How do you get 'additional' combinations when adding items to a list that I have already gotten all combinations for?

Question

Using python I would like to calculate all combinations of 3 from a list.

For example, list = [a,b,c,d] and combinations would be - [a,b,c], [a,b,d], [a,c,d], [b,c,d].

And then I would like to add some items to the original list and get only the additional combinations of 3.

For example, adding items [e,f] would generate new combinations - [a,b,e], [a,b,f], [a,c,e], [a,c,f], [a,d,e], [a,d,f], [a,e,f], [b,c,e], [b,c,f],...

The lists will be large so we need to avoid generating the combinations twice and then filtering in order to get the 'additional combinations'.

Background: I use itertools.combinations to get all combinations (of 3) for a list right now of about 100 items. That generates a lot of combinations and I doing a bunch of calculations and whatnot based on those combinations, looking for patterns and matches and stuff. I get through all that processing and if I don't have a 'successful' combination of 3 then I generate more candidates for the list (which in itself takes a long time). When I add the additional candidates to the list (usually like 10 or so), I then restart the analysis on the combinations which seems wasteful, so I would like to only be checking the 'additional' combinations.

Answer 1

Add the new items one by one:

from itertools import combinations

old = ['a', 'b', 'c', 'd']
new = ['e', 'f']

for item in new:
    for comb in combinations(old, 2):
        print(*comb, item)
    old.append(item)

Output (Attempt This Online!):

a b e
a c e
a d e
b c e
b d e
c d e
a b f
a c f
a d f
a e f
b c f
b d f
b e f
c d f
c e f
d e f

Or if order within each combination doesn't matter (inspired by a comment):

from math import comb
from itertools import combinations, islice

old = ['a', 'b', 'c', 'd']
new = ['e', 'f']

new_combs = comb(len(old) + len(new), 3) - comb(len(old), 3)
for comb in islice(combinations(new + old, 3), new_combs):
    print(*comb)

Output (Attempt This Online!):

e f a
e f b
e f c
e f d
e a b
e a c
e a d
e b c
e b d
e c d
f a b
f a c
f a d
f b c
f b d
f c d