Manacher

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Youtube Explanation

Manacher’s Algorithm Explained— Longest Palindromic Substring

Manacher.java

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/******************************************************************************
 *  Compilation:  javac Manacher.java
 *  Execution:    java Manacher text
 *  Dependencies: StdOut.java
 *
 *  Computes the longest palindromic substring in linear time
 *  using Manacher's algorithm.
 *
 *  Credits: The code is lifted from the following excellent reference
 *  http://www.leetcode.com/2011/11/longest-palindromic-substring-part-ii.html
 *
 ******************************************************************************/

public class Manacher {
    private int[]  p;  // p[i] = length of longest palindromic substring of t, centered at i
    private String s;  // original string
    private char[] t;  // transformed string

    public Manacher(String s) {
        this.s = s;
        preprocess();
        p = new int[t.length];

        int center = 0, right = 0;
        for (int i = 1; i < t.length-1; i++) {
            int mirror = 2*center - i;

            if (right > i)
                p[i] = Math.min(right - i, p[mirror]);
 
            // attempt to expand palindrome centered at i
            while (t[i + (1 + p[i])] == t[i - (1 + p[i])])
                p[i]++;
 
            // if palindrome centered at i expands past right,
            // adjust center based on expanded palindrome.
            if (i + p[i] > right) {
                center = i;
                right = i + p[i];
            }
        }

    }

    // Transform s into t.
    // For example, if s = "abba", then t = "$#a#b#b#a#@"
    // the # are interleaved to avoid even/odd-length palindromes uniformly
    // $ and @ are prepended and appended to each end to avoid bounds checking
    private void preprocess() {
        t = new char[s.length()*2 + 3];
        t[0] = '$';
        t[s.length()*2 + 2] = '@';
        for (int i = 0; i < s.length(); i++) {
            t[2*i + 1] = '#';
            t[2*i + 2] = s.charAt(i);
        }
        t[s.length()*2 + 1] = '#';
    }
 
    // longest palindromic substring
    public String longestPalindromicSubstring() {
        int length = 0;   // length of longest palindromic substring
        int center = 0;   // center of longest palindromic substring
        for (int i = 1; i < p.length-1; i++) {
            if (p[i] > length) {
                length = p[i];
                center = i;
            }
        }
        return s.substring((center - 1 - length) / 2, (center - 1 + length) / 2);
    }

    // longest palindromic substring centered at index i/2
    public String longestPalindromicSubstring(int i) {
        int length = p[i + 2];
        int center = i + 2;
        return s.substring((center - 1 - length) / 2, (center - 1 + length) / 2);
    }


    // test client
    public static void main(String[] args) {
        String s = args[0];
        Manacher manacher = new Manacher(s);
        StdOut.println(manacher.longestPalindromicSubstring());
        for (int i = 0; i < 2*s.length(); i++)
            StdOut.println(i +  ": " + manacher.longestPalindromicSubstring(i));
         
    }
}

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