原题

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.

• All numbers (including target) will be positive integers.
• The solution set must not contain duplicate combinations.

题目：

给出一个表示图像的 n x n 2D 矩阵。 将图像旋转90度 (顺时针方向)。

注意：

必须在就地旋转图像, 这意味着您必须直接修改输入2D 矩阵。不要分配另一个2D 矩阵并进行旋转。

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]
]

My Answer

思路分析

本题首先向尝试直接一步找出旋转矩阵的对应规律，发现比较困难。

次之，采用两步得到最终形态：先将矩阵转置，然后将矩阵的每一行翻转，就可以得到所要求的矩阵了。

class Solution:
    def rotate(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: void Do not return anything, modify matrix in-place instead.
        """
        
        for row in range(len(matrix)):
            for column in range(row, len(matrix)):
                matrix[row][column], matrix[column][row] = matrix[column][row], matrix[row][column]
        for row in range(len(matrix)):
            matrix[row].reverse()

反思：

1. 对于难以找到一步转换规律的问题，就尝试分多步实现；
2. 对于这种矩阵，无需再return matrix，自己在这个地方卡了很久，要注意。