<gh_stars>10-100
"""
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:
1. Transpose and reverse row
2. Rotate four rectangles
"""


# Transpose and reverse row
# Time: O(N^2), >45%, where N is the length of side of matrix
# Space: O(1)
class Solution(object):
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: None Do not return anything, modify matrix in-place instead.
        """
        row, col = len(matrix), len(matrix[0])
        # transpose
        for i in range(row):
            for j in range(col):
                if i < j:
                    matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
        
        # reverse row
        for i in range(row):
            matrix[i] = matrix[i][::-1]
        return matrix


# Rotate 4 rectangles
# Time: O(N^2), where N is the length of side of matrix
# Space: O(1)
class Solution:
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: void Do not return anything, modify matrix in-place instead.
        """
        n = len(matrix[0])        
        for i in range(n // 2 + n % 2):
            for j in range(n // 2):
                tmp = matrix[n - 1 - j][i]
                matrix[n - 1 - j][i] = matrix[n - 1 - i][n - j - 1]
                matrix[n - 1 - i][n - j - 1] = matrix[j][n - 1 -i]
                matrix[j][n - 1 - i] = matrix[i][j]
                matrix[i][j] = tmp
"""
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:
1. Transpose and reverse row
2. Rotate four rectangles
"""


# Transpose and reverse row
# Time: O(N^2), >45%, where N is the length of side of matrix
# Space: O(1)
class Solution(object):
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: None Do not return anything, modify matrix in-place instead.
        """
        row, col = len(matrix), len(matrix[0])
        # transpose
        for i in range(row):
            for j in range(col):
                if i < j:
                    matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
        
        # reverse row
        for i in range(row):
            matrix[i] = matrix[i][::-1]
        return matrix


# Rotate 4 rectangles
# Time: O(N^2), where N is the length of side of matrix
# Space: O(1)
class Solution:
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: void Do not return anything, modify matrix in-place instead.
        """
        n = len(matrix[0])        
        for i in range(n // 2 + n % 2):
            for j in range(n // 2):
                tmp = matrix[n - 1 - j][i]
                matrix[n - 1 - j][i] = matrix[n - 1 - i][n - j - 1]
                matrix[n - 1 - i][n - j - 1] = matrix[j][n - 1 -i]
                matrix[j][n - 1 - i] = matrix[i][j]
                matrix[i][j] = tmp
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: 1. Transpose and reverse row 2. Rotate four rectangles # Transpose and reverse row # Time: O(N^2), >45%, where N is the length of side of matrix # Space: O(1) :type matrix: List[List[int]]         :rtype: None Do not return anything, modify matrix in-place instead. # transpose # reverse row # Rotate 4 rectangles # Time: O(N^2), where N is the length of side of matrix # Space: O(1) :type matrix: List[List[int]]         :rtype: void Do not return anything, modify matrix in-place instead.