diff -r 3ffe978a5664 -r 085fefce672e main_templates4/knight1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_templates4/knight1.scala	Fri Nov 05 17:20:01 2021 +0000
@@ -0,0 +1,107 @@
+// Main Part 4 about finding Knight's tours
+//==========================================
+
+
+object M4a {
+
+// 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 = ???
+
+
+
+//(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] = ???
+
+
+//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 = ???
+
+def enum_tours(dim: Int, path: Path) : List[Path] = ???
+
+
+//(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 (4) 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()
+  } 
+}
+
+
+*/
+
+}