How to recursively create a list of permutations in python?

Question

I have a dictionary called possibilities where the key is an index and the values for that key are the values that can sit on that index in a list. See below:

possibilities = {0: [None, 'KLAX_1', 'KDEN_1'],
 1: [None, 'KLAX_1', 'KDEN_1'],
 2: [None, 'KLAX_1', 'KLAS_1', 'KDEN_1'],
 3: [None, 'KLAX_1', 'KLAS_1', 'KPHX_1', 'KDEN_1', 'KDFW_1'],
 4: [None, 'KPHX_1', 'KDEN_2', 'KDFW_2'],
 5: [None, 'KDEN_2', 'KDFW_2'],
 6: [None, 'KDEN_2']}

I want to save every permutation of this list in another list called permutations_list . My goal is to create this permutations_list from the possibilities dict. Currently I have a huge nested for loop that builds this (see below). But I want to have a function that takes in the possibilities_dict and generates my list automatically . I'm thinking that a recursive function will allow me to not specify the number of indexes I need.

for index_0 in possibilities[0]:
    for index_1 in possibilities[1]:
        for index_2 in possibilities[2]:
            for index_3 in possibilities[3]:
                for index_4 in possibilities[4]:
                    for index_5 in possibilities[5]:
                        for index_6 in possibilities[6]:
                            lst = [index_0,index_1,index_2,index_3,index_4,index_5,
                                  index_6]
                            permutations_list.append(lst)

The result from the code above is a list permutations_list of length 5184 . Each item in that list is a list that contains a specific permutation of all the values. This is not as simple as using itertools.permutations as only specific values can sit at specific indexes on the list. Can anyone help provide a recursive function for doing this? Thanks.

Answer 1

After some coding I have come up with a recursive solution. You can either use itertools.product or the functions below.

def rec_permutations(possibilities):
    counter = 0
    permutations_list=[]
    lst=[]
    return rec_permutations_helper(possibilities, permutations_list, counter, lst)

def rec_permutations_helper(possibilities, permutations_list, counter, lst):
    # Base case
    if counter == len(possibilities):
        permutations_list.append(lst)
        return
    # Recursive case
    else:
        locations = possibilities[counter]
        for location in locations:
            new_lst = lst + [location]      
            rec_permutations_helper(possibilities, permutations_list, counter+1, new_lst)

    return permutations_list