abstract class Rexp + −
case object NULL extends Rexp+ −
case object EMPTY extends Rexp+ −
case class CHAR(c: Char) extends Rexp+ −
case 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 constructor+ −
+ −
def nullable (r: Rexp) : Boolean = r match {+ −
case NULL => false+ −
case EMPTY => 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 NULL => NULL+ −
case EMPTY => NULL+ −
case CHAR(d) => if (c == d) EMPTY else NULL+ −
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) NULL else SEQ(der(c, r), NTIMES(r, 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 times+ −
def OPT(r: Rexp) = ALT(r, EMPTY)+ −
+ −
def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('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)+ −
}+ −
+ −
for (i <- 1 to 100) {+ −
println(i + ": " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i))))+ −
}+ −
+ −
//a bit bolder test+ −
for (i <- 1 to 1000 by 50) {+ −
println(i + " " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i))))+ −
}+ −
+ −
+ −