564
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// A version with simplification of derivatives;
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477
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// this keeps the regular expressions small, which
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// is good for run-time
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517
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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422
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abstract class Rexp
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case object ZERO extends Rexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case object ONE extends Rexp
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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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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case class NTIMES(r: Rexp, n: Int) extends Rexp
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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467
Christian Urban <christian dot urban at kcl dot ac dot uk>
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550
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623
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// the nullable function: tests whether the regular
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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// expression can recognise the empty string
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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def nullable (r: Rexp) : Boolean = r match {
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ZERO => false
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ONE => true
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case CHAR(_) => false
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case ALT(r1, r2) => nullable(r1) || nullable(r2)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case STAR(_) => true
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case NTIMES(r, i) => if (i == 0) true else nullable(r)
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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623
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// the derivative of a regular expression w.r.t. a character
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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def der (c: Char, r: Rexp) : Rexp = r match {
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ZERO => ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ONE => ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case CHAR(d) => if (c == d) ONE else ZERO
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case SEQ(r1, r2) =>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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else SEQ(der(c, r1), r2)
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440
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case STAR(r1) => SEQ(der(c, r1), STAR(r1))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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case NTIMES(r, i) =>
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477
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if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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564
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def simp(r: Rexp) : Rexp = r match {
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case ALT(r1, r2) => (simp(r1), simp(r2)) match {
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case (ZERO, r2s) => r2s
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case (r1s, ZERO) => r1s
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case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
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422
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}
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564
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case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
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case (ZERO, _) => ZERO
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case (_, ZERO) => ZERO
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case (ONE, r2s) => r2s
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case (r1s, ONE) => r1s
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case (r1s, r2s) => SEQ(r1s, r2s)
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}
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564
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case r => r
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}
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623
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// the derivative w.r.t. a string (iterates der)
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618
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def ders(s: List[Char], r: Rexp) : Rexp = s match {
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case Nil => r
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case c::s => ders(s, simp(der(c, r)))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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623
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// the derivative w.r.t. a string (iterates der)
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618
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def dersp(s: List[Char], r: Rexp) : Rexp = s match {
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case Nil => r
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case c::s => dersp(s, der(c, r))
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}
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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623
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// the main matcher function
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def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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623
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// tests
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val q = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z'))
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dersp("x".toList, q)
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dersp("xy".toList, q)
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dersp("xyz".toList, q)
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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623
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// one or zero
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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def OPT(r: Rexp) = ALT(r, ONE)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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477
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// Test Cases
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623
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// evil regular expressions: (a?){n} a{n} and (a*)* b
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def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
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440
Christian Urban <christian dot urban at kcl dot ac dot uk>
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val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
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422
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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def time_needed[T](i: Int, code: => T) = {
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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val start = System.nanoTime()
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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for (j <- 1 to i) code
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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val end = System.nanoTime()
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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(end - start)/(i * 1.0e9)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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434
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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//test: (a?{n}) (a{n})
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564
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for (i <- 1 to 7001 by 1000) {
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434
Christian Urban <christian dot urban at kcl dot ac dot uk>
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println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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}
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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564
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for (i <- 1 to 7001 by 1000) {
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415
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println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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434
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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//test: (a*)* b
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477
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for (i <- 1 to 6000001 by 500000) {
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println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
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}
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for (i <- 1 to 6000001 by 500000) {
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434
Christian Urban <christian dot urban at kcl dot ac dot uk>
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println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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477
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// size of a regular expressions - for testing purposes
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def size(r: Rexp) : Int = r match {
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case ZERO => 1
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case ONE => 1
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case CHAR(_) => 1
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case ALT(r1, r2) => 1 + size(r1) + size(r2)
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case SEQ(r1, r2) => 1 + size(r1) + size(r2)
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case STAR(r) => 1 + size(r)
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case NTIMES(r, _) => 1 + size(r)
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}
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477
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// now the size of the derivatives grows
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// much, much slower
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size(ders("".toList, EVIL2)) // 5
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size(ders("a".toList, EVIL2)) // 8
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size(ders("aa".toList, EVIL2)) // 8
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size(ders("aaa".toList, EVIL2)) // 8
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size(ders("aaaa".toList, EVIL2)) // 8
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size(ders("aaaaa".toList, EVIL2)) // 8
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544
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