1 // Part 3 about finding a single tour using the Warnsdorf Rule

     2 //=============================================================

     3 

     4 

     5 type Pos = (Int, Int)

     6 type Path = List[Pos]

     7 

     8 def print_board(dim: Int, path: Path): Unit = {

     9   println

    10   for (i <- 0 until dim) {

    11     for (j <- 0 until dim) {

    12       print(f"${path.reverse.indexOf((i, j))}%3.0f ")

    13     }

    14     println

    15   } 

    16 }

    17 

    18 def add_pair(x: Pos)(y: Pos): Pos = 

    19   (x._1 + y._1, x._2 + y._2)

    20 

    21 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = 

    22   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    23 

    24 def moves(x: Pos): List[Pos] = 

    25   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    26        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))

    27 

    28 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 

    29   moves(x).filter(is_legal(dim, path))

    30 

    31 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 

    32   legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)

    33 

    34 import scala.annotation.tailrec

    35 

    36 /*

    37 @tailrec

    38 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match {

    39   case Nil => None

    40   case x::xs => {

    41     val result = f(x)

    42     if (result.isDefined) result else first(xs, f)

    43   }

    44 }

    45 */

    46 

    47 def first[A, B](xs: List[A], f: A => Option[B]): Option[B] =

    48   xs.flatMap(f(_)).headOption

    49 

    50 

    51 def first_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = {

    52   if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path)

    53   else

    54     first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristics(dim, x::path))

    55 }

    56 

    57 /*

    58 for (dim <- 1 to 6) {

    59   val t = first_closed_tour_heuristics(dim, List((dim / 2, dim / 2)))

    60   println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))

    61 }

    62 */

    63 

    64 //@tailrec

    65 def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {

    66 

    67   @tailrec

    68   def aux(dim: Int, path: Path, moves: List[Position]): Option[Path 

    69   if (path.length == dim * dim) Some(path)

    70   else

    71     moves match {

    72       case Nil => None

    73       case x::xs => {

    74         val r = first_tour_heuristics(dim, x::path)

    75         if (r.isDefined) Some(r) else aux(dim, path, xs)

    76     }    

    77   aux(dim, path, ordered_moves(dim, path, path.head)) 

    78 }

    79 

    80 

    81 /*

    82 def first_tour_heuristics(dim: Int, path: Path): Option[Path] = {

    83   if (path.length == dim * dim) Some(path)

    84   else

    85     for (p <- ordered_moves(dim, path, path.head))

    86       val r = first_tour_heuristics(dim, x::path)

    87     //first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path))

    88     ordered_moves(dim, path, path.head).view.flatMap((x: Pos) => first_tour_heuristics(dim, x::path)).headOption

    89 }

    90 */ 

    91 

    92 /*

    93 for (dim <- 1 to 50) {

    94   val t = first_tour_heuristics(dim, List((dim / 2, dim / 2)))

    95   println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" }))

    96 }

    97 */

    98 

    99 print_board(50, first_tour_heuristics(50, (25,25)::Nil).get)