--- a/main_testing3/re.scala Mon Jan 03 00:59:32 2022 +0000
+++ b/main_testing3/re.scala Sun Jan 09 01:06:30 2022 +0000
@@ -1,4 +1,4 @@
-// Core Part about Regular Expression Matching
+// Main Part 3 about Regular Expression Matching
//=============================================
object M3 {
@@ -12,8 +12,8 @@
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
//the usual binary choice can be defined in terms of ALTs
def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
@@ -22,7 +22,6 @@
import scala.language.implicitConversions
import scala.language.reflectiveCalls
-
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => ONE
case c::Nil => CHAR(c)
@@ -53,12 +52,18 @@
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 STAR(_) => true
+ case CHAR(c) => false
+ case ALTs(rs) => {
+ if (rs.size == 0) false
+ else if (nullable(rs.head)) true
+ else nullable(ALTs(rs.tail))
+ }
+ case SEQ(c, s) => nullable(c) && nullable(s)
+ case STAR(r) => true
+ case _ => false
}
+
// (2) Complete the function der according to
// the definition given in the coursework; this
// function calculates the derivative of a
@@ -67,128 +72,138 @@
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 STAR(r1) => SEQ(der(c, r1), STAR(r1))
+ case CHAR(x) => {
+ if (x==c) ONE
+ else ZERO
+ }
+ case ALTs(rs) => ALTs(for (i <- rs) yield der(c, i))
+ case SEQ(x, y) => {
+ if (nullable(x)) ALTs(List(SEQ(der(c, x), y), der(c, y)))
+ else SEQ(der(c, x), y)
+ }
+ case STAR(x) => SEQ(der(c, x), STAR(x))
+}
+
+
+// (3) Implement the flatten function flts. It
+// deletes 0s from a list of regular expressions
+// and also 'spills out', or flattens, nested
+// ALTernativeS.
+
+def flts(rs: List[Rexp]) : List[Rexp] = rs match {
+ case Nil => Nil
+ case ZERO::rest => flts(rest)
+ case ALTs(rs_other)::rest => rs_other ::: flts(rest)
+ case r::rest => r::flts(rest)
}
-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)
-}
-
-// (3) Complete the simp function according to
-// the specification given in the coursework; this
-// function simplifies a regular expression from
+// (4) Complete the simp function according to
+// the specification given in the coursework description;
+// 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.
-
+// STAR-regular expressions. Use the _.distinct and
+// flts functions.
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(x, ZERO) => ZERO
+ case SEQ(ZERO, x) => ZERO
+ case SEQ(x, ONE) => x
+ case SEQ(ONE, x) => x
+ case SEQ(x, y) => SEQ(simp(x), simp(y))
+ case ALTs(rs) => {
+ val list = flts(for (x <- rs) yield simp(x)).distinct
+ if (list.size == 0) ZERO
+ else if (list.size == 1) list.head
+ else ALTs(list)
}
- 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
+ case x => x
}
-// (4) Complete the two functions below; the first
+// (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.
+// 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)))
+ case c::rest => {
+ val deriv = simp(der(c,r))
+ ders(rest, deriv)
+ }
}
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String): Boolean = nullable(ders(s.toList, r))
-// (5) Complete the size function for regular
+
+// (6) Complete the size function for regular
// expressions according to the specification
// given in the coursework.
-
def size(r: Rexp): Int = r match {
+ case Nil => 0
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 STAR(r1) => 1 + size(r1)
+ case CHAR(x) => 1
+ case ALTs(rs) => 1 + (for (x <- rs) yield size(x)).sum
+ case SEQ(x, y) => 1 + size(x) + size(y)
+ case STAR(x) => 1 + size(x)
}
-
// 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'))
-//println(matcher(EVIL, "a" * 1000 ++ "b")) // => true
-//println(matcher(EVIL, "a" * 1000)) // => false
+// matcher(EVIL, "a" * 1000 ++ "b") // => true
+// 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
+// size(der('a', der('a', EVIL))) // => 28
+// size(der('a', der('a', der('a', EVIL)))) // => 58
// size with simplification
-//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
+// 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()
- for (j <- 1 to i) code
- val end = System.nanoTime()
- "%.5f".format((end - start)/(i * 1.0e9))
-}
+// def time_needed[T](i: Int, code: => T) = {
+// val start = System.nanoTime()
+// for (j <- 1 to i) code
+// val end = System.nanoTime()
+// "%.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
+// 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 50 times.
-
+// This a dummy comment. Hopefully it works!
}
+