Longest palindromic substring DP solution

longest-palindromic-substring-dp.cpp

string longestPalindrome(string A) {
    int N = A.size();
    vector<vector<bool> > P(N+1, vector<bool>(N+1, true));
    int start = 0, len = 1;
    
    for (int k = 1; k < N; ++k) {
        for (int i = 1; i <= N-k; ++i) {
            P[i][i+k] = P[i+1][i+k-1] && (A[i-1] == A[i+k-1]);
            if (P[i][i+k] && k+1 > len)
                start = i-1, len = k+1;
        }
    }
    
    string result(A.begin() + start, A.begin() + start + len);
    return result;
}