48. Rotate Image

问题描述：

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.

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]
]

解题思路：

本题要求在原数组上直接进行操作，我先从四个角上找了找交换的坐标的关系，然后再对i，j的递增上界进行限定。

n*n的矩阵：

i < n/2 因为四个角一起转动，如果这个时候是n的话，那就要转180度了。

j < n-1-i 也是为了防止重复转动

当遇到两个循环嵌套的时候一定要注意自增的变量有没有写对！！！

代码：

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

别的解法：

参考链接：

http://www.cnblogs.com/grandyang/p/4389572.html