waterPouring.scala

class Pouring(capacity: Vector[Int]) {

  // States
  type State = Vector[Int]
  val initialState = capacity map (x => 0)

  // Moves
  trait Move {
    // A method that defines state changes
    def change(state: State): State
  }
  case class Empty(glass: Int) extends Move {
    def change(state: State) = state updated (glass, 0) // Remember: updated creates a new vector with an element changed
  }
  case class Fill(glass: Int) extends Move {
    def change(state: State) = state updated (glass, capacity(glass))
  }
  case class Pour(from: Int, to: Int) extends Move {
    def change(state: State) = {
      val amount = state(from) min (capacity(to) - state(to))
      state updated (to, state(to) + amount) updated (from, state(from) - amount)
    }
  }

  val glasses = 0 until capacity.length

  val moves =
    // for g 'taken from' glasses
    (for (g <- glasses) yield Empty(g)) ++ // Empty a glass
    (for (g <- glasses) yield Fill(g)) ++ // Fill up a glass
    (for (from <- glasses; to <- glasses if from != to) yield Pour(from, to))
    
  // Paths, sequences of moves
  class Path(history: List[Move], val endState: State) { // val: Available from outside
    def extend(move: Move) = new Path(move :: history, move change endState)
    override def toString = (history.reverse mkString " ") + "--> " + endState
  }
  
  val initialPath = new Path(Nil, initialState)
  
  // Path generating function (state exploration function)
  def from(paths: Set[Path], explored: Set[State]): Stream[Set[Path]] =
    if (paths.isEmpty) Stream.empty
    else {
      val more = for {
        path <- paths
        next <- moves map path.extend
        if !(explored contains next.endState) // Restrict moves to states that are unexplored
      } yield next
      paths #:: from(more, explored ++ (more map (_.endState)))
    }
  
  val pathSets = from(Set(initialPath), Set(initialState))
  
  def solutions(target: Int): Stream[Path] =
    for {
      pathSet <- pathSets
      path <- pathSet
      if path.endState contains target
    } yield path
}