# Set Matrix Zeroes

## Problem

Given a m x n matrix, if an element is 0, set its entire row and column to 0. Do it [**in-place**](https://en.wikipedia.org/wiki/In-place_algorithm).

**Example 1:**

```
Input:

[
  [1,1,1],
  [1,0,1],
  [1,1,1]
]

Output:

[
  [1,0,1],
  [0,0,0],
  [1,0,1]
]
```

**Example 2:**

```
Input:

[
  [0,1,2,0],
  [3,4,5,2],
  [1,3,1,5]
]

Output:

[
  [0,0,0,0],
  [0,4,5,0],
  [0,3,1,0]
]
```

**Follow up:**

* 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?

## Analysis

O(mn)的空间解法最直接暴力，就是开辟和输入matrix同等大小的matrix，用来存储新的matrix；

O(m + n)的空间复杂度则是一个提升，考虑到问题的本质其实是对于为0的元素，其对应下标(i, j)对应的行和列需要被记录，因此分别使用 m, n空间记录那些行和列中有0；

O(1)的空间复杂度则需要思考如何利用matrix本身来存储某行某列有0元素的情况，这里就是想到了使用首行`matrix[0][j]`和首列`matrix[i][0]`作为存储该行i 或者该列j 是否应该设为0的状态的空间，同时安排额外两个变量记录首行和首列本身是否应该设为全0.

## Code

```java
class Solution {
    public void setZeroes(int[][] matrix) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0)
            return;

        int m = matrix.length;
        int n = matrix[0].length;

        boolean firstRowZero = false;
        boolean firstColZero = false;

        //check if first row needs to be changed to zero
        for(int j = 0; j < n; j++) {
            if(matrix[0][j] == 0) {
                firstRowZero = true;
                break;
            }
        }

        //check if first col needs to be changed to zero
        for(int i = 0; i < m; i++) {
            if(matrix[i][0] == 0) {
                firstColZero = true;
                break;
            }
        }

        //mark the row col which have zero in first row and col
        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;
                }
            }
        }

        //fill in the zeroes
        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;
            }
        }

        //update first row
        if(firstRowZero) {
            for(int j = 0; j < n; j++)
                matrix[0][j] = 0;
        }

        //update first col
        if(firstColZero) {
            for(int i = 0; i < m; i++)
                matrix[i][0] = 0;
        }
    }
}
```
