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”.
Example 2:
Input:
“cbbd”
Output:
2

dp方法：数组dp[i][j]代表i到j的子字符串中回文子序列的最长长度，状态转移方程为：
若s[i]==s[j],dp[i][j] = dp[i+1][j-1]+2；
否则dp[i][j] = max(dp[i + 1][j],dp[i][j – 1])。

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        int l = s.length();
        int dp[l][l] = {1};
        for(int i = l - 1;i >= 0 ;i--){
            dp[i][i] = 1;
            for(int j = i + 1;j < l;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[0][l - 1];
    }
};