No. Replacement probability maintains equal inclusion probability after every prefix length.

The reservoir makes a promise after every prefix: each item seen so far is equally likely to be stored. The next replacement probability preserves that promise.

What the function promises: Return one item from a nonempty iterable using an injected random generator supporting randrange. Raise ValueError for empty input.

from random import Random

def reservoir_one(items, random_source):
    chosen = None
    count = 0
    for count, item in enumerate(items, 1):
        if random_source.randrange(count) == 0:
            chosen = item
    if count == 0: raise ValueError("Empty stream")
    return chosen

assert reservoir_one([10], Random(1)) == 10
assert reservoir_one(range(20), Random(7)) in range(20)

Work and storage: O(n) time, O(1) sample storage, and one random draw per item.

When to recognize it: Replacement probability maintains equal inclusion probability after every prefix length.

Check before applying it: Randomness quality matters, and weighted sampling needs a different rule.

Keep a reservoir of size k; item i>k replaces a uniformly selected reservoir slot with probability k/i.