feat: add Smith-Waterman algorithm for local sequence alignment

[AliAlimohammadi]

Description

This PR adds the Smith-Waterman algorithm implementation to the dynamic programming module.

Algorithm Overview

The Smith-Waterman algorithm is a dynamic programming algorithm for determining similar regions between two sequences (nucleotide or protein sequences). It performs local sequence alignment and is particularly useful in bioinformatics.

Key Features:

• Local alignment: Finds the best matching subsequence rather than aligning entire sequences
• Dynamic programming: O(m×n) time complexity where m and n are sequence lengths
• Configurable scoring: Supports custom match, mismatch, and gap penalties
• Case-insensitive: Automatically handles uppercase and lowercase inputs

Implementation Details:

• score_function: Calculates alignment scores for character pairs
• smith_waterman: Builds the scoring matrix using dynamic programming
• traceback: Reconstructs the optimal alignment from the scoring matrix

Testing

The implementation includes comprehensive tests:

• ✅ Multiple test cases with different sequence pairs
• ✅ Edge cases (empty sequences)
• ✅ Case-insensitive matching
• ✅ Traceback verification
• ✅ Score function validation

All tests pass:

cargo test smith_waterman

Documentation

• Detailed module-level documentation with algorithm overview
• Function-level documentation with examples
• References to original paper and Wikipedia

Checklist

• Algorithm implementation is correct
• All tests pass locally
• Code follows Rust best practices
• Documentation is comprehensive
• No clippy warnings
• Code is formatted with cargo fmt
• Added to appropriate module (dynamic_programming)

References

• Smith, T.F., Waterman, M.S. (1981). "Identification of Common Molecular Subsequences"
• Wikipedia: Smith-Waterman algorithm

[codecov-commenter]

Codecov Report

❌ Patch coverage is 93.71069% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.46%. Comparing base (700fd3a) to head (7a849ee).

Files with missing lines	Patch %	Lines
src/dynamic_programming/smith_waterman.rs	93.71%	10 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #960      +/-   ##
==========================================
- Coverage   95.48%   95.46%   -0.02%     
==========================================
  Files         335      336       +1     
  Lines       21797    21956     +159     
==========================================
+ Hits        20813    20961     +148     
- Misses        984      995      +11     

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[AliAlimohammadi]

@siriak, This is ready to merge.

[Copilot]

Pull request overview

This PR adds an implementation of the Smith-Waterman algorithm for local sequence alignment to the dynamic programming module. The Smith-Waterman algorithm is a well-known bioinformatics algorithm for finding optimal local alignments between sequences using dynamic programming with O(m×n) time and space complexity.

Key Changes:

• Implements Smith-Waterman algorithm with configurable scoring parameters (match, mismatch, gap penalties)
• Provides traceback functionality to reconstruct optimal alignments from the scoring matrix
• Includes comprehensive test coverage with multiple test cases
• Case-insensitive sequence handling

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 6 comments.

File	Description
src/dynamic_programming/smith_waterman.rs	New implementation of Smith-Waterman algorithm with score matrix generation, traceback, and helper scoring function
src/dynamic_programming/mod.rs	Module and public API declarations for smith_waterman functions
DIRECTORY.md	Documentation entry for Smith-Waterman algorithm, maintaining alphabetical order

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[siriak]

Please check the comments and address if they are relevant

[AliAlimohammadi]

Review completed.