Update Manacher.java

Author: Abhinavagarwa

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

@@ -1,30 +1,44 @@
 public class ManacherAlgorithm {
+
+    // Preprocesses the input string by adding boundary characters
     private String preprocess(String s) {
         StringBuilder sb = new StringBuilder();
-        sb.append('^');
+        sb.append('^');  // Add starting boundary
         for (int i = 0; i < s.length(); i++) {
-            sb.append('#');
+            sb.append('#');  // Add boundary between characters
             sb.append(s.charAt(i));
         }
-        sb.append("#$");
+        sb.append("#$");  // Add ending boundary
         return sb.toString();
     }
+
+    // Manacher's Algorithm to find the longest palindromic substring
     public String longestPalindrome(String s) {
         String T = preprocess(s);
         int n = T.length();
-        int[] P = new int[n];
-        int C = 0, R = 0; 
+        int[] P = new int[n];  // Array to store the lengths of palindromes
+        int C = 0, R = 0;  // C is the center, R is the right boundary
+
+        // Iterate through the transformed string
         for (int i = 1; i < n - 1; i++) {
-            int mirror = 2 * C - i; 
+            int mirror = 2 * C - i;  // Mirror of i with respect to the center C
+
+            // Use previously computed values or set P[i] to 0
             P[i] = (R > i) ? Math.min(R - i, P[mirror]) : 0;
+
+            // Expand around i
             while (T.charAt(i + 1 + P[i]) == T.charAt(i - 1 - P[i])) {
                 P[i]++;
-      }
+            }
+
+            // Update center and right boundary if the palindrome expands beyond R
             if (i + P[i] > R) {
                 C = i;
                 R = i + P[i];
             }
         }
+
+        // Find the longest palindrome in P
         int maxLen = 0;
         int centerIndex = 0;
         for (int i = 1; i < n - 1; i++) {
@@ -33,13 +47,10 @@ public String longestPalindrome(String s) {
                 centerIndex = i;
             }
         }
+
+        // Calculate the starting index of the longest palindromic substring
         int start = (centerIndex - maxLen) / 2;
         return s.substring(start, start + maxLen);
     }
-
-    public static void main(String[] args) {
-        ManacherAlgorithm ma = new ManacherAlgorithm();
-        String input = "babad";
-        System.out.println("Longest Palindromic Substring: " + ma.longestPalindrome(input));
-    }
 }
+