LeetCode 516. The longest palindrome subsequence (interval DP)

516. The longest palindrome subsequence
status: $dp\left[i\right]\left[j\right]$ represents the sequence$s[i,j]$ The length of the longest palindrome subsequence that can be generated.
Time complexity:$O(n^2)\; The$
large interval depends on its sub-intervals.
DP equation:
dp [i] [j] = max {dp [i] [j − 1], dp [i + 1] [j], dp [i + 1] [j − 1] + 2 ∗ (s [ i] = = s [j])} dp[i][j] = max\{dp[i][j-1],dp[i+1][j],dp[i+1][j- 1]+2*(s[i]==s[j])\}dp[i][j]=max{ dp[i][j−1],dp[i+1][j],dp[i+1][j−1]+2∗(s[i]==s[j])}

class Solution {
    
    
public:
    int dp[1010][1010] = {
    
    0};
    int longestPalindromeSubseq(string s) {
    
    
        int n = s.size();
        s = ' '+s;
        for(int i=1;i<=n;i++){
    
    
            dp[i][i] = 1; 
        }
        for(int j=1;j<=n;j++){
    
    
            for(int i=j-1;i>=1;i--){
    
    
                dp[i][j] = max(dp[i+1][j],dp[i][j-1]);
                if(s[i]==s[j]) dp[i][j] = max(dp[i][j],dp[i+1][j-1]+2);
            }
        }
        return dp[1][n];
    }
};