📌 Algorithms Template for Competitive Programming

This repository contains templates of useful algorithms and data structures coded in C++ for use in competitive programming.

Quick Start

Automatic Snippet Generation

This repository includes scripts to automatically generate code snippets for your editor:

For VS Code

python3 generate_vscode_snippets.py

This script automatically:

• Scans all .cpp files in the subdirectories
• Generates VS Code snippets in cpp.json
• Places them in your VS Code user snippets directory:
  • Windows: %APPDATA%\Code\User\snippets\cpp.json
  • Linux: ~/.config/Code/User/snippets/cpp.json
  • macOS: ~/Library/Application Support/Code/User/snippets/cpp.json
• Replaces Vim date placeholders with VS Code variables for template files

For Vim/Neovim (UltiSnips)

bash generate_snippets.sh

This script:

• Searches for all .cpp files recursively
• Generates UltiSnips format snippets
• Outputs to ~/.vim/UltiSnips/cpp/cpp_generate.snippets
• Each snippet is prefixed with the filename (without extension)

After running the appropriate script, you can use any algorithm by typing its prefix (e.g., graph_dijkstra_std) and triggering your editor's autocomplete.

Contents

Command - Description

• Misc

  • Debugging

    • misc_debug - Comprehensive debugging utilities with to_string methods for main data types, standard data structures, pairs, tuples, and bitsets.

  • Misc

    • misc_pragma - Compiler optimization pragmas for competitive programming.
    • misc_data_types - Macros to shorten the writing of numeric data types.
    • misc_pairs - Macros to shorten the writing of tuples and pairs.
    • misc_precise - Macros for setting decimal precision to format floating-point values on output operations.
    • misc_infinity - Macros defining the constants of infinity.
    • misc_loops - Macros to shorten loop writing.
    • misc_min_max - min and max functions by reference.
    • misc_directions - Array with the values to explore a 2D grid.
    • misc_references - Macros to shorten the code writing of vector references.
    • misc_math - Mathematical constants and utility functions.
    • misc_vector_n_d - Functions to create vectors of 2, 3 and 4 dimensions with shortened syntax.
    • misc_cond - Functions and macros to simplify conditional code writing.
    • misc_bits - Bit manipulation operations and tricks.
    • misc_unique - Remove duplicate values from a vector.
    • misc_y_combinator - Y Combinator pattern to define recursive lambda functions.
    • misc_argsort - Returns indices that would sort an array.
    • misc_coordinate_compression - Compress coordinates to a smaller range while preserving relative order.
    • misc_date - Date handling utilities and formatters.
    • misc_format_problem_answer - Utilities to format problem outputs consistently.
    • misc_integer128 - 128-bit integer support and operations.
    • misc_to_reverse - Utilities to reverse sequences and containers.
    • misc_unreachable - Macro to mark unreachable code paths for optimization.

• Geometry

  • 2d_geometry_point - Point representation in 2D space with basic operations (distance, dot product, cross product).
  • 2d_geometry_polygon - Polygon data structure for managing collections of points.
  • 2d_geometry_area - Computes the area of a polygon using the shoelace formula.
  • 2d_geometry_perimeter - Calculates the total perimeter length of a polygon.
  • 2d_geometry_convex_hull_mc - Finds the convex hull using the Monotone Chain algorithm (Andrew's algorithm).

• Math

  • math_primality_test - Primality test of a number.
  • math_divisors - Function to get all the divisors of a number.
  • math_gcd_recursive - Greatest common divisor (Recursive Implementation).
  • math_gcd_iterative - Greatest common divisor (Iterative Implementation).
  • math_lcm - Least common multiple.
  • math_prime_factors_vector - Function that calculates the prime factors of a number (returns vector).
  • math_prime_factors_map - Function that calculates the prime factors of a number with their frequencies (returns map).
  • math_sieve - Function to get all prime numbers in a given range using Sieve of Eratosthenes.
  • math_sieve_full - Complete implementation of Sieve of Eratosthenes with additional utilities.
  • math_is_power_of_n - Algorithm that checks if a number is a power of n.
  • math_matrix - Class that represents a 2D matrix with its matrix operations.
  • math_matrix_full - Complete matrix class with extended operations and utilities.
  • math_polynomial - Polynomial class with operations (Addition, Subtraction, Multiplication, Division and Modulo).
  • math_diophantine_best - Diophantine equation solver that meets the condition |x|, |y| <= max(|a|, |b|, |c|).
  • math_diophantine_std - Standard implementation of the Diophantine equation solver.
  • math_extgcd_iterative - Extended Euclidean Algorithm (Iterative).
  • math_extgcd_recursive - Extended Euclidean Algorithm (Recursive).
  • math_fft_recursive - Fast Fourier Transform Algorithm (Recursive).
  • math_factorial - Factorial implementation.
  • math_phi_euler_sqrt_n - Euler's totient function calculation in O(√n).
  • math_mex - Minimal excludant (MEX) - finds the smallest non-negative integer not in a set.
  • math_harmonic_lemma_trick - Harmonic lemma optimization trick for divisor-based problems.

• Query Range

  • range_query_segment_tree - Segment Tree data structure for efficient range queries and updates.
  • range_query_sum_immutable - Query sum in ranges with immutable array (Prefix Sum).
  • range_query_sum_2d_immutable - Query sum in 2D ranges with immutable matrix (2D Prefix Sum).
  • range_query_fenwick_tree_std - Standard Binary Indexed Tree (Fenwick Tree) for range sum queries and point updates.
  • range_query_segment_tree_lazy_compress - Segment Tree with lazy propagation - compressed implementation with (add, max, min, index) operations.
  • range_query_segment_tree_lazy_full - Segment Tree with lazy propagation - complete implementation including (add, max, min, index) operations, find_first and find_last methods.
  • range_query_segment_tree_lazy_template - Generic template for Segment Tree with lazy propagation.
  • range_query_sum_lower_bound_segment_tree_lazy - Lower bound algorithm on Segment Tree with lazy propagation.
  • range_query_less_than_segment_tree_lazy - Find the rightmost element less than a given value in Segment Tree with lazy propagation.
  • range_query_dynamic_segment_tree - Segment Tree with dynamic node allocation for sparse data.
  • range_query_persistent_segment_tree - Persistent Segment Tree implementation for maintaining query history.
  • range_query_sqrt_decomposition - Square Root Decomposition implementation using bucket technique.
  • range_query_sparse_table_std - Sparse Table for static range minimum/maximum queries in O(1).

• Graph

  • Graph Structures

    • graph_graph - Parent class of the representation of a graph.
    • graph_digraph - Child class representing a directed graph.
    • graph_undigraph - Child class representing an undirected graph.

  • Shortest Path Algorithms

    • graph_dijkstra_std - Implementation of Dijkstra's Algorithm for single-source shortest paths in weighted graphs.
    • graph_dijkstra_path - Dijkstra algorithm that allows path reconstruction.
    • graph_bellman_ford - Bellman-Ford algorithm for single-source shortest paths with negative weights detection.
    • graph_floyd_warshall - Floyd-Warshall algorithm for all-pairs shortest paths.

  • Minimum Spanning Tree

    • graph_kruskal - Kruskal's algorithm for finding Minimum Spanning Tree (MST).

  • Graph Connectivity

    • graph_dsu - Disjoint Set Union (Union-Find) data structure for connected components.
    • graph_scc_kosaraju - Kosaraju's algorithm to find Strongly Connected Components (SCC).

  • Graph Traversal & Ordering

    • graph_toposort_dfs - Topological sorting algorithm using depth-first search.
    • graph_find_cycle - Detect cycles in a graph.

  • Tree Algorithms

    • tree_diameter - Find the diameter (longest path) of a tree.
    • tree_binary_lifting_std - Binary lifting technique for LCA (Lowest Common Ancestor) queries.
    • tree_euler_tour - Euler tour technique for tree queries.
    • tree_subtree_queries - Handle subtree queries efficiently.
    • tree_distance_i - Calculate distances in trees.
    • tree_difference_array_technique_on_trees - Difference array technique adapted for trees.
    • tree_merge_trick_on_trees - Small-to-large merging optimization for tree problems.
    • graph_centroid_decomposition - Centroid decomposition technique for divide-and-conquer on trees.

• Data Structure

  • data_structure_mos_algorithm - Mo's Algorithm for efficient offline range query processing.
  • data_structure_trie_automaton - Prefix Tree (Trie) implementation using automaton-based approach.
  • data_structure_trie_dynamic - Prefix Tree (Trie) implementation with dynamic node allocation.
  • data_structure_tree_order_statistic - Order statistic tree implementation for Set and Map with rank queries.
  • data_structure_median - Data structure for efficient median tracking in dynamic datasets.
  • data_structure_minmax_heap_map - Min-Max heap implementation using map for dual-ended priority operations.
  • data_structure_minmax_heap_multiset - Min-Max heap implementation using multiset for handling duplicates.
  • data_structure_queue_min_max - Queue with O(1) minimum and maximum query operations.
  • data_structure_stack_min_max - Stack with O(1) minimum and maximum query operations.

• Numeric

  • numeric_mint_full - Complete modular arithmetic template with full operations support.
  • numeric_mint_medium - Medium-sized modular arithmetic template with balanced functionality.
  • numeric_mint_compress - Compressed modular arithmetic template with minimal overhead.
  • numeric_mod - Basic modular arithmetic operations and utilities.
  • numeric_mod_fast - Optimized fast modular arithmetic implementation.
  • numeric_bigint - Big integer template for arbitrary precision arithmetic operations.
  • numeric_fastpow - Fast exponentiation algorithm (binary exponentiation) for efficient power computation.

• String

  • Suffix Structures

    • string_suffix_array - Suffix Array construction algorithm for efficient substring operations.

  • Pattern Matching

    • string_kmp_std - Knuth-Morris-Pratt (KMP) algorithm for efficient pattern matching.
    • string_prefix_function - Prefix function (Longest prefix which is also suffix) used in KMP.
    • string_rabin_karp_std - Rabin-Karp algorithm for pattern matching using rolling hash.
    • string_aho_corasick_counter - Aho-Corasick algorithm for counting multiple pattern occurrences.
    • string_aho_corasick_occurrences - Aho-Corasick algorithm for finding all pattern occurrences in text.

  • Hashing

    • string_hashing_static_compress - Compressed string hashing implementation for static strings.
    • string_hashing_dynamic_compress - Compressed string hashing with dynamic updates support.

  • Palindrome & Special Algorithms

    • string_manacher - Manacher's algorithm to find all palindromic substrings in O(n).
    • string_minimum_expression - Find the lexicographically minimum rotation of a string.

  • Z-Algorithm

    • string_z_algorithm_std - Standard Z-algorithm for pattern matching and string analysis.
    • string_z_algorithm_compress - Compressed implementation of Z-algorithm.

  • Utilities

    • string_split - String splitting utility function.

• Combinatorics

  • combinatorics_combinations_permutations - Methods to count the number of combinations and permutations of a set of elements.
  • combinatorics_next_combination - Generate all combinations of k elements from a set of n elements (lexicographic order).
  • combinatorics_all_combinations_backtracking - Generate all combinations of k elements from a set of n elements using backtracking approach.
  • combinatorics_k_th_permutation - Find the k-th permutation in lexicographic order without generating all permutations.
  • combinatorics_ncr_compress - Compressed implementation for computing binomial coefficients (nCr) with modular arithmetic.

• Random

  • random_init - Initialize random number generator with seed.
  • random_permutation - Generate random permutation of integers.
  • random_vector - Generate a random vector with specified size and value range.

• Searches

  • Binary Search
    • searches_binary_search_I - Standard iterative binary search implementation for finding an element in a sorted array.
    • searches_binary_search_II - Alternative binary search implementation using different boundary handling.
    • searches_binary_search_III - Binary search implementation based on Binary Jumping technique for efficient searching.
  • Binary Search on Real Values
    • searches_binary_search_on_real_values_I - Binary search adapted for continuous/floating-point value ranges.
    • searches_binary_search_on_real_values_II - Second implementation of binary search for real numbers with precision handling.
    • searches_binary_search_on_real_values_III - Binary search on real values using Binary Jumping approach.
  • Ternary Search
    • searches_ternary_search_on_integers_I - Ternary search implementation for finding extremum (minimum/maximum) in unimodal integer sequences.
    • searches_ternary_search_on_real_values_I - Ternary search for finding extremum in continuous unimodal functions.
    • searches_ternary_search_on_real_values_II - Alternative ternary search implementation for real-valued unimodal functions with improved precision.

• Techniques

  • Divide and Conquer

    • techniques_divide_and_conquer - Divide and Conquer technique template for solving problems by breaking them into smaller subproblems.

  • Sliding Window

    • techniques_sliding_windows - Sliding Window technique for efficient processing of contiguous subarrays or substrings.

  • Sweep Line

    • techniques_sweep_line - Sweep Line algorithm template for solving geometric and interval-based problems.

  • Two Pointers

    • techniques_two_pointer1_pointer2 - Two Pointers technique for processing two sequences simultaneously.
    • techniques_two_pointer_left_right_boundary - Two Pointers technique using left and right boundary approach for array manipulation.
    • techniques_two_pointers_old_and_new_state - Two Pointers technique for tracking old and new state transitions.
    • techniques_two_pointers_slow_fast - Slow and Fast Pointer technique (Floyd's Algorithm) for cycle detection and linked list problems.

• Input/Output

  • io_print - Print utility for multiple variables with simplified syntax and automatic formatting.
  • io_read_write - Read and write utilities for standard containers (vector, list, forward_list, deque) with streamlined I/O operations.

• Template

  • template_header - Header template with common includes and configurations for C++17.
  • template_std - Standard template for competitive programming in C++17.
  • template_cases - Template for handling multiple test cases with automatic case numbering.
  • template_test_case - Test case snippet for quick testing and validation.
  • template_google - Template optimized for Google Code Jam and Kick Start competitions.
  • template_usaco - Template for USACO (USA Computing Olympiad) with file I/O support.
  • template_std_leetcode - Template adapted for LeetCode problems with class-based structure.
  • template_random - Template for generating random test cases and stress testing.

Credits

• Debugging

  • Some components of the source code of this folder were taken from the-tourist/algo misc > debug.cpp ➡️ By Gennady Korotkevich (Tourist)

• Graph

  • Some components of the source code of graph/graph_digraph.cpp, graph/graph_graph.cpp and graph/undigraph.cpp were taken from the-tourist/algo graph > ... ➡️ By Gennady Korotkevich (Tourist)

• Numeric

  • Some components of the source code of numeric/numeric_mint.cpp were taken from the-tourist/algo numeric > mint.cpp ➡️ By Gennady Korotkevich (Tourist)

  • Some components of the source code of numeric/bitint.cpp were taken from indy256/codelibrary numeric > bitint.cpp ➡️ By Andrei Navumenka

• String

  • Some components of the source code of string/string_suffix_array.cpp were taken from ekzhang/library suffix_array.cpp ➡️ By Eric Zhang

  • Some components of the source code of string/string_hashing.cpp were taken from mavd09/notebook_unal String/Hashing.cpp ➡️ By Osman Jimenez, Manuel Vergara and Víctor Ramírez

  • Some components of the source code of string/string_hashing_dynamic_compress.cpp were taken from ekzhang/library hashing_bit.cpp ➡️ By Eric Zhang

• Query Range

  • Some components of the source code of this folder were taken from the-tourist/algo data > segtree.cpp and sparsetable.cpp ➡️ By Gennady Korotkevich (Tourist)

• Combinatorics

  • Some components of the source code of this folder were taken from indy256/codelibrary cpp > combinatorics > enumerating_combinations.cpp ➡️ By Andrei Navumenka (indy256)