Set Matrix Zeroes

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-----QUESTION-----

Given a m x n matrix,if an element is 0, set its entire row and column to 0. Do it inplace.

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) {        if(matrix.empty()) return;                bool firstLineZero = false;        bool firstColumnZero = false;        if(matrix[0][0]==0){            firstLineZero = true;            firstColumnZero = true;        }        //the first line        for(int i = 1; i<matrix[0].size(); i++)        {            if(matrix[0][i]!=0) continue;            firstLineZero = true;            break;        }         //the first column        for(int i = 1; i<matrix.size(); i++)        {            if(matrix[i][0]!=0) continue;            firstColumnZero = true;            break;        }                  for(int i = 1; i < matrix.size(); i++)        {            for(int j = 1; j<matrix[0].size(); j++)            {                if(matrix[i][j] != 0) continue;                matrix[i][0] = 0;                matrix[0][j] = 0;            }        }        for(int i = 1; i<matrix[0].size(); i++)        {            if(matrix[0][i]!=0) continue;            for(int j = 1; j<matrix.size(); j++)            {                matrix[j][i]=0;            }        }        for(int i = 1; i<matrix.size(); i++)        {            if(matrix[i][0]!=0) continue;            for(int j = 1; j<matrix[0].size(); j++)            {                matrix[i][j]=0;            }        }        if(firstLineZero)        {            for(int i = 0 ; i< matrix[0].size(); i++)            {                matrix[0][i] = 0;            }        }        if(firstColumnZero)        {            for(int i = 0 ; i< matrix.size(); i++)            {                matrix[i][0] = 0;            }        }}};

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