--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_templates4-old/knight1.scala	Sat Nov 04 18:53:37 2023 +0000
@@ -0,0 +1,94 @@
+// Main Part 4 about finding Knight's tours
+//==========================================
+
+
+object M4a {
+
+// If you need any auxiliary functions, feel free to 
+// implement them, but do not make any changes to the
+// templates below. Also have a look whether the functions
+// at the end of the file are of any help.
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+// ADD YOUR CODE BELOW
+//======================
+
+
+
+//(1) 
+def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ???
+
+
+//(2) 
+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) 
+def count_tours(dim: Int, path: Path) : Int = ???
+
+def enum_tours(dim: Int, path: Path) : List[Path] = ???
+
+// (4) 
+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) 
+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()
+  } 
+}
+
+
+*/
+
+}