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abstract class Rexp
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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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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
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case class STAR(r: Rexp) extends Rexp
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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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}
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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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}
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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))
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}
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// main matcher function
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261
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
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258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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//example from the homework
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85
Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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//val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))
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119
Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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//der('a', r)
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85
Christian Urban <christian dot urban at kcl dot ac dot uk>
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changeset
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//der('b', r)
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258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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//der('c', r)
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258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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//optional: one or zero times
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def OPT(r: Rexp) = ALT(r, EMPTY)
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//n-times
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def NTIMES(r: Rexp, n: Int) : Rexp = n match {
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case 0 => EMPTY
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case 1 => r
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case n => SEQ(r, NTIMES(r, n - 1))
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}
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258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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// the evil regular expression a?{n} a{n}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
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258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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//for measuring time
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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 29) {
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261
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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println(i + ": " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i))))
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}
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