--- a/progs/knight3.scala	Sat Mar 11 23:12:49 2023 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,124 +0,0 @@
-// Part 3 about finding a single tour using the Warnsdorf Rule
-//=============================================================
-
-
-type Pos = (Int, Int)
-type Path = List[Pos]
-
-// for measuring time
-def time_needed[T](n: Int, code: => T) : T = {
-  val start = System.nanoTime()
-  for (i <- 0 until n) code
-  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 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))
-}
-
-// heuristic cannot be used to search for closed tours on 7 x 7
-for (dim <- 1 to 6) {
-  val t = time_needed(0, first_closed_tour_heuristics(dim, List((dim / 2, dim / 2))))
-  println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}
-
-
-//@tailrec
-/*
-def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {
-
-  @tailrec
-  def aux(dim: Int, path: Path, moves: List[Pos]): Option[Path] = 
-  if (path.length == dim * dim) Some(path)
-  else
-    moves match {
-      case Nil => None
-      case x::xs => {
-        val r = first_tour_heuristics(dim, x::path)
-        if (r.isDefined) r else aux(dim, path, xs)
-      }    
-    }
-
-  aux(dim, path, ordered_moves(dim, path, path.head)) 
-}
-*/ 
-
-@tailrec
-def tour_on_mega_board(dim: Int, paths: List[Path]): Option[Path] = paths match {
-  case Nil => None
-  case (path::rest) =>
-    if (path.length == dim * dim) Some(path)
-    else tour_on_mega_board(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)
-}
-
-
-
-/*
-def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {
-  if (path.length == dim * dim) Some(path)
-  else
-    for (p <- ordered_moves(dim, path, path.head))
-      val r = first_tour_heuristics(dim, x::path)
-    //first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path))
-    ordered_moves(dim, path, path.head).view.flatMap((x: Pos) => first_tour_heuristics(dim, x::path)).headOption
-}
-*/ 
-
-/*
-for (dim <- 1 to 50) {
-  val t = first_tour_heuristics(dim, List((dim / 2, dim / 2)))
-  println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))
-}
-*/
-
-val dim = 70
-println(s"${dim} x ${dim}:")
-print_board(dim, time_needed(0, tour_on_mega_board(dim, List(List((0, 0)))).get))
-