Asymptotic complexity in python for O-Upper

Question

I'm studying the complexity of functions in python, and I have this two there Im not sure, one because I think it's infinite loop and second is the not in method build in on python:

1- The function f1 receives a positive integer n and a list v. v is larger than n.

def f1(n, v): 
   b=n*n
   s=0
   while b > 1: 
      s += v[n]
      s += b
      b -= 2 
   return s

2- The function f2 receives a dictionary d and a list l.

def f2(d,l): 
   r = []
   for x in l:
      if x not in d:
         r.append(x)
return r

I am studying them on "O-Upper", O. ex O (n ^ 2) is quadratic. What is the complexity of this two functions?

You're not really asking a question. What is it you want to know? — Wes Hardaker, Mar 07 '21 at 11:43

score 0 · Accepted Answer · answered Mar 09 '21 at 13:43

0

f1 contains a loop that executes O(n²) times, and it performs only constant-time operations. Like EnderShadow8 explained, this makes your function O(n²).

f2 contains a loop that executes O(n) times, where n is the length of l. Since d is a Python dictionary, checking if x is in d runs in amortized O(1) time. This is because a dictionary does not in practice iterate through all its elements to find x, but rather it uses an underlying hash map data structure. Appending to a list is also in practice a constant-time operation in Python. Therefore, f2 is actually an O(n) time function.

answered Mar 09 '21 at 13:43

Berthur

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@Bertgur Thank you very much, my teacher explained that to me too, I just forgot it. Thanks – António Rocha Gonçalves Mar 10 '21 at 16:02
@AntónioRochaGonçalves No problem.This demonstrates the importance of using the right data structure for the right task. *O(n^2)* algorithms quickly become unpractical as the input scales. – Berthur Mar 10 '21 at 22:25

Asymptotic complexity in python for O-Upper

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