73. Set Matrix Zeroes java solutions

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

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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?

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public class Solution {
    public void setZeroes(int[][] matrix) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return;
        int m = matrix.length, n = matrix[0].length;
        int[] rowflag = new int[m];
        int[] colflag = new int[n];
        for(int i = 0; i < m; i++){
            for(int j = 0; j < n; j++){
                if(matrix[i][j] == 0){
                    rowflag[i] = 1;
                    colflag[j] = 1;
                }
            }
        }
        for(int i = 0; i < m; i++){
            if(rowflag[i] == 1){
                for(int j = 0; j < n; j++){
                    matrix[i][j] = 0;
                }
            }
        }
        for(int i = 0; i < n; i++){
            if(colflag[i] == 1){
                for(int j = 0; j < m; j++){
                    matrix[j][i] = 0;
                }
            }
        }
    }
}