import random
import itertools
from collections import Counter

iterable = [0, 1]
r = 4


#-- itertools ----------------------

print('itertools')
for comb in itertools.combinations_with_replacement(iterable, r):
    print(comb)


#-- from iterator ------------------

def random_combination_with_replacement_from_iterator(iterable, r):
    "Random selection from itertools.combinations_with_replacement(iterable, r)"
    iterator = itertools.combinations_with_replacement(iterable, r)
    return random.choice(list(iterator))


#-- current random recipe ----------

def random_combination_with_replacement(iterable, r):
    "Random selection from itertools.combinations_with_replacement(iterable, r)"
    pool = tuple(iterable)
    n = len(pool)
    indices = sorted(random.choices(range(n), k=r))
    return tuple(pool[i] for i in indices)


#-- proposed random recipe ---------

def random_combination_with_replacement_proposal(iterable, r):
    "Random selection from itertools.combinations_with_replacement(iterable, r)"
    pool = tuple(iterable)
    n = len(pool)
    indices = sorted(random.sample(range(n+r-1), k=r))
    return tuple(pool[i-j] for j, i in enumerate(indices))


#-- Comparison

for func in random_combination_with_replacement_from_iterator, random_combination_with_replacement, random_combination_with_replacement_proposal:
    print()
    print(func.__name__)
    N = 100000
    ctr = Counter(func(iterable, r) for _ in range(N))
    for comb, freq in sorted(ctr.items()):
        print(comb, f'{freq/N:6.2%}')