Sub Matrices with sum Zero

• Time : $O(n^2 * m^2)$
• Space : $O(nm)$

int Solution::solve(vector<vector<int>> &A) {
    int n = A.size(), m = A[0].size();
    vector<vector<int>> psum(n,vector<int>(m,0));
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < m; j++) {
            psum[i][j] += A[i][j];
            if(i) psum[i][j] += psum[i-1][j];
            if(j) psum[i][j] += psum[i][j-1];
            if(i and j) psum[i][j] -= psum[i-1][j-1];
        }
    }
    int res = 0;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < m; j++) {
            for(int k = 0; k <= i; k++) {
                for(int l = 0; l <= j; l++) {
                    int now = psum[i][j];
                    if(k) now -= psum[k-1][j];
                    if(l) now -= psum[i][l-1];
                    if(k and l) now += psum[k-1][l-1];
                    if(now == 0) res += 1;
                }
            }
        }
    }
    return res;
}