3212. Count Submatrices With Equal Frequency of X and Y

// Approach: Prefix sum to compute X and Y counts; for each cell check prefix X == prefix Y and X > 0.
// Time: O(mn) Space: O(mn)

public class Solution
{
    public int NumberOfSubmatrices(char[][] grid)
    {
        int m = grid.Length;
        int n = grid[0].Length;
        int ans = 0;
        // x[i,j] := the number of 'X' in grid[0..i)[0..j)
        int[,] x = new int[m + 1, n + 1];
        // y[i,j] := the number of 'Y' in grid[0..i)[0..j)
        int[,] y = new int[m + 1, n + 1];

        for (int i = 0; i < m; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                x[i + 1, j + 1] = (grid[i][j] == 'X' ? 1 : 0) + x[i, j + 1] + x[i + 1, j] - x[i, j];
                y[i + 1, j + 1] = (grid[i][j] == 'Y' ? 1 : 0) + y[i, j + 1] + y[i + 1, j] - y[i, j];
                if (x[i + 1, j + 1] > 0 && x[i + 1, j + 1] == y[i + 1, j + 1])
                    ++ans;
            }
        }

        return ans;
    }
}