// pattern-matching

// Pattern Matching

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

// A powerful tool which has even landed in Java during 

// the last few years (https://inside.java/2021/06/13/podcast-017/).

// ...Scala already has it for many years and the concept is

// older than your friendly lecturer, that is stone old  ;o)

// The general schema:

//

//    expression match {

//       case pattern1 => expression1

//       case pattern2 => expression2

//       ...

//       case patternN => expressionN

//    }

// recall

def len(xs: List[Int]) : Int = {

    if (xs == Nil) 0

    else 1 + len(xs.tail)

}    

def len(xs: List[Int]) : Int = xs match {

    case Nil => 0

    case _::xs => 1 + len(xs)

}  

len(Nil)

len(List(1,2,3,4))

List(1,2,3,4).map(x => x * x)

def my_map_int(lst: List[Int], f: Int => Int) : List[Int] = 

  lst match {

    case Nil => Nil

    case foo::xs => f(foo) :: my_map_int(xs, f)

  }

def my_map_option(opt: Option[Int], f: Int => Int) : Option[Int] = 

  opt match {

    case None => None

    case Some(x) => {

      Some(f(x))

    }

  }

my_map_option(None, x => x * x)

my_map_option(Some(8), x => x * x)

// you can also have cases combined

def season(month: String) : 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" => "It's winter"

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

  case _ => "Wrong month"

}

// pattern-match on integers

def fib(n: Int) : Int = n match { 

  case 0 | 1 => 1

  case _ => fib(n - 1) + fib(n - 2)

}

fib(10)

// pattern-match on results

// Silly: fizz buzz

def fizz_buzz(n: Int) : String = (n % 3, n % 5) match {

  case (0, 0) => "fizz buzz"

  case (0, _) => "fizz"

  case (_, 0) => "buzz"

  case _ => n.toString  

}

for (n <- 1 to 20) 

 println(fizz_buzz(n))

// guards in pattern-matching

def foo(xs: List[Int]) : String = xs match {

  case Nil => s"this list is empty"

  case x :: xs if x % 2 == 0 

     => s"the first elemnt is even"

  case x if len(x) ==

     => s"this list has exactly two elements"   

  case x :: y :: rest if x == y

     => s"this has two elemnts that are the same"

  case hd :: tl => s"this list is standard $hd::$tl"

}

foo(Nil)

foo(List(1,2,3))

foo(List(1,1))

foo(List(1,1,2,3))

foo(List(2,2,2,3))

abstract class Colour

case object Red extends Colour 

case object Green extends Colour 

case object Blue extends Colour

case object Yellow extends Colour

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

  case Green => true

  case Red => true

  case _  => false 

}

fav_colour(Blue)

// ... a tiny bit more useful: Roman Numerals

sealed abstract class RomanDigit 

case object I extends RomanDigit 

case object V extends RomanDigit 

case object X extends RomanDigit 

case object L extends RomanDigit 

case object C extends RomanDigit 

case object D extends RomanDigit 

case object M extends RomanDigit 

type RomanNumeral = List[RomanDigit] 

List(I, M,C,D,X,X,V,I,I, A)

/*

I    -> 1

II   -> 2

III  -> 3

IV   -> 4

V    -> 5

VI   -> 6

VII  -> 7

VIII -> 8

IX   -> 9

X    -> 10

*/

def RomanNumeral2Int(rs: RomanNumeral): Int = rs match { 

  case Nil => 0

  case M::r    => 1000 + RomanNumeral2Int(r)  

  case C::M::r => 900 + RomanNumeral2Int(r)

  case D::r    => 500 + RomanNumeral2Int(r)

  case C::D::r => 400 + RomanNumeral2Int(r)

  case C::r    => 100 + RomanNumeral2Int(r)

  case X::C::r => 90 + RomanNumeral2Int(r)

  case L::r    => 50 + RomanNumeral2Int(r)

  case X::L::r => 40 + RomanNumeral2Int(r)

  case X::r    => 10 + RomanNumeral2Int(r)

  case I::X::r => 9 + RomanNumeral2Int(r)

  case V::r    => 5 + RomanNumeral2Int(r)

  case I::V::r => 4 + RomanNumeral2Int(r)

  case I::r    => 1 + RomanNumeral2Int(r)

}

RomanNumeral2Int(List(I,V))             // 4

RomanNumeral2Int(List(I,I,I,I))         // 4 (invalid Roman number)

RomanNumeral2Int(List(V,I))             // 6

RomanNumeral2Int(List(I,X))             // 9

RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979

RomanNumeral2Int(List(M,M,X,V,I,I))     // 2017

abstract class Tree

case class Leaf(x: Int)

case class Branch(tl: Tree, tr: Tree)

abstract class Rexp

case object ZERO extends Rexp                      // matches nothing

case object ONE extends Rexp                       // matches the empty string

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

case class ALT(r1: Rexp, r2: Rexp) extends Rexp    // alternative

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

case class STAR(r: Rexp) extends Rexp              // star

def depth(r: Rexp) : Int = r match {

  case ZERO => 1

  case ONE => 1

  case CHAR(_) => 1

  case ALT(r1, r2) => 1 + List(depth(r1), depth(r2)).max

  case SEQ(r1, r2) => 1 + List(depth(r1), depth(r2)).max

  case STAR(r1) => 1 + depth(r1)

}

// Trees (example of an Algebraic Datatype)

abstract class Tree

case class Leaf(x: Int) extends Tree

case class Node(s: String, left: Tree, right: Tree) extends Tree 

val lf = Leaf(20)

val tr = Node("foo", Leaf(10), Leaf(23))

val lst : List[Tree] = List(lf, tr)

sealed abstract class Exp

println(e.toString)

// (....9 ....)

// Tail recursion

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

def fact(n: BigInt): BigInt = 

  if (n == 0) 1 else n * fact(n - 1)

fact(10)          

fact(1000)        

fact(100000)       

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

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

factT(10, 1)

println(factT(100000, 1))

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

import scala.annotation.tailrec

@tailrec

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

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

factT(100000, 1)

// for tail-recursive functions the Scala compiler

// generates loop-like code, which does not need

// to allocate stack-space in each recursive

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

// functions

// Moral: Whenever a recursive function is resource-critical

// (i.e. works with a large recursion depth), then you need to

// write it in tail-recursive fashion.

// 

// Unfortuantely, Scala because of current limitations in 

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

// only optimise "self-tail calls". This excludes the cases of 

// multiple functions making tail calls to each other. Well,

// nothing is perfect.