LeetCode Problem : Set Matrix Zeroes

Problem

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?

Code

void setZeroes(vector<vector<int> > &matrix) {
    // Start typing your C/C++ solution below
    // DO NOT write int main() function
    int m = matrix.size();
    int n = matrix[0].size();
    vector<bool> rows(m,false);
    vector<bool> cols(n,false);
    for(int i = 0; i < m; ++i){
        for(int j = 0; j < n ; ++j){
            if(matrix[i][j] == 0){
                rows[i] = true;
                cols[j] = true;
            }
        }
    }
    for(int i = 0; i < m; ++i){
        if(rows[i]){
            for(int j = 0; j < n ; ++j){
                matrix[i][j] = 0;
            }
        }
    }
    for(int j = 0; j < n; ++j){
        if(cols[j]){
            for(int i = 0; i < m ; ++i){
                matrix[i][j] = 0;
            }
        }
    }
}