# [面试题 01.08. 零矩阵](https://leetcode.cn/problems/zero-matrix-lcci)
[English Version](/lcci/01.08.Zero%20Matrix/README_EN.md)
## 题目描述
<!-- 这里写题目描述 -->
<p>编写一种算法，若M × N矩阵中某个元素为0，则将其所在的行与列清零。</p>
<p> </p>
<p><strong>示例 1：</strong></p>
<pre><strong>输入：</strong>
[
[1,1,1],
[1,0,1],
[1,1,1]
]
<strong>输出：</strong>
[
[1,0,1],
[0,0,0],
[1,0,1]
]
</pre>
<p><strong>示例 2：</strong></p>
<pre><strong>输入：</strong>
[
[0,1,2,0],
[3,4,5,2],
[1,3,1,5]
]
<strong>输出：</strong>
[
[0,0,0,0],
[0,4,5,0],
[0,3,1,0]
]
</pre>
## 解法
### 方法一：数组标记
我们分别用数组 `rows` 和 `cols` 标记待清零的行和列。
然后再遍历一遍矩阵，将 `rows` 和 `cols` 中标记的行和列对应的元素清零。
时间复杂度 $O(m \times n)$，空间复杂度 $O(m + n)$。其中 $m$ 和 $n$ 分别为矩阵的行数和列数。
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```python
class Solution:
def setZeroes(self, matrix: List[List[int]]) -> None:
m, n = len(matrix), len(matrix[0])
rows = [0] * m
cols = [0] * n
for i, row in enumerate(matrix):
for j, v in enumerate(row):
if v == 0:
rows[i] = cols[j] = 1
for i in range(m):
for j in range(n):
if rows[i] or cols[j]:
matrix[i][j] = 0
```
```java
class Solution {
public void setZeroes(int[][] matrix) {
int m = matrix.length, n = matrix[0].length;
boolean[] rows = new boolean[m];
boolean[] cols = new boolean[n];
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (matrix[i][j] == 0) {
rows[i] = true;
cols[j] = true;
}
}
}
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (rows[i] || cols[j]) {
matrix[i][j] = 0;
}
}
}
}
}
```
```cpp
class Solution {
public:
void setZeroes(vector<vector<int>>& matrix) {
int m = matrix.size(), n = matrix[0].size();
vector<bool> rows(m);
vector<bool> cols(n);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (!matrix[i][j]) {
rows[i] = 1;
cols[j] = 1;
}
}
}
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (rows[i] || cols[j]) {
matrix[i][j] = 0;
}
}
}
}
};
```
```go
func setZeroes(matrix [][]int) {
m, n := len(matrix), len(matrix[0])
rows := make([]bool, m)
cols := make([]bool, n)
for i, row := range matrix {
for j, v := range row {
if v == 0 {
rows[i] = true
cols[j] = true
}
}
}
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
if rows[i] || cols[j] {
matrix[i][j] = 0
}
}
}
}
```
```ts
/**
Do not return anything, modify matrix in-place instead.
*/
function setZeroes(matrix: number[][]): void {
const m = matrix.length;
const n = matrix[0].length;
const rows = new Array(m).fill(false);
const cols = new Array(n).fill(false);
for (let i = 0; i < m; i++) {
for (let j = 0; j < n; j++) {
if (matrix[i][j] === 0) {
rows[i] = true;
cols[j] = true;
}
}
}
for (let i = 0; i < m; i++) {
for (let j = 0; j < n; j++) {
if (rows[i] || cols[j]) {
matrix[i][j] = 0;
}
}
}
}
```
```rust
impl Solution {
pub fn set_zeroes(matrix: &mut Vec<Vec<i32>>) {
let m = matrix.len();
let n = matrix[0].len();
let mut rows = vec![false; m];
let mut cols = vec![false; n];
for i in 0..m {
for j in 0..n {
if matrix[i][j] == 0 {
rows[i] = true;
cols[j] = true;
}
}
}
for i in 0..m {
for j in 0..n {
if rows[i] || cols[j] {
matrix[i][j] = 0;
}
}
}
}
}
```
```js
/**
* @param {number[][]} matrix
* @return {void} Do not return anything, modify matrix in-place instead.
*/
var setZeroes = function (matrix) {
const m = matrix.length;
const n = matrix[0].length;
const rows = new Array(m).fill(false);
const cols = new Array(n).fill(false);
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
if (matrix[i][j] == 0) {
rows[i] = true;
cols[j] = true;
}
}
}
for (let i = 0; i < m; ++i) {
for (let j = 0; j < n; ++j) {
if (rows[i] || cols[j]) {
matrix[i][j] = 0;
}
}
}
};
```
```c
void setZeroes(int** matrix, int matrixSize, int* matrixColSize) {
int m = matrixSize;
int n = matrixColSize[0];
int* rows = (int*) malloc(sizeof(int) * m);
int* cols = (int*) malloc(sizeof(int) * n);
memset(rows, 0, sizeof(int) * m);
memset(cols, 0, sizeof(int) * n);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; ++j) {
if (matrix[i][j] == 0) {
rows[i] = 1;
cols[j] = 1;
}
}
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; ++j) {
if (rows[i] || cols[j]) {
matrix[i][j] = 0;
}
}
}
free(rows);
free(cols);
}
```
```swift
class Solution {
func setZeroes(_ matrix: inout [[Int]]) {
let m = matrix.count
guard m > 0 else { return }
let n = matrix[0].count
var rows = Array(repeating: false, count: m)
var cols = Array(repeating: false, count: n)
for i in 0..<m {
for j in 0..<n {
if matrix[i][j] == 0 {
rows[i] = true
cols[j] = true
}
}
}
for i in 0..<m {
for j in 0..<n {
if rows[i] || cols[j] {
matrix[i][j] = 0
}
}
}
}
}
```
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### 方法二：原地标记
方法一中使用了额外的数组标记待清零的行和列，实际上我们也可以直接用矩阵的第一行和第一列来标记，不需要开辟额外的数组空间。
由于第一行、第一列用来做标记，它们的值可能会因为标记而发生改变，因此，我们需要额外的变量 $i0$, $j0$ 来标记第一行、第一列是否需要被清零。
时间复杂度 $O(m \times n)$，其中 $m$ 和 $n$ 分别为矩阵的行数和列数。空间复杂度 $O(1)$。
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```python
class Solution:
def setZeroes(self, matrix: List[List[int]]) -> None:
m, n = len(matrix), len(matrix[0])
i0 = any(v == 0 for v in matrix[0])
j0 = any(matrix[i][0] == 0 for i in range(m))
for i in range(1, m):
for j in range(1, n):
if matrix[i][j] == 0:
matrix[i][0] = matrix[0][j] = 0
for i in range(1, m):
for j in range(1, n):
if matrix[i][0] == 0 or matrix[0][j] == 0:
matrix[i][j] = 0
if i0:
for j in range(n):
matrix[0][j] = 0
if j0:
for i in range(m):
matrix[i][0] = 0
```
```java
class Solution {
public void setZeroes(int[][] matrix) {
int m = matrix.length, n = matrix[0].length;
boolean i0 = false, j0 = false;
for (int j = 0; j < n; ++j) {
if (matrix[0][j] == 0) {
i0 = true;
break;
}
}
for (int i = 0; i < m; ++i) {
if (matrix[i][0] == 0) {
j0 = 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) {
for (int j = 1; j < n; ++j) {
if (matrix[i][0] == 0 || matrix[0][j] == 0) {
matrix[i][j] = 0;
}
}
}
if (i0) {
for (int j = 0; j < n; ++j) {
matrix[0][j] = 0;
}
}
if (j0) {
for (int i = 0; i < m; ++i) {
matrix[i][0] = 0;
}
}
}
}
```
```cpp
class Solution {
public:
void setZeroes(vector<vector<int>>& matrix) {
int m = matrix.size(), n = matrix[0].size();
bool i0 = false, j0 = false;
for (int j = 0; j < n; ++j) {
if (matrix[0][j] == 0) {
i0 = true;
break;
}
}
for (int i = 0; i < m; ++i) {
if (matrix[i][0] == 0) {
j0 = 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) {
for (int j = 1; j < n; ++j) {
if (matrix[i][0] == 0 || matrix[0][j] == 0) {
matrix[i][j] = 0;
}
}
}
if (i0) {
for (int j = 0; j < n; ++j) {
matrix[0][j] = 0;
}
}
if (j0) {
for (int i = 0; i < m; ++i) {
matrix[i][0] = 0;
}
}
}
};
```
```go
func setZeroes(matrix [][]int) {
m, n := len(matrix), len(matrix[0])
i0, j0 := false, false
for j := 0; j < n; j++ {
if matrix[0][j] == 0 {
i0 = true
break
}
}
for i := 0; i < m; i++ {
if matrix[i][0] == 0 {
j0 = true
break
}
}
for i := 1; i < m; i++ {
for j := 1; j < n; j++ {
if matrix[i][j] == 0 {
matrix[i][0], matrix[0][j] = 0, 0
}
}
}
for i := 1; i < m; i++ {
for j := 1; j < n; j++ {
if matrix[i][0] == 0 || matrix[0][j] == 0 {
matrix[i][j] = 0
}
}
}
if i0 {
for j := 0; j < n; j++ {
matrix[0][j] = 0
}
}
if j0 {
for i := 0; i < m; i++ {
matrix[i][0] = 0
}
}
}
```
```ts
/**
Do not return anything, modify matrix in-place instead.
*/
function setZeroes(matrix: number[][]): void {
const m = matrix.length;
const n = matrix[0].length;
let l0 = false;
let r0 = false;
for (let i = 0; i < m; i++) {
if (matrix[i][0] === 0) {
l0 = true;
break;
}
}
for (let j = 0; j < n; j++) {
if (matrix[0][j] === 0) {
r0 = true;
break;
}
}
for (let i = 0; i < m; i++) {
for (let j = 0; j < n; j++) {
if (matrix[i][j] === 0) {
matrix[i][0] = 0;
matrix[0][j] = 0;
}
}
}
for (let i = 1; i < m; i++) {
for (let j = 1; j < n; j++) {
if (matrix[i][0] === 0 || matrix[0][j] === 0) {
matrix[i][j] = 0;
}
}
}
if (l0) {
for (let i = 0; i < m; i++) {
matrix[i][0] = 0;
}
}
if (r0) {
for (let j = 0; j < n; j++) {
matrix[0][j] = 0;
}
}
}
```
```rust
impl Solution {
pub fn set_zeroes(matrix: &mut Vec<Vec<i32>>) {
let m = matrix.len();
let n = matrix[0].len();
let l0 = {
let mut res = false;
for j in 0..n {
if matrix[0][j] == 0 {
res = true;
break;
}
}
res
};
let r0 = {
let mut res = false;
for i in 0..m {
if matrix[i][0] == 0 {
res = true;
break;
}
}
res
};
for i in 0..m {
for j in 0..n {
if matrix[i][j] == 0 {
matrix[i][0] = 0;
matrix[0][j] = 0;
}
}
}
for i in 1..m {
for j in 1..n {
if matrix[i][0] == 0 || matrix[0][j] == 0 {
matrix[i][j] = 0;
}
}
}
if l0 {
for j in 0..n {
matrix[0][j] = 0;
}
}
if r0 {
for i in 0..m {
matrix[i][0] = 0;
}
}
}
}
```
```js
/**
* @param {number[][]} matrix
* @return {void} Do not return anything, modify matrix in-place instead.
*/
var setZeroes = function (matrix) {
const m = matrix.length;
const n = matrix[0].length;
let i0 = matrix[0].some(v => v == 0);
let j0 = false;
for (let i = 0; i < m; ++i) {
if (matrix[i][0] == 0) {
j0 = true;
break;
}
}
for (let i = 1; i < m; ++i) {
for (let j = 1; j < n; ++j) {
if (matrix[i][j] == 0) {
matrix[i][0] = 0;
matrix[0][j] = 0;
}
}
}
for (let i = 1; i < m; ++i) {
for (let j = 1; j < n; ++j) {
if (matrix[i][0] == 0 || matrix[0][j] == 0) {
matrix[i][j] = 0;
}
}
}
if (i0) {
for (let j = 0; j < n; ++j) {
matrix[0][j] = 0;
}
}
if (j0) {
for (let i = 0; i < m; ++i) {
matrix[i][0] = 0;
}
}
};
```
```c
void setZeroes(int** matrix, int matrixSize, int* matrixColSize) {
int m = matrixSize;
int n = matrixColSize[0];
int l0 = 0;
int r0 = 0;
for (int i = 0; i < m; i++) {
if (matrix[i][0] == 0) {
l0 = 1;
break;
}
}
for (int j = 0; j < n; j++) {
if (matrix[0][j] == 0) {
r0 = 1;
break;
}
}
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (matrix[i][j] == 0) {
matrix[i][0] = 0;
matrix[0][j] = 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 (l0) {
for (int i = 0; i < m; i++) {
matrix[i][0] = 0;
}
}
if (r0) {
for (int j = 0; j < n; j++) {
matrix[0][j] = 0;
}
}
}
```
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