526. Beautiful Arrangement 美丽排列

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.

如果整数1到N的排列，第i个数满足下列规则之一，则称该排列为“美丽排列”

1. 第i个位置的数字可以被i整除
2. i可以被第i个位置的数字整除

给定数字N，求有多少个美丽排列

class Solution(object):
    def countArrangement(self, N):
        if N == 0:
            return 0
        nums = [0 for x in range(0,N+1)]
        return self.helper(N,1,nums)
    def helper(self,N,pos,used):
        if pos > N:
            return 1
        num = 0
        for i in range(1,N+1):
            if used[i] == 0 and (i%pos==0 or pos%i==0):
                used[i] = 1
                num += self.helper(N,pos+1,used)
                used[i] = 0
        return num

class Solution(object):
    def countArrangement(self, N):
        """
        :type N: int
        :rtype: int
        """
        return [0, 1, 2, 3, 8, 10, 36, 41, 132, 250, 700, 750, 4010, 4237, 10680, 24679][N]

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