[LeetCode] 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.

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

旋转图像。

给定一个 n × n 的二维矩阵 matrix 表示一个图像。请你将图像顺时针旋转 90 度。 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。

思路

既然规定了要 in-place 做，只能想到对折之类的做法。但是如何对折呢？是先通过对角线对折（左上 - 右下），然后再左右对折。注意对角线对折部分 j 指针是从哪里开始的。

复杂度

时间O(n^2)
空间O(1)

代码

Java实现

class Solution {
    public void rotate(int[][] matrix) {
        // 按左上 - 右下对角线交换
        int m = matrix.length;
        for (int i = 0; i < m; i++) {
            for (int j = i; j < m; j++) {
                int temp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = temp;
            }
        }

        // 左右对折
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < m / 2; j++) {
                int temp = matrix[i][j];
                matrix[i][j] = matrix[i][m - 1 - j];
                matrix[i][m - 1 - j] = temp;
            }
        }
        return;
    }
}

JavaScript实现

/**
 * @param {number[][]} matrix
 * @return {void} Do not return anything, modify matrix in-place instead.
 */
var rotate = function (matrix) {
    let m = matrix.length;
    // 左上- 右下对角线交换
    for (let i = 0; i < m; i++) {
        for (let j = i; j < m; j++) {
            let temp = matrix[i][j];
            matrix[i][j] = matrix[j][i];
            matrix[j][i] = temp;
        }
    }

    // 左右对折
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < m / 2; j++) {
            let temp = matrix[i][j];
            matrix[i][j] = matrix[i][m - 1 - j];
            matrix[i][m - 1 - j] = temp;
        }
    }
};

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