【leetcode】Set Matrix Zeros

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?

 1 class Solution{
 2 public:
 3     void setZeroes(vector<vector<int> > &matrix){
 4         const size_t m=matrix.size();//row
 5         const size_t n=matrix[0].size();//col
 6         bool row_has_zero=false;
 7         bool col_has_zero=false;
 8
 9         for(size_t i=0;i<n;i++)
10         {
11             if(matrix[0][i]==0)
12             {
13                 row_has_zero=true;
14                 break;
15             }
16         }
17
18         for(size_t i=0;i<m;i++)
19         {
20             if(matrix[i][0]==0)
21             {
22                 col_has_zero=true;
23                 break;
24             }
25         }
26
27         for(size_t i=1;i<m;i++)
28         {
29             for(size_t j=1;j<n;j++)
30             {
31                 if(matrix[i][j]==0)
32                 {
33                     matrix[0][j]=0;
34                     matrix[i][0]=0;
35                 }
36             }
37
38         }
39
40         for(size_t i=1;i<m;i++)
41         {
42             for(size_t j=1;j<n;j++)
43             {
44                 if(matrix[i][0]==0||matrix[0][j]==0)
45                     matrix[i][j]=0;
46             }
47         }
48
49         if(row_has_zero)
50             for(size_t i=0;i<n;i++)
51                 matrix[0][i]=0;
52
53         if(col_has_zero)
54             for(size_t i=0;i<m;i++)
55                 matrix[i][0]=0;
56     }
57 };