Set Matrix Zeroes问题及解法

问题描述：

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

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?

问题分析：

想要在常量空间内解决问题，我们可以利用原有的matrix数组。在该数组中，将第一行和第一列设置为标志数组。先确定好第一行和第一列有没有0元素；然后看其他元素matrix[i][j]（i > 0, j > 0）是否等于0，若是便设置matrix[0][j] = matrix[i][0].。最后根据第一行和第一列的标志来设置每一列和每一行的值。

过程详见代码：

class Solution {public:    void setZeroes(vector<vector<int>>& matrix) {        int m = matrix.size();int n = matrix[0].size();int fr = 0, fc = 0;for (int i = 0; i < n; i++) if (!matrix[0][i]){ fr = 1; break; }for (int i = 0; i < m; i++) if (!matrix[i][0]){ fc = 1; break; }for (int i = 1; i < m; i++){for (int j = 1; j < n; j++){if (!matrix[i][j]){matrix[i][0] = 0;matrix[0][j] = 0;}}}for (int i = 1; i < m; i++){if (!matrix[i][0]){for (int j = 1; j < n; j++) matrix[i][j] = 0;}}for (int i = 1; i < n; i++){if (!matrix[0][i]){for (int j = 1; j < m; j++) matrix[j][i] = 0;}}if (fr){for (int i = 0; i < n; i++) matrix[0][i] = 0;}if (fc){for (int i = 0; i < m; i++) matrix[i][0] = 0;}    }};