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

You use reservoir sampling.

This is not too complicated nor expensive; it is the minimal approach given the constraints that you have (selecting an element from a stream).

It works just fine if you want a random sample size of 1 and if all the elements have the same weight.

When you've simplified the code with a k of 1 and no explicit weighting, its still reservoir sampling.

Not all pseudo random number generators run at the same speed; pick a fast one.

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Comments ask what would happen if you re-used the same random number rather than generating a new random number each step:

The Wikipedia link given shows the equivalence to the Yates-Fisher/Knuth shuffle. If you asked what would picking the same random number each step of the shuffle would be, you'd be barking.