Retrieve all possible combinations of ascending integers from sublists

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I have lists containing sublists. From theses lists I want to retrieve all combinations of integers that are in ascending order. Also the order of the sublists is important (see expected output).

It is not a bad thing when the function does also return the integers themselves (see optional sublists in expected output).

Also, when a sublist has more than one value, I want to consider these a seperate combinations as well. These values cannot occur together (see example 3).

example_list = [[1], [0], [4], [2]]
get_ascending_sublist_values(example_list)
>> [[1, 4], [1, 2], [0, 4], [0, 2] (optional: [1], [0], [4], [2])]

example_list2 = [[1], [0], [4], [2], [5]]
get_ascending_sublist_values(example_list2)
>> [[1, 4, 5], [1, 2, 5], [0, 4, 5], [0, 2, 5], [1, 4], [1, 2], [0, 4], [0, 2], [0, 5], [(optional: [1], [0], [4], [2], [5])]

example_list3 = [[0], [1, 4], [2]]
get_ascending_sublist_values(example_list3)
>> [[0, 1, 2], [0, 1], [0, 4], [0, 2], [1, 2], (optional: [1], [0], [4], [2])]
itertools python-3.x numpy arrays python
1 Answers

Use itertools.combinations and itertools.product. This is not an efficient solution, as this was not a requirement. Making this more efficient (i.e. using backtracking) will take quite some work, and still in theory it can't go below o(2^n).

from itertools import combinations
from itertools import product


def get_ascending_sublist_values(a):
    filtered = set()
    for comb_length in range(2, len(a)+1):
        combs = combinations(a, comb_length)

        results = []
        for comb in combs:
            for i in range(len(comb) - 1):
                prods = product(*comb)
                for prod in prods:
                    if sorted(prod) == list(prod):
                        results.append(tuple(sorted(prod)))

        for r in results:
            filtered.add(r)

    print(filtered)


a1 = [[1], [0], [4], [2]]
a2 = [[1], [0], [4], [2], [5]]
a3 = [[0], [1, 4], [2]]


get_ascending_sublist_values(a1)
print("----------")
get_ascending_sublist_values(a2)
print("----------")
get_ascending_sublist_values(a3)

out:

{(1, 2), (0, 2), (1, 4), (0, 4)}
----------
{(1, 2), (0, 4, 5), (4, 5), (1, 4), (1, 4, 5), (1, 5), (0, 5), (0, 2, 5), (0, 4), (2, 5), (1, 2, 5), (0, 2)}
----------
{(0, 1), (1, 2), (0, 1, 2), (0, 4), (0, 2)}
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