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);

    }

}

View Code

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。