author | Christian Urban <christian dot urban at kcl dot ac dot uk> |
Tue, 20 Sep 2016 12:40:57 +0100 | |
changeset 425 | d14a9bdac26f |
parent 422 | 5deefcc8cffa |
child 441 | 028816884f70 |
permissions | -rw-r--r-- |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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422 | 2 |
abstract class Rexp |
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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// nullable function: tests whether the regular |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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>
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def nullable (r: Rexp) : Boolean = r match { |
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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>
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case CHAR(_) => false |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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>
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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>
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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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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>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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// derivative of a regular expression w.r.t. a character |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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def der (c: Char, r: Rexp) : Rexp = r match { |
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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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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>
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case SEQ(r1, r2) => |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case NTIMES(r, i) => |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) |
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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>
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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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} |
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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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case NTIMES(r1, n) => simp(r1) match { |
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case ZERO => ZERO |
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case ONE => ONE |
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case r1s => NTIMES(r1s, n) |
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} |
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case r => r |
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} |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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// derivative w.r.t. a string (iterates der) |
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def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match { |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (Nil, r) => r |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, ZERO) => ZERO |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, ONE) => if (s == Nil) ONE else ZERO |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, CHAR(c)) => if (s == List(c)) ONE else |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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if (s == Nil) CHAR(c) else ZERO |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, ALT(r1, r2)) => ALT(ders2(s, r2), ders2(s, r2)) |
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case (c::s, r) => ders2(s, simp(der(c, r))) |
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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>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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// main matcher function |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r)) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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//one or zero |
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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>
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422 | 76 |
def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
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val EVIL2 = SEQ(STAR(CHAR('a')), CHAR('b')) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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>
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val start = System.nanoTime() |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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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>
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val end = System.nanoTime() |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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(end - start)/(i * 1.0e9) |
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} |
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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>
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// warmup |
412 | 88 |
val i = 5000 |
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println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i)))) |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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415 | 91 |
for (i <- 1 to 7000001 by 1000000) { |
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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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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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415 | 95 |
for (i <- 1 to 7500001 by 500000) { |
414 | 96 |
println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i)))) |
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} |
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