# HG changeset patch
# User Christian Urban <christian dot urban at kcl dot ac dot uk>
# Date 1484145997 0
# Node ID 139eb1ed2d579fcd2c70d1652d65234e14dfba12
# Parent  8f03f0dc3065e571208195103625fa929d67dcaf
updated

diff -r 8f03f0dc3065 -r 139eb1ed2d57 progs/re2_sol.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re2_sol.scala	Wed Jan 11 14:46:37 2017 +0000
@@ -0,0 +1,215 @@
+// 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)) 
+
+
+iter(200000, (x: Int) => x + 1, 0)
+iterT(200000, (x: Int) => x + 1, 0)
+iterT(100, (x: Int) => x * 2, 2)
+iterT(100, (x: BigInt) => x * 2, BigInt(2))
+iterT(10, (x: String) => x ++ "a", "a")
+
+// (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) 
+}
+
+fixpT((x:Int) => if (200000 < x) x else x + 1, 0)
+
+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)
+
+