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:
    def count(self, i, n, used):
        if i > n:
            return 1
        ctr = 0
        for j in range(1, n + 1):
            if j not in used and (j % i == 0 or i % j == 0):
                ctr += self.count(i + 1, n, used.union({j}))
        return ctr
    
    def countArrangement(self, n: int) -> int:
        return self.count(1, n, set())

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