How to generate the power set of a set in Scala

Question

I have a Set of items of some type and want to generate its power set.

I searched the web and couldn't find any Scala code that adresses this specific task.

This is what I came up with. It allows you to restrict the cardinality of the sets produced by the length parameter.

def power[T](set: Set[T], length: Int) = {
   var res = Set[Set[T]]()
   res ++= set.map(Set(_))

   for (i <- 1 until length)
      res = res.map(x => set.map(x + _)).flatten

   res
   }

This will not include the empty set. To accomplish this you would have to change the last line of the method simply to res + Set()

Any suggestions how this can be accomplished in a more functional style?

Answer 1

Here's another (lazy) version... since we're collecting ways of computing the power set, I thought I'd add it:

def powerset[A](s: Seq[A]) =
  Iterator.range(0, 1 << s.length).map(i =>
    Iterator.range(0, s.length).withFilter(j =>
      (i >> j) % 2 == 1
    ).map(s)
  )

Answer 2

All the other answers seemed a bit complicated, here is a simple function:

    def powerSet (l:List[_]) : List[List[Any]] =
      l match {
       case Nil => List(List())
       case x::xs =>
         var a = powerSet(xs)
         a.map(n => n:::List(x)):::a
      }

so

    powerSet(List('a','b','c'))

will produce the following result

    res0: List[List[Any]] = List(List(c, b, a), List(b, a), List(c, a), List(a), List(c, b), List(b), List(c), List())