#162 Set Matrix Zeroes

题目描述：

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

Have you met this question in a real interview?  Yes Example

Given a matrix

[ [1,2], [0,3] ],

return [ [0,2], [0,0] ]

Challenge 

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?

题目思路：

题目要求用constant space去解，那么就想到了把zero的信息写在matrix中。如果（i,j）的位置上位0，那么就意味着i行j列都为0。这里我会把(i,0)和(0, j)的位置标记为0，这表示i行都为0，j列都为0。需要注意的是(0,0)这个位置是分不清行和列的，所以我增加了两个bool：zero_row和zero_col，以此来区别(0,0)为0的时候到底是表示0行为0还是0列为0. 标记完了以后，就可以填0了。这里要注意的是，0行和0列要放在最后overwrite，不然有用的信息会被覆盖掉。

Mycode（AC = 44ms）：

class Solution { public: /** * @param matrix: A list of lists of integers * @return: Void */ void setZeroes(vector<vector<int> > &matrix) { // write your code here int num_rows = matrix.size(); if (num_rows == 0) return; int num_cols = matrix[0].size(); // if (i, j) is zero, then use first row and // first column to record the zero bool zero_row = false, zero_col = false; for (int i = 0; i < num_rows; i++) { for (int j = 0; j < num_cols; j++) { if (matrix[i][j] == 0) { matrix[0][j] = 0; matrix[i][0] = 0; zero_row = zero_row || (i == 0); zero_col = zero_col || (j == 0); } } } // zero-out all the columns except first column for (int j = 1; j < num_cols; j++) { if (matrix[0][j] == 0) { for (int i = 1; i < num_rows; i++) { matrix[i][j] = 0; } } } // zero-out all the rows except first row for (int i = 1; i < num_rows; i++) { if (matrix[i][0] == 0) { for (int j = 1; j < num_cols; j++) { matrix[i][j] = 0; } } } // zero-out the first row if needed if (zero_row) { for (int i = 0; i < num_cols; i++) { matrix[0][i] = 0; } } // zero-out the first column if needed if (zero_col) { for (int i = 0; i < num_rows; i++) { matrix[i][0] = 0; } } } };