Numerous significant improvements Beta

[lighting9999]

Describe your change:

butterfly_pattern.py

• Add doctests

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

• Added Comparable Protocol
  Implemented a Comparable protocol requiring __lt__ and __gt__ methods to ensure type safety for comparison operations.
• Fixed Type Constraint
  Constrained the generic type T with bound=Comparable to resolve mypy errors about unsupported comparison operations.
• Corrected Import Order
  Reorganized imports to satisfy ruff's I001 check by following PEP8 import sorting rules and adding proper blank lines.

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

• 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".