Added Smith-Waterman Algorithm

String Algorithms/Smith-Waterman Algorithm/Program.c

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+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+
+#define MAX(a, b) ((a) > (b) ? (a) : (b))
+#define MAX3(a, b, c) (MAX(MAX(a, b), c))
+
+// Function to find the maximum of 3 integers (match, insert, delete)
+
+// Function to initialize a 2D array for the scoring matrix
+int** createMatrix(int rows, int cols) {
+    int** matrix = (int**)malloc(rows * sizeof(int*));
+    for (int i = 0; i < rows; i++) {
+        matrix[i] = (int*)malloc(cols * sizeof(int));
+    }
+    return matrix;
+}
+
+// Function to perform the Smith-Waterman algorithm for local sequence alignment
+void smithWaterman(char* seq1, char* seq2, int matchScore, int mismatchPenalty, int gapPenalty) {
+    int len1 = strlen(seq1);
+    int len2 = strlen(seq2);
+
+    // Initialize scoring matrix with extra row and column for initial zeroes
+    int** scoreMatrix = createMatrix(len1 + 1, len2 + 1);
+
+    // Initialize maximum score to zero (for local alignment)
+    int maxScore = 0;
+    int endRow = 0, endCol = 0;
+
+    // Fill in the scoring matrix
+    for (int i = 0; i <= len1; i++) {
+        for (int j = 0; j <= len2; j++) {
+            if (i == 0 || j == 0) {
+                // Set first row and first column to 0
+                scoreMatrix[i][j] = 0;
+            } else {
+                // Calculate match, delete, and insert scores
+                int match = scoreMatrix[i - 1][j - 1] + (seq1[i - 1] == seq2[j - 1] ? matchScore : mismatchPenalty);
+                int delete = scoreMatrix[i - 1][j] + gapPenalty;
+                int insert = scoreMatrix[i][j - 1] + gapPenalty;
+
+                // Get the maximum score for this cell (including zero for local alignment)
+                scoreMatrix[i][j] = MAX3(0, match, MAX(delete, insert));
+
+                // Track the maximum score and the position for traceback
+                if (scoreMatrix[i][j] > maxScore) {
+                    maxScore = scoreMatrix[i][j];
+                    endRow = i;
+                    endCol = j;
+                }
+            }
+        }
+    }
+
+    // Output the maximum score
+    printf("Maximum Alignment Score: %d\n", maxScore);
+
+    // Traceback to find the aligned sequences
+    char alignedSeq1[100], alignedSeq2[100];
+    int idx1 = 0, idx2 = 0;
+
+    while (endRow > 0 && endCol > 0 && scoreMatrix[endRow][endCol] > 0) {
+        if (seq1[endRow - 1] == seq2[endCol - 1]) {
+            alignedSeq1[idx1++] = seq1[endRow - 1];
+            alignedSeq2[idx2++] = seq2[endCol - 1];
+            endRow--;
+            endCol--;
+        } else if (scoreMatrix[endRow][endCol] == scoreMatrix[endRow - 1][endCol] + gapPenalty) {
+            alignedSeq1[idx1++] = seq1[endRow - 1];
+            alignedSeq2[idx2++] = '-';
+            endRow--;
+        } else {
+            alignedSeq1[idx1++] = '-';
+            alignedSeq2[idx2++] = seq2[endCol - 1];
+            endCol--;
+        }
+    }
+
+    // Reverse the aligned sequences
+    alignedSeq1[idx1] = '\0';
+    alignedSeq2[idx2] = '\0';
+    strrev(alignedSeq1);
+    strrev(alignedSeq2);
+
+    // Print the aligned sequences
+    printf("Aligned Sequence 1: %s\n", alignedSeq1);
+    printf("Aligned Sequence 2: %s\n", alignedSeq2);
+
+    // Free allocated memory for the matrix
+    for (int i = 0; i <= len1; i++) {
+        free(scoreMatrix[i]);
+    }
+    free(scoreMatrix);
+}
+
+int main() {
+    char seq1[] = "ACACACTA";
+    char seq2[] = "AGCACACA";
+    int matchScore = 2;
+    int mismatchPenalty = -1;
+    int gapPenalty = -2;
+
+    printf("Sequence 1: %s\n", seq1);
+    printf("Sequence 2: %s\n", seq2);
+
+    // Call the Smith-Waterman function
+    smithWaterman(seq1, seq2, matchScore, mismatchPenalty, gapPenalty);
+
+    return 0;
+}

String Algorithms/Smith-Waterman Algorithm/README.md

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+# Smith-Waterman Algorithm
+
+## Description
+
+The Smith-Waterman algorithm is a dynamic programming algorithm used for local sequence alignment. It finds the optimal alignment of a subset of one sequence against another. Unlike global alignment algorithms, Smith-Waterman focuses on finding the most similar region between two sequences, making it ideal for biological applications such as DNA or protein sequence matching.
+
+### Problem Definition
+
+Given:
+- A sequence `seq1` of length `m`
+- A sequence `seq2` of length `n`
+
+Objective:
+- Find the best local alignment of `seq1` and `seq2`
+
+### Algorithm Overview
+
+1. **Initialization**:
+   - Create a scoring matrix with dimensions `(m+1) x (n+1)` initialized to zeros.
+
+2. **Scoring**:
+   - For each cell in the matrix, calculate the score based on the match/mismatch and gap penalties.
+   - Track the maximum score and its position.
+
+3. **Traceback**:
+   - Start from the cell with the highest score and trace back to reconstruct the optimal local alignment.
+
+### Key Features
+
+- Finds local alignments by allowing partial overlaps of sequences.
+- Uses a scoring system for matches, mismatches, and gaps.
+- Backtracks from the cell with the highest score to find the optimal alignment.
+- Time complexity: O(mn), where `m` and `n` are the lengths of the sequences.
+
+### Time Complexity
+
+- **Worst Case**: O(mn), where `m` is the length of `seq1` and `n` is the length of `seq2`
+
+### Space Complexity
+
+- O(mn), since a matrix of size `(m+1) x (n+1)` is required to store the scores.
+
+## Implementation
+
+The implementation in C demonstrates the Smith-Waterman algorithm for local sequence alignment. It includes:
+
+1. A function to initialize and populate the scoring matrix.
+2. The Smith-Waterman function to compute the alignment score and perform the traceback to find the aligned sequences.
+3. A demonstration of how to use the algorithm on two sample sequences.
+
+## Usage
+
+Compile the program and run it. The example in the `main` function demonstrates how the Smith-Waterman algorithm can be used to align two sequences.
+
+```bash
+gcc smith_waterman.c -o smith_waterman
+./smith_waterman
+```
+
+## Limitations
+
+- The algorithm works for short to medium-length sequences but can be memory-intensive for very long sequences due to the need for a full scoring matrix.
+- The current implementation assumes equal penalties for all types of mismatches and gaps. These can be adjusted as needed for specific applications.
+
+## Extensions
+
+- The algorithm can be extended by using affine gap penalties, which distinguish between opening and extending a gap.
+- It can also be adapted for approximate matching in non-biological contexts, such as comparing textual or binary data.