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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 NULL extends Rexp
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case object EMPTY 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 (NULL, r) => r
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case (r, NULL) => r
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case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
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case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
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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 (NULL, _) => NULL
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case (_, NULL) => NULL
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case (EMPTY, r) => r
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case (r, EMPTY) => 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 NULL => EMPTY
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case EMPTY => EMPTY
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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) EMPTY else
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r.simp match {
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case NULL => NULL
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case EMPTY => EMPTY
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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 => EMPTY
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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 NULL => false
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case EMPTY => 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 NULL => NULL
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case EMPTY => NULL
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case CHAR(d) => if (c == d) EMPTY else NULL
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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) NULL 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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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, EMPTY)
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def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
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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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for (i <- 1 to 11001 by 500) {
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println(i + " " + + " " + time_needed(1, matcher(RTEST(i), "a" * i)))
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}
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