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, and there exists one unique longest palindromic substring.

Solution: 1. Time O(n^2), Space O(n^2)
2. Time O(n^2), Space O(n)
3. Time O(n^2), Space O(1) (actually much more efficient than 1 & 2)
4. Time O(n), Space O(n) (Manacher's Algorithm)

class Solution {
public:
    string longestPalindrome(string s) {
        int N = s.size();
        bool dp[N][N];
        pair<int, int> res = make_pair(0,0);
        for(int k = 0; k < N; k++) {
            for(int i = 0; i < N-k; i++) {
                if(k == 0 || k == 1) {
                    dp[i][i+k] = s[i] == s[i+k];
                }
                else {
                    dp[i][i+k] = s[i] == s[i+k] ? dp[i+1][i+k-1] : false;
                }
                if(dp[i][i+k] && k +1 > res.second) {
                    res = make_pair(i,k+1);
                }
            }
        }
        return s.substr(res.first, res.second);
        
    }
};