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

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

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

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+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];
+    }
+}

src/test/java/com/thealgorithms/dynamicprogramming/NeedlemanWunschTest.java

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+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+/**
+ * Unit Tests for the {@code NeedlemanWunsch} class
+ */
+class NeedlemanWunschTest {
+
+    @Test
+    void testIdenticalStrings() {
+        int score = NeedlemanWunsch.align("GATTACA", "GATTACA", 1, -1, -2);
+        assertEquals(7, score); // All matches, 7*1
+    }
+
+    @Test
+    void testSimpleMismatch() {
+        int score = NeedlemanWunsch.align("GATTACA", "GACTATA", 1, -1, -2);
+        assertEquals(3, score);
+    }
+
+    @Test
+    void testInsertion() {
+        int score = NeedlemanWunsch.align("GATTACA", "GATACA", 1, -1, -2);
+        // One deletion (gap penalty)
+        assertEquals(4, score);
+    }
+
+    @Test
+    void testEmptyStrings() {
+        assertEquals(0, NeedlemanWunsch.align("", "", 1, -1, -2));
+    }
+
+    @Test
+    void testOneEmpty() {
+        assertEquals(-14, NeedlemanWunsch.align("GATTACA", "", 1, -1, -2)); // 7 gaps × -2
+    }
+
+    @Test
+    void testGapHeavyAlignment() {
+        int score = NeedlemanWunsch.align("AAAA", "AA", 1, -1, -2);
+        assertEquals(-2, score); // Two matches (2*1) + two gaps (2*-2)
+    }
+
+    @ParameterizedTest
+    @CsvSource({"null,ABC", "ABC,null", "null,null"})
+    void testNullInputs(String s1, String s2) {
+        // Interpret "null" literal as Java null
+        String first = "null".equals(s1) ? null : s1;
+        String second = "null".equals(s2) ? null : s2;
+
+        IllegalArgumentException ex = assertThrows(IllegalArgumentException.class, () -> NeedlemanWunsch.align(first, second, 1, -1, -2));
+        assertEquals("Input strings must not be null.", ex.getMessage());
+    }
+}