5. Longest Palindromic Substring - Unsolved

https://leetcode.com/problems/longest-palindromic-substring/#/description

Given a string s, find the longest palindromic substring in s. You may assume that the maximum length of s is 1000.

Example:

Input: "babad"

Output: "bab"

Note: "aba" is also a valid answer.

Example:

Input: "cbbd"

Output: "bb"

Sol 1: 

DP.

State transition equation:

 

 

The state is f(i, j) , it means the state transition equation in interval [i,j]. 

The next status is based on the previous status. We expand inner block by 1 char at a time. 

public class Solution {
    public String c(String s) {

        // DP
        // Time O(n2) Space O(n^2)
        final int n = s.length();
        final boolean [][] f = new boolean [n][n];
        int maxLen = 1, start = 0; // The start of the longestPalindrome

        for (int i = 0; i < n; i++){
            f[i][i] = true;
            for(int j = 0; j < i; j++){
                f[j][i] = (s.charAt(j) == s.charAt(i) && (i - j < 2 || f[j+1][i-1]));
            if (f[j][i] && maxLen < (i-j+1)){
                maxLen = i - j + 1;
                start = j;
            }
            }
        }

        return s.substring(start, start + maxLen);

    }
}

Sol 2:

Manacher algorithm in Python O(n)

https://discuss.leetcode.com/topic/10484/manacher-algorithm-in-python-o-n

WIKI

https://en.wikipedia.org/wiki/Longest_palindromic_substring