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 m = matrix.size();        if(!m) return ;        int n = matrix[0].size();        if(!n) return ;        int x = -1, y = -1;        for(int i = 0; i < m; ++i)            for(int j = 0; j < n; ++j)            {                if(!matrix[i][j])                {                    if(x == -1 && y == -1)                    {                        x = i;                        y = j;                    }                    else                    {                        matrix[i][y] = 0;                        matrix[x][j] = 0;                    }                }            }        if(x != -1 && y != -1)        {            for(int i = 0; i < n; ++i)            {                if(!matrix[x][i] && i != y)                {                    for(int j = 0; j < m; ++j) matrix[j][i] = 0;                }            }            for(int i = 0; i < m; ++i)            {                if(!matrix[i][y])                {                    for(int j = 0; j < n; ++j) matrix[i][j] = 0;                }            }            for(int i = 0; i < m; ++i) matrix[i][y] = 0;        }    }};