--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_testing4/knight2.scala	Mon Nov 02 02:31:44 2020 +0000
@@ -0,0 +1,94 @@
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
+
+object CW9b {
+
+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 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)
+  }
+}
+
+
+def tfirst_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path)
+  else
+    first(ordered_moves(dim, path, path.head), (x: Pos) => tfirst_closed_tour_heuristics(dim, x::path))
+}
+
+def first_closed_tour_heuristics(dim: Int, path: Path) =
+ time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path))
+
+def first_closed_tour_heuristic(dim: Int, path: Path) =
+ time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path))
+
+
+// heuristic cannot be used to search for closed tours on 7 x 7 an beyond
+//for (dim <- 1 to 6) {
+//  val t = time_needed(0, first_closed_tour_heuristics(dim, List((dim / 2, dim / 2))))
+//  println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
+//}
+
+
+def tfirst_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim) Some(path)
+  else
+    first(ordered_moves(dim, path, path.head), (x: Pos) => tfirst_tour_heuristics(dim, x::path))
+}
+
+
+def first_tour_heuristics(dim: Int, path: Path) = 
+  time_needed(tfirst_tour_heuristics(dim: Int, path: Path))
+
+def first_tour_heuristic(dim: Int, path: Path) = 
+  time_needed(tfirst_tour_heuristics(dim: Int, path: Path))
+
+// will be called with boards up to 30 x 30
+
+
+}