Longest Palindromic Substring

Longest Palindromic Substring

问题：

Given a string S, find the longest palindromic substring in S. You may assume that the maximum length of S is 1000, and there exists one unique longest palindromic substring.

思路：

　　动态规划

我的代码：

public class Solution {
    public String longestPalindrome(String s) {
        if(s == null || s.length() == 0) return s;
        int len = s.length();
        boolean[][] dp = new boolean[len][len];
        int start = 0;
        int max = 1;
        for(int i = 0; i < len; i++)
        {
            dp[i][i] = true;
            if(i < len- 1 && s.charAt(i) == s.charAt(i+1))
            {
                max = 2;
                start = i;
                dp[i][i+1] = true;
            }
        }
        for(int size = 3; size <= len; size++)
        {
            for(int i = 0; i <= len-size; i++)
            {
                int j = i+size-1;
                if(dp[i+1][j-1] && s.charAt(i)==s.charAt(j))
                {
                    max = size;
                    start = i;
                    dp[i][j] = true;
                }
            }
        }
        return s.substring(start,start+max);
    }
}

学习之处：

• 动归方程为dp[i][j] = (s.charAt(i) == s.charAt(j)) && dp[i+1][j-1] ? true : false;
• 想不出来动态规划的方程，就先想的dfs怎么做，然后再反向思维得出动态规划的方程，动态规划之所以快，是因为减少了好多的重复计算。