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[Leetcode]48. Rotate Image(C++)

题目描述

题目链接:48. Rotate Image

You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise).

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.

例子

例子 1

Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]

例子 2

Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
Output: [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

例子 3

Input: matrix = [[1]]
Output: [[1]]

Follow Up

Note

Constraints

  • matrix.length == n
  • matrix[i].length == n
  • 1 <= n <= 20
  • -1000 <= matrix[i][j] <= 1000

解题思路

观察一下矩阵变换的规律,可以发现顺时针旋转可以由以下两个操作完成:

  • 垂直翻转
  • 沿对角线翻转

代码如下:

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#include <vector>

class Solution {
public:
void rotate(std::vector<std::vector<int>>& matrix) {
int n = matrix.size();

for (int i = 0; i < n / 2; ++i) {
for (int j = 0; j < n; ++j) {
std::swap(matrix[i][j], matrix[n - 1 - i][j]);
}
}

for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
std::swap(matrix[i][j], matrix[j][i]);
}
}
}
};
  • 时间复杂度: O(n)
  • 空间复杂度: O(1)

GitHub 代码同步地址: 48.RotateImage.cpp

其他题目:
GitHub: Leetcode-C++-Solution
博客: Leetcode-Solutions