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Beautiful Arrangement

Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:

  • perm[i] is divisible by i.

  • i is divisible by perm[i].

Given an integer n, return the number of the beautiful arrangements that you can construct.

Example 1:

Input: n = 2
Output: 2
Explanation: 
The first beautiful arrangement is [1,2]:
    - perm[1] = 1 is divisible by i = 1
    - perm[2] = 2 is divisible by i = 2
The second beautiful arrangement is [2,1]:
    - perm[1] = 2 is divisible by i = 1
    - i = 2 is divisible by perm[2] = 1

Example 2:

Input: n = 1
Output: 1

Constraints:

  • 1 <= n <= 15

Solution:

class Solution {
int count = 0;

    public int countArrangement(int n) {
        int[] nums = new int[n];
        for (int i = 0; i < n; i++)
            nums[i] = i + 1;
        permute(nums, 0);
        return count;
    }

    private void permute(int[] nums, int k) {
        if (k == nums.length)
            count++;
        for (int i = k; i < nums.length; i++) {
            swap(nums, i, k);
            if (nums[k] % (k + 1) == 0 || (k + 1) % nums[k] == 0)
                permute(nums, k + 1);
            swap(nums, i, k);
        }
    }

    private void swap(int[] nums, int i, int j) {
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }
}

Happy Coding!

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