// 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 + −
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp + −
case class STAR(r: Rexp) extends Rexp + −
+ −
// 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 = r match {+ −
case ZERO => false+ −
case ONE => true+ −
case CHAR(_) => false+ −
case ALT(r1, r2) => nullable(r1) || nullable(r2)+ −
case SEQ(r1, r2) => nullable(r1) && nullable(r2)+ −
case STAR(_) => true+ −
}+ −
+ −
// (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 = r match {+ −
case ZERO => ZERO+ −
case ONE => ZERO+ −
case CHAR(d) => if (c == d) ONE else ZERO+ −
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(r1) => SEQ(der(c, r1), STAR(r1))+ −
}+ −
+ −
// (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 = r match {+ −
case ALT(r1, r2) => (simp(r1), simp(r2)) match {+ −
case (ZERO, r2s) => r2s+ −
case (r1s, ZERO) => r1s+ −
case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)+ −
}+ −
case SEQ(r1, r2) => (simp(r1), simp(r2)) match {+ −
case (ZERO, _) => ZERO+ −
case (_, ZERO) => ZERO+ −
case (ONE, r2s) => r2s+ −
case (r1s, ONE) => r1s+ −
case (r1s, r2s) => SEQ(r1s, r2s)+ −
}+ −
case r => r+ −
}+ −
+ −
// (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 = s match {+ −
case Nil => r+ −
case c::s => ders(s, simp(der(c, r)))+ −
}+ −
+ −
// main matcher function+ −
def matcher(r: Rexp, s: String): Boolean = nullable(ders(s.toList, r))+ −
+ −
+ −
// (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 splits(s: String): List[(String, String)] =+ −
(for (i <- (1 to s.length).toList) yield s.splitAt(i)).reverse+ −
+ −
splits("abcde")+ −
splits("")+ −
+ −
def first(r: Rexp, lst: List[(String, String)]): Option[String] = lst match {+ −
case Nil => None+ −
case (s1, s2)::xs => if (matcher(r, s1)) Some(s2) else first(r, xs)+ −
}+ −
+ −
"abcd".head+ −
+ −
def replace(r: Rexp, s1: String, s2: String): String = first(r, splits(s1)) match {+ −
case None if (s1 == "") => ""+ −
case None => s1.head.toString ++ replace(r, s1.tail, s2)+ −
case Some(s) => s2 ++ replace(r, s, s2) + −
}+ −
+ −
val s1 = "aabbbaaaaaaabaaaaabbaaaabb"+ −
val r: Rexp = "aa".% | "bb"+ −
splits(s1)+ −
first(r, splits(s1))+ −
+ −
replace(r, s1, "c")+ −
+ −
splits("bb")+ −
first(r, splits("bb"))+ −
replace(r, "abb", "c")+ −
+ −
+ −
// PART 2+ −
//========+ −
+ −
+ −
// (2a)+ −
+ −
import scala.annotation.tailrec+ −
+ −
@tailrec+ −
def iterT[A](n: Int, f: A => A, x: A): A = + −
if (n == 0) x else iterT(n - 1, f, f(x)) + −
+ −
+ −
//non-tail recursive iter+ −
+ −
//def iter[A](n: Int, f: A => A)(x: A): A = + −
// if (n == 0) x else f(iter(n - 1,f, x)) + −
+ −
+ −
+ −
// (2b)+ −
+ −
def size(r: Rexp): Int = r match {+ −
case ZERO => 1+ −
case ONE => 1+ −
case CHAR(_) => 1+ −
case ALT(r1, r2) => 1 + size(r1) + size (r2)+ −
case SEQ(r1, r2) => 1 + size(r1) + size (r2)+ −
case STAR(r1) => 1 + size(r1)+ −
}+ −
+ −
+ −
val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))+ −
size(iterT(20, (r: Rexp) => der('a', r), EVIL)) // should produce 7340068 + −
size(iterT(20, (r: Rexp) => simp(der('a', r)), EVIL)) // should produce 8+ −
+ −
+ −
// (2c)+ −
+ −
@tailrec+ −
def fixpT[A](f: A => A, x: A): A = {+ −
val fx = f(x)+ −
if (fx == x) x else fixpT(f, fx) + −
}+ −
+ −
def ctest(n: Long): Long =+ −
if (n == 1) 1 else+ −
if (n % 2 == 0) n / 2 else 3 * n + 1+ −
+ −
fixpT(ctest, 97L)+ −
fixpT(ctest, 871L)+ −
fixpT(ctest, 77031L)+ −
fixpT(ctest, 837799L)+ −
+ −
def foo(s: String): String = {+ −
if (matcher("a", s)) "a" else+ −
if (matcher("aa" ~ STAR("aa"), s)) s.take(s.length / 2) + −
else "a" ++ s * 3+ −
}+ −
+ −
fixpT(foo, "a" * 97)+ −
fixpT(foo, "a" * 871)+ −
+ −
+ −