add Zalgorithm

Author: princegupta22

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

@@ -0,0 +1,126 @@
+package com.thealgorithms.strings;
+
+/**
+ * Z Algorithm for Pattern Matching
+ * 
+ * The Z algorithm finds all occurrences of a pattern in a text in linear time.
+ * For a string S of length n, the Z array stores the length of the longest substring
+ * starting from S[i] which is also a prefix of S.
+ * 
+ * Time Complexity: O(n + m) where n is text length and m is pattern length
+ * Space Complexity: O(n + m)
+ * 
+ * Applications:
+ * - Pattern matching
+ * - String searching
+ * - Preprocessing for other string algorithms
+ * 
+ * @author YourName
+ */
+public final class ZAlgorithm {
+    
+    private ZAlgorithm() {
+        // Utility class
+    }
+    
+    /**
+     * Computes the Z array for given string
+     * Z[i] = length of longest substring starting from i which is also prefix of string
+     * 
+     * @param str input string
+     * @return Z array
+     */
+    public static int[] computeZArray(String str) {
+        if (str == null || str.isEmpty()) {
+            return new int[0];
+        }
+        
+        int n = str.length();
+        int[] z = new int[n];
+        z[0] = n; // First element is always equal to string length
+        
+        int left = 0;
+        int right = 0;
+        
+        for (int i = 1; i < n; i++) {
+            if (i > right) {
+                // Outside the current Z-box, compute from scratch
+                left = right = i;
+                while (right < n && str.charAt(right - left) == str.charAt(right)) {
+                    right++;
+                }
+                z[i] = right - left;
+                right--;
+            } else {
+                // Inside the Z-box, use previously computed values
+                int k = i - left;
+                if (z[k] < right - i + 1) {
+                    z[i] = z[k];
+                } else {
+                    left = i;
+                    while (right < n && str.charAt(right - left) == str.charAt(right)) {
+                        right++;
+                    }
+                    z[i] = right - left;
+                    right--;
+                }
+            }
+        }
+        
+        return z;
+    }
+    
+    /**
+     * Searches for all occurrences of pattern in text using Z algorithm
+     * 
+     * @param text the text to search in
+     * @param pattern the pattern to search for
+     * @return array of starting indices where pattern is found
+     */
+    public static int[] search(String text, String pattern) {
+        if (text == null || pattern == null || pattern.isEmpty() || text.length() < pattern.length()) {
+            return new int[0];
+        }
+        
+        // Concatenate pattern and text with a separator
+        String concat = pattern + "$" + text;
+        int[] z = computeZArray(concat);
+        
+        int patternLen = pattern.length();
+        java.util.List<Integer> results = new java.util.ArrayList<>();
+        
+        // Find positions where Z value equals pattern length
+        for (int i = patternLen + 1; i < z.length; i++) {
+            if (z[i] == patternLen) {
+                results.add(i - patternLen - 1);
+            }
+        }
+        
+        return results.stream().mapToInt(Integer::intValue).toArray();
+    }
+    
+    /**
+     * Main method for testing
+     */
+    public static void main(String[] args) {
+        // Test Z array computation
+        String str = "aabcaabxaaaz";
+        int[] z = computeZArray(str);
+        System.out.println("Z array for '" + str + "':");
+        for (int i = 0; i < z.length; i++) {
+            System.out.print(z[i] + " ");
+        }
+        System.out.println("\n");
+        
+        // Test pattern matching
+        String text = "ababcabcabababd";
+        String pattern = "ababd";
+        int[] matches = search(text, pattern);
+        
+        System.out.println("Searching for '" + pattern + "' in '" + text + "'");
+        System.out.println("Pattern found at indices: ");
+        for (int index : matches) {
+            System.out.print(index + " ");
+        }
+    }
+}