Generating All Possible Combinations

How to get all possible combinations of a list’s elements?

Have a look at itertools.combinations:

itertools.combinations(iterable, r)

Return r length subsequences of elements from
the input iterable.

Combinations are emitted in lexicographic sort order. So, if the
input iterable is sorted, the
combination tuples will be produced in
sorted order.

Since 2.6, batteries are included!

How to generate all possible combinations from the letters of strings in a list

I can propose you a trivial algorithm to do the same, it is using recursion:

def associations(entry):
    while len(entry) > 2:
        to_treat_later = entry.pop()
        print(f"We will treat {to_treat_later} later")
        entry = associations(entry)
        entry.append(to_treat_later)
    else:
        print(f"we can start with {entry}")
        associated_entry = []
        for elt_1 in entry[0]:
            for elt_2 in entry[1]:
                associated_entry.append(f"{elt_1}{elt_2}")
        return [associated_entry]


def convert_entry(entry):
    converted_entry = []
    for elt in entry:
        list_elt = []
        for letter in elt:
            list_elt.append(letter)
        converted_entry.append(list_elt)
    return converted_entry


the_entry = ["jkl", "ghi", "def", "cfe"]
associations(convert_entry(the_entry))

Getting all possible combination for [1,0] with length 3 [0,0,0] to [1,1,1]

You're looking for a Cartesian product, not a combination or permutation of [0, 1]. For that, you can use itertools.product.

from itertools import product

items = [0, 1]

for item in product(items, repeat=3):
    print(item)

This produces the output you're looking for (albeit in a slightly different order):

(0, 0, 0)
(0, 0, 1)
(0, 1, 0)
(0, 1, 1)
(1, 0, 0)
(1, 0, 1)
(1, 1, 0)
(1, 1, 1)

How to generate all the possible combinations for a list of elements grouped in different sizes?

You should take a look at the more-itertools library. And more particularly to the set_partitions method that should suits your needs.

from more-itertools import set_partitions

fruits = ['Apple', 'Orange', 'Banana', 'Watermelon']

for itm in set_partitions(fruits)):
    print(itm)

The ouput produce is :

[['Apple', 'Orange', 'Banana', 'Watermelon']]
[['Apple'], ['Orange', 'Banana', 'Watermelon']]
[['Apple', 'Orange'], ['Banana', 'Watermelon']]
[['Orange'], ['Apple', 'Banana', 'Watermelon']]
[['Apple', 'Orange', 'Banana'], ['Watermelon']]
[['Orange', 'Banana'], ['Apple', 'Watermelon']]
[['Apple', 'Banana'], ['Orange', 'Watermelon']]
[['Banana'], ['Apple', 'Orange', 'Watermelon']]
[['Apple'], ['Orange'], ['Banana', 'Watermelon']]
[['Apple'], ['Orange', 'Banana'], ['Watermelon']]
[['Apple'], ['Banana'], ['Orange', 'Watermelon']]
[['Apple', 'Orange'], ['Banana'], ['Watermelon']]
[['Orange'], ['Apple', 'Banana'], ['Watermelon']]
[['Orange'], ['Banana'], ['Apple', 'Watermelon']]
[['Apple'], ['Orange'], ['Banana'], ['Watermelon']]

EDIT:

And if you want all every combinations possible if you reorder your orignal list you can use the previous method in combination with the the permutations method of itertools with something like:

import itertools
from more_itertools import set_partitions

fruits = ['Apple', 'Orange', 'Banana', 'Watermelon']
output = list()

for x in itertools.permutations(fruits):
    output += list(set_partitions(x))

How to get all possible combinations of array elements without duplicate

Judging from your desired result, you want all the combinations with 2 choices of 'A', 'B', 'C', and '' (nothing). You can do it with nchoosek as follows

result = nchoosek(' ABC', 2) % note space for empty

Output

result =
  6×2 char array
    ' A'
    ' B'
    ' C'
    'AB'
    'AC'
    'BC'

Then removing the spaces and converting the combinations to a cell array:

result = strrep(cellstr(result), ' ', '')

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As Wolfie pointed out, this only works for single character input, for multi character inputs we can use string arrays instead of char arrays:

result = nchoosek(["","A1","B2","C3"], 2);
result = result(:,1) +  result(:,2) % string cat
% result = cellstr(result); % optional if want cell output

result = 
  6×1 string array
    "A1"
    "B2"
    "C3"
    "A1B2"
    "A1C3"
    "B2C3"

Create all possible combinations of lists of different sizes in numpy

Similar to Olvin Roght's comment, but if you put your sublists in a list you can do:

>>>> ls = [[1,2],[3,4],[5,6,7],[8,9,10]]
>>>> [item for cmb in combinations(ls, 2) for item in product(*cmb)]
[(1, 3), (1, 4), (2, 3), (2, 4), (1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (1, 8), (1, 9), (1, 10), (2, 8), (2, 9), (2, 10), (3, 5), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (3, 8), (3, 9), (3, 10), (4, 8), (4, 9), (4, 10), (5, 8), (5, 9), (5, 10), (6, 8), (6, 9), (6, 10), (7, 8), (7, 9), (7, 10)]

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