# Lowest complexity - Number closest to 0

I'm currently trying to improve my algorithm skills and I was trying a simple algorithm :

Given a list of integers. We want to find the one that is the closest to 0. If we have a number and his opposite, we want to return the positive one.

My current complexity on this algorithm is O(n). Is it possible to get a lower one ?

My current solution looks at all the values. I was thinking about a binary search, but we're not looking for a specific number, and the list of integers is not sorted.

Thanks for the help !

If you want an algorithm that is always correct you can not do better, precisely because you have to look at all the values at least once (except if you find a $$0$$ somewhere, then you can immediately return that).
Otherwise, suppose your run your algorithm $$A$$ some input $$I=[a_1,a_2,\ldots,a_n]$$, and it returns a value $$v\neq 0$$ without looking at all numbers in $$I$$. Say it didn't look at $$a_k$$. Then we could just as well set $$a_k=0$$ and $$A$$ wouldn't know about it (because it didn't look at $$a_k$$). Thus $$A$$ will be wrong on this (modified) input.
That is of course assuming that setting $$a_k = 0$$ doesn't contradict some assumption you have about the data (for example it being sorted).