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.

click to show follow up.

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?

 

方法一：扫到每个0元素，将其所在行和列中非0元素置为INF，最后在扫一遍，将所有INF的元素置0

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        for(int i=0; i<matrix.size(); ++i)  //将0元素所在行和列的非0元素置为INF
            for(int j=0; j<matrix[i].size(); ++j)
                if( !matrix[i][j] ) setINF(matrix, i, j);
        for(int i=0; i<matrix.size(); ++i)  //将所有INF元素置为0
            for(int j=0; j<matrix[i].size(); ++j)
                if( matrix[i][j] == INF ) matrix[i][j] = 0;
    }
    
    void setINF(vector<vector<int> > &matrix, int x, int y) {
        for(int i=0; i<matrix.size(); ++i)
            if( matrix[i][y] ) matrix[i][y] = INF;
        for(int i=0; i<matrix[x].size(); ++i)
            if( matrix[x][i] ) matrix[x][i] = INF;
    }
    
private:
    static const int INF = 0x3fffffff;
};

方法二：利用第一行和第一列标记哪行和哪列全部置0，需要注意，第一行和第一列需要额外标记

class Solution {
public:
    void setZeroes(vector<vector<int> > &matrix) {
        bool frow = false, fcol = false;
        for(int i=0; i<matrix[0].size(); ++i)   //判断第一行是否需要清0
            if( !matrix[0][i] ) {
                frow = true;
                break;
            }
        for(int i=0; i<matrix.size(); ++i)  //判断第一列是否需要清0
            if( !matrix[i][0] ) {
                fcol = true;
                break;
            }
        for(int i=1; i<matrix.size(); ++i)
            for(int j=1; j<matrix[i].size(); ++j)
                if( !matrix[i][j] ) {   //当前元素所在行和所在列，第一行和第一列对应的元素置0，作为标记
                    matrix[i][0] = matrix[0][j] = 0;
                }
        for(int i=1; i<matrix.size(); ++i)
            for(int j=1; j<matrix[i].size(); ++j)
                if( !matrix[i][0] || !matrix[0][j] ) matrix[i][j] = 0;  //按照标记来给对应的行和列置0
        if( frow )
            for(int i=0; i<matrix[0].size(); ++i) matrix[0][i] = 0;
        if( fcol )
            for(int i=0; i<matrix.size(); ++i) matrix[i][0] = 0;
    }
};