notes/OJ notes/pages/Leetcode Rotate-Image.md

# Leetcode Rotate-Image

2022-09-02 15:40

> ##### Algorithms:
>
> #algorithm #math
>
> ##### Data structures:
>
> #DS #array
>
> ##### Difficulty:
>
> #coding_problem #difficulty_medium
>
> ##### Additional tags:
>
> #leetcode #CS_list_need_understanding
>
> ##### Revisions:
>
> N/A

##### Links:

- [Link to problem](https://leetcode.com/problems/rotate-image/)
- [Solution and explanation](https://leetcode.com/problems/rotate-image/solution/)

---

### Problem

You are given an `n x n` 2D `matrix` representing an image, rotate the image by **90** degrees (clockwise).

You have to rotate the image [**in-place**](https://en.wikipedia.org/wiki/In-place_algorithm), which means you have to modify the input 2D matrix directly. **DO NOT** allocate another 2D matrix and do the rotation.

#### Examples

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/08/28/mat1.jpg)

```
**Input:** matrix = [[1,2,3],[4,5,6],[7,8,9]]
**Output:** [[7,4,1],[8,5,2],[9,6,3]]
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/08/28/mat2.jpg)

```
**Input:** matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
**Output:** [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]
```

#### Constraints

### Thoughts

> [!summary]
> This is a #math problem.

Mainly two ways

#### Method 1: rotate in rings

#TODO complete in this method.

#### Method 2: transpose and reflect

transpose reflects the matrix in `y = x`,
reflect changes matrix in axis y

### Solution

```cpp
class Solution {

  void reflect(vector<vector<int>> &mat) {
    // reflect in y axis.
    int n = mat.size();
    for (int i = 0; i < n; i++) {
      for (int j = 0, half = n / 2; j < half; j++) {
        swap(mat[i][j], mat[i][n - j - 1]);
      }
    }
  }

  void transpose(vector<vector<int>> &mat) {
    int n = mat.size();
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < i; j++) {
        swap(mat[i][j], mat[j][i]);
      }
    }
  }

public:
  void rotate(vector<vector<int>> &matrix) {
    // transpose and reflect

    transpose(matrix);
    reflect(matrix);
  }
};
```