--- a/main_testing3/re.scala Thu Nov 03 11:30:09 2022 +0000
+++ b/main_testing3/re.scala Tue Nov 08 00:27:47 2022 +0000
@@ -1,5 +1,5 @@
// Main Part 3 about Regular Expression Matching
-//=============================================
+//==============================================
object M3 {
@@ -8,13 +8,15 @@
case object ZERO extends Rexp
case object ONE extends Rexp
case class CHAR(c: Char) extends Rexp
-case class ALTs(rs: List[Rexp]) extends Rexp // alternatives
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence
-case class STAR(r: Rexp) extends Rexp // star
+case class ALTs(rs: List[Rexp]) extends Rexp // alternatives
+case class SEQs(rs: List[Rexp]) extends Rexp // sequences
+case class STAR(r: Rexp) extends Rexp // star
-//the usual binary choice can be defined in terms of ALTs
+//the usual binary choice and binary sequence can be defined
+//in terms of ALTs and SEQs
def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
+def SEQ(r1: Rexp, r2: Rexp) = SEQs(List(r1, r2))
// some convenience for typing in regular expressions
import scala.language.implicitConversions
@@ -41,83 +43,78 @@
def ~ (r: String) = SEQ(s, r)
}
-// (1) 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.
-
+// (1)
def nullable (r: Rexp) : Boolean = r match {
case ZERO => false
case ONE => true
case CHAR(_) => false
case ALTs(rs) => rs.exists(nullable)
- case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+ case SEQs(rs) => rs.forall(nullable)
case STAR(_) => true
}
-// (2) 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 {
+// (2)
+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 ALTs(rs) => ALTs(rs.map(der(c, _)))
- case SEQ(r1, r2) =>
- if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
- else SEQ(der(c, r1), r2)
+ case SEQs(Nil) => ZERO
+ case SEQs(r1::rs) =>
+ if (nullable(r1)) ALT(SEQs(der(c, r1)::rs), der(c, SEQs(rs)))
+ else SEQs(der(c, r1):: rs)
case STAR(r1) => SEQ(der(c, r1), STAR(r1))
}
-// (3) Implement the flatten function flts. It
-// deletes 0s from a list of regular expressions
-// and also 'spills out', or flattens, nested
-// ALTernativeS.
+// (3)
+def denest(rs: List[Rexp]) : List[Rexp] = rs match {
+ case Nil => Nil
+ case ZERO::tl => denest(tl)
+ case ALTs(rs1)::rs2 => rs1 ::: denest(rs2)
+ case r::rs => r :: denest(rs)
+}
-def flts(rs: List[Rexp]) : List[Rexp] = rs match {
- case Nil => Nil
- case ZERO::tl => flts(tl)
- case ALTs(rs1)::rs2 => rs1 ::: flts(rs2)
- case r::rs => r :: flts(rs)
+// (4)
+def flts(rs: List[Rexp], acc: List[Rexp] = Nil) : List[Rexp] = rs match {
+ case Nil => acc
+ case ZERO::rs => ZERO::Nil
+ case ONE::rs => flts(rs, acc)
+ case SEQs(rs1)::rs => flts(rs, acc ::: rs1)
+ case r::rs => flts(rs, acc :+ r)
}
-
+// (5)
+def ALTs_smart(rs: List[Rexp]) : Rexp = rs match {
+ case Nil => ZERO
+ case r::Nil => r
+ case rs => ALTs(rs)
+}
-// (4) 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 SEQs_smart(rs: List[Rexp]) : Rexp = rs match {
+ case Nil => ONE
+ case ZERO::nil => ZERO
+ case r::Nil => r
+ case rs => SEQs(rs)
+}
+// (6)
def simp(r: Rexp) : Rexp = r match {
- case ALTs(rs) => (flts(rs.map(simp)).distinct) match {
- case Nil => ZERO
- case r::Nil => r
- case rs => ALTs(rs)
- }
- 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 ALTs(rs) =>
+ ALTs_smart(denest(rs.map(simp)).distinct)
+ case SEQs(rs) =>
+ SEQs_smart(flts(rs.map(simp)))
case r => r
}
-simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE))
+//println("Simp tests")
+//println(simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE)))
+//println(simp(((CHAR('a') | ZERO) ~ ONE) |
+// (((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO))))
-// (5) 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.
+
+// (7)
def ders (s: List[Char], r: Rexp) : Rexp = s match {
case Nil => r
@@ -127,43 +124,40 @@
// main matcher function
def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
-// (6) Complete the size function for regular
-// expressions according to the specification
-// given in the coursework.
-
+// (8)
def size(r: Rexp): Int = r match {
case ZERO => 1
case ONE => 1
case CHAR(_) => 1
case ALTs(rs) => 1 + rs.map(size).sum
- case SEQ(r1, r2) => 1 + size(r1) + size (r2)
+ case SEQs(rs) => 1 + rs.map(size).sum
case STAR(r1) => 1 + size(r1)
}
// some testing data
-
-//matcher(("a" ~ "b") ~ "c", "abc") // => true
-//matcher(("a" ~ "b") ~ "c", "ab") // => false
+/*
+println(matcher(("a" ~ "b") ~ "c", "abc")) // => true
+println(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'))
-//println(matcher(EVIL, "a" * 1000 ++ "b")) // => true
-//println(matcher(EVIL, "a" * 1000)) // => false
+println(matcher(EVIL, "a" * 1000 ++ "b")) // => true
+println(matcher(EVIL, "a" * 1000)) // => false
// size without simplifications
-//println(size(der('a', der('a', EVIL)))) // => 28
-//println(size(der('a', der('a', der('a', EVIL))))) // => 58
+println(size(der('a', der('a', EVIL)))) // => 36
+println(size(der('a', der('a', der('a', EVIL))))) // => 83
// size with simplification
-//println(simp(der('a', der('a', EVIL))))
-//println(simp(der('a', der('a', der('a', EVIL)))))
+println(simp(der('a', der('a', EVIL))))
+println(simp(der('a', der('a', der('a', EVIL)))))
-//println(size(simp(der('a', der('a', EVIL))))) // => 8
-//println(size(simp(der('a', der('a', der('a', EVIL)))))) // => 8
+println(size(simp(der('a', der('a', EVIL))))) // => 7
+println(size(simp(der('a', der('a', der('a', EVIL)))))) // => 7
// 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
@@ -171,7 +165,7 @@
//
// 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.
+// few seconds.
def time_needed[T](i: Int, code: => T) = {
val start = System.nanoTime()
@@ -180,19 +174,20 @@
"%.5f".format((end - start)/(i * 1.0e9))
}
-//for (i <- 0 to 5000000 by 500000) {
-// println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.")
-//}
+for (i <- 0 to 5000000 by 500000) {
+ println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.")
+}
// another "power" test case
-//simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
+println(simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next()) == ONE)
// the Iterator produces the rexp
//
// SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
//
-// where SEQ is nested 50 times.
-
+// where SEQ is nested 100 times.
+*/
}
+