// Part 1 about Regular Expression Matching

//==========================================

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

// some convenience for typing in 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)

  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

def nullable (r: Rexp) : Boolean = ...

// (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 = ...

// (1c) Complete the function der according to

// the specification given in the coursework; this

// function simplifies a regular expression;

// however it does not simplify inside STAR-regular

// expressions

def simp(r: Rexp) : Rexp = ... 

// (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 function below: it searches (from the left to 

// right) in string s1 all the non-empty substrings that match the 

// regular expression -- these substrings are assumed to be

// the longest substrings matched by the regular expression and

// assumed to be non-overlapping. All these substrings in s1 are replaced

// by s2.

def replace(r: Rexp, s1: String, s2: String): String = ...

// some testing data

// the supposedly 'evil' regular expression (a*)* b

/*

val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))

println(matcher(EVIL, "a" * 1000 ++ "b"))

println(matcher(EVIL, "a" * 1000))

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 <- 1 to 5000001 by 500000) {

  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))

}

*/