2.1.19 Set Matrix Zeroes

Notes:
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?

Solution: Use first row and column as auxiliary spaces instead of newly allocating ones.

class Solution {public:    void setZeroes(vector<vector<int>> &matrix) {        if (matrix.empty()) return;        int N = matrix.size(), M = matrix[0].size();        bool setFirstRowZero = false;        bool setFirstColZero = false;        for (int i = 0; i < N && !setFirstColZero; ++i)            setFirstColZero = (matrix[i][0] == 0);        for (int j = 0; j < M && !setFirstRowZero; ++j)            setFirstRowZero = (matrix[0][j] == 0);        for (int i = 1; i < N; ++i)            for (int j = 1; j < M; ++j)                if (matrix[i][j] == 0) {                    matrix[0][j] = 0;                    matrix[i][0] = 0;                }        for (int i = 1; i < N; ++i)            if (matrix[i][0] == 0)                for (int j = 1; j < M; ++j)                    matrix[i][j] = 0;        for (int j = 1; j < M; ++j)            if (matrix[0][j] == 0)                for (int i = 1; i < N; ++i)                    matrix[i][j] = 0;        if (setFirstRowZero)            for (int j = 0; j < M; ++j)                matrix[0][j] = 0;        if (setFirstColZero)            for (int i = 0; i < N; ++i)                matrix[i][0] = 0;    }};