Leetcode(48) Rotate Image

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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:

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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:

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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]
]

解法

根据观察，可以首先对原数组取其转置矩阵，然后把每行的数字翻转可得到结果，如下所示：

1 2 3　　　 　　 1 4 7　　　　　 7 4 1

4 5 6　　–>　　 2 5 8　　 –> 　 8 5 2　　

7 8 9 　　　 　　3 6 9　　　　 9 6 3

注意转置的时候，或者翻转的时候不要重复交换位置。所以转置的时候j从i开始，而翻转的时候到中轴线停止翻转。

具体代码如下：

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class Solution {
    public void rotate(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = i; j < matrix[0].length; j++) {
                int tmp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = tmp;
            }
        }
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (j < matrix[0].length / 2) {
                    int tmp = matrix[i][j];
                    matrix[i][j] = matrix[i][matrix[0].length - 1 - j];
                    matrix[i][matrix[0].length - 1 - j] = tmp;
                }
            }
        }
    }
}