# Set Matrix Zeroes

### 描述​

Given a m × 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?

### 分析​

O(m+n)空间的方法很简单，设置两个 bool 数组，记录每行和每列是否存在 0。

### 代码 1​

// Set Matrix Zeroes// 时间复杂度O(m*n)，空间复杂度O(m+n)public class Solution {    public void setZeroes(int[][] matrix) {        final int m = matrix.length;        final int n = matrix[0].length;        boolean[] row = new boolean[m]; // 标记该行是否存在0        boolean[] col = new boolean[n]; // 标记该列是否存在0        for (int i = 0; i < m; ++i) {            for (int j = 0; j < n; ++j) {                if (matrix[i][j] == 0) {                    row[i] = col[j] = true;                }            }        }        for (int i = 0; i < m; ++i) {            if (row[i]) Arrays.fill(matrix[i], 0);        }        for (int j = 0; j < n; ++j) {            if (col[j]) {                for (int i = 0; i < m; ++i) {                    matrix[i][j] = 0;                }            }        }    }}

### 代码 2​

// Set Matrix Zeroes// 时间复杂度O(m*n)，空间复杂度O(1)public class Solution {    public void setZeroes(int[][] matrix) {        final int m = matrix.length;        final int n = matrix[0].length;        boolean row_has_zero = false; // 第一行是否存在 0        boolean col_has_zero = false; // 第一列是否存在 0        for (int i = 0; i < n; i++)            if (matrix[0][i] == 0) {                row_has_zero = true;                break;            }        for (int i = 0; i < m; i++)            if (matrix[i][0] == 0) {                col_has_zero = true;                break;            }        for (int i = 1; i < m; i++)            for (int j = 1; j < n; j++)                if (matrix[i][j] == 0) {                    matrix[0][j] = 0;                    matrix[i][0] = 0;                }        for (int i = 1; i < m; i++)            for (int j = 1; j < n; j++)                if (matrix[i][0] == 0 || matrix[0][j] == 0)                    matrix[i][j] = 0;        if (row_has_zero)            for (int i = 0; i < n; i++)                matrix[0][i] = 0;        if (col_has_zero)            for (int i = 0; i < m; i++)                matrix[i][0] = 0;    }};