import scala.annotation.tailrec + −
+ −
abstract class Rexp {+ −
def simp : Rexp = this+ −
}+ −
+ −
case object ZERO extends Rexp+ −
case object ONE extends Rexp+ −
case class CHAR(c: Char) extends Rexp+ −
case 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 expressions+ −
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)+ −
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// nullable function: tests whether the regular + −
// expression can recognise the empty string+ −
def 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 character+ −
def 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)+ −
@tailrec+ −
def ders (s: List[Char], r: Rexp) : Rexp = s match {+ −
case Nil => r+ −
case c::s => ders(s, der(c, r).simp)+ −
}+ −
+ −
+ −
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 function+ −
def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r))+ −
+ −
+ −
//one or zero+ −
def OPT(r: Rexp) = ALT(r, ONE)+ −
+ −
def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))+ −
+ −
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 = 5000000+ −
println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL(i), "a" * i))))+ −
+ −
for (i <- 1 to 800001 by 10000) {+ −
println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL(i), "a" * i))))+ −
}+ −
+ −
+ −