# 526. Beautiful Arrangement

### Problem:

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:

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

### Solutions:

``````public class Solution {
public int countArrangement(int N) {
boolean[] visited = new boolean[N + 1];
return process(1, visited);
}
private int process(int start, boolean[] visited) {
if (start == visited.length) {
return 1;
}
int count = 0;
for (int i = 1; i < visited.length; i ++) {
if (visited[i] == false && (start % i == 0 || i % start == 0)) {
visited[i] = true;
count += process(start + 1, visited);
visited[i] = false;
}
}
return count;
}
}
``````