// Scala Lecture 3

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

// - last week

//

// option type 

// higher-order function

def add(x: Int, y: Int) : Int = x + y

def plus5(x: Int) : Int = add(5, x)

plus5(6)

def add2(x: Int)(y: Int) : Int = x + y

def plus3(y: Int) : Int => Int = add2(3)(y)

plus3(9)

List(1,2,3,4,5).map(add2(3))

List(1,2,3,4,5).map(add(3, _))

type Pos = (Int, Int)

def test(p: Pos) = {

  if (p._1 < 5 && p._2 < 5) {

    Some(p)

  }

}

val l = List((1,2), (5,3), (2,5), (1,3))

l.map(test).flatten

// naive quicksort with "On" function

def sortOn(f: Int => Int, xs: List[Int]) : List[Int] = {

  if (xs.size < 2) xs

  else {

   val pivot = xs.head

   val (left, right) = xs.partition(f(_) < f(pivot))

   sortOn(f, left) ::: pivot :: sortOn(f, right.tail)

  }

} 

sortOn(identity, List(99,99,99,98,10,-3,2)) 

sortOn(n => - n, List(99,99,99,98,10,-3,2))

// Recursion Again ;o)

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

// A Web Crawler / Email Harvester

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

//

// the idea is to look for links using the

// regular expression "https?://[^"]*" and for

// email addresses using yet another regex.

import io.Source

import scala.util._

// gets the first 10K of a web-page

def get_page(url: String) : String = {

  Try(Source.fromURL(url)("ISO-8859-1").take(10000).mkString).

    getOrElse { println(s" Problem with: $url"); ""}

}

// regex for URLs and emails

val http_pattern = """"https?://[^"]*"""".r

val email_pattern = """([a-z0-9_\.-]+)@([\da-z\.-]+)\.([a-z\.]{2,6})""".r

//  val s = "foo bla christian@kcl.ac.uk 1234567"

//  email_pattern.findAllIn(s).toList

// drops the first and last character from a string

def unquote(s: String) = s.drop(1).dropRight(1)

def get_all_URLs(page: String): Set[String] = 

  http_pattern.findAllIn(page).map(unquote).toSet

// a naive version of crawl - searches until a given depth,

// visits pages potentially more than once

def crawl(url: String, n: Int) : Unit = {

  if (n == 0) ()

  else {

    println(s"  Visiting: $n $url")

    val page = get_page(url)

    for (u <- get_all_URLs(page)) crawl(u, n - 1)

  }

}

// some starting URLs for the crawler

val startURL = """https://nms.kcl.ac.uk/christian.urban/"""

crawl(startURL, 2)

for (x <- List(1,2,3,4,5,6)) println(x)

// a primitive email harvester

def emails(url: String, n: Int) : Set[String] = {

  if (n == 0) Set()

  else {

    println(s"  Visiting: $n $url")

    val page = get_page(url)

    val new_emails = email_pattern.findAllIn(page).toSet

    new_emails ++ (for (u <- get_all_URLs(page).par) yield emails(u, n - 1)).flatten

  }

}

emails(startURL, 3)

// if we want to explore the internet "deeper", then we

// first have to parallelise the request of webpages:

//

// scala -cp scala-parallel-collections_2.13-0.2.0.jar 

// import scala.collection.parallel.CollectionConverters._

// another well-known example

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

def move(from: Char, to: Char) =

  println(s"Move disc from $from to $to!")

def hanoi(n: Int, from: Char, via: Char, to: Char) : Unit = {

  if (n == 0) ()

  else {

    hanoi(n - 1, from, to, via)

    move(from, to)

    hanoi(n - 1, via, from, to)

  }

} 

hanoi(4, 'A', 'B', 'C')

// Jumping Towers

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

// the first n prefixes of xs

// for 1 => include xs

def moves(xs: List[Int], n: Int) : List[List[Int]] = (xs, n) match {

  case (Nil, _) => Nil

  case (_, 0) => Nil

  case (y::ys, n) => xs :: moves(ys, n - 1)

}

moves(List(5,1,0), 1)

moves(List(5,1,0), 2)

moves(List(5,1,0), 5)

// checks whether a jump tour exists at all

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

  case Nil => true

  case x::xs =>

    if (xs.length < x) true 

    else moves(xs, x).exists(search(_))

}

search(List(5,3,2,5,1,1))

search(List(3,5,1,0,0,0,1))

search(List(3,5,1,0,0,0,0,1))

search(List(3,5,1,0,0,0,1,1))

search(List(3,5,1))

search(List(5,1,1))

search(Nil)

search(List(1))

search(List(5,1,1))

search(List(3,5,1,0,0,0,0,0,0,0,0,1))

// generates *all* jump tours

//    if we are only interested in the shortest one, we could

//    shortcircut the calculation and only return List(x) in

//    case where xs.length < x, because no tour can be shorter

//    than 1

// 

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

  case Nil => Nil

  case x::xs => {

    val children = moves(xs, x)

    val results = children.map(cs => jumps(cs).map(x :: _)).flatten

    if (xs.length < x) List(x)::results else results

  }

}

jumps(List(5,3,2,5,1,1)).minBy(_.length)

jumps(List(3,5,1,2,1,2,1))

jumps(List(3,5,1,2,3,4,1))

jumps(List(3,5,1,0,0,0,1))

jumps(List(3,5,1))

jumps(List(5,1,1))

jumps(Nil)

jumps(List(1))

jumps(List(5,1,2))

moves(List(1,2), 5)

jumps(List(1,5,1,2))

jumps(List(3,5,1,0,0,0,0,0,0,0,0,1))

jumps(List(5,3,2,5,1,1)).minBy(_.length)

jumps(List(1,3,5,8,9,2,6,7,6,8,9)).minBy(_.length)

jumps(List(1,3,6,1,0,9)).minBy(_.length)

jumps(List(2,3,1,1,2,4,2,0,1,1)).minBy(_.length)

// User-defined Datatypes

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

abstract class Tree

case class Leaf(x: Int) extends Tree

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

List(Leaf(20), Node("foo", Leaf(1), Leaf(2)))

sealed 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 _  => false 

}

fav_colour(Green)

// ... 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(X,I,M,D)

/*

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

// String interpolations as patterns

val date = "2019-11-26"

val s"$year-$month-$day" = date

def parse_date(date: String) : Option[(Int, Int, Int)]= date match {

  case s"$year-$month-$day" => Some((day.toInt, month.toInt, year.toInt))

  case s"$day/$month/$year" => Some((day.toInt, month.toInt, year.toInt))

  case s"$day.$month.$year" => Some((day.toInt, month.toInt, year.toInt))

  case _ => None

} 

parse_date("2019-11-26")

parse_date("26/11/2019")

parse_date("26.11.2019")

// User-defined Datatypes and Pattern Matching

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

// Tail recursion

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

def fact(n: Long): Long = 

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

def factB(n: BigInt): BigInt = 

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

factB(100000)

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(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)

// 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

// tail recursive version that searches 

// for all solutions

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)

    }

  }

}

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

// tail recursive version that searches 

// for a single solution

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

  case Nil => None

  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)

    }

  }

}

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

time_needed(10, search1T(List(game3)))

// 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), Nil).map(pretty)

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

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

// (i.e. works with 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. 

//************

// Either

val either1 : Either[Exception,Int] = Right(1)

val either2: Either[Exception, Int] = Right(2)

for{

  one <- either1

  two <- either2

} yield one + two