Add pick generator specialized for indexed sequences

[lambdani]

Hi! Would there be interest in a pick generator specialized for IndexedSeqs? When choosing k elements from a sequence with n elements, the idea is to choose an element in the inclusive range [0,n-1], then another one in [0,n-2]... up to [0,n-k]. Then these indices must be translated to the whole range [0,n-1] while avoiding repetitions. For this, one can use a modified version of an order statistic tree that selects the i-th non negative integer not present in the tree.

This should pick k elements in O(k log k) time, using O(k) extra space for the tree. Additionally, the elements should be permuted in random order.

The names are horrible but I couldn't come up with better ones. Any help with that would be appreciated if you think it's worth to add this generator to Scalacheck. What do you think?

[satorg]

@lambdani just to clarify: is the suggested behavior different from this one?

def shuffledPick[T](n: Int, seq: IndexedSeq[T]): Gen[collection.Seq[T]] = {
  Arbitrary.arbitrary[Long].flatMap { seed =>
    val shuffledSeq = new scala.util.Random(seed).shuffle(seq)
    Gen.pick(n, shuffledSeq)
  }
}

I mean, I realize it works in a different way, but not sure if there's a difference in the results they both will be providing.

[lambdani]

No, it should have the same behavior. The only difference should be asymptotic efficiency (O(k log k) vs O(n)). But I don't know if it's faster in practice for enough use cases, and even then if it's worth the added complexity. I could try to write some benchmarks, but it's OK if you think it's not worth it :-).

[rossabaker]

Thanks! A quick benchmark would be interesting to see approximately what size collection is the break-even point.

[rossabaker]

Names that sort close to their relatives improve discoverability: how about pickIndexed?

[rossabaker]

A quick comment on the runtime improvement over pick would be helpful. Perhaps also that it doesn't repeat elements.