clean magic matrix code example

Example: clean magic matrix

int largestMagicSquare(vector<vector<int>>& grid) {
    int m = grid.size(), n = grid[0].size(), res = 0;
    vector<vector<int>> rows(m + 2, vector<int>(n + 2)), cols(rows), d1(rows), d2(rows);
    for (int i = 1; i <= m; ++i)
        for (int j = 1; j <= n; ++j) {
            rows[i][j] += grid[i - 1][j - 1] + rows[i][j - 1];
            cols[i][j] += grid[i - 1][j - 1] + cols[i - 1][j];
            d1[i][j] += grid[i - 1][j - 1] + d1[i - 1][j - 1];
            d2[i][j] += grid[i - 1][j - 1] + d2[i - 1][j + 1];
        }
    for (int i = 1; i <= m; ++i)
        for (int j = 1; j <= n; ++j)
            for (int k = min(m - i, n - j); k > res; --k) {
                int sum_d1 = d1[i + k][j + k] - d1[i - 1][j - 1];
                int sum_d2 = d2[i + k][j] - d2[i - 1][j + k + 1];
                bool match = sum_d1 == sum_d2; 
                for (int l = 0; l <= k && match; ++l) {
                    match &= sum_d1 == rows[i + l][j + k] - rows[i + l][j - 1];
                    match &= sum_d1 == cols[i + k][j + l] - cols[i - 1][j + l];
                }
                if (match)
                    res = k;
            }
    return res + 1;
}