You are given an n x n 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

Note:

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Example 1:

Input:

[
[1,2,3],
[4,5,6],
[7,8,9]
]


Output:

[
[7,4,1],
[8,5,2],
[9,6,3]
]


Example 1:

Input:

[
[ 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]
]


## Solution

from typing import List

class Solution:
def rotate(self, matrix: List[List[int]]) -> None:
n = len(matrix[0])
# transpose matrix
for i in range(n):
for j in range(i, n):
matrix[j][i], matrix[i][j] = matrix[i][j], matrix[j][i]

# reverse each row
for i in range(n):
matrix[i].reverse()


## Test Cases

test = Solution()
matrix = [
[1,2,3],
[4,5,6],
[7,8,9]
]
test.rotate(matrix)
assert matrix == [
[7,4,1],
[8,5,2],
[9,6,3]
]
print('All Passed!')


## Big O Analysis

Space Complexity: O(1)

Time Complexity: O(N2)