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?

class Solution {public:    void setZeroes(vector<vector<int>>& matrix) {    int col0 = 1, rows = matrix.size(), cols = matrix[0].size();    for (int i = 0; i < rows; i++) {        if (matrix[i][0] == 0) col0 = 0;        for (int j = 1; j < cols; j++)            if (matrix[i][j] == 0)                matrix[i][0] = matrix[0][j] = 0;    }    for (int i = rows - 1; i >= 0; i--) {        for (int j = cols - 1; j >= 1; j--)            if (matrix[i][0] == 0 || matrix[0][j] == 0)                matrix[i][j] = 0;        if (col0 == 0) matrix[i][0] = 0;    }    }};