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