# Question

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:

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

class Solution:
def rotate(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: void Do not return anything, modify matrix in-place instead.
"""
length = len(matrix)
if length <= 1:
return
half_i = length // 2 if length % 2 == 0 else length // 2 + 1
half_j = length // 2
length -= 1

for i in range(0, half_i):
for j in range(0, half_j):
# (i, j) -> (j, len-i) -> (len-i, len-j) -> (len-j, i) -> (i,j)
temp1 = matrix[i][j]
matrix[i][j] = matrix[length-j][i]
temp2 = matrix[j][length-i]
matrix[j][length-i] = temp1
temp1 = matrix[length-i][length-j]
matrix[length-i][length-j] = temp2
matrix[length-j][i] = temp1