import scala.annotation.tailrec import scala.language.implicitConversionsabstract class Rexp { def simp : Rexp = this}case object ZERO extends Rexpcase object ONE extends Rexpcase class CHAR(c: Char) extends Rexpcase class ALT(r1: Rexp, r2: Rexp) extends Rexp { override def simp = (r1.simp, r2.simp) match { case (ZERO, r) => r case (r, ZERO) => r case (r, ONE) => if (nullable(r)) r else ALT(r, ONE) case (ONE, r) => if (nullable(r)) r else ALT(r, ONE) case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2) }}case class SEQ(r1: Rexp, r2: Rexp) extends Rexp { override def simp = (r1.simp, r2.simp) match { case (ZERO, _) => ZERO case (_, ZERO) => ZERO case (ONE, r) => r case (r, ONE) => r case (r1, r2) => SEQ(r1, r2) }}case class STAR(r: Rexp) extends Rexp { override def simp = r.simp match { case ZERO => ONE case ONE => ONE case r => STAR(r) }}case class NTIMES(r: Rexp, n: Int) extends Rexp { override def simp = if (n == 0) ONE else r.simp match { case ZERO => ZERO case ONE => ONE case r => NTIMES(r, n) }}// some convenience for typing in regular expressionsdef 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)// nullable function: tests whether the regular // expression can recognise the empty stringdef nullable (r: Rexp) : Boolean = r match { case ZERO => false case ONE => true case CHAR(_) => false case ALT(r1, r2) => nullable(r1) || nullable(r2) case SEQ(r1, r2) => nullable(r1) && nullable(r2) case STAR(_) => true case NTIMES(r, i) => if (i == 0) true else nullable(r)}// derivative of a regular expression w.r.t. a characterdef der (c: Char, r: Rexp) : Rexp = r match { case ZERO => ZERO case ONE => ZERO case CHAR(d) => if (c == d) ONE else ZERO case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) case SEQ(r1, r2) => if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) else SEQ(der(c, r1), r2) case STAR(r) => SEQ(der(c, r), STAR(r)) case NTIMES(r, i) => if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))}// derivative w.r.t. a string (iterates der)def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match { case (Nil, r) => r case (s, ZERO) => ZERO case (s, ONE) => if (s == Nil) ONE else ZERO case (s, CHAR(c)) => if (s == List(c)) ONE else if (s == Nil) CHAR(c) else ZERO case (s, ALT(r1, r2)) => ALT(ders2(s, r2), ders2(s, r2)) case (c::s, r) => ders2(s, der(c, r).simp)}// main matcher functiondef matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r))//one or zerodef OPT(r: Rexp) = ALT(r, ONE)def EVIL1(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))val EVIL2 = SEQ(STAR("a"), "b")def time_needed[T](i: Int, code: => T) = { val start = System.nanoTime() for (j <- 1 to i) code val end = System.nanoTime() (end - start)/(i * 1.0e9)}val i = 5000println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i))))for (i <- 1 to 7000001 by 1000000) { println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))}for (i <- 1 to 7500001 by 500000) { println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))}