48. Rotate Image

🟠   🔖  数组 数学 矩阵  🔗 LeetCode

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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