leetcode73 Set Matrix Zeroes

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

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) {
        int m=matrix.size();
        if(!m)
            return;
        int n=matrix[0].size();
        vector<int> mlist(m,0);
        vector<int> nlist(n,0);
        int i,j;
        for(i=0;i<m;i++)
        {
            for(j=0;j<n;j++)
            {
                if(matrix[i][j]==0)
                {
                    mlist[i]=1;
                    nlist[j]=1;
                }
            }
        }
        for(i=0;i<m;i++)
        {
            if(mlist[i]==1)
            {
                for(j=0;j<n;j++)
                {
                    matrix[i][j]=0;
                }
            }
        }
        for(i=0;i<n;i++)
        {
            if(nlist[i]==1)
            {
                for(j=0;j<m;j++)
                {
                    matrix[j][i]=0;
                }
            }
        }
    }
};