// Scala Lecture 3
//=================
// 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 already for
// decades. I think I would be really upset if a programming language
// I have to use does not have pattern matching....its is just so
// useful. ;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] = {
if (xs == Nil) Nil
else if (xs.head == None) my_flatten(xs.tail)
else xs.head.get :: my_flatten(xs.tail)
}
val lst = List(None, Some(1), Some(2), None, Some(3))
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)
}
my_flatten(lst)
Nil == List()
// 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(10)
// 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"))
// we can also match more complicated pattern
//
// let's look at the Collatz function on binary strings
// adding two binary strings in a very, very lazy manner
def badd(s1: String, s2: String) : String =
(BigInt(s1, 2) + BigInt(s2, 2)).toString(2)
"111".dropRight(1)
"111".last
def bcollatz(s: String) : Long = (s.dropRight(1), s.last) match {
case ("", '1') => 1 // we reached 1
case (rest, '0') => 1 + bcollatz(rest)
// even number => divide by two
case (rest, '1') => 1 + bcollatz(badd(s + '1', s))
// odd number => s + '1' is 2 * s + 1
// add another s gives 3 * s + 1
}
bcollatz(6.toBinaryString)
bcollatz(837799.toBinaryString)
bcollatz(100000000000000000L.toBinaryString)
bcollatz(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))
// User-defined Datatypes
//========================
abstract class Colour
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)
// actually colors can be written with "object",
// because they do not take any arguments
// ... a bit more useful: Roman Numerals
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]
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
// another example
//=================
// Once upon a time, in a complete fictional country there were Persons...
abstract class Person
case object 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
case object Clown 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
case Clown => "My name is Boris Johnson"
}
title(Clown)
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
//================
def fact(n: Long): Long =
if (n == 0) 1 else n * fact(n - 1)
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)
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
// 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 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)
// 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.
// Polymorphic Types
//===================
// You do not want to write functions like contains, first
// and so on for every type of lists.
def length_string_list(lst: List[String]): Int = lst match {
case Nil => 0
case x::xs => 1 + length_string_list(xs)
}
def length_int_list(lst: List[Int]): Int = lst match {
case Nil => 0
case x::xs => 1 + length_int_list(xs)
}
length_string_list(List("1", "2", "3", "4"))
length_int_list(List(1, 2, 3, 4))
//-----
def length[A](lst: List[A]): Int = lst match {
case Nil => 0
case x::xs => 1 + length(xs)
}
length(List("1", "2", "3", "4"))
length(List(King, Knight("foo"), Clown))
length(List(1, 2, 3, 4))
def map[A, B](lst: List[A], f: A => B): List[B] = lst match {
case Nil => Nil
case x::xs => f(x)::map_int_list(xs, f)
}
map_int_list(List(1, 2, 3, 4), square)
// Remember?
def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = ...
// 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
// Regular expressions - the power of DSLs in Scala
//==================================================
abstract class Rexp
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 ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative r1 + r2
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence r1 o r2
case class STAR(r: Rexp) extends Rexp // star r*
// (ab)*
val r0 = STAR(SEQ(CHAR('a'), CHAR('b')))
// some convenience for typing in regular expressions
import scala.language.implicitConversions
import scala.language.reflectiveCalls
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => ONE
case c::Nil => CHAR(c)
case c::s => SEQ(CHAR(c), charlist2rexp(s))
}
implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)
val r1 = STAR("ab")
val r2 = STAR(ALT("ab"))
val r3 = STAR(ALT("ab", "baa baa black sheep"))
implicit def RexpOps (r: Rexp) = new {
def | (s: Rexp) = ALT(r, s)
def % = STAR(r)
def ~ (s: Rexp) = SEQ(r, s)
}
implicit def stringOps (s: String) = new {
def | (r: Rexp) = ALT(s, r)
def | (r: String) = ALT(s, r)
def % = STAR(s)
def ~ (r: Rexp) = SEQ(s, r)
def ~ (r: String) = SEQ(s, r)
}
//example regular expressions
val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
val sign = "+" | "-" | ""
val number = sign ~ digit ~ digit.%
// The End
//=========
// A function should do one thing, and only one thing.
// Make your variables immutable, unless there's a good
// reason not to.
// You can be productive on Day 1, but the language is deep.
//
// http://scalapuzzlers.com
//
// http://www.latkin.org/blog/2017/05/02/when-the-scala-compiler-doesnt-help/
List(1, 2, 3) contains "your mom"
// I like best about Scala that it lets me often write
// concise, readable code.