// Main Part 3 about Regular Expression Matching

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

object M3 {

abstract class Rexp

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 SEQs(rs: List[Rexp]) extends Rexp  // sequences

case class STAR(r: Rexp) extends Rexp         // star

//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 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)

}

// examples for the implicits:

// ALT(CHAR('a'), CHAR('b'))

// val areg : Rexp = "a" | "b"

// SEQ(CHAR('a'), CHAR('b')) 

// val sreg : Rexp = "a" ~ "b"

// ADD YOUR CODE BELOW

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

// (1)

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

// (2) 

def der (c: Char, r: Rexp) : Rexp = ???

// (3) 

def denest(rs: List[Rexp]) : List[Rexp] = ???

// (4)

def flts(rs: List[Rexp], acc: List[Rexp] = Nil) : List[Rexp] = ???

// (5)

def ALTs_smart(rs: List[Rexp]) : Rexp = ???

def SEQs_smart(rs: List[Rexp]) : Rexp = ???

// (6)

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

// (7)

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

def matcher(r: Rexp, s: String): Boolean = ???

// (8) 

def size(r: Rexp): Int = ???

// Some testing data

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

/*

simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE))   // => ALTs(List(ONE, CHAR(a)))

simp(((CHAR('a') | ZERO) ~ ONE) | 

     (((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO)))   // => CHAR(a)

matcher(("a" ~ "b") ~ "c", "ab")   // => false

matcher(("a" ~ "b") ~ "c", "abc")  // => true

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

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

matcher(EVIL, "a" * 1000)          // => false

matcher(EVIL, "a" * 1000 ++ "b")   // => true

// size without simplifications

size(der('a', der('a', EVIL)))             // => 36

size(der('a', der('a', der('a', EVIL))))   // => 83

// size with simplification

size(simp(der('a', der('a', EVIL))))           // => 7

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

// 30 seconds.

//

// Lets see how long it really takes to match strings with 

// 5 Million a's...it should be in the range of a few

// 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))

}

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(50).next()) == ONE

// the Iterator produces the rexp

//

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

//

//    where SEQ is nested 50 times.

*/

}