48. Rotate Image

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]
]

难度： medium

题目：给定n * n的矩阵表示一张图片。顺时针90度旋转。
注意：必须原地旋转不允许申请额外的空间。

思路：90度旋转有数学规律可寻。

Runtime: 1 ms, faster than 100.00% of Java online submissions for Rotate Image.
Memory Usage: 26.4 MB, less than 46.19% of Java online submissions for Rotate Image.

class Solution {
    public void rotate(int[][] matrix) {
        int n = matrix.length;
        int nIdx = n - 1;
        for (int i = 0; i < n / 2; i++) {
            int start = i;
            int end = nIdx - i;
            for (int j = start; j < end; j++) {
                int t = matrix[nIdx - j][i];
                matrix[nIdx - j][i]= matrix[end][nIdx - j];
                matrix[end][nIdx - j] = matrix[j][end];
                matrix[j][end] = matrix[i][j];
                matrix[i][j] = t;
             }
        }
    } 
}