73. Set Matrix Zeroes

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it in place.

click to show follow up.

Follow up:

Did you use extra space?
A straight forward solution using O(mn) space is probably a bad idea.
A simple improvement uses O(m + n) space, but still not the best solution.
Could you devise a constant space solution?

void setZeroes(vector<vector<int>>& matrix) {
	int m = matrix.size();
	int n = matrix[0].size();
	int col0 = 1;
	int row0 = 1;
	for (int y = 0;y < n;y++) if (matrix[0][y] == 0) row0 = 0;
	for (int x = 0;x < m;x++) {
		if (matrix[x][0] == 0) col0 = 0;
		for (int y = 0;y < n;y++) 
			if (matrix[x][y] == 0) matrix[0][y] = matrix[x][0] = 0;
	}
	for (int x = 1;x < m;x++) 
		for (int y = 1;y < n;y++) 
			if (matrix[0][y] == 0 || matrix[x][0] == 0) matrix[x][y] = 0;
	if (row0 == 0) for (int y = 0;y < n;y++) matrix[0][y] = 0;
	if (col0 == 0) for (int x = 0;x < m;x++) matrix[x][0] = 0;
}