Add Z-Algorithm for Linear-Time String Pattern Matching (#7124)

* Add Z-Algorithm (string pattern matching) with tests

* Add Z-Algorithm (string pattern matching) with tests

* Add Z-Algorithm (string pattern matching) with tests

* Fix checkstyle errors for ZAlgorithm

* Fix: clang-format and checkstyle compliance for ZAlgorithm

Author: Utkarsh-patel26

DIRECTORY.md

@@ -822,6 +822,7 @@
           - 📄 [Upper](src/main/java/com/thealgorithms/strings/Upper.java)
           - 📄 [ValidParentheses](src/main/java/com/thealgorithms/strings/ValidParentheses.java)
           - 📄 [WordLadder](src/main/java/com/thealgorithms/strings/WordLadder.java)
+          - 📄 [ZAlgorithm](src/main/java/com/thealgorithms/strings/ZAlgorithm.java)
           - 📁 **zigZagPattern**
             - 📄 [ZigZagPattern](src/main/java/com/thealgorithms/strings/zigZagPattern/ZigZagPattern.java)
         - 📁 **tree**
@@ -1579,6 +1580,7 @@
           - 📄 [UpperTest](src/test/java/com/thealgorithms/strings/UpperTest.java)
           - 📄 [ValidParenthesesTest](src/test/java/com/thealgorithms/strings/ValidParenthesesTest.java)
           - 📄 [WordLadderTest](src/test/java/com/thealgorithms/strings/WordLadderTest.java)
+          - 📄 [ZAlgorithmTest](src/test/java/com/thealgorithms/strings/ZAlgorithmTest.java)
           - 📁 **zigZagPattern**
             - 📄 [ZigZagPatternTest](src/test/java/com/thealgorithms/strings/zigZagPattern/ZigZagPatternTest.java)
         - 📁 **tree**

src/main/java/com/thealgorithms/strings/ZAlgorithm.java

@@ -0,0 +1,48 @@
+/*
+ * https://en.wikipedia.org/wiki/Z-algorithm
+ */
+package com.thealgorithms.strings;
+
+public final class ZAlgorithm {
+
+    private ZAlgorithm() {
+        throw new UnsupportedOperationException("Utility class");
+    }
+
+    public static int[] zFunction(String s) {
+        int n = s.length();
+        int[] z = new int[n];
+        int l = 0;
+        int r = 0;
+
+        for (int i = 1; i < n; i++) {
+            if (i <= r) {
+                z[i] = Math.min(r - i + 1, z[i - l]);
+            }
+
+            while (i + z[i] < n && s.charAt(z[i]) == s.charAt(i + z[i])) {
+                z[i]++;
+            }
+
+            if (i + z[i] - 1 > r) {
+                l = i;
+                r = i + z[i] - 1;
+            }
+        }
+
+        return z;
+    }
+
+    public static int search(String text, String pattern) {
+        String s = pattern + "$" + text;
+        int[] z = zFunction(s);
+        int p = pattern.length();
+
+        for (int i = 0; i < z.length; i++) {
+            if (z[i] == p) {
+                return i - p - 1;
+            }
+        }
+        return -1;
+    }
+}

src/test/java/com/thealgorithms/strings/ZAlgorithmTest.java

@@ -0,0 +1,25 @@
+package com.thealgorithms.strings;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class ZAlgorithmTest {
+
+    @Test
+    void testZFunction() {
+        int[] z = ZAlgorithm.zFunction("aaaaa");
+        assertArrayEquals(new int[] {0, 4, 3, 2, 1}, z);
+    }
+
+    @Test
+    void testSearchFound() {
+        assertEquals(2, ZAlgorithm.search("abcabca", "cab"));
+    }
+
+    @Test
+    void testSearchNotFound() {
+        assertEquals(-1, ZAlgorithm.search("abcdef", "gh"));
+    }
+}