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object WaterPouring
{
class Pouring(capacity: Vector[Int]) {
// States
type State = Vector[Int]
val initialState = capacity map ( x => 0) // empty glasses
// Moves
trait Move {
def change(state: State): State
}
case class Empty(glass: Int) extends Move {
def change(state: State): State = state updated (glass, 0)
}
case class Fill(glass: Int) extends Move {
def change(state: State): State = state updated (glass, capacity(glass))
}
case class Pour(from: Int, to: Int) extends Move {
def change(state: State): State = {
val amount = state(from) min (capacity(to) - state(to))
state updated (from, state(from) - amount) updated (to, state(to) + amount)
}
}
val glasses = 0 until capacity.length // range
val moves =
(for (g <- glasses) yield Empty(g)) ++
(for (g <- glasses) yield Fill(g)) ++
(for (from <- glasses; to <- glasses if from != to ) yield Pour(from, to))
// Paths
class Path(history: List[Move], val endState: State) {
// to be simplified…
/* def endState: State = trackState(history) */
/* private def trackState(xs: List[Move]): State = xs match { */
/* case Nil => initialState */
/* case move :: xs1 => move change trackState(xs1) */
/* } */
// recomputed over complete history
/* def endState: State = (history foldRight initialState) (_ change _) */
/* def extend(move: Move) = new Path(move :: history) */
def extend(move: Move) = new Path(move :: history, move change endState)
override def toString() = (history.reverse mkString " ") + "--> " + endState
}
val initialPath = new Path(Nil, initialState)
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)
} 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
}
def run = {
println("WaterPouring")
val problem = new Pouring(Vector(4, 7, 19))
problem.moves
println(problem.solutions(13))
}
}
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