526. Beautiful Arrangement 美丽排列
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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:
- 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”
- 第i个位置的数字可以被i整除
- 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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