Enumerating Oriented Gene Orderings

This is yet another problem with permutations. As in the previous problems of this type we get a positive integer n and are supposed to find some permutations. This time we are looking at signed permutations, that is, for all the positive integers in the range 1 to n we should also take into account their corresponding negative value. As in Enumerating Gene Orders, we should print the total number of permutations followed by each of the permutations.

Sample dataset:

2

Expected output:

8

-1 -2

-1 2

1 -2

1 2

-2 -1

-2 1

2 -1

2 1

Note that we should not count permutations of the same integer (i. e. -1 1, 2 -1 and so on should not be included).

For this problem we can once again utilise the itertools function permutations. However, this time we need to pair it to the itertools function product. The following is my code:

import itertools                                                           

n = 3                                                                      

permutation = []                                                           

nr = 0                                                                     

for i in itertools.permutations(list(range(1, n + 1))):                    

    for j in itertools.product([-1, 1], repeat=len(list(range(1, n + 1)))):

        perm = [a * sign for a, sign in zip(i, j)]                         

        permutation.append(perm)                                           

        nr += 1                                                            

print(nr)                                                                  

for i in range(len(permutation)):                                          

    print(*permutation[i], sep=' ')