03. Beautiful Arrangement.cpp

/*
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
*/

class Solution
{
  int count(vector<int> arr, int n)
  {
    if (n <= 0)
      return 1;
    int ans = 0;
    for (int i = 0; i < n; ++i)
    {
      if (arr[i] % n == 0 || n % arr[i] == 0)
      {
        swap(arr[i], arr[n - 1]);
        ans += count(arr, n - 1);
        swap(arr[i], arr[n - 1]);
      }
    }

    return ans;
  }

public:
  int countArrangement(int n)
  {
    vector<int> arr(n, 0);
    for (int i = 0; i < n; ++i)
      arr[i] = i + 1;
    return count(arr, n);
  }
};