All combinations of arbitrary number of sets using for comprehension - scala

Question

Let's look at following source of code:
def foo(s1: Set[Int], s2: Set[Int], s3: Set[Int]): Set[Set[Int]] = {
for {
ss1 <- s1
ss2 <- s2
ss3 <- s3
} yield Set(ss1, ss2, ss3)
}
How to define analogous function for def foo(ss: Set[Int]*) ?

Answer 1

It's almost the same as the usual cartesian product, except that you have to cram all the results into sets instead of collecting them in ordered tuples:
/** Forms cartesian product of sets,
* then collapses each resulting tuple into a set.
*/
def collapsedCartesian[A](sets: Set[A]*): Set[Set[A]] = sets match
case Seq() => Set(Set.empty)
case Seq(h, t # _*) => for a <- h; b <- collapsedCartesian(t: _*) yield (b + a)
Note that here, the + adds an element to a set: set + elem, which is an oddly asymmetric operation to be denoted by such a symmetric symbol.
The outcome seems reasonably irregular:
collapsedCartesian(Set(1, 2), Set(3, 4)).foreach(println)
println("---")
collapsedCartesian(Set(1, 2), Set(1, 2)).foreach(println)
println("---")
collapsedCartesian(Set(1, 2, 3), Set(4, 5), Set(6, 7)).foreach(println)
println("---")
collapsedCartesian(Set(1, 2, 3), Set(2, 3, 4), Set(4, 5)).foreach(println)
gives:
Set(3, 1)
Set(4, 1)
Set(3, 2)
Set(4, 2)
---
Set(1)
Set(2, 1)
Set(2)
---
Set(7, 5, 1)
Set(6, 4, 2)
Set(6, 4, 1)
Set(7, 4, 1)
Set(6, 5, 1)
Set(7, 5, 3)
Set(7, 4, 2)
Set(6, 5, 2)
Set(6, 4, 3)
Set(7, 5, 2)
Set(7, 4, 3)
Set(6, 5, 3)
---
Set(5, 3, 1)
Set(5, 4, 2)
Set(5, 4, 1)
Set(4, 2)
Set(4, 1)
Set(5, 3)
Set(5, 3, 2)
Set(5, 4, 3)
Set(4, 2, 1)
Set(5, 2, 1)
Set(4, 3, 1)
Set(4, 3, 2)
Set(5, 2)
Set(4, 3)
Please don't ask how to do it in Spark, this exponentially exploding stuff is obviously useless for any dataset with more than just a couple of entries.