Permutations without reversed sequences in Python

Question

I would like to generate a list of all permutations of 4 digits where :

All 4 digits are always present
Two reversed sequences are the same solution. For example. (1,2,3,4) = (4,3,2,1)

I would like to know:

What do you call this kind of permutations.
If it is possible to generate this list in one step. Below there is an example that generates it in two steps.

import itertools
inp_list = range(1, 5)

# 1. Create the list of all permutations.
permutations = list(itertools.permutations(inp_list))

# 2. Remove sequences that are the reverse of another.
for _p in permutations[::-1]:
    if _p[::-1] in permutations:
        permutations.remove(_p)

for _p in permutations:
    print("\t".join(map(str, _p)))

Kelly Bundy · Accepted Answer · 2021-11-12 15:36:36Z

3

You could just use the smaller one of each reversal pair:

from itertools import permutations

for p in permutations(range(1, 5)):
    if p < p[::-1]:
        print(*p)

Output:

answered Nov 12, 2021 at 15:36

Kelly Bundy

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1 Comment

nico Over a year ago

Very elegant solution!

mozway · Accepted Answer · 2021-11-12 13:45:32Z

3

To simplify your code and make it more efficient you could:

1- use a python set as the container (checking the presence of an element is much faster)

2- add the final output directly

3- avoid to create a temporary list with the permutations, keep it as a generator

from itertools import permutations
inp_list = range(1, 5)

out = set()
for p in permutations(inp_list): # loop over generator output
    p = '\t'.join(map(str,p))    # craft the desired output format
    if not p[::-1] in out:       # is the reverse not already in the set?
        out.add(p)               # then add the item
        print(p)                 # and print it

output:

1   2   3   4
1   2   4   3
1   3   2   4
1   3   4   2
1   4   2   3
1   4   3   2
2   1   3   4
2   1   4   3
2   3   1   4
2   4   1   3
3   1   2   4
3   2   1   4

answered Nov 12, 2021 at 13:45

mozway

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1 Comment

nico Over a year ago

Thank you for the advice about python sets.

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