1. Longest Palindromic Substring. (LeetCode 5)

1.  Longest Palindromic Substring. (LeetCode 5)

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

Example 1:

Input: "babad"
Output: "bab"
Note: "aba" is also a valid answer.

Example 2:

Input: "cbbd"
Output: "bb"

 

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class Solution {

   public String longestPalindrome(String s) {

       // corner case

       if (s == null){

           return null;

       }

       String res = new String();

       boolean[][] dp = new boolean[s.length()][s.length()];

       // base case

       dp[s.length() - 1][s.length() - 1] = true;

       int globalLength = 1;

       res = s.substring(s.length() - 1, s.length());

       for (int i = s.length() - 2; i >= 0; i--){//induction rule决定了必须从下往上，从中间往右填表

           for (int j = i; j < s.length(); j++){

               // case 1: a, aa, aba

               if ((s.charAt(i) == s.charAt(j)) && (j - i < 3)){

                   dp[i][j] = true;

               }else if((s.charAt(i) == s.charAt(j)) && (dp[i + 1][j - 1] == true)){ // case2: abba

                   dp[i][j] = true;

               }else{

                   dp[i][j] = false;

               }

               if (dp[i][j] == true && j - i + 1> globalLength){ // update globalLength and res

                   globalLength = j - i + 1;

                   res = s.substring(i, j + 1);

               }

           }

       }

       return res;

   }

}

Time : O(n^3)

Space: O(n^2)