Longest Palindromic Substring--LeetCode

1.题目

Longest Palindromic Substring

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”

2.题意

求最长回文子串

3.分析

动态规划 Dynamic Programming
维护一个二维数组dp
递推式如下：

if j == i
dp[j, i] = 1

if j == i - 1
dp[j, i] = s[j]==s[i]  

if j < i - 1                         
dp[j, i] = s[j]==s[i] && dp[j + 1][i - 1]            

之前的OJ使用vector<vector<int>>会超时，改成二维数组才能通过
注意maxLen初始值为1，最后return s.substr(left, maxLen);
若maxlen初始值为0，则应return s.substr(left, right-left+1);
考虑s为单个字符的情况

4.代码

class Solution {
public:
    string longestPalindrome(string s) {
        int sLen = s.size();
        // int dp[sLen][sLen] = {0};
        vector<vector<int>> dp(sLen, vector<int>(sLen, 0));

        int left = 0;
        int right = 0;
        int maxLen = 1;

        for(int i = 0; i < sLen; ++i)
        {
            dp[i][i] = 1;

            for(int j = 0; j < i; ++j)
            {
                dp[j][i] = s[j] == s[i] && (i - j < 2 || dp[j + 1][i - 1]);

                if(dp[j][i] && i - j + 1 > maxLen)
                {
                    maxLen = i - j + 1;
                    left = j;
                    right = i;
                }       
            }
        }

        return s.substr(left, maxLen);
    }
};