feat: add needleman–wunsch sequence alignment algorithm (#6707)

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

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

@@ -0,0 +1,60 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * The Needleman–Wunsch algorithm performs global sequence alignment between two strings.
+ * It computes the optimal alignment score using dynamic programming,
+ * given a scoring scheme for matches, mismatches, and gaps.
+ *
+ * Time Complexity: O(n * m)
+ * Space Complexity: O(n * m)
+ */
+public final class NeedlemanWunsch {
+
+    private NeedlemanWunsch() {
+        // Utility Class
+    }
+
+    /**
+     * Computes the Needleman–Wunsch global alignment score between two strings.
+     *
+     * @param s1 the first string
+     * @param s2 the second string
+     * @param matchScore score for a character match
+     * @param mismatchPenalty penalty for a mismatch (should be negative)
+     * @param gapPenalty penalty for inserting a gap (should be negative)
+     * @return the optimal 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[][] dp = new int[n + 1][m + 1];
+
+        // Initialize gap penalties for first row and column
+        for (int i = 0; i <= n; i++) {
+            dp[i][0] = i * gapPenalty;
+        }
+        for (int j = 0; j <= m; j++) {
+            dp[0][j] = j * gapPenalty;
+        }
+
+        // Fill the DP matrix
+        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(Math.max(dp[i - 1][j - 1] + matchOrMismatch, // match/mismatch
+                                        dp[i - 1][j] + gapPenalty // deletion (gap in s2)
+                                        ),
+                    dp[i][j - 1] + gapPenalty // insertion (gap in s1)
+                );
+            }
+        }
+
+        return dp[n][m];
+    }
+}