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// Scala Lecture 3
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//=================
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// Pattern Matching
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//==================
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// A powerful tool which is supposed to come to Java in a few years
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// time (https://www.youtube.com/watch?v=oGll155-vuQ)...Scala already
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// has it for many years. Other functional languages have it already for
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// decades. I think I would be really upset if a programming language
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// I have to use does not have pattern matching....its is just so
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// useful. ;o)
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// The general schema:
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//
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// expression match {
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// case pattern1 => expression1
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// case pattern2 => expression2
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// ...
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// case patternN => expressionN
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// }
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// remember
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val lst = List(None, Some(1), Some(2), None, Some(3)).flatten
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def my_flatten(xs: List[Option[Int]]): List[Int] = {
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if (xs == Nil) Nil
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else if (xs.head == None) my_flatten(xs.tail)
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else xs.head.get :: my_flatten(xs.tail)
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}
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val lst = List(None, Some(1), Some(2), None, Some(3))
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def my_flatten(lst: List[Option[Int]]): List[Int] = lst match {
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case Nil => Nil
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case None::xs => my_flatten(xs)
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case Some(n)::xs => n::my_flatten(xs)
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}
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my_flatten(lst)
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Nil == List()
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// another example including a catch-all pattern
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def get_me_a_string(n: Int): String = n match {
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case 0 => "zero"
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case 1 => "one"
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case 2 => "two"
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case _ => "many"
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}
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get_me_a_string(10)
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// you can also have cases combined
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def season(month: String) = month match {
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case "March" | "April" | "May" => "It's spring"
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case "June" | "July" | "August" => "It's summer"
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case "September" | "October" | "November" => "It's autumn"
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case "December" | "January" | "February" => "It's winter"
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}
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println(season("November"))
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// What happens if no case matches?
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println(season("foobar"))
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// we can also match more complicated pattern
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//
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// let's look at the Collatz function on binary strings
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// adding two binary strings in a very, very lazy manner
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def badd(s1: String, s2: String) : String =
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(BigInt(s1, 2) + BigInt(s2, 2)).toString(2)
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"111".dropRight(1)
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"111".last
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def bcollatz(s: String) : Long = (s.dropRight(1), s.last) match {
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case ("", '1') => 1 // we reached 1
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case (rest, '0') => 1 + bcollatz(rest)
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// even number => divide by two
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case (rest, '1') => 1 + bcollatz(badd(s + '1', s))
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// odd number => s + '1' is 2 * s + 1
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// add another s gives 3 * s + 1
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}
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bcollatz(6.toBinaryString)
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bcollatz(837799.toBinaryString)
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bcollatz(100000000000000000L.toBinaryString)
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bcollatz(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))
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// User-defined Datatypes
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//========================
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abstract class Colour
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case object Red extends Colour
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case object Green extends Colour
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case object Blue extends Colour
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def fav_colour(c: Colour) : Boolean = c match {
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case Red => false
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case Green => true
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case Blue => false
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}
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fav_colour(Green)
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// actually colors can be written with "object",
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// because they do not take any arguments
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// ... a bit more useful: Roman Numerals
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abstract class RomanDigit
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case object I extends RomanDigit
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case object V extends RomanDigit
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case object X extends RomanDigit
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case object L extends RomanDigit
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case object C extends RomanDigit
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case object D extends RomanDigit
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case object M extends RomanDigit
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type RomanNumeral = List[RomanDigit]
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def RomanNumeral2Int(rs: RomanNumeral): Int = rs match {
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case Nil => 0
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case M::r => 1000 + RomanNumeral2Int(r)
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case C::M::r => 900 + RomanNumeral2Int(r)
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case D::r => 500 + RomanNumeral2Int(r)
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case C::D::r => 400 + RomanNumeral2Int(r)
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case C::r => 100 + RomanNumeral2Int(r)
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case X::C::r => 90 + RomanNumeral2Int(r)
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case L::r => 50 + RomanNumeral2Int(r)
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case X::L::r => 40 + RomanNumeral2Int(r)
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case X::r => 10 + RomanNumeral2Int(r)
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case I::X::r => 9 + RomanNumeral2Int(r)
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case V::r => 5 + RomanNumeral2Int(r)
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case I::V::r => 4 + RomanNumeral2Int(r)
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case I::r => 1 + RomanNumeral2Int(r)
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}
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RomanNumeral2Int(List(I,V)) // 4
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RomanNumeral2Int(List(I,I,I,I)) // 4 (invalid Roman number)
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RomanNumeral2Int(List(V,I)) // 6
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RomanNumeral2Int(List(I,X)) // 9
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RomanNumeral2Int(List(M,C,M,L,X,X,I,X)) // 1979
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RomanNumeral2Int(List(M,M,X,V,I,I)) // 2017
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// another example
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//=================
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// Once upon a time, in a complete fictional country there were Persons...
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abstract class Person
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case object King extends Person
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case class Peer(deg: String, terr: String, succ: Int) extends Person
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case class Knight(name: String) extends Person
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case class Peasant(name: String) extends Person
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case object Clown extends Person
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def title(p: Person): String = p match {
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case King => "His Majesty the King"
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case Peer(deg, terr, _) => s"The ${deg} of ${terr}"
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case Knight(name) => s"Sir ${name}"
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case Peasant(name) => name
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case Clown => "My name is Boris Johnson"
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}
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title(Clown)
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def superior(p1: Person, p2: Person): Boolean = (p1, p2) match {
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case (King, _) => true
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case (Peer(_,_,_), Knight(_)) => true
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case (Peer(_,_,_), Peasant(_)) => true
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case (Peer(_,_,_), Clown) => true
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case (Knight(_), Peasant(_)) => true
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case (Knight(_), Clown) => true
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case (Clown, Peasant(_)) => true
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case _ => false
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}
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val people = List(Knight("David"),
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Peer("Duke", "Norfolk", 84),
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Peasant("Christian"),
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King,
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Clown)
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println(people.sortWith(superior(_, _)).mkString(", "))
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// Tail recursion
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//================
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def fact(n: Long): Long =
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if (n == 0) 1 else n * fact(n - 1)
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fact(10) //ok
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fact(10000) // produces a stackoverflow
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def factT(n: BigInt, acc: BigInt): BigInt =
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if (n == 0) acc else factT(n - 1, n * acc)
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factT(10, 1)
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factT(100000, 1)
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// there is a flag for ensuring a function is tail recursive
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import scala.annotation.tailrec
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@tailrec
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def factT(n: BigInt, acc: BigInt): BigInt =
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if (n == 0) acc else factT(n - 1, n * acc)
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// for tail-recursive functions the Scala compiler
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// generates loop-like code, which does not need
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// to allocate stack-space in each recursive
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// call; Scala can do this only for tail-recursive
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// functions
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// sudoku again
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val game0 = """.14.6.3..
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|62...4..9
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|.8..5.6..
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|.6.2....3
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|.7..1..5.
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|5....9.6.
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|..6.2..3.
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|1..5...92
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|..7.9.41.""".stripMargin.replaceAll("\\n", "")
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type Pos = (Int, Int)
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val EmptyValue = '.'
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val MaxValue = 9
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val allValues = "123456789".toList
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val indexes = (0 to 8).toList
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def empty(game: String) = game.indexOf(EmptyValue)
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def isDone(game: String) = empty(game) == -1
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def emptyPosition(game: String) =
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(empty(game) % MaxValue, empty(game) / MaxValue)
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def get_row(game: String, y: Int) =
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indexes.map(col => game(y * MaxValue + col))
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def get_col(game: String, x: Int) =
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indexes.map(row => game(x + row * MaxValue))
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def get_box(game: String, pos: Pos): List[Char] = {
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def base(p: Int): Int = (p / 3) * 3
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val x0 = base(pos._1)
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val y0 = base(pos._2)
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val ys = (y0 until y0 + 3).toList
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(x0 until x0 + 3).toList.flatMap(x => ys.map(y => game(x + y * MaxValue)))
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}
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// this is not mutable!!
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def update(game: String, pos: Int, value: Char): String =
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game.updated(pos, value)
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def toAvoid(game: String, pos: Pos): List[Char] =
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(get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos))
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def candidates(game: String, pos: Pos): List[Char] =
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allValues.diff(toAvoid(game,pos))
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//candidates(game0, (0,0))
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def pretty(game: String): String =
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"\n" + (game sliding (MaxValue, MaxValue) mkString "\n")
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/////////////////////
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// not tail recursive
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def search(game: String): List[String] = {
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if (isDone(game)) List(game)
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else {
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val cs = candidates(game, emptyPosition(game))
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cs.map(c => search(update(game, empty(game), c))).toList.flatten
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}
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}
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// tail recursive version that searches
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// for all solutions
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def searchT(games: List[String], sols: List[String]): List[String] = games match {
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case Nil => sols
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case game::rest => {
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if (isDone(game)) searchT(rest, game::sols)
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else {
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val cs = candidates(game, emptyPosition(game))
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searchT(cs.map(c => update(game, empty(game), c)) ::: rest, sols)
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}
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}
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}
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searchT(List(game3), List()).map(pretty)
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// tail recursive version that searches
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// for a single solution
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def search1T(games: List[String]): Option[String] = games match {
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case Nil => None
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case game::rest => {
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if (isDone(game)) Some(game)
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else {
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val cs = candidates(game, emptyPosition(game))
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search1T(cs.map(c => update(game, empty(game), c)) ::: rest)
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}
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}
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}
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search1T(List(game3)).map(pretty)
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// game with multiple solutions
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val game3 = """.8...9743
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|.5...8.1.
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|.1.......
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|8....5...
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|...8.4...
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|...3....6
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|.......7.
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|.3.5...8.
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|9724...5.""".stripMargin.replaceAll("\\n", "")
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searchT(List(game3), Nil).map(pretty)
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search1T(List(game3)).map(pretty)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// Moral: Whenever a recursive function is resource-critical
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// (i.e. works with large recursion depth), then you need to
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// write it in tail-recursive fashion.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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//
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// Unfortuantely, Scala because of current limitations in
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// the JVM is not as clever as other functional languages. It can
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// only optimise "self-tail calls". This excludes the cases of
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// multiple functions making tail calls to each other. Well,
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// nothing is perfect.
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// Polymorphic Types
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//===================
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// You do not want to write functions like contains, first
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// and so on for every type of lists.
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def length_string_list(lst: List[String]): Int = lst match {
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case Nil => 0
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case x::xs => 1 + length_string_list(xs)
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}
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def length_int_list(lst: List[Int]): Int = lst match {
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case Nil => 0
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case x::xs => 1 + length_int_list(xs)
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}
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length_string_list(List("1", "2", "3", "4"))
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length_int_list(List(1, 2, 3, 4))
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//-----
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def length[A](lst: List[A]): Int = lst match {
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case Nil => 0
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case x::xs => 1 + length(xs)
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}
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length(List("1", "2", "3", "4"))
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length(List(King, Knight("foo"), Clown))
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length(List(1, 2, 3, 4))
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def map[A, B](lst: List[A], f: A => B): List[B] = lst match {
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case Nil => Nil
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case x::xs => f(x)::map_int_list(xs, f)
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}
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map_int_list(List(1, 2, 3, 4), square)
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// Remember?
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def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = ...
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407 |
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158
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155
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// Cool Stuff
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413 |
//============
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72
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155
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415 |
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// Implicits
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417 |
//===========
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418 |
//
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419 |
// For example adding your own methods to Strings:
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420 |
// Imagine you want to increment strings, like
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//
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// "HAL".increment
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423 |
//
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424 |
// you can avoid ugly fudges, like a MyString, by
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|
425 |
// using implicit conversions.
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67
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426 |
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427 |
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155
|
428 |
implicit class MyString(s: String) {
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|
429 |
def increment = for (c <- s) yield (c + 1).toChar
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67
|
430 |
}
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431 |
|
155
|
432 |
"HAL".increment
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67
|
433 |
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53
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434 |
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435 |
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436 |
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71
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437 |
// Regular expressions - the power of DSLs in Scala
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|
438 |
//==================================================
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67
|
439 |
|
|
440 |
abstract class Rexp
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155
|
441 |
case object ZERO extends Rexp // nothing
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case object ONE extends Rexp // the empty string
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443 |
case class CHAR(c: Char) extends Rexp // a character c
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71
|
444 |
case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative r1 + r2
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155
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445 |
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence r1 o r2
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71
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446 |
case class STAR(r: Rexp) extends Rexp // star r*
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67
|
447 |
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448 |
|
158
|
449 |
|
67
|
450 |
// (ab)*
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72
|
451 |
val r0 = STAR(SEQ(CHAR('a'), CHAR('b')))
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67
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452 |
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453 |
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|
454 |
// some convenience for typing in regular expressions
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|
455 |
import scala.language.implicitConversions
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|
456 |
import scala.language.reflectiveCalls
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|
457 |
|
|
458 |
def charlist2rexp(s: List[Char]): Rexp = s match {
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|
459 |
case Nil => ONE
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|
460 |
case c::Nil => CHAR(c)
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|
461 |
case c::s => SEQ(CHAR(c), charlist2rexp(s))
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|
462 |
}
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|
463 |
implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)
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|
464 |
|
|
465 |
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|
466 |
val r1 = STAR("ab")
|
158
|
467 |
val r2 = STAR(ALT("ab"))
|
72
|
468 |
val r3 = STAR(ALT("ab", "baa baa black sheep"))
|
67
|
469 |
|
|
470 |
implicit def RexpOps (r: Rexp) = new {
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|
471 |
def | (s: Rexp) = ALT(r, s)
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|
472 |
def % = STAR(r)
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|
473 |
def ~ (s: Rexp) = SEQ(r, s)
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|
474 |
}
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|
475 |
|
|
476 |
implicit def stringOps (s: String) = new {
|
|
477 |
def | (r: Rexp) = ALT(s, r)
|
|
478 |
def | (r: String) = ALT(s, r)
|
|
479 |
def % = STAR(s)
|
|
480 |
def ~ (r: Rexp) = SEQ(s, r)
|
|
481 |
def ~ (r: String) = SEQ(s, r)
|
|
482 |
}
|
|
483 |
|
153
|
484 |
//example regular expressions
|
67
|
485 |
val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
|
|
486 |
val sign = "+" | "-" | ""
|
|
487 |
val number = sign ~ digit ~ digit.%
|
|
488 |
|
|
489 |
|
|
490 |
|
|
491 |
|
|
492 |
|
|
493 |
// The End
|
|
494 |
//=========
|
|
495 |
|
|
496 |
// A function should do one thing, and only one thing.
|
|
497 |
|
|
498 |
// Make your variables immutable, unless there's a good
|
|
499 |
// reason not to.
|
|
500 |
|
|
501 |
// You can be productive on Day 1, but the language is deep.
|
158
|
502 |
//
|
|
503 |
// http://scalapuzzlers.com
|
|
504 |
//
|
|
505 |
// http://www.latkin.org/blog/2017/05/02/when-the-scala-compiler-doesnt-help/
|
67
|
506 |
|
158
|
507 |
List(1, 2, 3) contains "your mom"
|
|
508 |
|
|
509 |
// I like best about Scala that it lets me often write
|
155
|
510 |
// concise, readable code.
|
68
|
511 |
|