000000 --- a/tree.md +++ /dev/null @@ -1,206 +0,0 @@ -``` - -. -├── array -│   ├── circular_counter.py -│   ├── flatten.py -│   ├── garage.py -│   ├── longest_non_repeat.py -│   ├── merge_intervals.py -│   ├── missing_ranges.py -│   ├── plus_one.py -│   ├── rotate_array.py -│   ├── summary_ranges.py -│   ├── three_sum.py -│   └── two_sum.py -├── backtrack -│   ├── anagram.py -│   ├── array_sum_combinations.py -│   ├── combination_sum.py -│   ├── expression_add_operators.py -│   ├── factor_combinations.py -│   ├── general_solution.md -│   ├── generate_abbreviations.py -│   ├── generate_parenthesis.py -│   ├── letter_combination.py -│   ├── palindrome_partitioning.py -│   ├── pattern_match.py -│   ├── permute.py -│   ├── permute_unique.py -│   ├── subsets.py -│   └── subsets_unique.py -├── bfs -│   ├── shortest_distance_from_all_buildings.py -│   └── word_ladder.py -├── bit -│   ├── count_ones.py -│   ├── power_of_two.py -│   ├── reverse_bits.py -│   ├── single_number2.py -│   ├── single_number.py -│   └── subsets.py -├── design -│   ├── alarm_system.md -│   ├── all_o_one_ds.md -│   ├── calculator.md -│   ├── excel_table.md -│   ├── LRUcache.md -│   ├── nearby_drivers.md -│   ├── ride_sharing.md -│   ├── task_runner.md -│   └── twitter_feeds.md -├── dfs -│   ├── all_factors.py -│   ├── count_islands.py -│   ├── pacific_atlantic.py -│   ├── sudoku_solver.py -│   └── walls_and_gates.py -├── dp -│   ├── buy_sell_stock.py -│   ├── climbing_stairs.py -│   ├── combination_sum.py -│   ├── house_robber.py -│   ├── longest_increasing.py -│   ├── max_product_subarray.py -│   ├── max_subarray.py -│   ├── num_decodings.py -│   ├── regex_matching.py -│   └── word_break.py -├── graph -│   ├── clone_graph.py -│   ├── find_path.py -│   ├── graph.py -│   └── traversal.py -├── heap -│   ├── merge_sorted_k_lists.py -│   ├── skyline.py -│   └── sliding_window_max.py -├── linkedlist -│   ├── add_two_numbers.py -│   ├── copy_random_pointer.py -│   ├── delete_node.py -│   ├── first_cyclic_node.py -│   ├── is_cyclic.py -│   ├── is_palindrome.py -│   ├── kth_to_last.py -│   ├── linkedlist.py -│   ├── remove_duplicates.py -│   ├── reverse.py -│   ├── rotate_list.py -│   └── swap_in_pairs.py -├── map -│   ├── hashtable.py -│   ├── longest_common_subsequence.py -│   ├── randomized_set.py -│   └── valid_sudoku.py -├── math -│   ├── generate_strobogrammtic.py -│   ├── is_strobogrammatic.py -│   ├── nth_digit.py -│   └── sqrt_precision_factor.py -├── matrix -│   ├── bomb_enemy.py -│   ├── matrix_rotation.txt -│   ├── rotate_image.py -│   ├── sparse_dot_vector.py -│   ├── sparse_mul.py -│   └── spiral_traversal.py -├── queue -│   ├── __init__.py -│   ├── max_sliding_window.py -│   ├── moving_average.py -│   ├── queue.py -│   ├── reconstruct_queue.py -│   └── zigzagiterator.py -├── README.md -├── search -│   ├── binary_search.py -│   ├── count_elem.py -│   ├── first_occurance.py -│   └── last_occurance.py -├── set -│   └── randomized_set.py -├── sort -│   ├── insertion_sort.py -│   ├── meeting_rooms.py -│   ├── merge_sort.py -│   ├── quick_sort.py -│   ├── selection_sort.py -│   ├── sort_colors.py -│   ├── topsort.py -│   └── wiggle_sort.py -├── stack -│   ├── __init__.py -│   ├── __init__.pyc -│   ├── longest_abs_path.py -│   ├── __pycache__ -│   │   ├── __init__.cpython-35.pyc -│   │   └── stack.cpython-35.pyc -│   ├── simplify_path.py -│   ├── stack.py -│   ├── stack.pyc -│   └── valid_parenthesis.py -├── string -│   ├── add_binary.py -│   ├── breaking_bad.py -│   ├── decode_string.py -│   ├── encode_decode.py -│   ├── group_anagrams.py -│   ├── int_to_roman.py -│   ├── is_palindrome.py -│   ├── license_number.py -│   ├── make_sentence.py -│   ├── multiply_strings.py -│   ├── one_edit_distance.py -│   ├── rabin_karp.py -│   ├── reverse_string.py -│   ├── reverse_vowel.py -│   ├── reverse_words.py -│   ├── roman_to_int.py -│   └── word_squares.py -├── tmp -│   └── temporary.md -├── tree -│   ├── binary_tree_paths.py -│   ├── bintree2list.py -│   ├── bst -│   │   ├── array2bst.py -│   │   ├── bst_closest_value.py -│   │   ├── BSTIterator.py -│   │   ├── delete_node.py -│   │   ├── is_bst.py -│   │   ├── kth_smallest.py -│   │   ├── lowest_common_ancestor.py -│   │   ├── predecessor.py -│   │   ├── serialize_deserialize.py -│   │   ├── successor.py -│   │   └── unique_bst.py -│   ├── deepest_left.py -│   ├── invert_tree.py -│   ├── is_balanced.py -│   ├── is_subtree.py -│   ├── is_symmetric.py -│   ├── longest_consecutive.py -│   ├── lowest_common_ancestor.py -│   ├── max_height.py -│   ├── max_path_sum.py -│   ├── min_height.py -│   ├── path_sum2.py -│   ├── path_sum.py -│   ├── pretty_print.py -│   ├── same_tree.py -│   ├── traversal -│   │   ├── inorder.py -│   │   ├── level_order.py -│   │   └── zigzag.py -│   ├── tree.py -│   └── trie -│   ├── add_and_search.py -│   └── trie.py -├── tree.md -└── union-find - └── count_islands.py - -26 directories, 173 files - -``` diff --git a/tree/binary_tree_paths.py b/tree/binary_tree_paths.py deleted file mode 100644 index aad327696..000000000 --- a/tree/binary_tree_paths.py +++ /dev/null @@ -1,14 +0,0 @@ -def binaryTreePaths(root): - res = [] - if not root: - return res - DFS(res, root, str(root.val)) - return res - -def DFS(res, root, cur): - if not root.left and not root.right: - res.append(cur) - if root.left: - DFS(res, root.left, cur+'->'+str(root.left.val)) - if root.right: - DFS(res, root.right, cur+'->'+str(root.right.val)) diff --git a/tree/bst/array2bst.py b/tree/bst/array2bst.py deleted file mode 100644 index cc147eac2..000000000 --- a/tree/bst/array2bst.py +++ /dev/null @@ -1,19 +0,0 @@ -""" -Given an array where elements are sorted in ascending order, -convert it to a height balanced BST. -""" -# class TreeNode(object): -# def __init__(self, x): -# self.val = x -# self.left = None -# self.right = None - - -def array2bst(nums): - if not nums: - return None - mid = len(nums)//2 - node = Node(nums[mid]) - node.left = array2bst(nums[:mid]) - node.right = array2bst(nums[mid+1:]) - return node diff --git a/tree/is_balanced.py b/tree/is_balanced.py deleted file mode 100644 index 69a420e83..000000000 --- a/tree/is_balanced.py +++ /dev/null @@ -1,33 +0,0 @@ - -def is_balanced(root): - """ - O(N) solution - """ - return -1 != get_depth(root) - -def get_depth(root): - """ - return 0 if unbalanced else depth + 1 - """ - if not root: - return 0 - left = get_depth(root.left) - right = get_depth(root.right) - if abs(left-right) > 1: - return -1 - return 1 + max(left, right) - -################################ - -def is_balanced(root): - """ - O(N^2) solution - """ - left = max_height(root.left) - right = max_height(root.right) - return abs(left-right) <= 1 and is_balanced(root.left) and is_balanced(root.right) - -def max_height(root): - if not root: - return 0 - return max(max_height(root.left), max_height(root.right)) + 1 diff --git a/tree/is_subtree.py b/tree/is_subtree.py deleted file mode 100644 index 9a6c91f95..000000000 --- a/tree/is_subtree.py +++ /dev/null @@ -1,69 +0,0 @@ -# Given two binary trees s and t, check if t is a subtree of s. -# A subtree of a tree t is a tree consisting of a node in t and -# all of its descendants in t. - -# Example 1: - -# Given s: - - # 3 - # / \ - # 4 5 - # / \ - # 1 2 - -# Given t: - - # 4 - # / \ - # 1 2 -# Return true, because t is a subtree of s. - -# Example 2: - -# Given s: - - # 3 - # / \ - # 4 5 - # / \ - # 1 2 - # / - # 0 - -# Given t: - - # 3 - # / - # 4 - # / \ - # 1 2 -# Return false, because even though t is part of s, -# it does not contain all descendants of t. - -# Follow up: -# What if one tree is significantly lager than the other? - - -def is_subtree(big, small): - flag = False - queue = collections.deque() - queue.append(big) - while queue: - node = queue.popleft() - if node.val == small.val: - flag = comp(node, small) - break - else: - queue.append(node.left) - queue.append(node.right) - return flag - -def comp(p, q): - if not p and not q: - return True - if p and q: - return p.val == q.val and comp(p.left,q.left) and comp(p.right, q.right) - return False - - diff --git a/tree/longest_consecutive.py b/tree/longest_consecutive.py deleted file mode 100644 index 498aaa6ca..000000000 --- a/tree/longest_consecutive.py +++ /dev/null @@ -1,45 +0,0 @@ -# Given a binary tree, find the length of the longest consecutive sequence path. - -# The path refers to any sequence of nodes from some starting node to any node -# in the tree along the parent-child connections. -# The longest consecutive path need to be from parent to child -# (cannot be the reverse). - -# For example, - # 1 - # \ - # 3 - # / \ - # 2 4 - # \ - # 5 -# Longest consecutive sequence path is 3-4-5, so return 3. - # 2 - # \ - # 3 - # / - # 2 - # / - # 1 - - -maxlen = 0 -def longestConsecutive(root): - """ - :type root: TreeNode - :rtype: int - """ - if not root: - return 0 - DFS(root, 0, root.val) - return maxlen - -def DFS(root, cur, target): - if not root: return - if root.val == target: - cur += 1 - else: - cur = 1 - maxlen = max(cur, maxlen) - DFS(root.left, cur, root.val+1) - DFS(root.right, cur, root.val+1) diff --git a/tree/max_path_sum.py b/tree/max_path_sum.py deleted file mode 100644 index 48c3e3fbf..000000000 --- a/tree/max_path_sum.py +++ /dev/null @@ -1,14 +0,0 @@ - -maximum = float("-inf") - -def max_path_sum(root): - helper(root) - return maximum - -def helper(root): - if not root: - return 0 - left = helper(root.left) - right = helper(root.right) - maximum = max(maximum, left+right+root.val) - return root.val + max(left, right) diff --git a/tree/pretty_print.py b/tree/pretty_print.py deleted file mode 100644 index dc58ab3ec..000000000 --- a/tree/pretty_print.py +++ /dev/null @@ -1,20 +0,0 @@ -# a -> Adam -> Book -> 4 -# b -> Bill -> Computer -> 5 - # -> TV -> 6 - # Jill -> Sports -> 1 -# c -> Bill -> Sports -> 3 -# d -> Adam -> Computer -> 3 - # Quin -> Computer -> 3 -# e -> Quin -> Book -> 5 - # -> TV -> 2 -# f -> Adam -> Computer -> 7 - -def treePrint(tree): - for key in tree: - print key, # comma prevents a newline character - treeElem = tree[key] # multiple lookups is expensive, even amortized O(1)! - for subElem in treeElem: - print " -> ", subElem, - if type(subElem) != str: # OP wants indenting after digits - print "\n " # newline and a space to match indenting - print "" # forces a newline diff --git a/union-find/count_islands.py b/union-find/count_islands.py deleted file mode 100644 index 15cd676ee..000000000 --- a/union-find/count_islands.py +++ /dev/null @@ -1,78 +0,0 @@ -""" -A 2d grid map of m rows and n columns is initially filled with water. -We may perform an addLand operation which turns the water at position -(row, col) into a land. Given a list of positions to operate, -count the number of islands after each addLand operation. -An island is surrounded by water and is formed by connecting adjacent -lands horizontally or vertically. -You may assume all four edges of the grid are all surrounded by water. - -Given m = 3, n = 3, positions = [[0,0], [0,1], [1,2], [2,1]]. -Initially, the 2d grid grid is filled with water. -(Assume 0 represents water and 1 represents land). - -0 0 0 -0 0 0 -0 0 0 -Operation #1: addLand(0, 0) turns the water at grid[0][0] into a land. - -1 0 0 -0 0 0 Number of islands = 1 -0 0 0 -Operation #2: addLand(0, 1) turns the water at grid[0][1] into a land. - -1 1 0 -0 0 0 Number of islands = 1 -0 0 0 -Operation #3: addLand(1, 2) turns the water at grid[1][2] into a land. - -1 1 0 -0 0 1 Number of islands = 2 -0 0 0 -Operation #4: addLand(2, 1) turns the water at grid[2][1] into a land. - -1 1 0 -0 0 1 Number of islands = 3 -0 1 0 -""" - - -class Solution(object): - def numIslands2(self, m, n, positions): - ans = [] - islands = Union() - for p in map(tuple, positions): - islands.add(p) - for dp in (0, 1), (0, -1), (1, 0), (-1, 0): - q = (p[0] + dp[0], p[1] + dp[1]) - if q in islands.id: - islands.unite(p, q) - ans += [islands.count] - return ans - -class Union(object): - def __init__(self): - self.id = {} - self.sz = {} - self.count = 0 - - def add(self, p): - self.id[p] = p - self.sz[p] = 1 - self.count += 1 - - def root(self, i): - while i != self.id[i]: - self.id[i] = self.id[self.id[i]] - i = self.id[i] - return i - - def unite(self, p, q): - i, j = self.root(p), self.root(q) - if i == j: - return - if self.sz[i] > self.sz[j]: - i, j = j, i - self.id[i] = j - self.sz[j] += self.sz[i] - self.count -= 1