# 48\_Rotate Image

You are given an `nxn` 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

**Note:**

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.

**Example 1:**

```
Given input matrix = 
[
  [1,2,3],
  [4,5,6],
  [7,8,9]
],

rotate the input matrix in-place such that it becomes:
[
  [7,4,1],
  [8,5,2],
  [9,6,3]
]
```

**Example 2:**

```
Given input matrix =
[
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
], 

rotate the input matrix in-place such that it becomes:
[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]
```

## Solution 1:

If there is no constraint of in-place rotation, a brute force method is to initiate a new `nxn` matrix and put each row in the original matrix into the column of the new matrix in a reversed order.

## Solution 2:

**Idea**: (In-place rotation)

* split the whole matrix into 4 parts: upper-left, upper-right, bottom-right, bottom-left, loop over all the elements in the upper left part, and rotate the corresponding 3 elements in the other 3 parts.

**Time Complexity**: $$O(n^2)$$

**Space Complexity**: $$O(1)$$

```python
def rotate(matrix):
    """
    :type matrix: List[List[int]]
    :rtype: void Do not return anything, modify matrix in-place instead.
    """
    n = len(matrix)
    for i in range(n//2):
        for j in range(n-n//2):
            matrix[i][j], matrix[j][~i], matrix[~i][~j], matrix[~j][i] \
            = matrix[~j][i], matrix[i][j], matrix[j][~i], matrix[~i][~j]
```

Note that `[~i]` means `[n-1-i],` and it's easier to read.

Reference: [https://leetcode.com/problems/rotate-image/discuss/18884/Seven-Short-Solutions-(1-to-7-lines)](https://leetcode.com/problems/rotate-image/discuss/18884/Seven-Short-Solutions-%281-to-7-lines%29)


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