題目描述

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.
意思就是給你一個矩陣，順時針旋轉90度，並進行打印

解法

睡完午覺起來，又看到了這個題目，不知道爲什麼靈感就來了，總覺得這種幾何題目肯定要在上面施加什麼操作，思路會更加清晰，於是乎，冒出了一個想法
1. 首先沿着主對角線進行對稱變換
2. 然後沿着垂直線進行鏡面變換
即

  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]

變成

  [ 5, 2, 13, 15],
  [ 1, 4, 3, 14],
  [ 9, 8, 6, 12],
  [11, 10, 7, 16]

再變成

  [ 15, 13, 2, 5],
  [ 14, 3, 4, 1],
  [ 12, 6, 8, 9],
  [16, 7, 10, 11]

即可
代碼如下：

class Solution { public void rotate(int[][] matrix) { for(int I = 0; I < matrix.length; I ++) { for(int J = I + 1; J < matrix.length; J ++) { int T = matrix[I][J]; matrix[I][J] = matrix[J][I]; matrix[J][I] = T; } } for(int I = 0; I < matrix.length; I ++) { for(int J = 0, M = matrix.length - 1; J < matrix.length / 2; J ++, M --) { int T = matrix[I][J]; matrix[I][J] = matrix[I][M]; matrix[I][M] = T; } } } }