Rotate Image

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

Note:

• 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:

 Given input matrix =
 [
    [1,2,3],
    [4,5,6],
    [7,8,9]
 ],

rotate the input matrix in-place such that it becomes:
[
    [7,4,1],
    [8,5,2],
    [9,6,3]
]

Example 2:

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

rotate the input matrix in-place such that it becomes:
[
    [15,13, 2, 5],
    [14, 3, 4, 1],
    [12, 6, 8, 9],
    [16, 7,10,11]
]

Solution:

/**
* @param {number[][]} matrix
* @return {void} Do not return anything, modify matrix in-place instead.
*/
function rotate1(matrix) {
    const last = matrix.length - 1;
    for (let i = 0; i < matrix.length / 2; i++) {  i is layer level
        for (let j = i; j < last - i; j++) {
            swap(matrix, i, j, j, last - i);
            swap(matrix, i, j, last - i, last - j);
            swap(matrix, i, j, last - j, i);
        }
    }
}

function swap(m, x1, y1, x2, y2) {
    [m[x1][y1], m[x2][y2]] = [m[x2][y2], m[x1][y1]];
}

1. Swap three times from outside to inside

    Step 1: 1 -> 3 -> 9 -> 7, then 2 -> 6 -> 8 -> 4
    1 2 3 3 2 1 9 2 1 7 2 1
    4 5 6 -> 4 5 6 => 4 5 6 -> 4 5 6
    7 8 9 7 8 9 7 8 3 9 8 3
   

2. Step 2: from outside to inside

3. Reverse up to down, then swap the symmetry

Solution 2:

• To clockwise rotate, reverse up to down, then swap the symmetry
• To anticlockwise rotate, reverse left to right, then swap the symmetry)

Example

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

function rotate(matrix) {
    matrix.reverse();
    for (let i = 0; i < matrix.length; i++) {
        for (let j = i + 1; j < matrix[i].length; j++){
            [matrix[i][j], matrix[j][i]] = [matrix[j][i], matrix[i][j]];
        }
    }
}