Given an unknown length list, return a random item in it by scanning it only 1 time

Question

Given an unknown length list, return a random item in it by scanning it only 1 time.

My idea:

A similar algorithm is Reservoir Sampling (posted by others). But

Answer 1

Why are you against reservoir sampling? You happen to be doing it with k = 1. There are minor optimizations (e.g. you don't need to select 1 out of the k, since k = 1) but it's the right approach. You could try to optimize by keeping processing a fixed window at a time, do the math to figure out with equal probability if you should choose any of the items in your window instead of the one you have, etc. to minimize rand() calls at the expensive of a more complicated algorithm, but you're going to wind up back at reservoir sampling more or less anyhow.