// version with explicit n-times regular expressionabstract class Rexp case object ZERO extends Rexpcase object ONE extends Rexpcase class CHAR(c: Char) extends Rexpcase class ALT(r1: Rexp, r2: Rexp) extends Rexp case class SEQ(r1: Rexp, r2: Rexp) extends Rexp case class STAR(r: Rexp) extends Rexp case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructordef 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)}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(r1) => SEQ(der(c, r1), STAR(r1)) case NTIMES(r1, i) => if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1))}def ders (s: List[Char], r: Rexp) : Rexp = s match { case Nil => r case c::s => ders(s, der(c, r))}def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))//optional: one or zero timesdef OPT(r: Rexp) = ALT(r, ONE)//evil regular expressionsdef EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('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)}//test: (a?{n}) (a{n})for (i <- 1 to 1001 by 100) { println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))}for (i <- 1 to 1001 by 100) { println(i + " " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))}//test: (a*)* bfor (i <- 1 to 20) { println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i))))}for (i <- 1 to 20) { println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i))))}