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.

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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?

Solution:

class Solution {public:    void setZeroes(vector<vector<int> > &matrix)     {        int n = matrix.size();        if(n == 0)            return;        int m = matrix[0].size();        if(m == 0)            return;        bool* flag_row = new bool[n];        for(int i=0; i<n; i++)            flag_row[i] = false;        bool* flag_col = new bool[m];        for(int i=0; i<m; i++)            flag_col[i] = false;        for(int i=0; i<n; i++)        {            for(int j=0; j<m; j++)            {                if(matrix[i][j] == 0)                {                    flag_row[i] = true;                    flag_col[j] = true;                }            }        }        for(int i=0; i<n; i++)        {            if(flag_row[i] == true)            {                for(int j=0; j<m; j++)                    matrix[i][j] = 0;            }        }        for(int i=0; i<m; i++)        {            if(flag_col[i] == true)            {                for(int j=0; j<n; j++)                    matrix[j][i] = 0;            }        }        return ;    }};