CODE 60. Set Matrix Zeroes

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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?

public void setZeroes(int[][] matrix) {
	// Note: The Solution object is instantiated only once and is reused by
	// each test case.
	int zeroH = -1;
	int rows = matrix.length;
	int cols = matrix[0].length;
	if (0 == matrix[0][0]) {
		zeroH = 0;
	}
	for (int i = 1; i < rows; i++) {
		if (0 == matrix[i][0]) {
			matrix[0][0] = 0;
			break;
		}
	}
	for (int i = 1; i < cols; i++) {
		if (0 == matrix[0][i]) {
			zeroH = 0;
			break;
		}
	}
	for (int i = 1; i < rows; i++) {
		for (int j = 1; j < cols; j++) {
			if (0 == matrix[i][j]) {
				matrix[i][0] = 0;
				matrix[0][j] = 0;
			}
		}
	}

	for (int i = 1; i < rows; i++) {
		if (0 == matrix[i][0]) {
			for (int j = 0; j < cols; j++) {
				matrix[i][j] = 0;
			}
		}
	}
	for (int i = 0; i < cols; i++) {
		if (0 == matrix[0][i]) {
			for (int j = 0; j < rows; j++) {
				matrix[j][i] = 0;
			}
		}
	}
	if (0 == zeroH) {
		for (int j = 0; j < cols; j++) {
			matrix[0][j] = 0;
		}
	}
}