# 526. Beautiful Arrangement

## 1. Question

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.
• iis divisible by perm[i].

Given an integer n, return the number of the beautiful arrangements that you can construct.

## 2. Examples

Example 1:

Input: n = 2
Output: 2
Explanation:
The first beautiful arrangement is [1,2]:
- perm = 1 is divisible by i = 1
- perm = 2 is divisible by i = 2
The second beautiful arrangement is [2,1]:
- perm = 2 is divisible by i = 1
- i = 2 is divisible by perm = 1


Example 2:

Input: n = 1
Output: 1


## 3. Constraints

• 1 <= n <= 15

# Solutions

class Solution {

ArrayList<Integer>[] list;
boolean[] visited;
int res = 0;

public int countArrangement(int n) {

list = new ArrayList[n + 1];
visited = new boolean[n + 1];

for (int i = 1; i <= n; i++) {
list[i] = new ArrayList();
for (int j = 1; j <= n; j++) {
if (i % j == 0 || j % i == 0) {
}
}
}

backtrace(1, n);
return res;
}

private void backtrace(int index, int n) {
if (index == n + 1) {
res++;
return;
}
for (int k : list[index]) {
if (!visited[k]) {
visited[k] = true;
backtrace(index + 1, n);
visited[k] = false;
}
}
}
}