--- a/progs/re1.scala	Thu Jul 25 14:39:37 2019 +0100
+++ b/progs/re1.scala	Sun Jul 28 01:00:41 2019 +0100
@@ -1,8 +1,8 @@
-// Simple matcher for basic regular expressions
+// A simple matcher for basic regular expressions
 
 abstract class Rexp
 case object ZERO extends Rexp                    // matches nothing
-case object ONE extends Rexp                     // matches the empty string
+case object ONE extends Rexp                     // matches an empty string
 case class CHAR(c: Char) extends Rexp            // matches a character c
 case class ALT(r1: Rexp, r2: Rexp) extends Rexp  // alternative
 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp  // sequence
@@ -19,9 +19,7 @@
   case STAR(_) => true
 }
 
-
-
-// derivative of a regular expression w.r.t. a character
+// 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
@@ -33,18 +31,18 @@
   case STAR(r1) => SEQ(der(c, r1), STAR(r1))
 }
 
-// derivative w.r.t. a string (iterates der)
+// the derivative w.r.t. a string (iterates der)
 def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
   case c::s => ders(s, der(c, r))
 }
 
-// main matcher function
+// the main matcher function
 def matches(r: Rexp, s: String) : Boolean = 
   nullable(ders(s.toList, r))
 
 
-//examples from the homework
+// examples from the homework
 
 val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))
 der('a', r)
@@ -57,10 +55,10 @@
 der('z', der('y', der('x', r2)))
 
 
-//optional regular expression (one or zero times)
+// the optional regular expression (one or zero times)
 def OPT(r: Rexp) = ALT(r, ONE)
 
-//n-times regular expression (explicitly expanded)
+// the n-times regular expression (explicitly expanded)
 def NTIMES(r: Rexp, n: Int) : Rexp = n match {
   case 0 => ONE
   case 1 => r
@@ -76,40 +74,31 @@
 // the evil regular expression (a*)*b
 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
 
-//for measuring time
+// for measuring time
 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)
+  "%.5f".format((end - start) / (i * 1.0e9))
 }
 
 
-//test: (a?{n}) (a{n})
+// test: (a?{n}) (a{n})
 println("Test (a?{n}) (a{n})")
-for (i <- 1 to 20) {
-  println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))
-}
 
-for (i <- 1 to 20) {
-  println(i + ": " + "%.5f".format(time_needed(2, matches(EVIL1(i), "a" * i))))
+for (i <- 0 to 20 by 2) {
+  println(s"$i: ${time_needed(2, matches(EVIL1(i), "a" * i))}")
 }
 
-//test: (a*)* b
+// test: (a*)* b
 println("Test (a*)* b")
 
-for (i <- 1 to 20) {
-  println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i))))
-}
-
-for (i <- 1 to 20) {
-  println(i + " " + "%.5f".format(time_needed(2, matches(EVIL2, "a" * i))))
+for (i <- 0 to 20 by 2) {
+  println(s"$i: ${time_needed(2, matches(EVIL2, "a" * i))}")
 }
 
 
-
-
-// size of a regular expressions - for testing purposes 
+// the size of a regular expressions - for testing purposes 
 def size(r: Rexp) : Int = r match {
   case ZERO => 1
   case ONE => 1
@@ -126,7 +115,7 @@
 size(EVIL1(3))  // 17
 size(EVIL1(5))  // 29
 size(EVIL1(7))  // 41
-
+size(EVIL1(20)) // 119
 
 // given a regular expression and building successive
 // derivatives might result into bigger and bigger
@@ -147,6 +136,6 @@
 
 size(ders(("ab" * 200).toList, BIG))    // 366808
 
-for (i <- 1 to 21) {
-  println(i + " " + "%.5f".format(time_needed(2, matches(BIG, "ab" * i))))
+for (i <- 0 to 200 by 10) {
+  println(s"$i: ${time_needed(2, matches(BIG, "ab" * i))}")
 }