Beautiful Arrangement

Description

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 i_th position (1 <= i <= N) in this array:

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

 

Solution(javascript)

/**
 * @param {number} N
 * @return {number}
 */
const countArrangement = function (N) {
  const list = new Array(N).fill(0).map((_, index) => index + 1)
  let result = 0
  const aux = (currentList = []) => {
    if (currentList.length === 0) {
      result += 1
      return
    }
    currentList.forEach((v) => {
      const index = N - currentList.length + 1
      if (Number.isInteger(index / v) || Number.isInteger(v / index)) {
        aux(currentList.filter(x => x !== v))
      }
    })
  }
  aux(list)
  return result
}