How to calculate time complexity with variable list elements?

Question

I got a really long time complexity for this function, not sure if we can simplify it.

# Let n = # of file names in the input
# Overall Time Complexity: O(n + k_0 + k_1 + k_2 + ... + k_n + 1) = O(n + k_0 + k_1 + k_2 + ... + k_n)
def split_input(input):

    # Time Complexity: O(n)
    file_names = input.split(",")

    # Let k_i = file name length for the i^th element
    # Time Complexity: O(k_0 + k_1 + k_2 + ... + k_n)
    for index, value in enumerate(file_names):
        # O(k_i)
        file_names[index] = file_names[index].strip()

    # Time Complexity: O(1)
    return file_names

Berthur · Accepted Answer · 2022-11-30 12:02:39Z

1

You have already defined n here as the total length of your input string, which includes all your file names, so

n > k_0 + k_1 + ... + k_n.

Therefore, your time complexity is just O(n).

answered Nov 30, 2022 at 12:02

Berthur

4,5242 gold badges20 silver badges32 bronze badges

Sign up to request clarification or add additional context in comments.

3 Comments

NoName Over a year ago

So we define "n" as the # of characters in the string rather than the # of actual file names in the string? e.g. "abc.csv, def.csv, ghi.csv"

Berthur Over a year ago

@NoName Well you already claim that input.split(",") is O(n) so clearly you have chosen the total length of the string as your n, right? str.split() does have to go through all characters of the string.

Berthur Over a year ago

If you prefer to define n as your number of file names, then your time complexity would be O(k0 + k1 + ... + kn)) just O(n * k_avg) where k_avg is your average file name length. Can also express it as O(n * k_longest), though that might be a less tight bound.

Collectives™ on Stack Overflow

How to calculate time complexity with variable list elements?

1 Answer 1

3 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

3 Comments

Your Answer

Sign up or log in

Post as a guest

Related