73 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.

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size();
        if ( m == 0 ) return;
        int n = matrix[0].size();
        if ( n == 0 ) return;
        bool row = false, column = false;
        for ( int i = 0; i < m; i++ ) {
            if ( matrix[i][0] == 0 ) {
                column = true;
                break;
            } 
        }
        for ( int j = 0; j < n; j++ ) {
            if ( matrix[0][j] == 0 ) {
                row = true;
                break;
            }
        }
        for ( int i = 1; i < m; i++ ) {
            for ( int j = 1; j < n; j++ ) {
                if ( matrix[i][j] == 0 ) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        for ( int i = 1; i < m; i++ ) {
            if ( matrix[i][0] == 0 ) {
                for ( int j = 1; j < n; j++ ) matrix[i][j] = 0;
            }
        }
        for ( int j = 1; j < n; j++ ) {
            if ( matrix[0][j] == 0 ) {
                for ( int i = 0; i < m; i++ ) matrix[i][j] = 0;
            }
        }
        if ( column ) {
            for ( int i = 0; i < m; i++ ) matrix[i][0] = 0;
        }
        if ( row ) {
            for ( int j = 0; j < n; j++ ) matrix[0][j] = 0;
        }
        return;
    }
};