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

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

     3 

     4 object CW8c { // for preparing the jar

     5 

     6 type Pos = (Int, Int)

     7 type Path = List[Pos]

     8 

     9 

    10 // for measuring time in the JAR

    11 def time_needed[T](code: => T) : T = {

    12   val start = System.nanoTime()

    13   val result = code

    14   val end = System.nanoTime()

    15   println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")

    16   result

    17 }

    18 

    19 

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

    21   println

    22   for (i <- 0 until dim) {

    23     for (j <- 0 until dim) {

    24       print(f"${path.reverse.indexOf((i, j))}%4.0f ")

    25     }

    26     println

    27   } 

    28 }

    29 

    30 def add_pair(x: Pos, y: Pos): Pos = 

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

    32 

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

    34   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    35 

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

    37   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    38        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x, _))

    39 

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

    41   moves(x).filter(is_legal(dim, path, _))

    42  

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

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

    45 

    46 import scala.annotation.tailrec

    47 

    48 @tailrec

    49 def tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match {

    50   case Nil => None

    51   case (path::rest) =>

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

    53     else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)

    54 }

    55 

    56 def ttour_on_mega_board(dim: Int, path: Path): Option[Path] =

    57   tour_on_mega_board_aux(dim, List(path))

    58 

    59 

    60 def tour_on_mega_board(dim: Int, path: Path) =

    61   time_needed(ttour_on_mega_board(dim: Int, path: Path))

    62 

    63 }