What is the time complexity of this function using a built-in function?

Question

Assume you have the following compute function, using python built-in sum function:

def compute(a_list):
    for i in range(0, n):                        #Line 1
        number = sum(a_list[0:i + 1])/(i+1)      #Line 2
    return number

What would the time-complexity for something like this look like?

Line 1 is executed n number of times, but Line 2, having the built-in sum function (O(n)), would it execute n^2 number of times? Therefore the algorithm would be O(n^2).

For each iteration of i, Line 2 is executed 1 + 2 + 3 + ... + n-2 + n-1 + n. The sum of these terms is

Is this correct?

where does n come from? I'd guess either n = len(a_list) or def compute(a_list, n)… — Sam Mason
– Sam Mason, Commented Feb 20, 2019 at 8:37

Sam Mason · Accepted Answer · 2019-02-20 08:29:19Z

1

I'd say that line 1 is executed once, and this causes line 2 to be executed n times. the list subscript is O(n), and the sum is also O(n). division, addition and assignment are all O(1).

compute is therefore O(N^2) as the largest terms are evaluating an O(n) operation O(n) times.

note that, as written, it discards all intermediate results, so it could be rewritten as:

def compute(a_list):
    return sum(a_list[0:n])/n

which would be O(n).

answered Feb 20, 2019 at 8:29

Sam Mason

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2 Comments

Patrick Artner Over a year ago

your "rewritten" part uses n => NameError

Sam Mason Over a year ago

@PatrickArtner yup, OP also has this… they didn't say where n is coming from!

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