Prerequisite

Permutations

Problem Statement

uppose 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

Problem Link

Beautiful Arrangement - LeetCode

Code

class Solution {
public:
    vector<int> nums;
    int res = 0;
    int countArrangement(int n) {
        
        nums.resize(n);
        
        for(int i=0;i<n;i++)
            nums[i] = i+1;
        
        solve(0,n);
        
        return res;
        
        
    }
   
    void solve(int l,int n)
    {
        if(l==n)
        {
            res++;
            return;
        }
        
        for(int i=l;i<n;i++)
        {
            if(nums[i]%(l+1)==0 || (l+1)%nums[i]==0)
            {
                swap(nums[i],nums[l]);
            
                solve(l+1,n);
            
                swap(nums[i],nums[l]);
            }
        }
    }
};