// Part 1 about Regular Expression Matching+ −
//==========================================+ −
+ −
+ −
object CW8a {+ −
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abstract class Rexp+ −
case object ZERO extends Rexp+ −
case object ONE extends Rexp+ −
case class CHAR(c: Char) extends Rexp+ −
case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative + −
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence+ −
case class STAR(r: Rexp) extends Rexp // star+ −
+ −
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// some convenience for typing in regular expressions+ −
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import scala.language.implicitConversions + −
import scala.language.reflectiveCalls + −
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def charlist2rexp(s: List[Char]): Rexp = s match {+ −
case Nil => ONE+ −
case c::Nil => CHAR(c)+ −
case c::s => SEQ(CHAR(c), charlist2rexp(s))+ −
}+ −
implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)+ −
+ −
implicit def RexpOps (r: Rexp) = new {+ −
def | (s: Rexp) = ALT(r, s)+ −
def % = STAR(r)+ −
def ~ (s: Rexp) = SEQ(r, s)+ −
}+ −
+ −
implicit def stringOps (s: String) = new {+ −
def | (r: Rexp) = ALT(s, r)+ −
def | (r: String) = ALT(s, r)+ −
def % = STAR(s)+ −
def ~ (r: Rexp) = SEQ(s, r)+ −
def ~ (r: String) = SEQ(s, r)+ −
}+ −
+ −
// (1a) Complete the function nullable according to+ −
// the definition given in the coursework; this + −
// function checks whether a regular expression+ −
// can match the empty string and Returns a boolean+ −
// accordingly.+ −
+ −
//def nullable (r: Rexp) : Boolean = ...+ −
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// (1b) Complete the function der according to+ −
// the definition given in the coursework; this+ −
// function calculates the derivative of a + −
// regular expression w.r.t. a character.+ −
+ −
//def der (c: Char, r: Rexp) : Rexp = ...+ −
+ −
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// (1c) Complete the simp function according to+ −
// the specification given in the coursework; this+ −
// function simplifies a regular expression from+ −
// the inside out, like you would simplify arithmetic + −
// expressions; however it does not simplify inside + −
// STAR-regular expressions.+ −
+ −
//def simp(r: Rexp) : Rexp = ... + −
+ −
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// (1d) Complete the two functions below; the first + −
// calculates the derivative w.r.t. a string; the second+ −
// is the regular expression matcher taking a regular+ −
// expression and a string and checks whether the+ −
// string matches the regular expression+ −
+ −
//def ders (s: List[Char], r: Rexp) : Rexp = ... + −
+ −
//def matcher(r: Rexp, s: String): Boolean = ...+ −
+ −
+ −
// (1e) Complete the size function for regular+ −
// expressions according to the specification + −
// given in the coursework.+ −
+ −
//def size(r: Rexp): Int = ...+ −
+ −
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// some testing data+ −
+ −
/*+ −
matcher(("a" ~ "b") ~ "c", "abc") // => true+ −
matcher(("a" ~ "b") ~ "c", "ab") // => false+ −
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// the supposedly 'evil' regular expression (a*)* b+ −
val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))+ −
+ −
matcher(EVIL, "a" * 1000 ++ "b") // => true+ −
matcher(EVIL, "a" * 1000) // => false+ −
+ −
// size without simplifications+ −
size(der('a', der('a', EVIL))) // => 28+ −
size(der('a', der('a', der('a', EVIL)))) // => 58+ −
+ −
// size with simplification+ −
size(simp(der('a', der('a', EVIL)))) // => 8+ −
size(simp(der('a', der('a', der('a', EVIL))))) // => 8+ −
+ −
// Java needs around 30 seconds for matching 28 a's with EVIL. + −
//+ −
// Lets see how long it takes to match strings with + −
// 0.5 Million a's...it should be in the range of some+ −
// seconds.+ −
+ −
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 <- 0 to 5000000 by 500000) {+ −
println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))+ −
}+ −
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*/+ −
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+ −
}+ −