526. Beautiful Arrangement

#### QUESTION:

Suppose you have N integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these N numbers successfully if one of the following is true for the ith position (1 ≤ i ≤ N) in this array:

1. The number at the ith position is divisible by i.
2. i is divisible by the number at the ith position.

Now given N, how many beautiful arrangements can you construct?

Example 1:

``````Input: 2
Output: 2
Explanation:

The first beautiful arrangement is [1, 2]:

Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).

Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).

The second beautiful arrangement is [2, 1]:

Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).

Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.

``````

Note:

1. N is a positive integer and will not exceed 15.

#### EXPLANATION:

``````procedure bt(c)
if reject(P,c) then return
if accept(P,c) then output(P,c)
s ← first(P,c)
while s ≠ Λ do
bt(s)
s ← next(P,s)
``````

#### SOLUTION:

``````public class Solution {
int count = 0;
public ArrayList<Integer> countArrangementList = new ArrayList<>();
public int countArrangement(int N) {
countArrangementHelper(N,1);
return count;
}
public void countArrangementHelper(int N,int index){
if(index>N){
count++;
return;
}
for(int i = 1;i<=N;i++){
if(isValid(index,i)){