Performance around functional programming in scala

Question

I'm working with below stuff as a way to learn functional programming and scala, I came from a python background.

case class Point(x: Int, y:Int)
object Operation extends Enumeration {
  type Operation = Value
  val TurnOn, TurnOff, Toggle = Value
}

object Status extends Enumeration {
  type Status = Value
  val On, Off = Value
}

val inputs: List[String]
def parseInputs(s: String): (Point, Point, Operation)

Idea is that we have a light matrix(Point), each Point can be either On or Off as describe in Status. My inputs is a series of command, asking to either TurnOn, TurnOff or Toggle all the lights from one Point to another Point (The rectangular area defined using two points are bottom-left corner and upper-right corner).

My original solution is like this:

type LightStatus = mutable.Map[Point, Status]
val lightStatus = mutable.Map[Point, Status]()

def updateStatus(p1: Point, p2: Point, op: Operation): Unit = {
  (p1, p2) match {
    case (Point(x1, y1), Point(x2, y2)) =>
      for (x <- x1 to x2)
        for (y <- y1 to y2) {
          val p = Point(x, y)
          val currentStatus = lightStatus.getOrElse(p, Off)
          (op, currentStatus) match {
            case (TurnOn, _) => lightStatus.update(p, On)
            case (TurnOff, _) => lightStatus.update(p, Off)
            case (Toggle, On) => lightStatus.update(p, Off)
            case (Toggle, Off) => lightStatus.update(p, On)
          }
        }
  }
}

for ((p1, p2, op) <- inputs.map(parseInputs)) {
  updateStatus(p1, p2, op)
}

Now I have lightStatus as a map to describe the end status of the entire matrix. This works, but seems less functional to me as I was using a mutable Map instead of an immutable object, so I tried to re-factor this into a more functional way, I ended up with this:

inputs.flatMap(s => parseInputs(s) match {
  case (Point(x1, y1), Point(x2, y2), op) =>
    for (x <- x1 to x2;
         y <- y1 to y2)
    yield (Point(x, y), op)
}).foldLeft(Map[Point, Status]())((m, item) => {
  item match {
    case (p, op) =>
      val currentStatus = m.getOrElse(p, Off)
      (op, currentStatus) match {
        case (TurnOn, _) => m.updated(p, On)
        case (TurnOff, _) => m.updated(p, Off)
        case (Toggle, On) => m.updated(p, Off)
        case (Toggle, Off) => m.updated(p, On)
      }
  }
})

I have couple questions regarding this process:

1. My second version doesn't seem as clean and straightforward as the first version to me, I'm not sure if this is because I'm not that familiar with functional programming or I just wrote bad functional code.
2. Is there someway to simplify the syntax on second piece? Especially the (m, item) => ??? function in the foldLeft part? Something like (m, (point, operation)) => ??? gives me syntax error
3. The second piece of code takes significantly longer to run, which surprise me a bit as these two code essentially is doing the same thing, As I don't have too much Java background, Any idea what might be causing the performance issue?

Many thanks!

Answer 1

From a Functional Programming perspective, your code suffers from the fact that...

1. The lightStatus Map "maintains state" and thus requires mutation.
2. A large "area" of status changes == a large number of data updates.

If you can accept each light status as a Boolean value, here's a design that requires no mutation and has fast status updates even over very large areas.

case class Point(x: Int, y:Int)

class LightGrid private (status: Point => Boolean) {
  def apply(p: Point): Boolean = status(p)

  private def isWithin(p:Point, ll:Point, ur:Point) =
    ll.x <= p.x && ll.y <= p.y && p.x <= ur.x && p.y <= ur.y

  //each light op returns a new LightGrid
  def turnOn(lowerLeft: Point, upperRight: Point): LightGrid =
    new LightGrid(point =>
      isWithin(point, lowerLeft, upperRight) || status(point))

  def turnOff(lowerLeft: Point, upperRight: Point): LightGrid =
    new LightGrid(point =>
      !isWithin(point, lowerLeft, upperRight) && status(point))

  def toggle(lowerLeft: Point, upperRight: Point): LightGrid =
    new LightGrid(point =>
      isWithin(point, lowerLeft, upperRight) ^ status(point))
}
object LightGrid {  //the public constructor
  def apply(): LightGrid = new LightGrid(_ => false)
}

usage:

val ON  = true
val OFF = false
val lg = LightGrid().turnOn(Point(2,2), Point(11,11)) //easy numbers
                    .turnOff(Point(8,8), Point(10,10))
                    .toggle(Point(1,1), Point(9,9))
lg(Point(1,1))    //ON
lg(Point(7,7))    //OFF
lg(Point(8,8))    //ON
lg(Point(9,9))    //ON
lg(Point(10,10))  //OFF
lg(Point(11,11))  //ON
lg(Point(12,12))  //OFF