Enhance exponential_search doctests with comprehensive examples

[JesunAhmadUshno]

Summary

Enhanced doctest coverage for exponential_search() with 14 comprehensive test examples covering:

• Valid searches (first, middle, last elements)
• Invalid searches (element not found)
• Edge cases (single-element list)
• Various array sizes (small, large ranges)
• Different value distributions
• Large arrays (up to 100 elements)

Changes

• Added 10 new doctest examples (from 4 → 14 total)
• Improved docstring to explain the exponential doubling strategy
• Added complexity notes (O(log i) where i is the index)
• All tests pass locally

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 enhances documentation and doctest coverage around exponential_search(), and also includes a handful of broader typing/documentation cleanups in other modules.

Changes:

• Expanded exponential_search() docstring with additional explanation, complexity notes, and 10 new doctest examples.
• Migrated some type annotations to PEP 695 generic syntax (jump_search, valid_input) and generalized bipartite graph function typing.
• Minor small refactor in hash table linked-list storage (deque([]) → deque()).

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
searches/jump_search.py	Updates generic typing syntax for jump_search() and removes the old TypeVar declaration.
searches/exponential_search.py	Adds more explanatory docstring text and expands doctest examples from 4 to 14.
machine_learning/linear_discriminant_analysis.py	Updates valid_input() typing to PEP 695 generic syntax and removes TypeVar usage/import.
graphs/check_bipatrite.py	Broadens accepted graph typing to hashable nodes and updates docs/annotations for DFS/BFS variants.
data_structures/hashing/hash_table_with_linked_list.py	Minor simplification of deque construction in _set_value.

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[Copilot]

Docstring says neighbor nodes not appearing as keys are treated as “isolated nodes,” but those nodes can still have incoming edges (they just have no outgoing adjacency list). Consider rewording to “treated as nodes with no outgoing edges/neighbor list” to match the behavior more precisely.

[Copilot]

Docstring says neighbor nodes not appearing as keys are treated as “isolated nodes,” but those nodes can still have incoming edges (they just have no outgoing adjacency list). Consider rewording to “treated as nodes with no outgoing edges/neighbor list” to match the behavior more precisely.

[Copilot]

The PR title/description focus on enhancing exponential_search() doctests, but this PR also changes type syntax in jump_search, updates typing in linear_discriminant_analysis.valid_input, adjusts bipartite graph typing/docs, and tweaks a hash table implementation. Please update the PR title/description to reflect the full scope or split these unrelated changes into separate PRs for easier review and revertability.

[Copilot]

The docstring says exponential search is “particularly efficient for unbounded or infinite arrays,” but this implementation requires a finite, sized list (it uses len() and direct indexing). Consider rephrasing to avoid implying this function works on truly unbounded/infinite collections.

Suggested change

	It's particularly efficient for unbounded or infinite arrays.
	In theory, exponential search is particularly useful for unbounded or very large
	sorted collections, but this implementation operates on finite Python lists.