Describe your change:

butterfly_pattern.py

• Add doctests

shuffled_shift_cipher.py

• Fixed negative modulus in decrypt: Changed (position - self.__shift_key) % -len(self.__key_list) to (position - self.__shift_key) % key_len
• Fixed passcode type consistency: Changed __passcode_creator return type from list to string
• Optimized __str__ method: Simplified return "".join(self.__passcode) to return self.__passcode
• Fixed character appending: Changed temp_list.extend(i) to temp_list.append(i)
• Added length caching: Introduced key_len = len(self.__key_list) in encrypt/decrypt
• Improved variable naming: Renamed loop variable i to char for readability
• Fixed negative shift handling: Ensured modulus uses positive length consistently
• Corrected passcode generation: Added ''.join() to convert list to string
• Removed redundant conversion: Eliminated unnecessary list-to-string conversion
• Fixed doctest compatibility: Maintained backward-compatible encryption/decryption behavior

pascal_triangle.py

• Replaced List → list everywhere
• Changed List[List[int]] → list[list[int]]
• Removed typing module import
• Changed Callable import source: typing → collections.abc
• Alphabetized imports: collections.abc before timeit
• Fixed bracket issues in list comprehensions
• Added missing closing brackets
• Removed redundant parentheses
• Simplified elif → if where possible
• Renamed variables:
  above_to_left_elt → above_left
above_to_right_elt → above_right
• Improved spacing around operators

sum_of_digits.py

• Moved imports to top:

from collections.abc import Callable
from timeit import timeit

• Fixed recursive function:

return n if n < 10 else n % 10 + sum_of_digits_recursion(n // 10)

minimum_spanning_tree_kruskal2.py

• Removed Generic and TypeVar imports since they're no longer needed
• Updated class declarations to use new-style generics with [T]
• Removed the top-level T = TypeVar("T") as it's now redundant

lru_cache.py

• Removed top-level TypeVar definitions for T and U since they're no longer needed
• Converted class definitions to use new type parameter syntax:
  • class DoubleLinkedListNode(Generic[T, U]) → class DoubleLinkedListNode[T, U]
  • class DoubleLinkedList(Generic[T, U]) → class DoubleLinkedList[T, U]
  • class LRUCache(Generic[T, U]) → class LRUCache[T, U]

lfu_cache.py

• UpdatedDoubleLinkedListNode,DoubleLinkedList,andLFUCache to use modern Python 3.12+ generic syntax.
• Replaced class ClassName(Generic[T, U]) with cleaner class ClassName[T, U].
• Maintained identical functionality while fixing flake8 UP046 errors.

stack_with_doubly_linked_list.py

• Removed the Generic import and TypeVar declaration
• Updated class definitions to use the new [T] syntax instead of subclassing Generic[T]

skew_heap.py

• Fixed "Unsupported left operand type" error by removing generic type parameter T
• Replaced T with Any type throughout the implementation
• Added customizable comparison function parameter comp to constructor
• Default comparison remains lambda a, b: a < b for min-heap behavior
• Passed comparison function to all merge operations
• Updated type annotations to modern X | None syntax
• Organized imports according to Python standards
• Maintained all original functionality and doctests
• Enabled both min-heap and max-heap configurations
• Preserved O(log n) time complexity for operations
• Removed unused imports and cleaned up type hints

test_digital_image_processing.py

• Replaced array() with np.array(): Due to removal of from numpy import array
• Replaced uint8 with np.uint8: Due to removal of from numpy import uint8

minimum_spanning_tree_prims2.py

• Fixed missing colon in for loop syntax
• Changed Optional[T] to T | None
• Replaced dict comprehensions with dict.fromkeys()
• Corrected weight calculation in Prim's algorithm
• Optimized priority queue initialization
• Added precise type annotations
• Improved neighbor iteration using items()
• Updated docstring tests and expected results
• Fixed import ordering issues
• Modernize the code to use Python 3.12's native generics syntax (PEP 695)
• Remove outdated typing module dependencies

matrix_class.py

• Fixed __hash__ type conflict with base class
• Added proper type annotations throughout
• Resolved float/int type inconsistencies
• Corrected indentation issues (E111)
• Fixed line length violations (E501)
• Resolved syntax errors from improper indentation
• Added @final decorator to mark class as unhashable
• Removed explicit __hash__ assignment
• Replaced integer values 0/1 with 0.0/1.0 in identity matrix
• Added tolerance check (1e-10) for determinant comparison
• Removed unnecessary int() conversion
• Changed all element types from int to float
• Used modern union syntax (X | Y) instead of Union
• Added proper return type declarations
• Replaced list concatenation with unpacking in:
  • add_row() method
  • add_column() method
• Leveraged @final decorator
• Utilized __future__ annotations

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".