How could I obtain some possible permutations of a string of characters using Python?

Question

I would like to write a Python code to be able to obtain some of the possible permutations of a string of characters.

I present two examples to show what I would like to do.

Example 1: Let's say that I have a string of characters that I write

my_list=['1','2','3','4']

What I would like to obtain are the 3 possible permutations starting the pairing from the left, meaning

['1', '2', '3','4'], ['1', '3', '2', '4'], ['1', '4', '2', '3'] 

So, the first value '1' can be paired with '2' or '3' or '4', and then the remaining pair is '3','4' or '2','4' or '2','3'.

Example 2: Let's say that I have a string of characters that I write

my_list=['1','2','3','4','5','6']

What I would like to obtain are the 15 possible permutations starting the pairing from the left, meaning

['1', '2', '3', '4', '5', '6'],
['1', '2', '3', '5', '4', '6'],
['1', '2', '3', '6', '4', '5'],
['1', '3', '2', '4', '5', '6'],
['1', '3', '2', '5', '4', '6'],
['1', '3', '2', '6', '4', '5'],
['1', '4', '2', '3', '5', '6'],
['1', '4', '2', '5', '3', '6'],
['1', '4', '2', '6', '3', '5'],
['1', '5', '2', '3', '4', '6'],
['1', '5', '2', '4', '3', '6'],
['1', '5', '2', '6', '3', '4'],
['1', '6', '2', '3', '4', '5'],
['1', '6', '2', '4', '3', '5'],
['1', '6', '2', '5', '3', '4']

Where again we have the same kind of pairing as for the first example.

I would also like to obtain the possible permutations of longer strings (8, 10, ...). I would like to use Python because a string of 8 characters leads to 105 possible permutations when starting pairing from the left. Of course, I would like a single code that could give me these permutations for a string of arbitrary length.

The first example is not that difficult but I struggle a lot for the second example. For the first example, I tried using pairs of characters. I define my_list and then another list for the first pair. Then, I remove from my_list the first pair and the resulting string is given by concatenating the first pair and the remaining of my_list. Here is the code for the first example:

my_list_a = ['1', '2', '3', '4']
my_list_b = ['2', '3', '4']

for i in range(1,len(my_list_b)+1):
    tmp_list=['2', '3', '4']
    c = [my_list_a[0],my_list_a[i]]
    tmp_list.remove(my_list_a[i])
    print(c+tmp_list)

I tried to adapt this code for the second example but without success so far. I have seen that to deal with permutations we can use itertools but I did not manage to use it for my purpose.

Answer 1

Updated my answer with the correct solution after feedback from the author.

a = ['1','2','3','4','5','6']

def get_pairs(a, exc_val: int = None):

    if exc_val is not None:
        a = a[:exc_val] + a[exc_val+1:]

    if len(a) <=2:
        return [a]
    
    a0 = a.pop(0)
    t = [[a0, k] + b  for i, k in enumerate(a) for b in get_pairs(a,i)]
    return t

get_pairs(a)

Answer 2

Here is an algorithm for your task:

def generate_permutations_left(input_list):
    permutations = [input_list.copy()]  # Include the original list

    for i in range(1, len(input_list) - 1):
        # Swap elements and save the list
        input_list[i], input_list[i + 1] = input_list[i + 1], input_list[i]
        permutations.append(input_list.copy())

        # Back to original order
        input_list[i], input_list[i + 1] = input_list[i + 1], input_list[i]

    return permutations

In each iteration it swaps the current element with the next element in the list, then it saves that modified list, finally it sets back the original order.

Answer 3

Simple recursion with still available values and already built partial output:

def pair(unpaired, paired=[]):
    if not unpaired:
        print(paired)
    for i in range(len(unpaired) - 1):
        first, *rest = unpaired
        pair(rest, paired + [first, rest.pop(i)])

pair(['1','2','3','4','5','6'])

Output (Attempt This Online!):

['1', '2', '3', '4', '5', '6']
['1', '2', '3', '5', '4', '6']
['1', '2', '3', '6', '4', '5']
['1', '3', '2', '4', '5', '6']
['1', '3', '2', '5', '4', '6']
['1', '3', '2', '6', '4', '5']
['1', '4', '2', '3', '5', '6']
['1', '4', '2', '5', '3', '6']
['1', '4', '2', '6', '3', '5']
['1', '5', '2', '3', '4', '6']
['1', '5', '2', '4', '3', '6']
['1', '5', '2', '6', '3', '4']
['1', '6', '2', '3', '4', '5']
['1', '6', '2', '4', '3', '5']
['1', '6', '2', '5', '3', '4']