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128 lines
2.9 KiB
Markdown
Executable File
128 lines
2.9 KiB
Markdown
Executable File
# [48. Rotate Image](https://leetcode.com/problems/rotate-image/)
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## 题目
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You are given an *n* x *n* 2D matrix representing an image.
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Rotate the image by 90 degrees (clockwise).
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**Note**:
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You have to rotate the image **[in-place](https://en.wikipedia.org/wiki/In-place_algorithm)**, which means you have to modify the input 2D matrix directly. **DO NOT** allocate another 2D matrix and do the rotation.
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**Example 1**:
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Given input matrix =
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[
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[1,2,3],
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[4,5,6],
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[7,8,9]
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],
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rotate the input matrix in-place such that it becomes:
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[
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[7,4,1],
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[8,5,2],
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[9,6,3]
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]
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**Example 2**:
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Given input matrix =
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[
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[ 5, 1, 9,11],
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[ 2, 4, 8,10],
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[13, 3, 6, 7],
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[15,14,12,16]
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],
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rotate the input matrix in-place such that it becomes:
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[
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[15,13, 2, 5],
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[14, 3, 4, 1],
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[12, 6, 8, 9],
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[16, 7,10,11]
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]
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## 题目大意
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给定一个 n × n 的二维矩阵表示一个图像。将图像顺时针旋转 90 度。说明：你必须在原地旋转图像，这意味着你需要直接修改输入的二维矩阵。请不要使用另一个矩阵来旋转图像。
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## 解题思路
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- 给出一个二维数组，要求顺时针旋转 90 度。
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- 这一题比较简单，按照题意做就可以。这里给出 2 种旋转方法的实现，顺时针旋转和逆时针旋转。
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```c
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/*
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* clockwise rotate 顺时针旋转
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* first reverse up to down, then swap the symmetry
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* 1 2 3 7 8 9 7 4 1
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* 4 5 6 => 4 5 6 => 8 5 2
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* 7 8 9 1 2 3 9 6 3
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*/
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void rotate(vector<vector<int> > &matrix) {
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reverse(matrix.begin(), matrix.end());
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for (int i = 0; i < matrix.size(); ++i) {
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for (int j = i + 1; j < matrix[i].size(); ++j)
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swap(matrix[i][j], matrix[j][i]);
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}
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}
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/*
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* anticlockwise rotate 逆时针旋转
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* first reverse left to right, then swap the symmetry
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* 1 2 3 3 2 1 3 6 9
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* 4 5 6 => 6 5 4 => 2 5 8
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* 7 8 9 9 8 7 1 4 7
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*/
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void anti_rotate(vector<vector<int> > &matrix) {
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for (auto vi : matrix) reverse(vi.begin(), vi.end());
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for (int i = 0; i < matrix.size(); ++i) {
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for (int j = i + 1; j < matrix[i].size(); ++j)
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swap(matrix[i][j], matrix[j][i]);
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}
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}
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```
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## 代码
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```go
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package leetcode
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func rotate(matrix [][]int) {
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row := len(matrix)
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if row <= 0 {
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return
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}
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column := len(matrix[0])
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// rotate by diagonal 对角线变换
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for i := 0; i < row; i++ {
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for j := i + 1; j < column; j++ {
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tmp := matrix[i][j]
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matrix[i][j] = matrix[j][i]
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matrix[j][i] = tmp
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}
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}
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// rotate by vertical centerline 竖直轴对称翻转
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halfColumn := column / 2
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for i := 0; i < row; i++ {
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for j := 0; j < halfColumn; j++ {
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tmp := matrix[i][j]
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matrix[i][j] = matrix[i][column-j-1]
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matrix[i][column-j-1] = tmp
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}
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}
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}
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```
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