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

[AliAlimohammadi]

@dynamitechetan, This PR is ready to merge.