feat: added new algorithm Z Algorithm

Author: Mrinal Chauhan

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

@@ -4,58 +4,57 @@
 import java.util.List;
 
 /**
- * Class to implement the Z Algorithm for pattern matching in strings.
- * The Z Algorithm finds all occurrences of a pattern within a text.
+ * Z-algorithm implementation to find all occurrences of a pattern in a text.
  */
 public final class Zalgorithm {
     private Zalgorithm() {
     }
 
     /**
-     * Calculates the Z array for a given string.
+     * Finds the occurrences of a pattern in a text using Z-algorithm.
      *
-     * @param s the input string
-     * @return the Z array where Z[i] indicates the length of the longest substring
-     *         starting from s[i] that is also a prefix of s
+     * @param text    the input text in which we are searching the pattern
+     * @param pattern the pattern to search for
+     * @return a list of indices where the pattern occurs in the text
      */
-    public static int[] calculateZ(String s) {
-        int n = s.length();
-        int[] Z = new int[n];
-        int left = 0, right = 0;
+    public static List<Integer> findPatternOccurrences(String text, String pattern) {
+        String combined = pattern + "$" + text;
+        int[] zArray = calculateZ(combined);
+        List<Integer> occurrences = new ArrayList<>();
+        int patternLength = pattern.length();
 
-        for (int i = 1; i < n; i++) {
-            if (i <= right) {
-                Z[i] = Math.min(right - i + 1, Z[i - left]);
-            }
-            while (i + Z[i] < n && s.charAt(Z[i]) == s.charAt(i + Z[i])) {
-                Z[i]++;
-            }
-            if (i + Z[i] - 1 > right) {
-                left = i;
-                right = i + Z[i] - 1;
+        for (int i = 0; i < zArray.length; i++) {
+            if (zArray[i] == patternLength) {
+                occurrences.add(i - patternLength - 1);
             }
         }
-        return Z;
+        return occurrences;
     }
 
     /**
-     * Finds all occurrences of a pattern in the text using the Z Algorithm.
+     * Helper method to calculate Z-array for a given string.
      *
-     * @param text the text in which to search for the pattern
-     * @param pattern the pattern to search for
-     * @return a list of starting indices of occurrences of the pattern in the text
+     * @param s the input string
+     * @return the Z-array where Z[i] is the length of the longest substring
+     * starting from i that is also a prefix of s
      */
-    public static List<Integer> findPatternOccurrences(String text, String pattern) {
-        String combined = pattern + "$" + text;
-        int[] Z = calculateZ(combined);
-        List<Integer> occurrences = new ArrayList<>();
-        int patternLength = pattern.length();
+    private static int[] calculateZ(String s) {
+        int n = s.length();
+        int[] z = new int[n];
+        int l = 0, r = 0;
 
-        for (int i = 0; i < Z.length; i++) {
-            if (Z[i] == patternLength) {
-                occurrences.add(i - patternLength - 1);
+        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 occurrences;
+        return z;
     }
 }