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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 1 public class Solution {
 2     public void setZeroes(int[][] matrix) {
 3         if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return;
 4         int m = matrix.length, n = matrix[0].length;
 5         int[] rowflag = new int[m];
 6         int[] colflag = new int[n];
 7         for(int i = 0; i < m; i++){
 8             for(int j = 0; j < n; j++){
 9                 if(matrix[i][j] == 0){
10                     rowflag[i] = 1;
11                     colflag[j] = 1;
12                 }
13             }
14         }
15         for(int i = 0; i < m; i++){
16             if(rowflag[i] == 1){
17                 for(int j = 0; j < n; j++){
18                     matrix[i][j] = 0;
19                 }
20             }
21         }
22         for(int i = 0; i < n; i++){
23             if(colflag[i] == 1){
24                 for(int j = 0; j < m; j++){
25                     matrix[j][i] = 0;
26                 }
27             }
28         }
29     }
30 }