Combination items of List in Python

Question

I have a list:

[0, 1, 2, 3, 4, 5]

I would like to combine the first item all others except the last. The result should be a list, as the list below:

[[0], [0,1], [0,2], [0,3], [0,4], [0,1,2], [0,1,3] [0,1, 4], [0,2,3], [0,2,4], [0,3,4], [0,1,2,3], [0,1,2,4], [0, 2,3,4], [0,1,2,3,4]]

How can I do this? Thank you!

Answer 1

import itertools

a = [0, 1, 2, 3, 4, 5]

base = (a[0],)
items = a[1:-1]
combos = [base + combo for length in range(len(items)+1) for combo in itertools.combinations(items, length)]

# In case it matters that the sublists are lists rather than tuples:
combos = [list(combo) for combo in combos]

print combos
# [[0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]]

Answer 2

First compute the power set of the all but the first item. Searching on "python power set" you'll get several hits, including this one . You didn't specifically mention it, but you probably want the results in lexographical order, and the implementation I selected gets you most of the way there.

That will give you all the combinations you need, .eg [[], 1 , ..., [1,2,3,4,5]] (note this includes the empty set and the whole set itself). Now just prepend 0 to each of these gives [[0],[0,1],...[0,1,2,3,4,5]].

Answer 3

This problem is related to powersets

>>> L = [0, 1, 2, 3, 4, 5]
>>> [[L[0]] + [k for j,k in enumerate(L[1:-1]) if i>>j&1] for i in range(1<<(len(L)-2))]
[[0], [0, 1], [0, 2], [0, 1, 2], [0, 3], [0, 1, 3], [0, 2, 3], [0, 1, 2, 3], [0, 4], [0, 1, 4], [0, 2, 4], [0, 1, 2, 4], [0, 3, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]]

If you want them sorted shortest to longest:

>>> M = [[L[0]] + [k for j,k in enumerate(L[1:-1]) if i>>j&1] for i in range(1<<(len(L)-2))
>>> sorted(M, key=len)
[[0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 1, 2], [0, 1, 3], [0, 2, 3], [0, 1, 4], [0, 2, 4], [0, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]]

Answer 4

Its a combination of the first element plus the powerset of all the elements minus the first and last elements:

from itertools import chain, combinations

test = [0, 1, 2, 3, 4, 5]

def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))


print [test[:1] + list(c) for c in powerset(test[1:-1])]

# [[0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]]   

Answer 5

Here is a generator.

from itertools import combinations

def custom_combination_gen(l):
    start = [l[0]]
    L = l[1:-1]
    yield start
    for y in range(1, len(L)+1):
        for x in combinations(L, y):
            yield start + list(x)

Running the code:

print list(custom_combination_gen([0,1,2,3,4,5]))
[[0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 3], [0, 2, 4], [0, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 3, 4], [0, 2, 3, 4], [0, 1, 2, 3, 4]]

Answer 6

import itertools
a = [0, 1, 2, 3, 4, 5]
myList = []
myFinalList = []
for i in xrange(0,len(a)-2): myList += list(itertools.combinations(a[1:-1],i))
for item in myList: myFinalList.append(list(item)+[a[0]])
print myFinalList