Set Matrix Zeros

Given a matrix, A of size M x N of 0s and 1s. If an element is 0, set its entire row and column to 0.

Note: This will be evaluated on the extra memory used. Try to minimize the space and time complexity.

Input Format:

The first and the only argument of input contains a 2-d integer matrix, A, of size M x N.

Output Format:

Return a 2-d matrix that satisfies the given conditions.

Constraints:

1 <= N, M <= 1000
0 <= A[i][j] <= 1

Examples:

Input 1:
    [   [1, 0, 1],
        [1, 1, 1], 
        [1, 1, 1]   ]

Output 1:
    [   [0, 0, 0],
        [1, 0, 1],
        [1, 0, 1]   ]

Input 2:
    [   [1, 0, 1],
        [1, 1, 1],
        [1, 0, 1]   ]

Output 2:
    [   [0, 0, 0],
        [1, 0, 1],
        [0, 0, 0]   ]

public class Solution {
    // Basic explanation:
    // We are using the first row and column as a memory to keep track of all the
    // 0's in the entire matrix.
    public void setZeroes(int[][] matrix) {
        boolean firstRow = false, firstCol = false;
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (matrix[i][j] == 0) {
                    if (i == 0)
                        firstRow = true;
                    if (j == 0)
                        firstCol = true;
                    matrix[0][j] = 0;
                    matrix[i][0] = 0;
                }
            }
        }
        for (int i = 1; i < matrix.length; i++)
            for (int j = 1; j < matrix[0].length; j++)
                if (matrix[i][0] == 0 || matrix[0][j] == 0)
                    matrix[i][j] = 0;
        if (firstRow)
            for (int j = 0; j < matrix[0].length; j++)
                matrix[0][j] = 0;
        if (firstCol)
            for (int i = 0; i < matrix.length; i++)
                matrix[i][0] = 0;
    }
}