diff -r 3020f8c76baa -r 9e7897f25e13 testing3/knight1.scala
--- a/testing3/knight1.scala	Wed Nov 28 23:26:47 2018 +0000
+++ b/testing3/knight1.scala	Thu Nov 29 17:15:11 2018 +0000
@@ -1,13 +1,105 @@
-// Part 1 about finding and counting Knight's tours
-//==================================================
+// Part 1 about finding Knight's tours
+//=====================================
 
-//object CW8a {   // for preparing the jar
+// If you need any auxiliary function, feel free to 
+// implement it, but do not make any changes to the
+// templates below. Also have a look whether the functions
+// at the end are of any help.
+
 
 type Pos = (Int, Int)    // a position on a chessboard 
 type Path = List[Pos]    // a path...a list of positions
 
+//(1) Complete the function that tests whether the position x
+//    is inside the board and not yet element in the path.
 
-// for measuring time in the JAR
+def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ((!(path.contains(x))) && (x._1 < dim) && (x._2 < dim))
+
+
+
+//(2) Complete the function that calculates for a position x
+//    all legal onward moves that are not already in the path. 
+//    The moves should be ordered in a "clockwise" manner.
+
+
+def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] ={
+  val y = List((x._1 + 1, x._2 + 2),
+               (x._1 + 2, x._2 + 1),
+               (x._1 + 2, x._2 - 1),
+               (x._1 + 1, x._2 - 2),
+               (x._1 - 1, x._2 - 2),
+               (x._1 - 2, x._2 - 1),
+               (x._1 - 2, x._2 + 1),
+               (x._1 - 1, x._2 + 2)
+   )
+  y.filter(next => is_legal(dim, path, next))
+}
+
+//some test cases
+//
+//assert(legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
+//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
+//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) ==  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
+//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
+
+
+//(3) Complete the two recursive functions below. 
+//    They exhaustively search for knight's tours starting from the 
+//    given path. The first function counts all possible tours, 
+//    and the second collects all tours in a list of paths.
+
+def count_tours(dim: Int, path: Path) : Int = {
+  if(path.length == dim*dim) 1 else
+    (for(i <- legal_moves(dim, path, path.head)) yield
+      count_tours(dim, i :: path)
+    ).sum
+}
+
+def enum_tours(dim: Int, path: Path) : List[Path] ={
+  if(path.length == dim*dim) List(path) else
+    (for(i <- legal_moves(dim, path, path.head)) yield
+      enum_tours(dim, i :: path)
+    ).flatten
+}
+
+//(5) Implement a first-function that finds the first 
+//    element, say x, in the list xs where f is not None. 
+//    In that case Return f(x), otherwise None. If possible,
+//    calculate f(x) only once.
+
+def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = {
+  if(xs == Nil) None
+  else(
+    for(x <- xs) yield{
+      val a = f(x)
+      if(a != None) a
+      else first(xs.drop(1), f)
+    }
+  ).head
+}
+
+// test cases
+//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None
+//
+//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo)   // Some(List((4,0)))
+//first(List((1, 0),(2, 0),(3, 0)), foo)          // None
+
+
+
+
+//(6) Implement a function that uses the first-function from (5) for
+//    trying out onward moves, and searches recursively for a
+//    knight tour on a dim * dim-board.
+
+
+// def first_tour(dim: Int, path: Path) : Option[Path] = {
+//   first(legal_moves(dim, path, path.head), (x : Pos => ))
+// }
+ 
+/* Helper functions
+
+
+// for measuring time
 def time_needed[T](code: => T) : T = {
   val start = System.nanoTime()
   val result = code
@@ -16,6 +108,11 @@
   result
 }
 
+// can be called for example with
+//     time_needed(count_tours(dim, List((0, 0))))
+// in order to print out the time that is needed for 
+// running count_tours
+
 // for printing a board
 def print_board(dim: Int, path: Path): Unit = {
   println
@@ -27,144 +124,5 @@
   } 
 }
 
-def is_legal(dim: Int, path: Path, x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
 
-// testcases
-//assert(is_legal(8, Nil, (3, 4)) == true)
-//assert(is_legal(8, List((4, 1), (1, 0)), (4, 1)) == false)
-//assert(is_legal(2, Nil, (0, 0)) == true)
-
-
-def add_pair(x: Pos, y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def moves(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x, _))
-
-// 1 mark
-
-def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves(x).filter(is_legal(dim, path, _))
-
-// testcases
-//assert(legal_moves(8, Nil, (2,2)) == 
-//  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
-//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
-//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 
-//  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
-//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
-//assert(legal_moves(1, Nil, (0,0)) == List())
-//assert(legal_moves(2, Nil, (0,0)) == List())
-//assert(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
-
-// 2 marks
-
-def tcount_tours(dim: Int, path: Path): Int = {
-  if (path.length == dim * dim) 1
-  else 
-    (for (x <- legal_moves(dim, path, path.head)) yield tcount_tours(dim, x::path)).sum
-}
-
-def count_tours(dim: Int, path: Path) =
-  time_needed(tcount_tours(dim: Int, path: Path))
-
-
-def tenum_tours(dim: Int, path: Path): List[Path] = {
-  if (path.length == dim * dim) List(path)
-  else 
-    (for (x <- legal_moves(dim, path, path.head)) yield tenum_tours(dim, x::path)).flatten
-}
-
-def enum_tours(dim: Int, path: Path) =
-  time_needed(tenum_tours(dim: Int, path: Path))
-
-// test cases
-
-/*
-def count_all_tours(dim: Int) = {
-  for (i <- (0 until dim).toList; 
-       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
-}
-
-def enum_all_tours(dim: Int): List[Path] = {
-  (for (i <- (0 until dim).toList; 
-        j <- (0 until dim).toList) yield enum_tours(dim, List((i, j)))).flatten
-}
-
-
-println("Number of tours starting from (0, 0)")
-
-for (dim <- 1 to 5) {
-  println(s"${dim} x ${dim} " + time_needed(0, count_tours(dim, List((0, 0)))))
-}
-
-println("Number of tours starting from all fields")
-
-for (dim <- 1 to 5) {
-  println(s"${dim} x ${dim} " + time_needed(0, count_all_tours(dim)))
-}
-
-for (dim <- 1 to 5) {
-  val ts = enum_tours(dim, List((0, 0)))
-  println(s"${dim} x ${dim} ")   
-  if (ts != Nil) {
-    print_board(dim, ts.head)
-    println(ts.head)
-  }
-}
 */
-
-// 1 mark
-
-def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
-  case Nil => None
-  case x::xs => {
-    val result = f(x)
-    if (result.isDefined) result else first(xs, f)
-  }
-}
-
-// test cases
-//def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None
-//
-//first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo)
-//first(List((1, 0),(2, 0),(3, 0)), foo)
-
-
-// 1 mark
-
-def tfirst_tour(dim: Int, path: Path): Option[Path] = {
-  if (path.length == dim * dim) Some(path)
-  else
-    first(legal_moves(dim, path, path.head), (x:Pos) => tfirst_tour(dim, x::path))
-}
-
-def first_tour(dim: Int, path: Path) = 
-  time_needed(tfirst_tour(dim: Int, path: Path))
-
-
-/*
-for (dim <- 1 to 8) {
-  val t = first_tour(dim, List((0, 0)))
-  println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}
-*/
-
-// 15 secs for 8 x 8
-//val ts1 = time_needed(0,first_tour(8, List((0, 0))).get)
-
-// no result for 4 x 4
-//val ts2 = time_needed(0, first_tour(4, List((0, 0))))
-
-// 0.3 secs for 6 x 6
-//val ts3 = time_needed(0, first_tour(6, List((0, 0))))
-
-// 15 secs for 8 x 8
-//time_needed(0, print_board(8, first_tour(8, List((0, 0))).get))
-
-
-//}
-
-