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;
}
}
};