526. Beautiful Arrangement

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LeetCode

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Problem

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

Code

class Solution {
    int res = 0;
    
    public int countArrangement(int n) {
        helper(n, 1, new boolean[n + 1]);
        return res;
    }
    
    private void helper(int n, int curr, boolean[] visited) {
        if (curr > n) {
            res++;
            return;
        }
        
        for (int i = 1; i <= n; i++) {
            if(visited[i]) continue;
            
            if (i % curr == 0 || curr % i == 0) {
                visited[i] = true;
                helper(n, curr + 1, visited);
                visited[i] = false;
            }
        }
    }
}