LeetCode 5: Longest Palindromic Substring

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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"

 题目描述:给定字符串,求出最大的回文串,结果可能有多种,返回一种即可;

算法分析:

采用动态规划的思想,用二维数组DP[j][i]来表示第j个字符到第i个字符是否是回文,因此可以用两个for循环来解决填表问题,填表的时候应当使i、j从同一点开始,一次循环中,保证i不动,j从i往前直到0,这样才能保证动态规划表达式的正确性。动态规划表达式为DP[j][i]=(DP[j+1][i-1] | | i-j<=2)&&s[i]==s[j]

代码:

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

 

 

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