I have two list, which we can call
def check_comps(self, comps):
for a in self.A:
for b in comps:
Your solution has the worst-case O(nm) time complexity, that is O(n^2) if n ~ m. You can easily reduce it to O(n log(n)) and even O(log(n)). Here is how.
Consider a list of words (your
comps attrubute) and a target (your
words = ['abdc', 'abd', 'acb', 'abcabc', 'abc'] target = "abcd"
Observe, that by sorting the list of words in lexicographical order, you get a list of prefixes
prefixes = ['abc', 'abcabc', 'abd', 'abdc', 'acb']
It is degenerate, because
prefixes is a prefix of
prefixes, hence everything that starts with
prefixes starts with
prefixes just as well. This is a bit problematic. Let's see why. Let's use the fast (binary) search to find the proper place of the target in the
import bisect bisect.bisect(prefixes, target) # -> 2
This is because the
prefixes share a prefix, but
target > prefixes, hence lexicographically it should go after. Hence, if there is a prefix of the
target in the
prefixes, it should be to the left of index
2. Obviously, the
target doesn't start with
prefixes hence in the worst case we would have to search all the way to the left to find whether there is a prefix. Now observe, that if we transform these
prefixes into a nondegenerate list, the only possible prefix of a target will always be to the left of the position returned by
bisect.bisect. Let's reduce the list of prefixes and write a helper function that will check whether there is a prefix of a target.
from functools import reduce def minimize_prefixes(prefixes): """ Note! `prefixes` must be sorted lexicographically ! """ def accum_prefs(prefixes, prefix): if not prefix.startswith(prefixes[-1]): return prefixes.append(prefix) or prefixes return prefixes prefs_iter = iter(prefixes) return reduce(accum_prefs, prefs_iter, [next(prefs_iter)]) if prefixes else  def hasprefix(minimized_prefixes, target): position = bisect.bisect(minimized_prefixes, target) return target.startswith(minimized_prefixes[position-1]) if position else False
Now let's see
min_prefixes = minimize_prefixes(prefixes) print(min_prefixes) # -> ['abc', 'abd', 'acb'] hasprefix(min_prefixes, target) # -> True
Let's make a test that must fail:
min_prefs_fail = ["abcde"] hasprefix(min_prefs_fail, target) # -> False
This way you get O(n log(n)) search, which is asymptotically faster than your O(n^2) solution. Note! You can (and you really should) store the
minimize_prefixes(sorted(comps)) prefix set as an attribute in your object, making any prefix search O(log (n)), which is even more faster than what you have now.