feat: add smith-waterman sequence alignment algorithm (#6708)

Co-authored-by: a <alexanderklmn@gmail.com>

src/main/java/com/thealgorithms/dynamicprogramming/SmithWaterman.java

@@ -0,0 +1,56 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Smith–Waterman algorithm for local sequence alignment.
+ * Finds the highest scoring local alignment between substrings of two sequences.
+ *
+ * Time Complexity: O(n * m)
+ * Space Complexity: O(n * m)
+ */
+public final class SmithWaterman {
+
+    private SmithWaterman() {
+        // Utility Class
+    }
+
+    /**
+     * Computes the Smith–Waterman local alignment score between two strings.
+     *
+     * @param s1 first string
+     * @param s2 second string
+     * @param matchScore score for a match
+     * @param mismatchPenalty penalty for mismatch (negative)
+     * @param gapPenalty penalty for insertion/deletion (negative)
+     * @return the maximum local alignment score
+     */
+    public static int align(String s1, String s2, int matchScore, int mismatchPenalty, int gapPenalty) {
+        if (s1 == null || s2 == null) {
+            throw new IllegalArgumentException("Input strings must not be null.");
+        }
+
+        int n = s1.length();
+        int m = s2.length();
+        int maxScore = 0;
+
+        int[][] dp = new int[n + 1][m + 1];
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= m; j++) {
+                int matchOrMismatch = (s1.charAt(i - 1) == s2.charAt(j - 1)) ? matchScore : mismatchPenalty;
+
+                dp[i][j] = Math.max(0,
+                    Math.max(Math.max(dp[i - 1][j - 1] + matchOrMismatch, // match/mismatch
+                                 dp[i - 1][j] + gapPenalty // deletion
+                                 ),
+                        dp[i][j - 1] + gapPenalty // insertion
+                        ));
+
+                if (dp[i][j] > maxScore) {
+                    maxScore = dp[i][j];
+                }
+            }
+        }
+
+        return maxScore;
+    }
+}