Enhance double_linear_search doctests with comprehensive examples

[JesunAhmadUshno]

Summary

Enhanced doctest coverage for double_linear_search() with 17 comprehensive test examples covering:

• Valid searches (first, middle, last element, various positions)
• Invalid searches (element not found)
• Edge cases (empty list, single-element list)
• Duplicates (all elements same, finding first occurrence)
• Negative numbers and various array sizes
• Algorithm behavior explanation in docstring

Changes

• Added 13 new doctest examples (from 4 → 17 total)
• Improved docstring to explain the two-pointer search approach
• All tests pass locally: python -m doctest -v double_linear_search.py

Checklist

• I have read the CONTRIBUTING.md file
• This is my own work and not plagiarized
• My work will be distributed under the MIT License once merged
• My submission follows the coding style and standards of this repository
• I have tested my changes locally
• All doctest examples pass
• Code passes ruff linting

[Copilot]

Pull request overview

This PR claims to enhance doctest coverage for double_linear_search() but actually contains multiple unrelated changes across different files. The main changes include:

Changes:

• Added 13 new doctest examples to double_linear_search() (lines 26-63)
• Migrated several files from TypeVar to PEP 695 generic syntax
• Updated type hints in check_bipatrite.py to be more generic
• Minor code cleanup in hash_table_with_linked_list.py

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
searches/double_linear_search.py	Enhanced docstring with 13 new doctests covering edge cases, duplicates, and negative numbers
searches/jump_search.py	Migrated from TypeVar to PEP 695 syntax (def jump_search[T: Comparable])
machine_learning/linear_discriminant_analysis.py	Migrated valid_input function from TypeVar to PEP 695 syntax
graphs/check_bipatrite.py	Improved type hints to use Mapping[Hashable, Iterable[Hashable]] and removed FIXME comments
data_structures/hashing/hash_table_with_linked_list.py	Changed deque([]) to deque() for cleaner initialization

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[Copilot]

The PR description states "Enhanced doctest coverage for double_linear_search()" but this file contains unrelated changes migrating from TypeVar to PEP 695 generic syntax. This change (along with similar changes in machine_learning/linear_discriminant_analysis.py, graphs/check_bipatrite.py, and data_structures/hashing/hash_table_with_linked_list.py) should either be mentioned in the PR description or submitted as a separate PR focused on type annotation modernization.