【Rosalind】Enumerating Oriented Gene Orderings - 排列与组合

最近更新比较少，做题也比较慢，因为手头事情多起来了，而且这些题目真是很难了，不静下来在纸上算一会我是真写不出来。今天就分享一道和之前两道题有关的一道习题吧。

Problem

A signed permutation of length nn is some ordering of the positive integers {1,2,…,n} in which each integer is then provided with either a positive or negative sign (for the sake of simplicity, we omit the positive sign). For example, π=(5,−3,−2,1,4) is a signed permutation of length 5.

Given: A positive integer n≤6.

Return: The total number of signed permutations of length n, followed by a list of all such permutations (you may list the signed permutations in any order).

Sample Dataset

2

Sample Output

8
-1 -2
-1 2
1 -2
1 2
-2 -1
-2 1
2 -1
2 1

思路

这道题和之前的一道题非常类似，首先要生成全排列，然后需要对每个位置的正负进行组合。

首先收集(1,2,...,n)的全排列到一个列表里。

然后从(1,-1)这两个元素中随机选n次，得到的所有组合放到一个列表里。

假如n=3，全排列表里应该有个(1,2,3)，符号的组合里应该有一个(1,-1,1)，我们再把这两个列表里的列表或元组对应相乘，前面这个例子输出就应该是(1,-2,3)。

全排列的数量是n!，符号组合的数目是2^n，所以总的输出的可能数应该是n!*(2**n)。

我的代码

"""
	Rosalind Problems: Enumerating Oriented Gene Orderings

	Problem ID: SIGN

	http://rosalind.info/problems/sign/

	A signed permutation of length n is some ordering of the positive integers {1,2,…,n} in which each integer is then provided with either a positive or negative sign (for the sake of simplicity, we omit the positive sign). For example, π=(5,−3,−2,1,4) is a signed permutation of length 5.

	Given: A positive integer n≤6.

	Return: The total number of signed permutations of length n, followed by a list of all such permutations (you may list the signed permutations in any order).
"""

from itertools import product

def fac(x):
	if x==1:
		return x
	else:
		return x*fac(x-1)

def perm(n):
	elem = [