feat(algorithms, dynamic-programming): unique paths

[BrianLusina]

Describe your change:

Unique Paths in a grid moving only right and down

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• 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 have a URL in its comments that points to Wikipedia or other similar explanation.
• If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

Summary by CodeRabbit

• Documentation
  • Enhanced complexity analysis with comprehensive time and space details.
• Refactor
  • Clarified parameter naming for improved API usability.
  • Optimized performance through memoization support.
  • Restructured algorithmic implementation for better maintainability.
• Tests
  • Reorganized test suite using parameterized testing approach for improved organization.

_{✏️ Tip: You can customize this high-level summary in your review settings.}

[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

The unique paths dynamic programming module is refactored to add lru_cache memoization to the top-down approach, rename parameters from (m, n) to (rows, cols) for clarity, and restructure the bottom-up implementation with explicit DP table initialization. The test suite is consolidated from multiple classes into parameterized tests using shared test cases.

Changes

Cohort / File(s)	Summary
Core Algorithm Updates algorithms/dynamic_programming/unique_paths/__init__.py	Added lru_cache import and decorator for memoization in top-down helper. Renamed unique_paths_bottom_up(m, n) → unique_paths_bottom_up(rows, cols). Restructured bottom-up implementation with explicit DP table initialization, base case setup, and recurrence computation. Expanded docstring with fuller Complexity Analysis section.
Test Consolidation algorithms/dynamic_programming/unique_paths/test_unique_paths.py	Consolidated three separate test classes into parameterized tests. Introduced shared UNIQUE_PATHS_TEST_CASES data structure. Replaced individual test methods with three parameterized equivalents (one per implementation). Reduced duplication and simplified test structure.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~15 minutes

Poem

🐰 Hops through paths with caches in place,
Parameters renamed to set a new pace,
Bottom-up tables built explicit and clear,
Tests unified—duplication's no longer here!
A cleaner code garden, row by column we tread. 🌿

✨ Finishing touches

• 📝 Generate docstrings

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