test_combination.py

import itertools
from pprint import pprint

hotdogs = ['SimpleHotdog', 'SpecialHotdog']
ingredients = ['Sausage', 'Bacon',
               'Egg', 'Cheese', 'MashedPotatoes',
               'PotatoSticks']

classnames = []
for ingredient in ingredients:
    for i, j in itertools.combinations(range(len(ingredients) + 1), 2):
        if ingredient in ingredients[i:j]:
            continue

        value = set([ingredient, *ingredients[i:j]])

        if value in classnames:
            continue

        classnames.append(value)

all_classnames = []
for hotdog in hotdogs:
    for classname in sorted(classnames, key=lambda item: ''.join(item)):
        all_classnames.append(f'{hotdog}Bread{"".join(classname)}')

pprint(all_classnames)
pprint(len(all_classnames))

"""
['SimpleHotdogBreadBaconCheeseEggPotatoSticks',
 'SimpleHotdogBreadBaconEggPotatoSticks',
 'SimpleHotdogBreadCheeseBacon',
 'SimpleHotdogBreadCheeseEggBacon',
 'SimpleHotdogBreadCheeseEggPotatoSticks',
 'SimpleHotdogBreadCheeseMashedPotatoesEggBacon',
 'SimpleHotdogBreadCheesePotatoSticksBaconMashedPotatoesEgg',
 'SimpleHotdogBreadEggBacon',
 'SimpleHotdogBreadEggCheese',
 'SimpleHotdogBreadEggMashedPotatoesBacon',
 'SimpleHotdogBreadEggPotatoSticks',
 'SimpleHotdogBreadEggSausageMashedPotatoesBacon',
 'SimpleHotdogBreadMashedPotatoesBacon',
 'SimpleHotdogBreadMashedPotatoesCheese',
 'SimpleHotdogBreadMashedPotatoesCheeseBacon',
 'SimpleHotdogBreadMashedPotatoesEgg',
 'SimpleHotdogBreadMashedPotatoesEggCheese',
 'SimpleHotdogBreadMashedPotatoesEggPotatoSticks',
 'SimpleHotdogBreadMashedPotatoesPotatoSticks',
 'SimpleHotdogBreadMashedPotatoesPotatoSticksCheeseBacon',
 'SimpleHotdogBreadMashedPotatoesPotatoSticksEggCheese',
 'SimpleHotdogBreadPotatoSticksBacon',
 'SimpleHotdogBreadPotatoSticksCheese',
 'SimpleHotdogBreadPotatoSticksMashedPotatoesBacon',
 'SimpleHotdogBreadPotatoSticksMashedPotatoesCheese',
 'SimpleHotdogBreadSausageBacon',
 'SimpleHotdogBreadSausageBaconCheese',
 'SimpleHotdogBreadSausageBaconEggPotatoSticks',
 'SimpleHotdogBreadSausageBaconPotatoSticks',
 'SimpleHotdogBreadSausageCheese',
 'SimpleHotdogBreadSausageCheeseBaconMashedPotatoesEgg',
 'SimpleHotdogBreadSausageCheeseEggBacon',
 'SimpleHotdogBreadSausageCheesePotatoSticksBaconEgg',
 'SimpleHotdogBreadSausageCheesePotatoSticksBaconMashedPotatoesEgg',
 'SimpleHotdogBreadSausageEgg',
 'SimpleHotdogBreadSausageEggBacon',
 'SimpleHotdogBreadSausageEggCheese',
 'SimpleHotdogBreadSausageMashedPotatoes',
 'SimpleHotdogBreadSausageMashedPotatoesBacon',
 'SimpleHotdogBreadSausageMashedPotatoesCheese',
 'SimpleHotdogBreadSausageMashedPotatoesEggCheese',
 'SimpleHotdogBreadSausageMashedPotatoesPotatoSticks',
 'SimpleHotdogBreadSausagePotatoSticks',
 'SimpleHotdogBreadSausagePotatoSticksCheeseMashedPotatoesEgg',
 'SimpleHotdogBreadSausagePotatoSticksMashedPotatoesCheese',
 'SpecialHotdogBreadBaconCheeseEggPotatoSticks',
 'SpecialHotdogBreadBaconEggPotatoSticks',
 'SpecialHotdogBreadCheeseBacon',
 'SpecialHotdogBreadCheeseEggBacon',
 'SpecialHotdogBreadCheeseEggPotatoSticks',
 'SpecialHotdogBreadCheeseMashedPotatoesEggBacon',
 'SpecialHotdogBreadCheesePotatoSticksBaconMashedPotatoesEgg',
 'SpecialHotdogBreadEggBacon',
 'SpecialHotdogBreadEggCheese',
 'SpecialHotdogBreadEggMashedPotatoesBacon',
 'SpecialHotdogBreadEggPotatoSticks',
 'SpecialHotdogBreadEggSausageMashedPotatoesBacon',
 'SpecialHotdogBreadMashedPotatoesBacon',
 'SpecialHotdogBreadMashedPotatoesCheese',
 'SpecialHotdogBreadMashedPotatoesCheeseBacon',
 'SpecialHotdogBreadMashedPotatoesEgg',
 'SpecialHotdogBreadMashedPotatoesEggCheese',
 'SpecialHotdogBreadMashedPotatoesEggPotatoSticks',
 'SpecialHotdogBreadMashedPotatoesPotatoSticks',
 'SpecialHotdogBreadMashedPotatoesPotatoSticksCheeseBacon',
 'SpecialHotdogBreadMashedPotatoesPotatoSticksEggCheese',
 'SpecialHotdogBreadPotatoSticksBacon',
 'SpecialHotdogBreadPotatoSticksCheese',
 'SpecialHotdogBreadPotatoSticksMashedPotatoesBacon',
 'SpecialHotdogBreadPotatoSticksMashedPotatoesCheese',
 'SpecialHotdogBreadSausageBacon',
 'SpecialHotdogBreadSausageBaconCheese',
 'SpecialHotdogBreadSausageBaconEggPotatoSticks',
 'SpecialHotdogBreadSausageBaconPotatoSticks',
 'SpecialHotdogBreadSausageCheese',
 'SpecialHotdogBreadSausageCheeseBaconMashedPotatoesEgg',
 'SpecialHotdogBreadSausageCheeseEggBacon',
 'SpecialHotdogBreadSausageCheesePotatoSticksBaconEgg',
 'SpecialHotdogBreadSausageCheesePotatoSticksBaconMashedPotatoesEgg',
 'SpecialHotdogBreadSausageEgg',
 'SpecialHotdogBreadSausageEggBacon',
 'SpecialHotdogBreadSausageEggCheese',
 'SpecialHotdogBreadSausageMashedPotatoes',
 'SpecialHotdogBreadSausageMashedPotatoesBacon',
 'SpecialHotdogBreadSausageMashedPotatoesCheese',
 'SpecialHotdogBreadSausageMashedPotatoesEggCheese',
 'SpecialHotdogBreadSausageMashedPotatoesPotatoSticks',
 'SpecialHotdogBreadSausagePotatoSticks',
 'SpecialHotdogBreadSausagePotatoSticksCheeseMashedPotatoesEgg',
 'SpecialHotdogBreadSausagePotatoSticksMashedPotatoesCheese']
90
"""