--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/knight3_sol.scala	Sat Mar 11 23:22:05 2023 +0000
@@ -0,0 +1,99 @@
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
+
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+def print_board(dim: Int, path: Path): Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
+
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path))
+
+def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+
+import scala.annotation.tailrec
+
+/*
+@tailrec
+def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {
+  case Nil => None
+  case x::xs => {
+    val result = f(x)
+    if (result.isDefined) result else first(xs, f)
+  }
+}
+*/
+
+def first[A, B](xs: List[A], f: A => Option[B]): Option[B] =
+  xs.flatMap(f(_)).headOption
+
+
+def first_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path)
+  else
+    first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristics(dim, x::path))
+}
+
+/*
+for (dim <- 1 to 6) {
+  val t = first_closed_tour_heuristics(dim, List((dim / 2, dim / 2)))
+  println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
+}
+*/
+
+//@tailrec
+def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+
+  @tailrec
+  def aux(dim: Int, path: Path, moves: List[Position]): Option[Path 
+  if (path.length == dim * dim) Some(path)
+  else
+    moves match {
+      case Nil => None
+      case x::xs => {
+        val r = first_tour_heuristics(dim, x::path)
+        if (r.isDefined) Some(r) else aux(dim, path, xs)
+    }    
+  aux(dim, path, ordered_moves(dim, path, path.head)) 
+}
+
+
+/*
+def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {
+  if (path.length == dim * dim) Some(path)
+  else
+    for (p <- ordered_moves(dim, path, path.head))
+      val r = first_tour_heuristics(dim, x::path)
+    //first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path))
+    ordered_moves(dim, path, path.head).view.flatMap((x: Pos) => first_tour_heuristics(dim, x::path)).headOption
+}
+*/ 
+
+/*
+for (dim <- 1 to 50) {
+  val t = first_tour_heuristics(dim, List((dim / 2, dim / 2)))
+  println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
+}
+*/
+
+print_board(50, first_tour_heuristics(50, (25,25)::Nil).get)