// Part 1 about Regular Expression Matching+
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//==========================================+
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+
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abstract class Rexp+
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case object ZERO extends Rexp+
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case object ONE extends Rexp+
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case class CHAR(c: Char) extends Rexp+
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case class ALT(r1: Rexp, r2: Rexp) extends Rexp   // alternative +
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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence+
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case class STAR(r: Rexp) extends Rexp             // star+
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+
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+
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// some convenience for typing in regular expressions+
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+
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import scala.language.implicitConversions    +
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import scala.language.reflectiveCalls +
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+
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def charlist2rexp(s: List[Char]): Rexp = s match {+
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  case Nil => ONE+
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  case c::Nil => CHAR(c)+
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  case c::s => SEQ(CHAR(c), charlist2rexp(s))+
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}+
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implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)+
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+
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implicit def RexpOps (r: Rexp) = new {+
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  def | (s: Rexp) = ALT(r, s)+
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  def % = STAR(r)+
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  def ~ (s: Rexp) = SEQ(r, s)+
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}+
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+
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implicit def stringOps (s: String) = new {+
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  def | (r: Rexp) = ALT(s, r)+
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  def | (r: String) = ALT(s, r)+
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  def % = STAR(s)+
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  def ~ (r: Rexp) = SEQ(s, r)+
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  def ~ (r: String) = SEQ(s, r)+
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}+
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+
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// (1a) Complete the function nullable according to+
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// the definition given in the coursework; this +
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// function checks whether a regular expression+
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// can match the empty string+
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+
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def nullable (r: Rexp) : Boolean = ...+
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+
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+
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// (1b) Complete the function der according to+
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// the definition given in the coursework; this+
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// function calculates the derivative of a +
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// regular expression w.r.t. a character+
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+
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def der (c: Char, r: Rexp) : Rexp = ...+
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+
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// (1c) Complete the function der according to+
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// the specification given in the coursework; this+
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// function simplifies a regular expression;+
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// however it does not simplify inside STAR-regular+
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// expressions+
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+
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def simp(r: Rexp) : Rexp = ... +
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+
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// (1d) Complete the two functions below; the first +
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// calculates the derivative w.r.t. a string; the second+
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// is the regular expression matcher taking a regular+
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// expression and a string and checks whether the+
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// string matches the regular expression+
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+
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def ders (s: List[Char], r: Rexp) : Rexp = ... +
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+
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def matcher(r: Rexp, s: String): Boolean = ...+
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+
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+
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// (1e) Complete the function below: it searches (from the left to +
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// right) in string s1 all the non-empty substrings that match the +
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// regular expression -- these substrings are assumed to be+
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// the longest substrings matched by the regular expression and+
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// assumed to be non-overlapping. All these substrings in s1 are replaced+
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// by s2.+
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+
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def replace(r: Rexp, s1: String, s2: String): String = ...+
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+
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+
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+
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// some testing data+
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// the supposedly 'evil' regular expression (a*)* b+
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/*+
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val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))+
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println(matcher(EVIL, "a" * 1000 ++ "b"))+
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println(matcher(EVIL, "a" * 1000))+
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+
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+
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def time_needed[T](i: Int, code: => T) = {+
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  val start = System.nanoTime()+
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  for (j <- 1 to i) code+
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  val end = System.nanoTime()+
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  (end - start)/(i * 1.0e9)+
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}+
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+
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for (i <- 1 to 5000001 by 500000) {+
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  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))+
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}+
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*/+
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