// Part 1 about Regular Expression Matching

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

// Regular Expressions

abstract class Rexp

case object ZERO extends Rexp

case object ONE extends Rexp

case class CHAR(c: Char) extends Rexp

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)

}

// (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.

def nullable (r: Rexp) : Boolean = r match {

}

// (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 {

}

// (3) 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 {

}

// (4) 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

def ders (s: List[Char], r: Rexp) : Rexp = s match {

}

// (5) Complete the size function for regular

// expressions according to the specification 

// given in the coursework.

def size(r: Rexp): Int = r match {

}

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

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

// size without simplifications

// size with simplification

// 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

//

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)

}

// another "power" test case 

// the Iterator produces the rexp

//

//      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)

//