Question

There are three arrays a1, a2, a3 of size n. Function searches for common number in these arrays.
Algorithm is the next:

foreach n in a1
    if n is found in a2
        if n is found in a3
            return true

return false

My guess that worse case will be the next: a1 and a2 are equal, a3 does not contain any common number with a1.

Complexity to iterate through array a1 will be O(i).
Complexity to search array a2 or a3 is f(n) (we do not know how they are searched).
My guess that overall complexity for worse case would be:

O(n) = n * f(n) * f(n) = n * (f(n))^2

I was told that that it is wrong.
What is correct answer then?

Answer 1

n * f(n) * f(n) = n * (f(n))^2 

I was told that that it is wrong. What is correct answer then?

The correct answer for the given algorithm:

n * (f(n) + f(n)) = O(n*f(n))

You don’t search a3 array f(n) times for each n in a1 so you should use + instead of *.