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

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

     3 

     4 object CW7c {

     5 

     6 type Pos = (Int, Int)

     7 type Path = List[Pos]

     8 

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

    10   println

    11   for (i <- 0 until dim) {

    12     for (j <- 0 until dim) {

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

    14     }

    15     println

    16   } 

    17 }

    18 

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

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

    21 

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

    23   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    24 

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

    26   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    27        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))

    28 

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

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

    31 

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

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

    34 

    35 

    36 import scala.annotation.tailrec

    37 

    38 @tailrec

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

    40   case Nil => None

    41   case x::xs => {

    42     val result = f(x)

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

    44   }

    45 }

    46 

    47 

    48 def first_closed_tour_heuristic(dim: Int, path: Path): Option[Path] = {

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

    50   else

    51     first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristic(dim, x::path))

    52 }

    53 

    54 /*

    55 for (dim <- 1 to 6) {

    56   val t = first_closed_tour_heuristic(dim, List((dim / 2, dim / 2)))

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

    58 }*/

    59 

    60 

    61 def first_tour_heuristic(dim: Int, path: Path): Option[Path] = {

    62 

    63   @tailrec

    64   def aux(dim: Int, path: Path, moves: List[Pos]): Option[Path] =  

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

    66   else

    67     moves match {

    68       case Nil => None

    69       case x::xs => {

    70         val r = first_tour_heuristic(dim, x::path)

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

    72     }

    73   }    

    74  

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

    76 }

    77 

    78 /*

    79 def first_tour_heuristic(dim: Int, path: Path): Option[Path] = {

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

    81   else

    82     first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristic(dim, x::path))

    83 }

    84 */

    85 

    86 /*

    87 for (dim <- 1 to 50) {

    88   val t = first_tour_heuristic(dim, List((dim / 2, dim / 2)))

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

    90 }

    91 */

    92 

    93 }

    94 

    95 

    96 //CW7c.first_tour_heuristic(50, List((0,0))).get