diff -r 40657f9a4e4a -r 663c2a9108d1 pre_testing4/knight1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pre_testing4/knight1.scala	Sun Nov 01 01:21:31 2020 +0000
@@ -0,0 +1,147 @@
+// Preliminary Part about finding Knight's tours
+//===============================================
+
+
+object CW9a {
+
+// 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.
+
+def is_legal(dim: Int, path: Path, x: Pos) : Boolean = { 
+  if ((!(path.contains(x))) && (x._1 >= 0) && (x._2 >= 0) && (x._1 < dim) && (x._2 < dim))
+    true
+  else false
+}
+
+//(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] = {//List[Pos]
+  val changes = List((1,2),(2,1),(2,-1),(1,-2),(-1,-2),(-2,-1),(-2,1),(-1,2))
+  val returnList = (for ((y,z) <- changes) yield(
+    //println(y,z)-2,-1
+    if ((is_legal(dim,path,((x._1 + y) , (x._2 + z)))) == true)
+      Some(x._1 + y , x._2 + z)
+    else
+      None
+  ))
+  returnList.flatten
+}
+
+
+//some 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)))
+
+
+//(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 = (dim,path) match {//Int
+  case (_, Nil) => 0
+  case (0, path) => 0
+  case (dim, path) => { if (legal_moves(dim,path, path.head).size == 0) 
+				if(path.size < dim*dim) 
+					0 
+				else 
+					1
+			else (for (j <- legal_moves(dim,path, path.head)) yield count_tours(dim,j::path)).sum
+			}
+}
+
+def enum_tours(dim: Int, path: Path) : List[Path] = (dim,path) match {
+  case (_, Nil) => Nil
+  case (0, path) => Nil
+  case (dim, path) =>	{ if (legal_moves(dim,path, path.head).size == 0) 
+				if(path.size < dim*dim) 
+					Nil
+				else 
+					List(path)
+			else (for (j <- legal_moves(dim,path, path.head)) yield enum_tours(dim,j::path)).flatten
+			}
+			
+}
+
+
+//(4) 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] = ...
+
+
+// testcases
+//
+//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
+
+
+//(5) 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] = ...
+ 
+
+
+
+
+
+/* Helper functions
+
+
+// for measuring time
+def time_needed[T](code: => T) : T = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
+  result
+}
+
+// can be called for example with
+//     time_needed(count_tours(dim, List((0, 0))))
+// in order to print out the time that is needed for 
+// running count_tours
+
+
+
+
+// for printing a board
+def print_board(dim: Int, path: Path): Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ")
+    }
+    println
+  } 
+}
+
+
+*/
+
+}