feat: add Smith-Waterman algorithm for local sequence alignment

[AliAlimohammadi]

Description

This PR adds the Smith-Waterman algorithm implementation to the dynamic_programming directory.

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
• Traceback functionality: Reconstructs the optimal alignment

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

Code Quality

The implementation follows TheAlgorithms/C-Plus-Plus standards:

• ✅ Doxygen-style documentation
• ✅ Namespace organization (dynamic_programming::smith_waterman)
• ✅ Modern C++ practices (C++11 and above)
• ✅ STL usage (no bits/stdc++.h)
• ✅ Comprehensive self-tests (8 test cases)
• ✅ Example usage in main function

Testing

The implementation includes 8 comprehensive test cases:

• ✅ Simple exact match
• ✅ Partial match
• ✅ Traceback verification
• ✅ No match scenario
• ✅ Empty string handling
• ✅ Sequences with gaps
• ✅ Custom scoring parameters
• ✅ Case sensitivity

All tests pass:

g++ -std=c++11 -O2 -Wall dynamic_programming/smith_waterman.cpp -o smith_waterman
./smith_waterman

Documentation

• Detailed file-level Doxygen documentation
• Function-level documentation with parameters and returns
• Algorithm explanation with complexity analysis
• References to original paper and Wikipedia

Checklist

• Algorithm implementation is correct
• All tests pass locally
• Code follows C++ best practices
• Uses standard library (no bits/stdc++.h)
• Organized with namespace
• Doxygen documentation complete
• No compiler warnings
• Added to appropriate directory (dynamic_programming)
• Example usage provided

References

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

[github-actions]

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[Copilot]

Pull request overview

This PR introduces a Smith-Waterman algorithm implementation for local sequence alignment in bioinformatics applications. The implementation uses dynamic programming to find optimal local alignments between two sequences with configurable scoring parameters.

Key changes:

• Adds a complete Smith-Waterman algorithm with matrix scoring and traceback functionality
• Includes 8 test cases covering various scenarios including edge cases
• Provides comprehensive Doxygen documentation following project standards

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[Copilot]

Pull request overview

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

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[AliAlimohammadi]

@poyea, revisions completed.

[AliAlimohammadi]

@realstealthninja, this is ready to be merged.

[realstealthninja]

I think we need to think about AI assisted contributions and AI assisted reviewing before this can be merged. An official policy needs to be drafted and discussed, before any commits be entered into the repository.