LeetCode: 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) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        int m = matrix.size();        if (m == 0) return;        int n = matrix[0].size();        if (n == 0) return;                bool isFirstRowZero = false;        bool isFirstColZero = false;        for (int i = 0; i < n; ++i)        {            if (matrix[0][i] == 0)            {                isFirstRowZero = true;                break;            }        }                for (int i = 0; i < m; ++i)        {            if (matrix[i][0] == 0)            {                isFirstColZero = true;                break;            }        }                for (int i = 1; i < m; ++i)        {            for (int j = 1; j < n; ++j)            {                if (matrix[i][j] == 0)                {                    matrix[0][j] = 0;                    matrix[i][0] = 0;                }            }        }                for (int i = 1; i < m; ++i)        {            for (int j = 1; j < n; ++j)            {                if (matrix[0][j] == 0 || matrix[i][0] == 0)                    matrix[i][j] = 0;            }        }                if (isFirstRowZero)        {            for (int i = 0; i < n; ++i)                matrix[0][i] = 0;        }        if (isFirstColZero)        {            for (int i = 0; i < m; ++i)                matrix[i][0] = 0;        }    }};