updated
authorChristian Urban <urbanc@in.tum.de>
Fri, 24 Nov 2017 03:10:23 +0000
changeset 155 371acb50643d
parent 154 39c6b93718f0
child 156 cc6d036401f4
updated
cws/cw03.pdf
cws/cw03.tex
progs/catastrophic.py
progs/lecture2.scala
progs/lecture3.scala
slides/slides03.pdf
slides/slides03.tex
Binary file cws/cw03.pdf has changed
--- a/cws/cw03.tex	Fri Nov 24 01:26:01 2017 +0000
+++ b/cws/cw03.tex	Fri Nov 24 03:10:23 2017 +0000
@@ -517,7 +517,11 @@
   given brainfu** program and memory, and the program counter and memory counter
   set to~$0$. Like \texttt{run} it returns the memory after the execution
   of the program finishes. You can test your brainf**k interpreter with the
-  Sierpinski triangle or the Hello world programs.\\\mbox{}\hfill[2 Marks]
+  Sierpinski triangle or the Hello world programs or have a look at
+
+  \begin{center}
+  \url{https://esolangs.org/wiki/Brainfuck}
+  \end{center}\hfill[2 Marks]
   
   \begin{figure}[p]
   \begin{center}
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/catastrophic.py	Fri Nov 24 03:10:23 2017 +0000
@@ -0,0 +1,24 @@
+#!/usr/bin/env python
+import re
+import sys
+
+# case of catastrophic backtracking in Python
+#
+# regex: (a?){n} a{n}
+# strings: aa...
+#
+# call with timing as:
+#
+#   > time ./catastrophic.py 20
+
+# counter n given on the command line
+cn = sys.argv[1]
+
+# constructing the regex
+r1 = '((a?){%s})' % cn
+r2 = 'a{%s}' % cn
+
+# calling the matching function
+m = re.match(r1 + r2 , "a" * int(cn)) 
+
+print m.group(0)
--- a/progs/lecture2.scala	Fri Nov 24 01:26:01 2017 +0000
+++ b/progs/lecture2.scala	Fri Nov 24 03:10:23 2017 +0000
@@ -346,126 +346,6 @@
 better_first_word("").map(duplicate).map(valid_msg)
 
 
-// Pattern Matching
-//==================
-
-// A powerful tool which is supposed to come to Java in a few years
-// time (https://www.youtube.com/watch?v=oGll155-vuQ)...Scala already
-// has it for many years ;o)
-
-// The general schema:
-//
-//    expression match {
-//       case pattern1 => expression1
-//       case pattern2 => expression2
-//       ...
-//       case patternN => expressionN
-//    }
-
-
-// remember
-val lst = List(None, Some(1), Some(2), None, Some(3)).flatten
-
-
-def my_flatten(xs: List[Option[Int]]): List[Int] = {
-  ...?
-}
-
-
-
-
-
-def my_flatten(lst: List[Option[Int]]): List[Int] = lst match {
-  case Nil => Nil
-  case None::xs => my_flatten(xs)
-  case Some(n)::xs => n::my_flatten(xs)
-}
-
-
-// another example including a catch-all pattern
-def get_me_a_string(n: Int): String = n match {
-  case 0 => "zero"
-  case 1 => "one"
-  case 2 => "two"
-  case _ => "many"
-}
-
-get_me_a_string(0)
-
-// you can also have cases combined
-def season(month: String) = month match {
-  case "March" | "April" | "May" => "It's spring"
-  case "June" | "July" | "August" => "It's summer"
-  case "September" | "October" | "November" => "It's autumn"
-  case "December" | "January" | "February" => "It's winter"
-}
- 
-println(season("November"))
-
-// What happens if no case matches?
-
-println(season("foobar"))
-
-
-// User-defined Datatypes
-//========================
-
-abstract class Colour
-case class Red() extends Colour 
-case class Green() extends Colour 
-case class Blue() extends Colour
-
-def fav_colour(c: Colour) : Boolean = c match {
-  case Red()   => false
-  case Green() => true
-  case Blue()  => false 
-}
-
-
-// actually colors can be written with "object",
-// because they do not take any arguments
-
-
-// another example
-//=================
-
-// Once upon a time, in a complete fictional country there were persons...
-
-abstract class Person
-case class King() extends Person
-case class Peer(deg: String, terr: String, succ: Int) extends Person
-case class Knight(name: String) extends Person
-case class Peasant(name: String) extends Person
-
-
-def title(p: Person): String = p match {
-  case King() => "His Majesty the King"
-  case Peer(deg, terr, _) => s"The ${deg} of ${terr}"
-  case Knight(name) => s"Sir ${name}"
-  case Peasant(name) => name
-}
-
-
-def superior(p1: Person, p2: Person): Boolean = (p1, p2) match {
-  case (King(), _) => true
-  case (Peer(_,_,_), Knight(_)) => true
-  case (Peer(_,_,_), Peasant(_)) => true
-  case (Peer(_,_,_), Clown()) => true
-  case (Knight(_), Peasant(_)) => true
-  case (Knight(_), Clown()) => true
-  case (Clown(), Peasant(_)) => true
-  case _ => false
-}
-
-val people = List(Knight("David"), 
-                  Peer("Duke", "Norfolk", 84), 
-                  Peasant("Christian"), 
-                  King(), 
-                  Clown())
-
-println(people.sortWith(superior(_, _)).mkString(", "))
-
-
 
 
 
@@ -509,24 +389,8 @@
 time_needed(10, count_intersection2(A, B))
 
 
-// Implicits (Cool Feature)
-//=========================
-//
-// For example adding your own methods to Strings:
-// Imagine you want to increment strings, like
-//
-//     "HAL".increment
-//
-// you can avoid ugly fudges, like a MyString, by
-// using implicit conversions.
 
 
-implicit class MyString(s: String) {
-  def increment = for (c <- s) yield (c + 1).toChar 
-}
-
-"HAL".increment
-
 
 
 // No returns in Scala
--- a/progs/lecture3.scala	Fri Nov 24 01:26:01 2017 +0000
+++ b/progs/lecture3.scala	Fri Nov 24 03:10:23 2017 +0000
@@ -1,7 +1,72 @@
 // Scala Lecture 3
 //=================
 
-// adding two binary strings very, very lazy manner
+// Pattern Matching
+//==================
+
+// A powerful tool which is supposed to come to Java in a few years
+// time (https://www.youtube.com/watch?v=oGll155-vuQ)...Scala already
+// has it for many years. Other functional languages have it for
+// decades. I think I would refuse to program in a language that
+// does not have pattern matching....its is just so elegant. ;o)
+
+// The general schema:
+//
+//    expression match {
+//       case pattern1 => expression1
+//       case pattern2 => expression2
+//       ...
+//       case patternN => expressionN
+//    }
+
+
+// remember
+val lst = List(None, Some(1), Some(2), None, Some(3)).flatten
+
+
+def my_flatten(xs: List[Option[Int]]): List[Int] = {
+  ...?
+}
+
+
+
+
+
+def my_flatten(lst: List[Option[Int]]): List[Int] = lst match {
+  case Nil => Nil
+  case None::xs => my_flatten(xs)
+  case Some(n)::xs => n::my_flatten(xs)
+}
+
+
+// another example including a catch-all pattern
+def get_me_a_string(n: Int): String = n match {
+  case 0 => "zero"
+  case 1 => "one"
+  case 2 => "two"
+  case _ => "many"
+}
+
+get_me_a_string(0)
+
+// you can also have cases combined
+def season(month: String) = month match {
+  case "March" | "April" | "May" => "It's spring"
+  case "June" | "July" | "August" => "It's summer"
+  case "September" | "October" | "November" => "It's autumn"
+  case "December" | "January" | "February" => "It's winter"
+}
+ 
+println(season("November"))
+
+// What happens if no case matches?
+
+println(season("foobar"))
+
+
+// Collatz function on binary strings
+
+// adding two binary strings in a very, very lazy manner
 
 def badd(s1: String, s2: String) : String = 
   (BigInt(s1, 2) + BigInt(s2, 2)).toString(2)
@@ -21,33 +86,26 @@
 bcollatz(100000000000000000L.toBinaryString)
 bcollatz(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))
 
-def conv(c: Char) : Int = c match {
-  case '0' => 0
-  case '1' => 1
+
+
+
+// User-defined Datatypes
+//========================
+
+abstract class Colour
+case class Red() extends Colour 
+case class Green() extends Colour 
+case class Blue() extends Colour
+
+def fav_colour(c: Colour) : Boolean = c match {
+  case Red()   => false
+  case Green() => true
+  case Blue()  => false 
 }
 
-def badds(s1: String, s2: String, carry: Int) : String = (s1, s2, carry) match {
-  case ("", "", 1) => "1"
-  case ("", "", 0) => ""
-  case (cs1, cs2, carry) => (conv(cs1.last) + conv(cs2.last) + carry) match {
-    case 3 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '1'
-    case 2 => badds(cs1.dropRight(1), cs2.dropRight(1), 1) + '0'
-    case 1 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '1'
-    case 0 => badds(cs1.dropRight(1), cs2.dropRight(1), 0) + '0'
-  }
-} 
 
-def bcollatz2(s: String) : Long = (s.dropRight(1), s.last) match {
-  case ("", '1') => 1                                          // we reached 1
-  case (rest, '0') => 1 + bcollatz2(rest)                      // even number => divide by two
-  case (rest, '1') => 1 + bcollatz2(badds(s + '1', '0' + s, 0))   // odd number => s + '1' is 2 * s + 1
-                                                                  //         add another s gives 3 * s + 1  
-} 
-
-bcollatz2(9.toBinaryString)
-bcollatz2(837799.toBinaryString)
-bcollatz2(100000000000000000L.toBinaryString)
-bcollatz2(BigInt("1000000000000000000000000000000000000000000000000000000000000000000000000000").toString(2))
+// actually colors can be written with "object",
+// because they do not take any arguments
 
 
 
@@ -88,108 +146,190 @@
 RomanNumeral2Int(List(M,M,X,V,I,I))     // 2017
 
 
-// Tail recursion
-//================
+
+// another example
+//=================
+
+// Once upon a time, in a complete fictional country there were persons...
 
-def my_contains(elem: Int, lst: List[Int]): Boolean = lst match {
-  case Nil => false
-  case x::xs => 
-    if (x == elem) true else my_contains(elem, xs)
+abstract class Person
+case class King() extends Person
+case class Peer(deg: String, terr: String, succ: Int) extends Person
+case class Knight(name: String) extends Person
+case class Peasant(name: String) extends Person
+
+
+def title(p: Person): String = p match {
+  case King() => "His Majesty the King"
+  case Peer(deg, terr, _) => s"The ${deg} of ${terr}"
+  case Knight(name) => s"Sir ${name}"
+  case Peasant(name) => name
 }
 
-my_contains(4, List(1,2,3))
-my_contains(2, List(1,2,3))
 
-my_contains(1000000, (1 to 1000000).toList)
-my_contains(1000001, (1 to 1000000).toList)
+def superior(p1: Person, p2: Person): Boolean = (p1, p2) match {
+  case (King(), _) => true
+  case (Peer(_,_,_), Knight(_)) => true
+  case (Peer(_,_,_), Peasant(_)) => true
+  case (Peer(_,_,_), Clown()) => true
+  case (Knight(_), Peasant(_)) => true
+  case (Knight(_), Clown()) => true
+  case (Clown(), Peasant(_)) => true
+  case _ => false
+}
+
+val people = List(Knight("David"), 
+                  Peer("Duke", "Norfolk", 84), 
+                  Peasant("Christian"), 
+                  King(), 
+                  Clown())
+
+println(people.sortWith(superior(_, _)).mkString(", "))
 
 
-//factorial V0.1
-import scala.annotation.tailrec
+
+
+// Tail recursion
+//================
 
 
 def fact(n: Long): Long = 
   if (n == 0) 1 else n * fact(n - 1)
 
-fact(10000)                        // produces a stackoverflow
+fact(10)              //ok
+fact(10000)           // produces a stackoverflow
+
+def factT(n: BigInt, acc: BigInt): BigInt =
+  if (n == 0) acc else factT(n - 1, n * acc)
+
+factT(100000, 1)
+
+// there is a flag for ensuring a function is tail recursive
+import scala.annotation.tailrec
 
 @tailrec
 def factT(n: BigInt, acc: BigInt): BigInt =
   if (n == 0) acc else factT(n - 1, n * acc)
 
 
-println(factT(10000, 1))
 
-// the functions my_contains and factT are tail-recursive 
-// you can check this with 
-
-import scala.annotation.tailrec
-
-// and the annotation @tailrec
-
-// for tail-recursive functions the scala compiler
+// for tail-recursive functions the Scala compiler
 // generates loop-like code, which does not need
 // to allocate stack-space in each recursive
-// call; scala can do this only for tail-recursive
+// call; Scala can do this only for tail-recursive
 // functions
 
-// consider the following "stupid" version of the
-// coin exchange problem: given some coins and a
-// total, what is the change can you get?
+
+
+// sudoku again
+
+val game0 = """.14.6.3..
+              |62...4..9
+              |.8..5.6..
+              |.6.2....3
+              |.7..1..5.
+              |5....9.6.
+              |..6.2..3.
+              |1..5...92
+              |..7.9.41.""".stripMargin.replaceAll("\\n", "")
 
-val coins = List(4,5,6,8,10,13,19,20,21,24,38,39,40)
+type Pos = (Int, Int)
+val EmptyValue = '.'
+val MaxValue = 9
+
+val allValues = "123456789".toList
+val indexes = (0 to 8).toList
+
+
+def empty(game: String) = game.indexOf(EmptyValue)
+def isDone(game: String) = empty(game) == -1 
+def emptyPosition(game: String) = 
+  (empty(game) % MaxValue, empty(game) / MaxValue)
+
 
-def first_positive[B](lst: List[Int], f: Int => Option[B]): Option[B] = lst match {
-  case Nil => None
-  case x::xs => 
-    if (x <= 0) first_positive(xs, f)
-    else {
-      val fx = f(x)
-      if (fx.isDefined) fx else first_positive(xs, f)
+def get_row(game: String, y: Int) = 
+  indexes.map(col => game(y * MaxValue + col))
+def get_col(game: String, x: Int) = 
+  indexes.map(row => game(x + row * MaxValue))
+
+def get_box(game: String, pos: Pos): List[Char] = {
+    def base(p: Int): Int = (p / 3) * 3
+    val x0 = base(pos._1)
+    val y0 = base(pos._2)
+    val ys = (y0 until y0 + 3).toList
+    (x0 until x0 + 3).toList.flatMap(x => ys.map(y => game(x + y * MaxValue)))
+}
+
+// this is not mutable!!
+def update(game: String, pos: Int, value: Char): String = 
+  game.updated(pos, value)
+
+def toAvoid(game: String, pos: Pos): List[Char] = 
+  (get_col(game, pos._1) ++ get_row(game, pos._2) ++ get_box(game, pos))
+
+def candidates(game: String, pos: Pos): List[Char] = 
+  allValues.diff(toAvoid(game,pos))
+
+//candidates(game0, (0,0))
+
+def pretty(game: String): String = 
+  "\n" + (game sliding (MaxValue, MaxValue) mkString "\n")
+
+// not tail recursive 
+def search(game: String): List[String] = {
+  if (isDone(game)) List(game)
+  else {
+    val cs = candidates(game, emptyPosition(game))
+    cs.map(c => search(update(game, empty(game), c))).toList.flatten
   }
 }
 
-
-import scala.annotation.tailrec
-
-def search(total: Int, coins: List[Int], cs: List[Int]): Option[List[Int]] = {
-  if (total < cs.sum) None 
-  else if (cs.sum == total) Some(cs) 
-  else first_positive(coins, (c: Int) => search(total, coins, c::cs))
+// tail recursive version that searches 
+// for all solution
+def searchT(games: List[String], sols: List[String]): List[String] = games match {
+  case Nil => sols
+  case game::rest => {
+    if (isDone(game)) searchT(rest, game::sols)
+    else {
+      val cs = candidates(game, emptyPosition(game))
+      searchT(cs.map(c => update(game, empty(game), c)) ::: rest, sols)
+    }
+  }
 }
 
-search(11, coins, Nil)
-search(111, coins, Nil)
-search(111111, coins, Nil)
-
-val junk_coins = List(4,-2,5,6,8,0,10,13,19,20,-3,21,24,38,39, 40)
-search(11, junk_coins, Nil)
-search(111, junk_coins, Nil)
-
-
-import scala.annotation.tailrec
-
-@tailrec
-def searchT(total: Int, coins: List[Int], 
-            acc_cs: List[List[Int]]): Option[List[Int]] = acc_cs match {
+// tail recursive version that searches 
+// for a single solution
+def search1T(games: List[String]): Option[String] = games match {
   case Nil => None
-  case x::xs => 
-    if (total < x.sum) searchT(total, coins, xs)
-    else if (x.sum == total) Some(x) 
-    else searchT(total, coins, coins.filter(_ > 0).map(_::x) ::: xs)
+  case game::rest => {
+    if (isDone(game)) Some(game)
+    else {
+      val cs = candidates(game, emptyPosition(game))
+      search1T(cs.map(c => update(game, empty(game), c)) ::: rest)
+    }
+  }
 }
 
-val start_acc = coins.filter(_ > 0).map(List(_))
-searchT(11, junk_coins, start_acc)
-searchT(111, junk_coins, start_acc)
-searchT(111111, junk_coins, start_acc)
+// game with multiple solutions
+val game3 = """.8...9743
+              |.5...8.1.
+              |.1.......
+              |8....5...
+              |...8.4...
+              |...3....6
+              |.......7.
+              |.3.5...8.
+              |9724...5.""".stripMargin.replaceAll("\\n", "")
+
+searchT(List(game3), List()).map(pretty)
+search1T(List(game3)).map(pretty)
 
 // Moral: Whenever a recursive function is resource-critical
 // (i.e. works with large recursion depths), then you need to
 // write it in tail-recursive fashion.
 // 
-// Unfortuantely, the Scala is because of current limitations in 
-// the JVM not as clever as other functional languages. It can 
+// Unfortuantely, Scala because of current limitations in 
+// the JVM is not as clever as other functional languages. It can 
 // only optimise "self-tail calls". This excludes the cases of 
 // multiple functions making tail calls to each other. Well,
 // nothing is perfect. 
@@ -230,59 +370,43 @@
 def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = ...
 
 
-// polymorphic classes
-//(trees with some content)
-
-abstract class Tree[+A]
-case class Node[A](elem: A, left: Tree[A], right: Tree[A]) extends Tree[A]
-case object Leaf extends Tree[Nothing]
 
-val t0 = Node('4', Node('2', Leaf, Leaf), Node('7', Leaf, Leaf))
+// Cool Stuff
+//============
 
-def insert[A](tr: Tree[A], n: A): Tree[A] = tr match {
-  case Leaf => Node(n, Leaf, Leaf)
-  case Node(m, left, right) => 
-    if (n == m) Node(m, left, right) 
-    else if (n < m) Node(m, insert(left, n), right)
-    else Node(m, left, insert(right, n))
-}
+
 
 
-// the A-type needs to be ordered
-
-abstract class Tree[+A <% Ordered[A]]
-case class Node[A <% Ordered[A]](elem: A, left: Tree[A], 
-                                 right: Tree[A]) extends Tree[A]
-case object Leaf extends Tree[Nothing]
+// Implicits 
+//===========
+//
+// For example adding your own methods to Strings:
+// Imagine you want to increment strings, like
+//
+//     "HAL".increment
+//
+// you can avoid ugly fudges, like a MyString, by
+// using implicit conversions.
 
 
-def insert[A <% Ordered[A]](tr: Tree[A], n: A): Tree[A] = tr match {
-  case Leaf => Node(n, Leaf, Leaf)
-  case Node(m, left, right) => 
-    if (n == m) Node(m, left, right) 
-    else if (n < m) Node(m, insert(left, n), right)
-    else Node(m, left, insert(right, n))
+implicit class MyString(s: String) {
+  def increment = for (c <- s) yield (c + 1).toChar 
 }
 
+"HAL".increment
 
-val t1 = Node(4, Node(2, Leaf, Leaf), Node(7, Leaf, Leaf))
-insert(t1, 3)
-
-val t2 = Node('b', Node('a', Leaf, Leaf), Node('f', Leaf, Leaf))
-insert(t2, 'e')
 
 
 
 // Regular expressions - the power of DSLs in Scala
 //==================================================
 
-
 abstract class Rexp
-case object ZERO extends Rexp
-case object ONE extends Rexp
-case class CHAR(c: Char) extends Rexp
+case object ZERO extends Rexp                       // nothing
+case object ONE extends Rexp                        // the empty string
+case class CHAR(c: Char) extends Rexp               // a character c
 case class ALT(r1: Rexp, r2: Rexp) extends Rexp     // alternative  r1 + r2
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp     // sequence     r1 r2  
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp     // sequence     r1 o r2  
 case class STAR(r: Rexp) extends Rexp               // star         r*
 
 
@@ -326,63 +450,6 @@
 val number = sign ~ digit ~ digit.% 
 
 
-//implement print_re
-
-
-
-// Lazyness with style
-//=====================
-
-// The concept of lazy evaluation doesn’t really exist in 
-// non-functional languages, but it is pretty easy to grasp. 
-// Consider first 
-
-def square(x: Int) = x * x
-
-square(42 + 8)
-
-// this is called strict evaluation
-
-
-def expensiveOperation(n: BigInt): Boolean = expensiveOperation(n + 1) 
-val a = "foo"
-val b = "bar"
-
-val test = if ((a == b) || expensiveOperation(0)) true else false
-
-// this is called lazy evaluation
-// you delay compuation until it is really 
-// needed; once calculated though, does not 
-// need to be re-calculated
-
-// a useful example is
-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) + " secs"
-}
-
-
-// streams (I do not care how many)
-// primes: 2, 3, 5, 7, 9, 11, 13 ....
-
-def generatePrimes (s: Stream[Int]): Stream[Int] =
-  s.head #:: generatePrimes(s.tail filter (_ % s.head != 0))
-
-val primes: Stream[Int] = generatePrimes(Stream.from(2))
-
-primes.take(10).toList
-
-primes.filter(_ > 100).take(2000).toList
-
-time_needed(1, primes.filter(_ > 100).take(2000).toList)
-time_needed(1, primes.filter(_ > 100).take(2000).toList)
-
-
-
-// streams are useful for implementing search problems ;o)
-
 
 
 
@@ -397,5 +464,5 @@
 // You can be productive on Day 1, but the language is deep.
 
 // I like best about Scala that it lets me write
-// concise, readable code
+// concise, readable code.
 
Binary file slides/slides03.pdf has changed
--- a/slides/slides03.tex	Fri Nov 24 01:26:01 2017 +0000
+++ b/slides/slides03.tex	Fri Nov 24 03:10:23 2017 +0000
@@ -2,7 +2,7 @@
 \usepackage{../slides}
 \usepackage{../graphics}
 \usepackage{../langs}
-%\usepackage{../data}
+%%\usepackage{../data}
 \usepackage[export]{adjustbox}
 
 \hfuzz=220pt 
@@ -21,9 +21,59 @@
 % beamer stuff 
 \renewcommand{\slidecaption}{PEP (Scala) 03, King's College London}
 
+\begin{filecontents}{re3a.data}
+1 0.00003
+500001 0.22527
+1000001 0.62752
+1500001 0.88485
+2000001 1.39815
+2500001 1.68619
+3000001 1.94957
+3500001 2.15878
+4000001 2.59918
+4500001 5.90679
+5000001 13.11295
+5500001 19.15376
+6000001 40.16373
+\end{filecontents}
+\begin{filecontents}{re-python2.data}
+1 0.033
+5 0.036
+10 0.034
+15 0.036
+18 0.059
+19 0.084
+20 0.141
+21 0.248
+22 0.485
+23 0.878
+24 1.71
+25 3.40
+26 7.08
+27 14.12
+28 26.69
+\end{filecontents}
+
+\begin{filecontents}{re-java.data}
+5  0.00298
+10  0.00418
+15  0.00996
+16  0.01710
+17  0.03492
+18  0.03303
+19  0.05084
+20  0.10177
+21  0.19960
+22  0.41159
+23  0.82234
+24  1.70251
+25  3.36112
+26  6.63998
+27  13.35120
+28  29.81185
+\end{filecontents}
 
 \begin{document}
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{%
@@ -35,9 +85,11 @@
   \normalsize
   \begin{center}
   \begin{tabular}{ll}
-  Email:  & christian.urban at kcl.ac.uk\\
-  Office: & S1.27 (1st floor Strand Building)\\
-  Slides \& Code: & KEATS
+    Email:  & christian.urban at kcl.ac.uk\\
+    Office: & N7.07 (North Wing, Bush House)\\
+    Slides \& Code: & KEATS\medskip\\
+    Scala Office & \\
+    Hours: &  Thursdays 11 -- 13\\
   \end{tabular}
   \end{center}
 
@@ -45,181 +97,79 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
-\begin{frame}[c, fragile]
-\frametitle{The Joy of Immutability}
-
-\begin{itemize}
-\item If you need to manipulate some data in a list say, then you make
-  a new list with the updated values, rather than revise the original
-  list. Easy!\medskip
-
-  {\small
-  \begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
-    val old_list = List(1, 2, 3, 5)
-    val new_list = 0 :: old_list
-  \end{lstlisting}}  
-  
-\item You do not have to be defensive about who can access the data
-  (concurrency, lazyness).
-\end{itemize}  
-\end{frame}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Email: Hate 'val'}
-
-\mbox{}\\[-25mm]\mbox{}
-
-\begin{center}
-  \begin{bubble}[10.5cm]
-  Subject: \textbf{Hate '\textbf{\texttt{val}}'}\hfill 01:00 AM\medskip\\
-
-  Hello Mr Urban,\medskip\\
-
-  I just wanted to ask, how are we suppose to work
-  with the completely useless \textbf{\texttt{val}}, that can’t be changed ever? Why is
-  this rule active at all? I’ve spent 4 hours not thinking on the
-  coursework, but how to bypass this annoying rule. What’s the whole
-  point of all these coursework, when we can’t use everything Scala
-  gives us?!?\medskip\\
-
-  Regards.\\
-  \mbox{}\hspace{5mm}\textcolor{black!50}{<<deleted>>}\\
-  \end{bubble}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-
-\mbox{}\\[-25mm]\mbox{}
-
-\begin{center}
-  \begin{bubble}[10.5cm]
-  Subject: \textbf{Re: Hate '\textbf{\texttt{val}}'}\hfill 01:02 AM\bigskip\bigskip\\
-
-  \textcolor{black!70}{
-    \textit{\large<<my usual rant about fp\ldots\\ concurrency bla bla\ldots{} better programs
-    yada>>}}\bigskip\bigskip\bigskip
-  
-  PS: What are you trying to do where you desperately want to use \texttt{var}?
-  \end{bubble}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c,fragile]
 
 \begin{textblock}{6}(0.5,0.5)
 \begin{bubble}[11.5cm]
-  \small  
-  Subject: \textbf{Re: Re: Hate '\textbf{\texttt{val}}'}\hfill 01:04 AM\medskip\\
+\footnotesize
+\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
+import java.util.concurrent._
+import java.util.concurrent.atomic._
 
-  \textbf{Right now my is\_legal function works fine:}
-  
-\footnotesize\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
- def is_legal(dim: Int, path: Path)(x: Pos): Boolean = {
-   var boolReturn = false
-   if(x._1 > dim || x._2 > dim || x._1 < 0 || x._2 < 0) {
-   else { var breakLoop = false
-          if(path == Nil) { boolReturn = true }
-          else { for(i <- 0 until path.length) {
-                    if(breakLoop == false) {
-                      if(path(i) == x) {
-                        boolReturn = true
-                        breakLoop = true
-                      }
-                      else { boolReturn = false }
-                    } else breakLoop
+  def collatz(input:Int){
+          CollatzConjecture(input);
+          println(count.get());
+      }
+      def collatz_max(input:Int){
+          val List = new Array[Int](input)
+            for (i <- 0 to input-1){
+                CollaĵConjecture(i);
+                List(i)=count.get();
+                count.set(0);
             }
-          }
-          boolReturn
-   }
+            val max = new AtomicInteger();
+            max.set(List(0));
+            val index = new AtomicInteger();
+            index.set(1);
+ 
 \end{lstlisting}
 \end{bubble}
 \end{textblock}
 
-\begin{textblock}{6}(8.2,11.8)
-\begin{bubble}[5.5cm]\footnotesize\bf
-\ldots{}but I can’t make it work with boolReturn being val. What approach would
-you recommend in this case, and is using var in this case justified?
-\end{bubble}
-\end{textblock}
-
-\only<2>{
-\begin{textblock}{6}(0.3,11.8)
-  \begin{bubble}[3.1cm]
-    \textbf{Me:} \includegraphics[scale=0.08, valign=t]{../pics/throwup.jpg}
-  \end{bubble}
-\end{textblock}}
-
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-
-\mbox{}\\[-25mm]\mbox{}
+\begin{frame}[c,fragile]
 
-\begin{textblock}{6}(0.5,2)
-  \begin{bubble}[11.5cm]
-  Subject: \textbf{Re: Re: Re: Hate '\textbf{\texttt{val}}'}\hfill 01:06 AM\bigskip\\
-  \small
-  
-  OK. So you want to make sure that the \texttt{x}-position is not outside the
-  board....and furthermore you want to make sure that the \texttt{x}-position
-  is not yet in the path list. How about something like\bigskip
+\begin{textblock}{6}(0.5,0.5)
+\begin{bubble}[11.5cm]
+\footnotesize
+\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
+             for(i<-0 to input-1){
+                val temp :Int=max.get();
+                if (temp < List(i)){
+                    max.set(List(i));
+                    index.set(i);
+                }
+            }
+            println("("+max.get() +","+ index.get()+ ")");
+      }
 
-\footnotesize\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
- def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 
- ...<<some board conditions>>... && !path.contains(x)
-\end{lstlisting}\bigskip
-  
-  \small Does not even contain a \texttt{val}.
-  \end{bubble}
-\end{textblock}
-
-\begin{textblock}{6}(7,12)
-\footnotesize\textcolor{black!50}{(This is all on one line)}
+      def CollatzConjecture(n: Long): Long = {
+        count.incrementAndGet();
+        if (n <= 1)
+            1
+        else if (n\%2 ==0)
+            CollatzConjecture(n/2);
+            else
+               CollatzConjecture((3*n)+1);
+   }
+ }
+\end{lstlisting}
+\end{bubble}
 \end{textblock}
 
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t,fragile]
-
-\mbox{}\\[-15mm]\mbox{}
-
-\begin{textblock}{6}(1,3)
-  \begin{bubble}[10.5cm]
-    Subject: \textbf{Re: Re: Re: Re: Hate '\textbf{\texttt{val}}'}\hfill 11:02 AM\bigskip\bigskip\\
-    
-    THANK YOU! You made me change my coding perspective. Because of you,
-    I figured out the next one\ldots
-  \end{bubble}
-\end{textblock}
-
-\only<2>{
-\begin{textblock}{6}(0.3,11.8)
-  \begin{bubble}[3.1cm]
-    \textbf{Me:} \includegraphics[scale=0.08]{../pics/happy.jpg}
-  \end{bubble}
-\end{textblock}}
-
-\end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-  \frametitle{CW3: Regexes (1 Part)}
+  \frametitle{CW3 (1 Part): Regexes}
   
 \begin{center}
   Graphs: $(a^*)^* b$ and strings $\underbrace{\;a\ldots a\;}_{n}$\bigskip
@@ -287,32 +237,77 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}\\[3cm]\alert{Questions?}\end{tabular}}
+\begin{frame}[c,fragile]
+\frametitle{\alert{Questions?}}
 
-\mbox{}\footnotesize
-Thanks: ``\it{}By the way -  Scala is really getting quite fun
-when you start to get the hang of it\ldots''
+{\tiny
+\begin{verbatim}
+                               *
+                              * *
+                             *   *
+                            * * * *
+                           *       *
+                          * *     * *
+                         *   *   *   *
+                        * * * * * * * *
+                       *               *
+                      * *             * *
+                     *   *           *   *
+                    * * * *         * * * *
+                   *       *       *       *
+                  * *     * *     * *     * *
+                 *   *   *   *   *   *   *   *
+                * * * * * * * * * * * * * * * *
+               *                               *
+              * *                             * *
+             *   *                           *   *
+            * * * *                         * * * *
+           *       *                       *       *
+          * *     * *                     * *     * *
+         *   *   *   *                   *   *   *   *
+        * * * * * * * *                 * * * * * * * *
+       *               *               *               *
+      * *             * *             * *             * *
+     *   *           *   *           *   *           *   *
+    * * * *         * * * *         * * * *         * * * *
+   *       *       *       *       *       *       *       *
+  * *     * *     * *     * *     * *     * *     * *     * *
+ *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *
+* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
+\end{verbatim}}
 
+
+\begin{textblock}{6}(8.5,3.5)
+\begin{bubble}[5cm]
+\footnotesize
+\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
+++++++++[>+>++++<<-]>++>>
++<[-[>>+<<-]+>>]>+[-<<<[-
+>[+[-]+>++>>>-<<]<[<]>>++
+++++[<<+++++>>-]+<<++.[-]
+<<]>.>+[>>]>+]
+\end{lstlisting}
+\end{bubble}
+\end{textblock}
+  
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 \begin{frame}[c]
-\frametitle{Marks for CW6 (Part 1)}
+\frametitle{Marks for CW6 (Part 1 + 2)}
 
-Absolute raw marks, alleged collusions still included:
+Raw marks:
 
 \begin{itemize}
-\item 0\%: 18 students
-\item 1\%: 2
-\item 2\%: 11
-\item 3\%: 29
+\item 0\%: 21 students
+\item 1\%: 1
+\item 2\%: 2
+\item 3\%: 13
 \item 4\%: 18
-\item 5\%: 33
-\item 6\%: 55
-\item 7\%: 62 
+\item 5\%: 66
+\item 6\%: 154
 \end{itemize}  
 \end{frame}