--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_solution4/knight3.scala	Mon Nov 02 02:31:44 2020 +0000
@@ -0,0 +1,63 @@
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
+
+object CW9c { // for preparing the jar
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+
+// for measuring time in the JAR
+def time_needed[T](code: => T) : T = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
+  result
+}
+
+
+def print_board(dim: Int, path: Path): Unit = {
+  println()
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%4.0f ")
+    }
+    println()
+  } 
+}
+
+def add_pair(x: Pos, y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+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)
+
+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, _))
+
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path, _))
+ 
+def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+
+import scala.annotation.tailrec
+
+@tailrec
+def tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match {
+  case Nil => None
+  case (path::rest) =>
+    if (path.length == dim * dim) Some(path)
+    else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)
+}
+
+def ttour_on_mega_board(dim: Int, path: Path): Option[Path] =
+  tour_on_mega_board_aux(dim, List(path))
+
+
+def tour_on_mega_board(dim: Int, path: Path) =
+  time_needed(ttour_on_mega_board(dim: Int, path: Path))
+
+}