How to incrementally sample without replacement?

Question

Python has my_sample = random.sample(range(100), 10) to randomly sample without replacement from [0, 100).

Suppose I have sampled n

Answer 1

Here's a way that doesn't build the difference set explicitly. But it does use a form of @Veedrac's "accept/reject" logic. If you're not willing to mutate the base sequence as you go along, I'm afraid that's unavoidable:

def sample(n, base, forbidden):
    # base is iterable, forbidden is a set.
    # Every element of forbidden must be in base.
    # forbidden is updated.
    from random import random
    nusable = len(base) - len(forbidden)
    assert nusable >= n
    result = []
    if n == 0:
        return result
    for elt in base:
        if elt in forbidden:
            continue
        if nusable * random() < n:
            result.append(elt)
            forbidden.add(elt)
            n -= 1
            if n == 0:
                return result
        nusable -= 1
    assert False, "oops!"

Here's a little driver:

base = list(range(100))
forbidden = set()
for i in range(10):
    print sample(10, base, forbidden)