| author | Christian Urban <urbanc@in.tum.de> |
| Tue, 19 Nov 2019 00:40:27 +0000 | |
| changeset 320 | 90aed247c8cf |
| parent 318 | f1215a72cd88 |
| child 321 | f6cb539e0ffb |
| permissions | -rw-r--r-- |
| 67 | 1 |
// Scala Lecture 3 |
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//================= |
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// - last week |
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// |
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// option type |
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// higher-order function |
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// Recursion Again ;o) |
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//==================== |
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// A Web Crawler / Email Harvester |
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//================================= |
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// |
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// the idea is to look for links using the |
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// regular expression "https?://[^"]*" and for |
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// email addresses using yet another regex. |
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import io.Source |
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import scala.util._ |
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// gets the first 10K of a web-page |
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def get_page(url: String) : String = {
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Try(Source.fromURL(url)("ISO-8859-1").take(10000).mkString).
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getOrElse { println(s" Problem with: $url"); ""}
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} |
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// regex for URLs and emails |
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val http_pattern = """"https?://[^"]*"""".r |
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val email_pattern = """([a-z0-9_\.-]+)@([\da-z\.-]+)\.([a-z\.]{2,6})""".r
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// val s = "foo bla christian@kcl.ac.uk 1234567" |
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// email_pattern.findAllIn(s).toList |
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// drops the first and last character from a string |
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def unquote(s: String) = s.drop(1).dropRight(1) |
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def get_all_URLs(page: String): Set[String] = |
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http_pattern.findAllIn(page).map(unquote).toSet |
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// a naive version of crawl - searches until a given depth, |
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// visits pages potentially more than once |
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def crawl(url: String, n: Int) : Unit = {
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if (n == 0) () |
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else {
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println(s" Visiting: $n $url") |
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for (u <- get_all_URLs(get_page(url))) crawl(u, n - 1) |
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} |
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} |
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// some starting URLs for the crawler |
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val startURL = """https://nms.kcl.ac.uk/christian.urban/""" |
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crawl(startURL, 2) |
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// a primitive email harvester |
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def emails(url: String, n: Int) : Set[String] = {
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if (n == 0) Set() |
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else {
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println(s" Visiting: $n $url") |
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val page = get_page(url) |
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val new_emails = email_pattern.findAllIn(page).toSet |
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new_emails ++ (for (u <- get_all_URLs(page)) yield emails(u, n - 1)).flatten |
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} |
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} |
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emails(startURL, 2) |
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// if we want to explore the internet "deeper", then we |
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// first have to parallelise the request of webpages: |
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// |
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// scala -cp scala-parallel-collections_2.13-0.2.0.jar |
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// import scala.collection.parallel.CollectionConverters._ |
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// another well-known example |
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//============================ |
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def move(from: Char, to: Char) = |
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println(s"Move disc from $from to $to!") |
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def hanoi(n: Int, from: Char, via: Char, to: Char) : Unit = {
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if (n == 0) () |
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else {
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hanoi(n - 1, from, to, via) |
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move(from, to) |
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hanoi(n - 1, via, from, to) |
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} |
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} |
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hanoi(4, 'A', 'B', 'C') |
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// Jumping Towers |
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//================ |
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// the first n prefixes of xs |
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// for 1 => include xs |
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def moves(xs: List[Int], n: Int) : List[List[Int]] = (xs, n) match {
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case (Nil, _) => Nil |
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case (xs, 0) => Nil |
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case (x::xs, n) => (x::xs) :: moves(xs, n - 1) |
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} |
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moves(List(5,1,0), 1) |
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moves(List(5,1,0), 2) |
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moves(List(5,1,0), 5) |
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// checks whether a jump tour exists at all |
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def search(xs: List[Int]) : Boolean = xs match {
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case Nil => true |
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case (x::xs) => |
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if (xs.length < x) true else moves(xs, x).exists(search(_)) |
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} |
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search(List(5,3,2,5,1,1)) |
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search(List(3,5,1,0,0,0,1)) |
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search(List(3,5,1,0,0,0,0,1)) |
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search(List(3,5,1,0,0,0,1,1)) |
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search(List(3,5,1)) |
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search(List(5,1,1)) |
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search(Nil) |
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search(List(1)) |
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search(List(5,1,1)) |
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search(List(3,5,1,0,0,0,0,0,0,0,0,1)) |
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// generates *all* jump tours |
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// if we are only interested in the shortes one, we could |
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// shortcircut the calculation and only return List(x) in |
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// case where xs.length < x, because no tour can be shorter |
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// than 1 |
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// |
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def jumps(xs: List[Int]) : List[List[Int]] = xs match {
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case Nil => Nil |
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case (x::xs) => {
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val children = moves(xs, x) |
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val results = children.map(cs => jumps(cs).map(x :: _)).flatten |
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if (xs.length < x) List(x)::results else results |
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} |
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} |
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jumps(List(5,3,2,5,1,1)).minBy(_.length) |
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jumps(List(3,5,1,2,1,2,1)) |
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jumps(List(3,5,1,2,3,4,1)) |
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jumps(List(3,5,1,0,0,0,1)) |
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jumps(List(3,5,1)) |
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jumps(List(5,1,1)) |
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jumps(Nil) |
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jumps(List(1)) |
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jumps(List(5,1,2)) |
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moves(List(1,2), 5) |
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jumps(List(1,5,1,2)) |
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jumps(List(3,5,1,0,0,0,0,0,0,0,0,1)) |
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jumps(List(5,3,2,5,1,1)).minBy(_.length) |
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jumps(List(1,3,5,8,9,2,6,7,6,8,9)).minBy(_.length) |
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jumps(List(1,3,6,1,0,9)).minBy(_.length) |
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jumps(List(2,3,1,1,2,4,2,0,1,1)).minBy(_.length) |
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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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// ... a tiny 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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List(X,I) |
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/* |
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I -> 1 |
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II -> 2 |
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III -> 3 |
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IV -> 4 |
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V -> 5 |
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VI -> 6 |
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VII -> 7 |
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VIII -> 8 |
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IX -> 9 |
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X -> 10 |
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*/ |
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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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// String interpolations as patterns |
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val date = "2019-11-26" |
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val s"$year-$month-$day" = date |
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def parse_date(date: String) : Option[(Int, Int, Int)]= date match {
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case s"$year-$month-$day" => Some((day.toInt, month.toInt, year.toInt)) |
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case s"$day/$month/$year" => Some((day.toInt, month.toInt, year.toInt)) |
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case s"$day.$month.$year" => Some((day.toInt, month.toInt, year.toInt)) |
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case _ => None |
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} |
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parse_date("2019-11-26")
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parse_date("26/11/2019")
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parse_date("26.11.2019")
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// User-defined Datatypes and Pattern Matching |
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//============================================= |
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// trees |
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abstract class Exp |
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case class N(n: Int) extends Exp // for numbers |
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case class Plus(e1: Exp, e2: Exp) extends Exp |
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case class Times(e1: Exp, e2: Exp) extends Exp |
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def string(e: Exp) : String = e match {
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case N(n) => s"$n" |
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case Plus(e1, e2) => s"(${string(e1)} + ${string(e2)})"
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case Times(e1, e2) => s"(${string(e1)} * ${string(e2)})"
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} |
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val e = Plus(N(9), Times(N(3), N(4))) |
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println(string(e)) |
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def eval(e: Exp) : Int = e match {
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case N(n) => n |
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case Plus(e1, e2) => eval(e1) + eval(e2) |
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case Times(e1, e2) => eval(e1) * eval(e2) |
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} |
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println(eval(e)) |
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def simp(e: Exp) : Exp = e match {
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case N(n) => N(n) |
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case Plus(e1, e2) => (simp(e1), simp(e2)) match {
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case (N(0), e2s) => e2s |
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case (e1s, N(0)) => e1s |
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case (e1s, e2s) => Plus(e1s, e2s) |
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} |
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case Times(e1, e2) => (simp(e1), simp(e2)) match {
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case (N(0), _) => N(0) |
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case (_, N(0)) => N(0) |
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case (N(1), e2s) => e2s |
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case (e1s, N(1)) => e1s |
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case (e1s, e2s) => Times(e1s, e2s) |
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} |
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} |
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310 |
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val e2 = Times(Plus(N(0), N(1)), Plus(N(0), N(9))) |
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println(string(e2)) |
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println(string(simp(e2))) |
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// Tokens and Reverse Polish Notation |
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317 |
abstract class Token |
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318 |
case class T(n: Int) extends Token |
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case object PL extends Token |
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case object TI extends Token |
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321 |
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def rp(e: Exp) : List[Token] = e match {
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case N(n) => List(T(n)) |
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case Plus(e1, e2) => rp(e1) ::: rp(e2) ::: List(PL) |
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case Times(e1, e2) => rp(e1) ::: rp(e2) ::: List(TI) |
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} |
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println(string(e2)) |
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println(rp(e2)) |
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def comp(ls: List[Token], st: List[Int]) : Int = (ls, st) match {
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case (Nil, st) => st.head |
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case (T(n)::rest, st) => comp(rest, n::st) |
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case (PL::rest, n1::n2::st) => comp(rest, n1 + n2::st) |
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case (TI::rest, n1::n2::st) => comp(rest, n1 * n2::st) |
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} |
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336 |
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337 |
comp(rp(e), Nil) |
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338 |
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339 |
def proc(s: String) : Token = s match {
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case "+" => PL |
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case "*" => TI |
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342 |
case _ => T(s.toInt) |
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} |
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344 |
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345 |
comp("1 2 + 4 * 5 + 3 +".split(" ").toList.map(proc), Nil)
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347 |
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348 |
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349 |
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// Sudoku |
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351 |
//======== |
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352 |
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353 |
// THE POINT OF THIS CODE IS NOT TO BE SUPER |
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354 |
// EFFICIENT AND FAST, just explaining exhaustive |
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355 |
// depth-first search |
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356 |
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| 155 | 357 |
|
358 |
val game0 = """.14.6.3.. |
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359 |
|62...4..9 |
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360 |
|.8..5.6.. |
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361 |
|.6.2....3 |
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362 |
|.7..1..5. |
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|5....9.6. |
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364 |
|..6.2..3. |
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|1..5...92 |
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366 |
|..7.9.41.""".stripMargin.replaceAll("\\n", "")
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type Pos = (Int, Int) |
369 |
val EmptyValue = '.' |
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370 |
val MaxValue = 9 |
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371 |
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372 |
val allValues = "123456789".toList |
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373 |
val indexes = (0 to 8).toList |
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374 |
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375 |
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376 |
def empty(game: String) = game.indexOf(EmptyValue) |
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377 |
def isDone(game: String) = empty(game) == -1 |
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378 |
def emptyPosition(game: String) = |
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379 |
(empty(game) % MaxValue, empty(game) / MaxValue) |
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380 |
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| 67 | 381 |
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| 155 | 382 |
def get_row(game: String, y: Int) = |
383 |
indexes.map(col => game(y * MaxValue + col)) |
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384 |
def get_col(game: String, x: Int) = |
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385 |
indexes.map(row => game(x + row * MaxValue)) |
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386 |
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387 |
def get_box(game: String, pos: Pos): List[Char] = {
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388 |
def base(p: Int): Int = (p / 3) * 3 |
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389 |
val x0 = base(pos._1) |
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390 |
val y0 = base(pos._2) |
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391 |
val ys = (y0 until y0 + 3).toList |
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392 |
(x0 until x0 + 3).toList.flatMap(x => ys.map(y => game(x + y * MaxValue))) |
|
393 |
} |
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394 |
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| 217 | 395 |
//get_row(game0, 0) |
396 |
//get_row(game0, 1) |
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| 218 | 397 |
//get_col(game0, 0) |
398 |
//get_box(game0, (3, 1)) |
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| 217 | 399 |
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400 |
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| 155 | 401 |
// this is not mutable!! |
402 |
def update(game: String, pos: Int, value: Char): String = |
|
403 |
game.updated(pos, value) |
|
404 |
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405 |
def toAvoid(game: String, pos: Pos): List[Char] = |
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406 |
(get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos)) |
|
407 |
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408 |
def candidates(game: String, pos: Pos): List[Char] = |
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| 218 | 409 |
allValues.diff(toAvoid(game, pos)) |
| 155 | 410 |
|
411 |
//candidates(game0, (0,0)) |
|
412 |
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413 |
def pretty(game: String): String = |
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| 218 | 414 |
"\n" + (game.sliding(MaxValue, MaxValue).mkString("\n"))
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| 155 | 415 |
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| 218 | 416 |
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| 155 | 417 |
def search(game: String): List[String] = {
|
418 |
if (isDone(game)) List(game) |
|
419 |
else {
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420 |
val cs = candidates(game, emptyPosition(game)) |
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| 320 | 421 |
cs.map(c => search(update(game, empty(game), c))).toList.flatten |
| 67 | 422 |
} |
423 |
} |
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424 |
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| 217 | 425 |
search(game0).map(pretty) |
426 |
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427 |
val game1 = """23.915... |
|
428 |
|...2..54. |
|
429 |
|6.7...... |
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430 |
|..1.....9 |
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431 |
|89.5.3.17 |
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432 |
|5.....6.. |
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433 |
|......9.5 |
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434 |
|.16..7... |
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435 |
|...329..1""".stripMargin.replaceAll("\\n", "")
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436 |
||
437 |
||
438 |
// game that is in the hard category |
|
439 |
val game2 = """8........ |
|
440 |
|..36..... |
|
441 |
|.7..9.2.. |
|
442 |
|.5...7... |
|
443 |
|....457.. |
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444 |
|...1...3. |
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445 |
|..1....68 |
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446 |
|..85...1. |
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447 |
|.9....4..""".stripMargin.replaceAll("\\n", "")
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448 |
||
449 |
// game with multiple solutions |
|
450 |
val game3 = """.8...9743 |
|
451 |
|.5...8.1. |
|
452 |
|.1....... |
|
453 |
|8....5... |
|
454 |
|...8.4... |
|
455 |
|...3....6 |
|
456 |
|.......7. |
|
457 |
|.3.5...8. |
|
458 |
|9724...5.""".stripMargin.replaceAll("\\n", "")
|
|
459 |
||
460 |
||
461 |
search(game1).map(pretty) |
|
462 |
search(game3).map(pretty) |
|
463 |
search(game2).map(pretty) |
|
464 |
||
465 |
// for measuring time |
|
466 |
def time_needed[T](i: Int, code: => T) = {
|
|
467 |
val start = System.nanoTime() |
|
468 |
for (j <- 1 to i) code |
|
469 |
val end = System.nanoTime() |
|
470 |
((end - start) / 1.0e9) + " secs" |
|
471 |
} |
|
472 |
||
473 |
time_needed(1, search(game2)) |
|
474 |
||
| 320 | 475 |
|
476 |
||
477 |
||
478 |
// Tail recursion |
|
479 |
//================ |
|
480 |
||
481 |
||
482 |
def fact(n: Long): Long = |
|
483 |
if (n == 0) 1 else n * fact(n - 1) |
|
484 |
||
485 |
def factB(n: BigInt): BigInt = |
|
486 |
if (n == 0) 1 else n * factB(n - 1) |
|
487 |
||
488 |
factB(100000) |
|
489 |
||
490 |
fact(10) //ok |
|
491 |
fact(10000) // produces a stackoverflow |
|
492 |
||
493 |
def factT(n: BigInt, acc: BigInt): BigInt = |
|
494 |
if (n == 0) acc else factT(n - 1, n * acc) |
|
495 |
||
496 |
factT(10, 1) |
|
497 |
println(factT(100000, 1)) |
|
498 |
||
499 |
// there is a flag for ensuring a function is tail recursive |
|
500 |
import scala.annotation.tailrec |
|
501 |
||
502 |
@tailrec |
|
503 |
def factT(n: BigInt, acc: BigInt): BigInt = |
|
504 |
if (n == 0) acc else factT(n - 1, n * acc) |
|
505 |
||
506 |
||
507 |
||
508 |
// for tail-recursive functions the Scala compiler |
|
509 |
// generates loop-like code, which does not need |
|
510 |
// to allocate stack-space in each recursive |
|
511 |
// call; Scala can do this only for tail-recursive |
|
512 |
// functions |
|
513 |
||
| 155 | 514 |
// tail recursive version that searches |
| 158 | 515 |
// for all solutions |
516 |
||
| 155 | 517 |
def searchT(games: List[String], sols: List[String]): List[String] = games match {
|
518 |
case Nil => sols |
|
519 |
case game::rest => {
|
|
520 |
if (isDone(game)) searchT(rest, game::sols) |
|
521 |
else {
|
|
522 |
val cs = candidates(game, emptyPosition(game)) |
|
523 |
searchT(cs.map(c => update(game, empty(game), c)) ::: rest, sols) |
|
524 |
} |
|
525 |
} |
|
| 67 | 526 |
} |
527 |
||
| 158 | 528 |
searchT(List(game3), List()).map(pretty) |
529 |
||
530 |
||
| 155 | 531 |
// tail recursive version that searches |
532 |
// for a single solution |
|
| 158 | 533 |
|
| 155 | 534 |
def search1T(games: List[String]): Option[String] = games match {
|
| 67 | 535 |
case Nil => None |
| 155 | 536 |
case game::rest => {
|
537 |
if (isDone(game)) Some(game) |
|
538 |
else {
|
|
539 |
val cs = candidates(game, emptyPosition(game)) |
|
540 |
search1T(cs.map(c => update(game, empty(game), c)) ::: rest) |
|
541 |
} |
|
542 |
} |
|
| 67 | 543 |
} |
544 |
||
| 158 | 545 |
search1T(List(game3)).map(pretty) |
| 217 | 546 |
time_needed(10, search1T(List(game3))) |
547 |
||
| 158 | 548 |
|
| 155 | 549 |
// game with multiple solutions |
550 |
val game3 = """.8...9743 |
|
551 |
|.5...8.1. |
|
552 |
|.1....... |
|
553 |
|8....5... |
|
554 |
|...8.4... |
|
555 |
|...3....6 |
|
556 |
|.......7. |
|
557 |
|.3.5...8. |
|
558 |
|9724...5.""".stripMargin.replaceAll("\\n", "")
|
|
559 |
||
| 158 | 560 |
searchT(List(game3), Nil).map(pretty) |
| 155 | 561 |
search1T(List(game3)).map(pretty) |
| 67 | 562 |
|
|
77
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
563 |
// Moral: Whenever a recursive function is resource-critical |
| 158 | 564 |
// (i.e. works with large recursion depth), then you need to |
|
77
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
565 |
// write it in tail-recursive fashion. |
|
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
566 |
// |
| 155 | 567 |
// Unfortuantely, Scala because of current limitations in |
568 |
// the JVM is not as clever as other functional languages. It can |
|
|
77
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
569 |
// only optimise "self-tail calls". This excludes the cases of |
|
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
570 |
// multiple functions making tail calls to each other. Well, |
|
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
571 |
// nothing is perfect. |
|
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
572 |
|
|
3cbe3d90b77f
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
73
diff
changeset
|
573 |
|
| 67 | 574 |
|
575 |
||
| 71 | 576 |
|
| 67 | 577 |