// Scala Lecture 3

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

// - last week

//

// option type 

// higher-order function

// 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")

  }

}

// some starting URLs for the crawler

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

crawl(startURL, 2)

// 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)) yield emails(u, n - 1)).flatten

  }

}

emails(startURL, 2)

// 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 (xs, 0) => Nil

  case (x::xs, n) => (x::xs) :: moves(xs, 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

}

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

//    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

    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

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

case object Red extends Colour 

case object Green extends Colour 

case object Blue extends Colour

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

  case Red   => false

  case Green => true

  case Blue  => false 

}

fav_colour(Green)

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

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)

/*

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

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

// trees

case class N(n: Int) extends Exp                  // for numbers

case class Plus(e1: Exp, e2: Exp) extends Exp

case class Times(e1: Exp, e2: Exp) extends Exp

def string(e: Exp) : String = e match {

  case N(n) => s"$n"

  case Plus(e1, e2) => s"(${string(e1)} + ${string(e2)})" 

  case Times(e1, e2) => s"(${string(e1)} * ${string(e2)})"

}

val e = Plus(N(9), Times(N(3), N(4)))

println(string(e))

def eval(e: Exp) : Int = e match {

  case N(n) => n

  case Plus(e1, e2) => eval(e1) + eval(e2) 

  case Times(e1, e2) => eval(e1) * eval(e2) 

}

println(eval(e))

def simp(e: Exp) : Exp = e match {

  case N(n) => N(n)

  case Plus(e1, e2) => (simp(e1), simp(e2)) match {

    case (N(0), e2s) => e2s

    case (e1s, N(0)) => e1s

    case (e1s, e2s) => Plus(e1s, e2s)

  }  

  case Times(e1, e2) => (simp(e1), simp(e2)) match {

    case (N(0), _) => N(0)

    case (_, N(0)) => N(0)

    case (N(1), e2s) => e2s

    case (e1s, N(1)) => e1s

    case (e1s, e2s) => Times(e1s, e2s)

  }  

}

val e2 = Times(Plus(N(0), N(1)), Plus(N(0), N(9)))

println(string(e2))

println(string(simp(e2)))

// Tokens and Reverse Polish Notation

case class T(n: Int) extends Token

case object PL extends Token

case object TI extends Token

def rp(e: Exp) : List[Token] = e match {

  case N(n) => List(T(n))

  case Plus(e1, e2) => rp(e1) ::: rp(e2) ::: List(PL) 

  case Times(e1, e2) => rp(e1) ::: rp(e2) ::: List(TI) 

}

println(string(e2))

println(rp(e2))

def comp(ls: List[Token], st: List[Int]) : Int = (ls, st) match {

  case (Nil, st) => st.head 

  case (T(n)::rest, st) => comp(rest, n::st)

  case (PL::rest, n1::n2::st) => comp(rest, n1 + n2::st)

  case (TI::rest, n1::n2::st) => comp(rest, n1 * n2::st)

}

comp(rp(e), Nil)

def proc(s: String) : Token = s match {

  case  "+" => PL

  case  "*" => TI

  case  _ => T(s.toInt) 

}

comp("1 2 + 4 * 5 + 3 +".split(" ").toList.map(proc), Nil)

// Sudoku 

//========

// THE POINT OF THIS CODE IS NOT TO BE SUPER

// EFFICIENT AND FAST, just explaining exhaustive

// depth-first search

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)))

}

//get_row(game0, 0)

//get_row(game0, 1)

//get_col(game0, 0)

//get_box(game0, (3, 1))

// 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"))

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

  }

}

search(game0).map(pretty)

val game1 = """23.915...

              |...2..54.

              |6.7......

              |..1.....9

              |89.5.3.17

              |5.....6..

              |......9.5

              |.16..7...

              |...329..1""".stripMargin.replaceAll("\\n", "")

// game that is in the hard category

val game2 = """8........

              |..36.....

              |.7..9.2..

              |.5...7...

              |....457..

              |...1...3.

              |..1....68

              |..85...1.

              |.9....4..""".stripMargin.replaceAll("\\n", "")

// 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", "")

search(game1).map(pretty)

search(game3).map(pretty)

search(game2).map(pretty)

// for measuring time

def time_needed[T](i: Int, code: => T) = {

  val start = System.nanoTime()

  for (j <- 1 to i) code

  val end = System.nanoTime()

  ((end - start) / 1.0e9) + " secs"

}

time_needed(1, search(game2))

// 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)