The best case possible is to iterate the list once - you sum the list from left to right holding cumulative answers and if the final sum is zero, that index is

The best case possible is to iterate the list once - you sum the list from left to right holding cumulative answers and if the final sum is zero, that index is a valid answer. The worst case of the best algorithm is to iterate twice - firstly as above, and then again in the opposite direction, comparing values from the first iteration.