// Pattern Matching

//==================

// A powerful tool which is supposed to come to Java in a few years

// time (https://www.youtube.com/watch?v=oGll155-vuQ)...Scala already

// has it for many years. Other functional languages have it for

// decades. I think I would refuse to program in a language that

// does not have pattern matching....its is just so elegant. ;o)

// The general schema:

//

//    expression match {

//       case pattern1 => expression1

//       case pattern2 => expression2

//       ...

//       case patternN => expressionN

//    }

// remember

val lst = List(None, Some(1), Some(2), None, Some(3)).flatten

def my_flatten(xs: List[Option[Int]]): List[Int] = {

  ...?

}

def my_flatten(lst: List[Option[Int]]): List[Int] = lst match {

  case Nil => Nil

  case None::xs => my_flatten(xs)

  case Some(n)::xs => n::my_flatten(xs)

}

// another example including a catch-all pattern

def get_me_a_string(n: Int): String = n match {

  case 0 => "zero"

  case 1 => "one"

  case 2 => "two"

  case _ => "many"

}

get_me_a_string(0)

// you can also have cases combined

def season(month: String) = month match {

  case "March" | "April" | "May" => "It's spring"

  case "June" | "July" | "August" => "It's summer"

  case "September" | "October" | "November" => "It's autumn"

  case "December" | "January" | "February" => "It's winter"

}

println(season("November"))

// What happens if no case matches?

println(season("foobar"))

// Collatz function on binary strings

// adding two binary strings in a very, very lazy manner

// User-defined Datatypes

//========================

abstract class Colour

case class Red() extends Colour 

case class Green() extends Colour 

case class Blue() extends Colour

def fav_colour(c: Colour) : Boolean = c match {

  case Red()   => false

  case Green() => true

  case Blue()  => false 

// actually colors can be written with "object",

// because they do not take any arguments

// another example

//=================

// Once upon a time, in a complete fictional country there were persons...

abstract class Person

case class King() extends Person

case class Peer(deg: String, terr: String, succ: Int) extends Person

case class Knight(name: String) extends Person

case class Peasant(name: String) extends Person

def title(p: Person): String = p match {

  case King() => "His Majesty the King"

  case Peer(deg, terr, _) => s"The ${deg} of ${terr}"

  case Knight(name) => s"Sir ${name}"

  case Peasant(name) => name

def superior(p1: Person, p2: Person): Boolean = (p1, p2) match {

  case (King(), _) => true

  case (Peer(_,_,_), Knight(_)) => true

  case (Peer(_,_,_), Peasant(_)) => true

  case (Peer(_,_,_), Clown()) => true

  case (Knight(_), Peasant(_)) => true

  case (Knight(_), Clown()) => true

  case (Clown(), Peasant(_)) => true

  case _ => false

}

val people = List(Knight("David"), 

                  Peer("Duke", "Norfolk", 84), 

                  Peasant("Christian"), 

                  King(), 

                  Clown())

println(people.sortWith(superior(_, _)).mkString(", "))

// Tail recursion

//================

fact(10)              //ok

fact(10000)           // produces a stackoverflow

def factT(n: BigInt, acc: BigInt): BigInt =

  if (n == 0) acc else factT(n - 1, n * acc)

factT(100000, 1)

// there is a flag for ensuring a function is tail recursive

import scala.annotation.tailrec

// for tail-recursive functions the Scala compiler

// call; Scala can do this only for tail-recursive

// sudoku again

val game0 = """.14.6.3..

              |62...4..9

              |.8..5.6..

              |.6.2....3

              |.7..1..5.

              |5....9.6.

              |..6.2..3.

              |1..5...92

              |..7.9.41.""".stripMargin.replaceAll("\\n", "")

type Pos = (Int, Int)

val EmptyValue = '.'

val MaxValue = 9

val allValues = "123456789".toList

val indexes = (0 to 8).toList

def empty(game: String) = game.indexOf(EmptyValue)

def isDone(game: String) = empty(game) == -1 

def emptyPosition(game: String) = 

  (empty(game) % MaxValue, empty(game) / MaxValue)

def get_row(game: String, y: Int) = 

  indexes.map(col => game(y * MaxValue + col))

def get_col(game: String, x: Int) = 

  indexes.map(row => game(x + row * MaxValue))

def get_box(game: String, pos: Pos): List[Char] = {

    def base(p: Int): Int = (p / 3) * 3

    val x0 = base(pos._1)

    val y0 = base(pos._2)

    val ys = (y0 until y0 + 3).toList

    (x0 until x0 + 3).toList.flatMap(x => ys.map(y => game(x + y * MaxValue)))

}

// this is not mutable!!

def update(game: String, pos: Int, value: Char): String = 

  game.updated(pos, value)

def toAvoid(game: String, pos: Pos): List[Char] = 

  (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos))

def candidates(game: String, pos: Pos): List[Char] = 

  allValues.diff(toAvoid(game,pos))

//candidates(game0, (0,0))

def pretty(game: String): String = 

  "\n" + (game sliding (MaxValue, MaxValue) mkString "\n")

// not tail recursive 

def search(game: String): List[String] = {

  if (isDone(game)) List(game)

  else {

    val cs = candidates(game, emptyPosition(game))

    cs.map(c => search(update(game, empty(game), c))).toList.flatten

// tail recursive version that searches 

// for all solution

def searchT(games: List[String], sols: List[String]): List[String] = games match {

  case Nil => sols

  case game::rest => {

    if (isDone(game)) searchT(rest, game::sols)

    else {

      val cs = candidates(game, emptyPosition(game))

      searchT(cs.map(c => update(game, empty(game), c)) ::: rest, sols)

    }

  }

// tail recursive version that searches 

// for a single solution

def search1T(games: List[String]): Option[String] = games match {

  case game::rest => {

    if (isDone(game)) Some(game)

    else {

      val cs = candidates(game, emptyPosition(game))

      search1T(cs.map(c => update(game, empty(game), c)) ::: rest)

    }

  }

// game with multiple solutions

val game3 = """.8...9743

              |.5...8.1.

              |.1.......

              |8....5...

              |...8.4...

              |...3....6

              |.......7.

              |.3.5...8.

              |9724...5.""".stripMargin.replaceAll("\\n", "")

searchT(List(game3), List()).map(pretty)

search1T(List(game3)).map(pretty)

// Unfortuantely, Scala because of current limitations in 

// the JVM is not as clever as other functional languages. It can 

// Cool Stuff

//============

// Implicits 

//===========

//

// For example adding your own methods to Strings:

// Imagine you want to increment strings, like

//

//     "HAL".increment

//

// you can avoid ugly fudges, like a MyString, by

// using implicit conversions.

implicit class MyString(s: String) {

  def increment = for (c <- s) yield (c + 1).toChar 

"HAL".increment

case object ZERO extends Rexp                       // nothing

case object ONE extends Rexp                        // the empty string

case class CHAR(c: Char) extends Rexp               // a character c

case class SEQ(r1: Rexp, r2: Rexp) extends Rexp     // sequence     r1 o r2  

// concise, readable code.