Question

I was asked this today and i know the answer is damn sure simple but he kept me the twist to the last.

Question

Write a program to remove even numbers stored in ArrayList containing 1 - 100.

I just said wow

Here you go this is how i have implemented it.

ArrayList source = new ArrayList(100);
for (int i = 1; i < 100; i++)
{
    source.Add(i);
}


for (int i = 0; i < source.Count; i++)
{
    if (Convert.ToInt32(source[i]) % 2 ==0)
    {
        source.RemoveAt(i);
    }
}

//source contains only Odd elements

The twist

He asked me what is the computational complexity of this give him a equation. I just did and said this is Linear directly proportional to N (Input).

he said : hmmm.. so that means i need to wait longer to get results when the input size increases am i right? Yes sirr you are

Tune it for me, make it Log(N) try as much as you can he said. I failed miserably in this part.

• Hence come here for the right logic, answer or algorithm to do this.

note: He wanted no Linq, No extra bells and whistles. Just plain loops or other logic to do it

Answer 1

Let’s think it this way:

The number of delete actions you are doing is, forcely, the half of array lenght (if the elements are stored in array). So the complexity is at least O(N) .

The question you received let me suppose that your professor wanted you to reason about different ways of storing the numbers.

Usually when you have log complexity you are working with different structures, like graphs or trees.

The only way I can think of having logartmic complexity is having the numbers stored in a tree (ordered tree, b-tree… we colud elaborate on this), but it is actually out of the constraints of your exam (sotring numbers in array).

Does it make sense to you?