import scala.annotation.tailrec
import scala.language.implicitConversions

abstract class Rexp

case object NULL extends Rexp
case object EMPTY extends Rexp
case object ALLCHAR extends Rexp
case class CHAR(c: Char) extends Rexp
case class STR(s: String) extends Rexp
case class ALT(r1: Rexp, r2: Rexp) extends Rexp 
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
case class STAR(r: Rexp) extends Rexp 
case class NOT(r: Rexp) extends Rexp
case class REP(r: Rexp, n: Int) extends Rexp 

// some convenience for typing in regular expressions
implicit def string2rexp(s : String) : Rexp = STR(s)

implicit def RexpOps(r: Rexp) : Rexp = new {
  def | (s: Rexp) = ALT(r, s)
  def % = STAR(r)
  def %(n: Int) = REP(r, n) 
  def %%(n: Int) = SEQ(REP(r, n), STAR(r)) 
  def ? = ALT(EMPTY, r)
  def unary_! = NOT(r)
  def ~ (s: Rexp) = SEQ(r, s)
}

implicit def stringOps(s: String) : Rexp = new {
  def | (r: Rexp) = ALT(s, r)
  def | (r: String) = ALT(s, r)
  def % = STAR(s)
  def %(n: Int) = REP(s, n)
  def %%(n: Int) = SEQ(REP(s, n), STAR(s)) 
  def ? = ALT(EMPTY, s)
  def unary_! = NOT(s)
  def ~ (r: Rexp) = SEQ(s, r)
  def ~ (r: String) = SEQ(s, r)
}


// nullable function: tests whether the regular 
// expression can recognise the empty string

def nullable (r: Rexp) : Boolean = r match {
  case NULL => false
  case EMPTY => true
  case ALLCHAR => false
  case CHAR(_) => false
  case STR(s) => s.isEmpty
  case ALT(r1, r2) => nullable(r1) || nullable(r2)
  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
  case STAR(_) => true
  case NOT(r) => !(nullable(r))
  case REP(r, i) => if (i == 0) true else nullable(r)
}

// derivative of a regular expression w.r.t. a character
def der (c: Char, r: Rexp) : Rexp = r match {
  case NULL => NULL
  case EMPTY => NULL
  case ALLCHAR => EMPTY
  case CHAR(d) => if (c == d) EMPTY else NULL
  case STR(s) => if (s.isEmpty || s.head != c) NULL else STR(s.tail)
  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
  case SEQ(r1, r2) => 
    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
    else SEQ(der(c, r1), r2)
  case STAR(r) => SEQ(der(c, r), STAR(r))
  case NOT(r) => NOT(der (c, r))
  case REP(r, i) => 
    if (i == 0) NULL else SEQ(der(c, r), REP(r, i - 1))
}


// derivative w.r.t. a string (iterates der)
@tailrec
def ders (s: List[Char], r: Rexp) : Rexp = s match {
  case Nil => r
  case c::s => ders(s, der(c, r))
}

// main matcher function
def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))

//examples
val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
val int = ("+" | "-").? ~ digit.%%(1)
val real = ("+" | "-").? ~ digit.%%(1) ~ ("." ~ digit.%%(1)).? ~ (("e" | "E") ~ ("+" | "-").? ~ digit.%%(1)).?

val ints = List("0", "-4534", "+049", "99")
val reals = List("0.9", "-12.8", "+91.0", "9e12", "+9.21E-12", "-512E+01")
val errs = List("", "-", "+", "+-1", "-+2", "2-")

ints.map(s => matcher(int, s))
reals.map(s => matcher(int, s))
errs.map(s => matcher(int, s))

ints.map(s => matcher(real, s))
reals.map(s => matcher(real, s))
errs.map(s => matcher(real, s))



def RTEST(n: Int) = ("a".? %(n)) ~ ("a" %(n))

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 12000 by 500) {
  println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i))))
}