Okay so as I understand it this is an example of the "dynamic programming approach" to this classic challenge with a slight twist I still don't quite get. The classic approach might start with both current and total maximums equal to the first element. In each iteration it would compare the current element to currentMax + a instead of comparing it with zero. Aside from that, it's the same and you can Google it. So, why are you using zeros instead of elements? Does this always work?

Sure, but could someone explain it?