feat: add Smith-Waterman algorithm for local sequence alignment

dynamic_programming/smith_waterman.cpp

@@ -0,0 +1,322 @@
+/**
+ * @file
+ * @brief Implementation of the [Smith-Waterman
+ * algorithm](https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm)
+ * for local sequence alignment
+ *
+ * @details
+ * 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, which identifies the best
+ * matching subsequence rather than aligning entire sequences.
+ *
+ * The algorithm works by:
+ * 1. Creating a scoring matrix where each cell represents the maximum
+ *    alignment score ending at that position
+ * 2. Using match, mismatch, and gap penalties to calculate scores
+ * 3. Allowing scores to reset to 0 (ensuring local rather than global
+ *    alignment)
+ * 4. Tracing back from the highest scoring position to reconstruct the
+ *    alignment
+ *
+ * ### Algorithm
+ * Given two sequences S1 and S2 of lengths m and n:
+ * - Initialize a (m+1) × (n+1) matrix H with H[i][0] = H[0][j] = 0
+ * - For each cell H[i][j]:
+ *   - H[i][j] = max(0, H[i-1][j-1] + match/mismatch_score,
+ *                   H[i-1][j] + gap_penalty, H[i][j-1] + gap_penalty)
+ * - Find the maximum value in H matrix
+ * - Traceback from maximum value to cell with value 0
+ *
+ * Time Complexity: O(m × n) where m and n are the lengths of the sequences
+ * Space Complexity: O(m × n) for the scoring matrix
+ *
+ * @author [Ali Alimohammadi](https://github.com/AliAlimohammadi)
+ */
+
+#include <algorithm>  /// for std::max
+#include <cassert>    /// for assert
+#include <iostream>   /// for IO operations
+#include <string>     /// for std::string
+#include <utility>    /// for std::pair
+#include <vector>     /// for std::vector
+
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+/**
+ * @namespace smith_waterman
+ * @brief Functions for the Smith-Waterman algorithm
+ */
+namespace smith_waterman {
+
+/**
+ * @enum Direction
+ * @brief Direction indicators for traceback in the scoring matrix
+ */
+enum Direction {
+    NONE = 0,      ///< No direction (score is 0)
+    DIAGONAL = 1,  ///< Match or mismatch
+    UP = 2,        ///< Gap in subject sequence
+    LEFT = 3       ///< Gap in query sequence
+};
+
+/**
+ * @brief Calculate the score for a character pair
+ * 
+ * @param a First character
+ * @param b Second character
+ * @param match_score Score for matching characters (typically positive)
+ * @param mismatch_score Score for mismatching characters (typically negative)
+ * @return int The calculated score
+ */
+int score_function(char a, char b, int match_score, int mismatch_score) {
+    return (a == b) ? match_score : mismatch_score;
+}
+
+/**
+ * @brief Compute the Smith-Waterman scoring matrix
+ * @details
+ * The Smith-Waterman algorithm uses dynamic programming to find the optimal
+ * local alignment. The recurrence relation is:
+ * 
+ * H(i,j) = max {
+ *     H(i-1,j-1) + s(a_i, b_j),  // diagonal: match/mismatch
+ *     H(i-1,j) + gap_score,      // up: gap in subject
+ *     H(i,j-1) + gap_score,      // left: gap in query
+ *     0                          // start new alignment
+ * }
+ * 
+ * Additionally stores direction information for efficient traceback.
+ * When multiple paths have equal scores, the algorithm prioritizes diagonal
+ * moves, then up, then left.
+ * 
+ * @param query First sequence
+ * @param subject Second sequence
+ * @param match_score Score for matching characters (default: 2)
+ * @param mismatch_score Penalty for mismatching characters (default: -1)
+ * @param gap_score Penalty for gaps (default: -1)
+ * @return std::pair of scoring matrix and direction matrix
+ */
+std::pair<std::vector<std::vector<int>>, std::vector<std::vector<Direction>>>
+smith_waterman(const std::string &query, const std::string &subject,
+               int match_score = 2, int mismatch_score = -1,
+               int gap_score = -1) {
+    size_t m = query.length();
+    size_t n = subject.length();
+
+    // Initialize scoring matrix with zeros
+    std::vector<std::vector<int>> score(m + 1, std::vector<int>(n + 1, 0));
+
+    // Initialize direction matrix for traceback
+    std::vector<std::vector<Direction>> direction(m + 1, 
+                                                   std::vector<Direction>(n + 1, NONE));
+
+    // Fill matrices using dynamic programming
+    for (size_t i = 1; i <= m; ++i) {
+        for (size_t j = 1; j <= n; ++j) {
+            // Calculate scores from three possible sources
+            int match_mismatch = score[i - 1][j - 1] + 
+                score_function(query[i - 1], subject[j - 1], 
+                              match_score, mismatch_score);
+            int delete_gap = score[i - 1][j] + gap_score;
+            int insert_gap = score[i][j - 1] + gap_score;
+
+            // Take maximum of all options, including 0 (local alignment)
+            int max_score = std::max({match_mismatch, delete_gap, insert_gap, 0});
+            score[i][j] = max_score;
+
+            // Store direction for traceback
+            if (max_score == 0) {
+                direction[i][j] = NONE;
+            } else if (max_score == match_mismatch) {
+                direction[i][j] = DIAGONAL;
+            } else if (max_score == delete_gap) {
+                direction[i][j] = UP;
+            } else {
+                direction[i][j] = LEFT;
+            }
+        }
+    }
+
+    return {score, direction};
+}
+
+/**
+ * @brief Perform traceback to reconstruct the optimal local alignment
+ * @details
+ * Starting from the cell with maximum score, follows the direction matrix
+ * backwards until reaching a cell with score 0, reconstructing the alignment.
+ * 
+ * @param score The scoring matrix from smith_waterman()
+ * @param direction The direction matrix from smith_waterman()
+ * @param query First sequence
+ * @param subject Second sequence
+ * @return std::pair<std::string, std::string> The aligned sequences
+ */
+std::pair<std::string, std::string>
+traceback(const std::vector<std::vector<int>> &score,
+          const std::vector<std::vector<Direction>> &direction,
+          const std::string &query, const std::string &subject) {
+    // Find the cell with maximum score
+    int max_value = 0;
+    size_t i_max = 0;
+    size_t j_max = 0;
+
+    for (size_t i = 0; i < score.size(); ++i) {
+        for (size_t j = 0; j < score[i].size(); ++j) {
+            if (score[i][j] > max_value) {
+                max_value = score[i][j];
+                i_max = i;
+                j_max = j;
+            }
+        }
+    }
+
+    // If no significant alignment found, return empty strings
+    if (max_value == 0) {
+        return {"", ""};
+    }
+
+    // Traceback from maximum score position
+    std::string align1;
+    std::string align2;
+    size_t i = i_max;
+    size_t j = j_max;
+
+    // Follow direction matrix until we hit NONE (score of 0)
+    while (i > 0 && j > 0 && direction[i][j] != NONE) {
+        switch (direction[i][j]) {
+            case DIAGONAL:
+                // Match or mismatch
+                align1 = query[i - 1] + align1;
+                align2 = subject[j - 1] + align2;
+                --i;
+                --j;
+                break;
+            case UP:
+                // Gap in subject
+                align1 = query[i - 1] + align1;
+                align2 = '-' + align2;
+                --i;
+                break;
+            case LEFT:
+                // Gap in query
+                align1 = '-' + align1;
+                align2 = subject[j - 1] + align2;
+                --j;
+                break;
+            default:
+                break;
+        }
+    }
+
+    return {align1, align2};
+}
+
+}  // namespace smith_waterman
+}  // namespace dynamic_programming
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    using dynamic_programming::smith_waterman::smith_waterman;
+    using dynamic_programming::smith_waterman::traceback;
+
+    // Test 1: Simple exact match
+    auto [score1, dir1] = smith_waterman("AGCT", "AGCT");
+    auto result1 = traceback(score1, dir1, "AGCT", "AGCT");
+    assert(result1.first == "AGCT");
+    assert(result1.second == "AGCT");
+    std::cout << "Test 1 passed: Simple exact match\n";
+
+    // Test 2: Partial match
+    auto [score2, dir2] = smith_waterman("AGCT", "AGT");
+    auto result2 = traceback(score2, dir2, "AGCT", "AGT");
+    assert(!result2.first.empty());
+    assert(!result2.second.empty());
+    std::cout << "Test 2 passed: Partial match\n";
+
+    // Test 3: Traceback verification
+    auto [score3, dir3] = smith_waterman("AGCT", "AGCT");
+    auto result3 = traceback(score3, dir3, "AGCT", "AGCT");
+    assert(result3.first == "AGCT");
+    assert(result3.second == "AGCT");
+    std::cout << "Test 3 passed: Traceback verification\n";
+
+    // Test 4: No match scenario
+    auto [score4, dir4] = smith_waterman("AAAA", "TTTT");
+    auto result4 = traceback(score4, dir4, "AAAA", "TTTT");
+    assert(result4.first.empty());
+    assert(result4.second.empty());
+    std::cout << "Test 4 passed: No match scenario\n";
+
+    // Test 5: Empty string handling
+    auto [score5, dir5] = smith_waterman("", "AGCT");
+    auto result5 = traceback(score5, dir5, "", "AGCT");
+    assert(result5.first.empty());
+    assert(result5.second.empty());
+    std::cout << "Test 5 passed: Empty string handling\n";
+
+    // Test 6: Sequences with gaps
+    auto [score6, dir6] = smith_waterman("AGCT", "AGT");
+    auto result6 = traceback(score6, dir6, "AGCT", "AGT");
+    assert(!result6.first.empty());
+    assert(!result6.second.empty());
+    assert(result6.first.length() == result6.second.length());
+    std::cout << "Test 6 passed: Sequences with gaps\n";
+
+    // Test 7: Custom scoring parameters
+    auto [score7, dir7] = smith_waterman("AGCT", "AGCT", 3, -2, -2);
+    auto result7 = traceback(score7, dir7, "AGCT", "AGCT");
+    assert(result7.first == "AGCT");
+    assert(result7.second == "AGCT");
+    std::cout << "Test 7 passed: Custom scoring parameters\n";
+
+    // Test 8: Case sensitivity
+    auto [score8, dir8] = smith_waterman("agct", "AGCT");
+    auto result8 = traceback(score8, dir8, "agct", "AGCT");
+    assert(result8.first.empty());
+    assert(result8.second.empty());
+    std::cout << "Test 8 passed: Case sensitivity\n";
+
+    std::cout << "\nAll tests passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    std::cout << "Smith-Waterman Algorithm for Local Sequence Alignment\n";
+    std::cout << "======================================================\n\n";
+
+    // Example usage
+    std::string query = "GCATGCT";
+    std::string subject = "GATTACA";
+
+    std::cout << "Query:   " << query << "\n";
+    std::cout << "Subject: " << subject << "\n\n";
+
+    auto [score_matrix, direction_matrix] = 
+        dynamic_programming::smith_waterman::smith_waterman(query, subject);
+    auto alignment = 
+        dynamic_programming::smith_waterman::traceback(score_matrix, 
+                                                       direction_matrix,
+                                                       query, subject);
+
+    std::cout << "Optimal Local Alignment:\n";
+    std::cout << "Query:   " << alignment.first << "\n";
+    std::cout << "Subject: " << alignment.second << "\n\n";
+
+    // Run tests
+    std::cout << "Running tests...\n";
+    std::cout << "================\n";
+    test();
+
+    return 0;
+}