add ZAlgorithm for linear pattern matching

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

@@ -0,0 +1,110 @@
+package com.thealgorithms.strings;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Z Algorithm for pattern matching in linear time
+ *
+ * The Z-algorithm computes, for each position i in a string,
+ * the length of the longest substring starting at i which is
+ * also a prefix of the string.
+ *
+ * Time Complexity: O(n + m) where n is text length, m is pattern length
+ * Space Complexity: O(n + m)
+ *
+ * @author Your Name
+ */
+public final class ZAlgorithm {
+    private ZAlgorithm() {
+    }
+
+    /**
+     * Finds all occurrences of pattern in text using Z-algorithm
+     *
+     * @param text the text to search in
+     * @param pattern the pattern to search for
+     * @return list of starting indices where pattern occurs
+     * @throws IllegalArgumentException if text or pattern is null
+     */
+    public static List<Integer> search(String text, String pattern) {
+        if (text == null || pattern == null) {
+            throw new IllegalArgumentException("Text and pattern cannot be null");
+        }
+
+        List<Integer> result = new ArrayList<>();
+
+        if (pattern.isEmpty() || pattern.length() > text.length()) {
+            return result;
+        }
+
+        // Concatenate pattern and text with a separator
+        String combined = pattern + "$" + text;
+        int[] zArray = computeZArray(combined);
+
+        int patternLength = pattern.length();
+
+        // Find positions where Z-value equals pattern length
+        for (int i = patternLength + 1; i < combined.length(); i++) {
+            if (zArray[i] == patternLength) {
+                result.add(i - patternLength - 1);
+            }
+        }
+
+        return result;
+    }
+
+    /**
+     * Computes the Z-array for the given string
+     * Z[i] = length of longest substring starting at i which is also a prefix
+     *
+     * @param str input string
+     * @return Z-array
+     */
+    private static int[] computeZArray(String str) {
+        int n = str.length();
+        int[] zArray = new int[n];
+
+        int left = 0;
+        int right = 0;
+
+        for (int i = 1; i < n; i++) {
+            if (i > right) {
+                left = right = i;
+                while (right < n && str.charAt(right - left) == str.charAt(right)) {
+                    right++;
+                }
+                zArray[i] = right - left;
+                right--;
+            } else {
+                int k = i - left;
+                if (zArray[k] < right - i + 1) {
+                    zArray[i] = zArray[k];
+                } else {
+                    left = i;
+                    while (right < n && str.charAt(right - left) == str.charAt(right)) {
+                        right++;
+                    }
+                    zArray[i] = right - left;
+                    right--;
+                }
+            }
+        }
+        return zArray;
+    }
+
+    /**
+     * Computes only the Z-array for a given string
+     * Useful for other applications beyond pattern matching
+     *
+     * @param str input string
+     * @return Z-array where Z[i] is length of longest prefix match at position i
+     * @throws IllegalArgumentException if string is null
+     */
+    public static int[] getZArray(String str) {
+        if (str == null) {
+            throw new IllegalArgumentException("String cannot be null");
+        }
+        return computeZArray(str);
+    }
+}