48. Rotate Image

摘要： 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 ima...

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]
]

難度： medium

題目：給定n * n的矩陣表示一張圖片。順時針90度旋轉。

注意：必須原地旋轉不允許申請額外的空間。

思路：90度旋轉有數學規律可尋。

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;
}
}
} 
}