What's the complexity of this function?

Question

I'm practising in Codeacademy and I have to make the following function:

Define a function called anti_vowel that takes one string, text, as input and returns the text with all of the vowels removed

This is my solution.

def anti_vowel(text):
md = ""
for ch in text:
    if ch not in "aeiouAEIOU":
        md =  md + ch
return md 

It works well but I'm wondering what the complexity of the function is.

I think it's O(nk) where n:="length of text" and k:="length of "aeoiuAEIOU"".
I take one element of text and compare it with all vowels, that takes O(k) time. But I repeat that n times, so I do it all in O(nk). Is my analysis correct? How could I improve my function? Could it be linear?

Answer 1

Big-O complexity doesn't work like that. k (the length of the vowels) is a constant, it doesn't change depending on the length of the input. So we discount it in calculating the complexity.

Your function is just O(n), ie linear complexity.