1 // Part 2 about finding a single tour for a board

     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 

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

    33   case Nil => None

    34   case x::xs => {

    35     val result = f(x)

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

    37   }

    38 }

    39 

    40 

    41 def first_tour(dim: Int, path: Path): Option[Path] = {

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

    43   else

    44     first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path))

    45 }

    46 

    47 for (dim <- 1 to 8) {

    48   val t = first_tour(dim, List((0, 0)))

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

    50 }

    51