題目： 

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]
]

分析：

很明顯，題目要求矩陣順時針旋轉90度，且要求不開闢新的空間。我們可以先求矩陣的轉置，之後再將轉置好的矩陣前後列交換，如下圖。

程式：

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        int n = matrix.size();
        for (int i = 0; i < n-1; i++){
            for (int j = i+1; j < n; j++){
                swap(matrix[i][j], matrix[j][i]);
            }
        }
        
 
for (int i = 0; i < n/2; i++){
            for (int j = 0; j < n; j++){
                swap(matrix[j][i],matrix[j][n-1-i]);
            }
        }
    }
};