【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?

 

class Solution{
public:
    void setZeroes(vector<vector<int> > &matrix){
        const size_t m=matrix.size();//row
        const size_t n=matrix[0].size();//col
        bool row_has_zero=false;
        bool col_has_zero=false;

        for(size_t i=0;i<n;i++)
        {
            if(matrix[0][i]==0)
            {
                row_has_zero=true;
                break;
            }
        }

        for(size_t i=0;i<m;i++)
        {
            if(matrix[i][0]==0)
            {
                col_has_zero=true;
                break;
            }
        }

        for(size_t i=1;i<m;i++)
        {
            for(size_t j=1;j<n;j++)
            {
                if(matrix[i][j]==0)
                {
                    matrix[0][j]=0;
                    matrix[i][0]=0;
                }
            }

        }

        for(size_t i=1;i<m;i++)
        {
            for(size_t j=1;j<n;j++)
            {
                if(matrix[i][0]==0||matrix[0][j]==0)
                    matrix[i][j]=0;
            }
        }

        if(row_has_zero)
            for(size_t i=0;i<n;i++)
                matrix[0][i]=0;

        if(col_has_zero)
            for(size_t i=0;i<m;i++)
                matrix[i][0]=0;
    }
};