--- a/testing4/re.scala Tue Dec 03 11:07:09 2019 +0000
+++ b/testing4/re.scala Mon Jan 27 10:18:13 2020 +0000
@@ -8,16 +8,16 @@
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
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
-case class STAR(r: Rexp) 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
-// some convenience for typing in regular expressions
+
+// some convenience for typing regular expressions
import scala.language.implicitConversions
import scala.language.reflectiveCalls
-
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => ONE
case c::Nil => CHAR(c)
@@ -39,117 +39,137 @@
def ~ (r: String) = SEQ(s, r)
}
-// (1) Complete the function nullable according to
+// (5) 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 = r match {
- case ZERO => false
- case ONE => true
- case CHAR(_) => false
- case ALT(r1, r2) => nullable(r1) || nullable(r2)
- case SEQ(r1, r2) => nullable(r1) && nullable(r2)
- case STAR(_) => true
+def nullable (r: Rexp) : Boolean = {
+ r match {
+ case ZERO => false
+ case ONE => true
+ case CHAR(c) => false
+ case ALT(r1, r2) => (nullable(r1) || nullable(r2))
+ case SEQ(r1, r2) => (nullable(r1) && nullable(r2))
+ case STAR(r) => true
+ }
}
-// (2) Complete the function der according to
+// (6) 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 = r match {
- case ZERO => ZERO
- case ONE => ZERO
- case CHAR(d) => if (c == d) ONE else ZERO
- 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(r1) => SEQ(der(c, r1), STAR(r1))
+def der (c: Char, r: Rexp) : Rexp = {
+ r match {
+ case ZERO => ZERO
+ case ONE => ZERO
+ case CHAR(d) => if(d == c) ONE else ZERO
+ 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))
+ }
}
-// (3) Complete the simp function according to
+
+// (7) 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 = r match {
- case ALT(r1, r2) => (simp(r1), simp(r2)) match {
- case (ZERO, r2s) => r2s
- case (r1s, ZERO) => r1s
- case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
- }
- case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
- case (ZERO, _) => ZERO
- case (_, ZERO) => ZERO
- case (ONE, r2s) => r2s
- case (r1s, ONE) => r1s
- case (r1s, r2s) => SEQ(r1s, r2s)
- }
- case r => r
+def simp(r: Rexp) : Rexp = {
+ r match {
+ case STAR(r) => STAR(r) // does not process r star
+ case SEQ(r1, r2) => {
+ val x = (simp(r1), simp(r2))
+ if(x._1 == ZERO) ZERO else
+ if(x._2 == ZERO) ZERO else
+ if(x._1 == ONE) simp(x._2) else
+ if(x._2 == ONE) simp(x._1) else
+ if(x._1 == x._2) simp(x._2) else
+ SEQ(simp(x._1), simp(x._2))
+ }
+ case ALT(r1, r2) => {
+ val x = (simp(r1), simp(r2))
+ if(x._1 == ZERO) simp(x._2) else
+ if(x._2 == ZERO) simp(x._1) else
+ if(x._1 == x._2) simp(x._2) else
+ ALT(simp(x._1), simp(x._2))
+ }
+ case r => r // if single regex, return it
+ }
}
-// (4) Complete the two functions below; the first
+// (8) 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.
+// string matches the regular expression
-def ders (s: List[Char], r: Rexp) : Rexp = s match {
- case Nil => r
- case c::s => ders(s, simp(der(c, r)))
+def ders (s: List[Char], r: Rexp) : Rexp = {
+ s match {
+ case Nil => r
+ case c :: cs => ders(cs, simp(der(c,r)))
+ }
}
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String): Boolean = {
+ val listOfCharacters = s.toList
+ val result = ders(listOfCharacters, r)
+ nullable(result)
+}
-// (5) Complete the size function for regular
+
+// (9) Complete the size function for regular
// expressions according to the specification
// given in the coursework.
-
-def size(r: Rexp): Int = r match {
- case ZERO => 1
- case ONE => 1
- case CHAR(_) => 1
- case ALT(r1, r2) => 1 + size(r1) + size (r2)
- case SEQ(r1, r2) => 1 + size(r1) + size (r2)
- case STAR(r1) => 1 + size(r1)
+def size(r: Rexp): Int = {
+ r match {
+ case ZERO => 1
+ case ONE => 1
+ case CHAR(c) => 1
+ case ALT(r1, r2) => 1 + size(r1) + size(r2)
+ case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+ case STAR(r) => 1 + size(r)
+ }
}
-
-
// some testing data
-//matcher(("a" ~ "b") ~ "c", "abc") // => true
-//matcher(("a" ~ "b") ~ "c", "ab") // => false
+/*
+matcher(("a" ~ "b") ~ "c", "abc") // => true
+matcher(("a" ~ "b") ~ "c", "ab") // => false
// the supposedly 'evil' regular expression (a*)* b
-val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+// val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-//matcher(EVIL, "a" * 1000 ++ "b") // => true
-//matcher(EVIL, "a" * 1000) // => false
+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(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
+size(simp(der('a', der('a', EVIL)))) // => 8
+size(simp(der('a', der('a', der('a', EVIL))))) // => 8
// Python needs around 30 seconds for matching 28 a's with EVIL.
// Java 9 and later increase this to an "astonishing" 40000 a's in
-// around 30 seconds.
+// 30 seconds.
//
-// Lets see how long it takes to match strings with
-// 5 Million a's...it should be in the range of a
-// couple of seconds.
+// Lets see how long it really takes to match strings with
+// 5 Million a's...it should be in the range of a couple
+// of seconds.
def time_needed[T](i: Int, code: => T) = {
val start = System.nanoTime()
@@ -158,19 +178,19 @@
(end - start)/(i * 1.0e9)
}
-//for (i <- 0 to 5000000 by 500000) {
-// println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.")
-//}
+for (i <- 0 to 5000000 by 500000) {
+ println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))
+}
// another "power" test case
-//simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
+simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE
// the Iterator produces the rexp
//
// SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
//
-// where SEQ is nested 100 times.
-
+// where SEQ is nested 50 times.
+*/
}