Description：
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]
]

题意：将一个n维矩阵顺时针方向旋转90°；要求直接对此矩阵进行操作，不再额外的分配空间；

解法：对n维矩阵旋转90°相当于先将其转置后再对矩阵左右两边的元素进行交换即可；
例如：对于矩阵

matrix = [
   [ 5, 1, 9,11],
     [ 2, 4, 8,10],
     [13, 3, 6, 7],
     [15,14,12,16]
]
matrix.T = [
   [5, 2, 13, 15],
     [1, 4,  3, 14],
     [9, 8,  6, 12],
     [11,10, 7, 16]
]
matrix90 = [
     [15,13, 2, 5],
     [14, 3, 4, 1],
     [12, 6, 8, 9],
     [16, 7,10,11]
]
Java
class Solution {
    public void rotate(int[][] matrix) {
        for (int i=0; i<matrix.length; i++) {
            for (int j=0; j<i; j++) {
                matrix[i][j] = matrix[i][j] ^ matrix[j][i];
                matrix[j][i] = matrix[i][j] ^ matrix[j][i];
                matrix[i][j] = matrix[i][j] ^ matrix[j][i];
            }
        }
        for (int i=0; i<matrix.length; i++) {
            for (int j=0; j<matrix.length/2; j++) {
                matrix[i][j] = matrix[i][j] ^ matrix[i][matrix.length-j-1];
                matrix[i][matrix.length-j-1] = matrix[i][j] ^ matrix[i][matrix.length-j-1];
                matrix[i][j] = matrix[i][j] ^ matrix[i][matrix.length-j-1];
            }
        }
    }
}