Largest Palindrome

class Solution {
  public:
    string longestPalin (string S) {
        int min_i=0, max_j=0, N = S.length();
        for (int i=0; i<N; i++) {
            int p1 = i, p2 = i+1;
            while (p1>=0 && p2<N && S[p1]==S[p2]) {
                if (p2-p1 > max_j-min_i){
                    max_j = p2;
                    min_i = p1;
                }
                p1--;
                p2++;
            }
        }
        for (int i=1; i<N-1; i++) {
            int j=1;
            while(i-j>=0 && i+j<N && S[i+j]==S[i-j]) {
                if ( (i+j)-(i-j) > (max_j-min_i) ) {
                    max_j = i+j;
                    min_i = i-j;
                }
                j++;
            }
        }
        return S.substr(min_i, max_j-min_i+1);
    }
};