Rotate image

Time: O(N^2); Space: O(1); medium

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: matrix =

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

Output:

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

Example 2:

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]
]

[4]:

class Solution1(object):
    """
    Rotate the image in-place
    Time: O(N^2)
    Space: O(1)
    """
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: List[List[int]]
        """
        n = len(matrix)

        # anti-diagonal mirror
        for i in range(n):
            for j in range(n - i):
                matrix[i][j], matrix[n-1-j][n-1-i] = matrix[n-1-j][n-1-i], matrix[i][j]

        # horizontal mirror
        for i in range(n // 2):
            for j in range(n):
                matrix[i][j], matrix[n-1-i][j] = matrix[n-1-i][j], matrix[i][j]

        return matrix

[5]:

s = Solution1()
matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]
s.rotate(matrix)
assert matrix == [
    [7,4,1],
    [8,5,2],
    [9,6,3]
]

matrix = [
      [ 5, 1, 9,11],
      [ 2, 4, 8,10],
      [13, 3, 6, 7],
      [15,14,12,16]
    ]
s.rotate(matrix)
assert matrix == [
      [15,13, 2, 5],
      [14, 3, 4, 1],
      [12, 6, 8, 9],
      [16, 7,10,11]
    ]

[6]:

class Solution2(object):
    """
    Time: O(N^2)
    Space: O(N^2)
    """
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: List[List[int]]
        """
        return [list(reversed(x)) for x in zip(*matrix)]

[7]:

s = Solution2()
matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]
assert s.rotate(matrix) == [
    [7,4,1],
    [8,5,2],
    [9,6,3]
]

matrix = [
      [ 5, 1, 9,11],
      [ 2, 4, 8,10],
      [13, 3, 6, 7],
      [15,14,12,16]
    ]
assert s.rotate(matrix) == [
      [15,13, 2, 5],
      [14, 3, 4, 1],
      [12, 6, 8, 9],
      [16, 7,10,11]
    ]