526. Beautiful Arrangement

Problem Link

Description

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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

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Python3

class Solution:
    def countArrangement(self, n: int) -> int:
        
        def dfs(count, used):
            if count == 0: return 1
            
            res = 0
            for i in range(1, n+1):
                if not used[i] and (not i%count or not count%i):
                    used[i] = True
                    res += dfs(count-1, used)
                    used[i] = False
            
            return res
        
        return dfs(n, [False]*(n+1))