48. 旋转图像
48. 旋转图像
题目
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.
Example 1:
Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]
Example 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]]
Constraints:
n == matrix.length == matrix[i].length
1 <= n <= 20
-1000 <= matrix[i][j] <= 1000
题目大意
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。
解题思路
- 给出一个二维数组,要求顺时针旋转 90 度,这一题比较简单;
- 这里给出 2 种旋转方法的实现,顺时针旋转和逆时针旋转;
- 顺时针旋转:先将二维数组上下翻转,然后将二维数组沿对角线交换;
- 逆时针旋转:先将二维数组左右翻转,然后将二维数组沿对角线交换;
/*
* clockwise rotate 顺时针旋转
* first reverse up to down, then swap the symmetry
* 1 2 3 7 8 9 7 4 1
* 4 5 6 => 4 5 6 => 8 5 2
* 7 8 9 1 2 3 9 6 3
*/
/*
* anticlockwise rotate 逆时针旋转
* first reverse left to right, then swap the symmetry
* 1 2 3 3 2 1 3 6 9
* 4 5 6 => 6 5 4 => 2 5 8
* 7 8 9 9 8 7 1 4 7
*/
代码
/**
* @param {number[][]} matrix
* @return {void} Do not return anything, modify matrix in-place instead.
*/
var rotate = function (matrix) {
const len = matrix.length;
// 上下翻转
// 此处要注意:只能针对一半的行数翻转
// 否则翻转两遍等于没变
for (let i = 0; i < len / 2; i++) {
for (let j = 0; j < len; j++) {
let temp = matrix[i][j];
matrix[i][j] = matrix[len - i - 1][j];
matrix[len - i - 1][j] = temp;
}
}
// 沿对角线翻转
// 此处要注意:只能对左下角或者右上角的一半数据做翻转
// 否则翻转两遍等于没变
for (let i = 0; i < len; i++) {
for (let j = i + 1; j < len; j++) {
let temp = matrix[i][j];
matrix[i][j] = matrix[j][i];
matrix[j][i] = temp;
}
}
};
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