516. Longest Palindromic Subsequence

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

Example 1:
Input:

"bbbab"
Output:
4
One possible longest palindromic subsequence is "bbbb".

判断字符串中最长的回文子串，子串不一定要连续。

动态规划的方法：

1、s[i]==s[j]，s[i,j]的最长子串就是s[i+1, j-1]能构成的回文串+2；

2、不相等，也就是s[i]，s[j]不能同时加入子串，s[i,j]的最长子串就是s[i, j-1]或s[i+1, j]能构成的回文串

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int len = s.length();
        if (len == 0)
            return 0;
        vector<vector<int>> dp(len, vector<int>(len));
        for (int i=0; i<len; ++i)
            dp[i][i] = 1;
        for (int i=0; i<len; ++i) 
            for (int j=i-1; j>=0; --j) {
                if (s[i] == s[j]) {
                    dp[i][j] = dp[i-1][j+1] + 2;
                }
                else {
                    dp[i][j] = max(dp[i-1][j], dp[i][j+1]);  
                }
                     
            }
        return dp[len-1][0];        
    }
};