关于“ in” Python时间复杂度的简单查询

Question

I have a function strip_punctuation(text) which takes in a string of text and removes all punctuation in it using a punctuation list. I am not sure about the time complexity whether it is O(N)*N or O(N^2). I think that it works where it is O(N) for N text length, and then O(N) for length of punctuation. May someone clarify the time complexity for this code?

def strip_punctuation(text):
    punctuations = '''!()-[]{};:'"\,<>./?@#$%^&*_~'''
    stripped = ""
    for i in text:
        if i not in punctuations:
            stripped = stripped + i

    return stripped

Answer 1

If N is len(text) , then this is O(N):

for i in text

If M is len(punctuations) , then this code is O(M^2):

if i not in punctuations:
    stripped = stripped + i

That is because the whole stripped (which has length >= M) has to be copied M times ( stripped + i makes a copy of stripped ).

So, if both text and punctuations were inputs, the complexity would be O(N) * O(M^2), but in this case, M is a constant, so the complexity is O(N) .

Note that if punctuations was very very big, the function would be very very slow, but its complexity would still be just O(N), which only means that it is N times slower when the input is N times bigger.