LeetCode 5. Longest Palindromic Substring

class Solution {
public:
    string longestPalindrome(string s) {
        vector<vector<int>> dp(s.size(), vector<int>(s.size(), 0));
        // dp[a][b]: ```true``` expresses s[a..b] is a palindromic substring;
        //           otherwise is not. assert a <= b.
        int mx = -1;
        string substr;
        for (int i = 0; i < s.size(); i++) {
            int a, b;
            for (int delta = 0; delta < 2; delta++) {
                a = b = i;
                b += delta;
                while (a >= 0 && b < s.size()) {
                    if (a + 1 <= b - 1 && dp[a+1][b-1] == 0) {
                        dp[a][b] = 0;
                    } else {
                        if (s[a] == s[b]) {
                            if (a + 1 <= b - 1) {
                                dp[a][b] = dp[a+1][b-1] + 2;
                            } else {
                                dp[a][b] = b - a + 1;
                            }
                        } else {
                            dp[a][b] = 0;
                        }
                        if (dp[a][b] > mx) {
                            mx = dp[a][b];
                            substr = s.substr(a, b - a + 1);
                        }
                    }
                    --a;
                    ++b; 
                }
            }
        }
        return substr;
    }
};