progs/re4.scala
author Christian Urban <urbanc@in.tum.de>
Tue, 23 Aug 2016 12:26:13 +0200
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import scala.annotation.tailrec    
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import scala.language.implicitConversions
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abstract class Rexp {
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  def simp : Rexp = this
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}
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case object ZERO extends Rexp
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case object ONE extends Rexp
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case class CHAR(c: Char) extends Rexp
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case class ALT(r1: Rexp, r2: Rexp) extends Rexp {
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  override def simp = (r1.simp, r2.simp) match {
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    case (ZERO, r) => r
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    case (r, ZERO) => r
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    case (r, ONE) => if (nullable(r)) r else ALT(r, ONE)
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    case (ONE, r) => if (nullable(r)) r else ALT(r, ONE)
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    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
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  }
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}
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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
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  override def simp = (r1.simp, r2.simp) match {
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    case (ZERO, _) => ZERO
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    case (_, ZERO) => ZERO
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    case (ONE, r) => r
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    case (r, ONE) => r
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    case (r1, r2) => SEQ(r1, r2)
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  }
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}
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case class STAR(r: Rexp) extends Rexp {
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  override def simp = r.simp match {
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    case ZERO => ONE
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    case ONE => ONE
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    case r => STAR(r)
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  }
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}
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case class NTIMES(r: Rexp, n: Int) extends Rexp {
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  override def simp = if (n == 0) ONE else 
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    r.simp match {
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      case ZERO => ZERO
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      case ONE => ONE
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      case r => NTIMES(r, n)
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    }
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}
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// some convenience for typing in regular expressions
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def charlist2rexp(s : List[Char]) : Rexp = s match {
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  case Nil => ONE
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  case c::Nil => CHAR(c)
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  case c::s => SEQ(CHAR(c), charlist2rexp(s))
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}
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implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
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// nullable function: tests whether the regular 
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// expression can recognise the empty string
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def nullable (r: Rexp) : Boolean = r match {
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  case ZERO => false
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  case ONE => true
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  case CHAR(_) => false
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  case ALT(r1, r2) => nullable(r1) || nullable(r2)
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  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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  case STAR(_) => true
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  case NTIMES(r, i) => if (i == 0) true else nullable(r)
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}
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// derivative of a regular expression w.r.t. a character
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def der (c: Char, r: Rexp) : Rexp = r match {
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  case ZERO => ZERO
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  case ONE => ZERO
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  case CHAR(d) => if (c == d) ONE else ZERO
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  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
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  case SEQ(r1, r2) => 
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    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
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    else SEQ(der(c, r1), r2)
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  case STAR(r) => SEQ(der(c, r), STAR(r))
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  case NTIMES(r, i) => 
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    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
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}
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// derivative w.r.t. a string (iterates der)
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@tailrec
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def ders (s: List[Char], r: Rexp) : Rexp = s match {
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  case Nil => r
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  case c::s => ders(s, der(c, r).simp)
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}
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// main matcher function
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def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
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//one or zero
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def OPT(r: Rexp) = ALT(r, ONE)
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def EVIL1(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
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val EVIL2 = SEQ(STAR("a"), "b")
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def time_needed[T](i: Int, code: => T) = {
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  val start = System.nanoTime()
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  for (j <- 1 to i) code
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  val end = System.nanoTime()
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  (end - start)/(i * 1.0e9)
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}
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val i = 5000
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println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i))))
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for (i <- 1 to 9001 by 1000) {
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  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
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}
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for (i <- 1 to 7500001 by 500000) {
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  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
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}
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