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

One possible longest palindromic subsequence is "bb".

class Solution {
public:
  int longestPalindromeSubseq(string s) {
    int N = s.size();
    vector
 
<vector<int>> dp(N, vector<int>(N,0));
    for(int i=0; i<N; i++) {
      dp[i][i] = 1;
    }   
    for(int gap=1; gap<s.size(); gap++) {
      for(int i=0; i<N; i++) {
        int j = i+gap;
        if(i+gap >= N) continue;
        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][N-1];
  }
};

LC 516. Longest Palindromic Subsequence