Leetcode-48 Rotate Image

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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

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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]
]

解题思路

顺时针旋转 90°，等价于先将 matrix 倒立，再求 matrix 的对称阵。

复杂度分析

  • 时间复杂度：$O(n^2)$，求矩阵的对称阵。
  • 空间复杂度：$O(1)$。

代码

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class Solution {
public:
	void rotate(vector<vector<int>>& matrix) {
		int n = matrix.size();
		for (int i = 0; i < n / 2; ++i) {
			swap(matrix[i], matrix[n - 1 - i]); //交换矩阵的上下层,使其倒立
		}
		for (int i = 0; i < n; ++i) {
			for (int j = i + 1; j < n; ++j) {
				swap(matrix[i][j], matrix[j][i]); //求对称阵
			}
		}
	}
};