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)