1 // Part 4 about finding a single tour on "mutilated" chessboards

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

     3 

     4 object M4d { // for preparing the jar

     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))}%4.0f ")

    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 import scala.annotation.tailrec

    33 

    34 @tailrec

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

    36   case Nil => None

    37   case x::xs => {

    38     val result = f(x)

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

    40   }

    41 }

    42 

    43 

    44 def one_tour_pred(dim: Int, path: Path, n: Int, pred: Pos => Boolean): Option[Path] = {

    45   if (path.length == n) Some(path)

    46   else

    47     first(legal_moves(dim, path, path.head).filter(pred), (x: Pos) => one_tour_pred(dim, x::path, n, pred))

    48 }

    49 

    50 //print_board(8, one_tour_pred(8, List((0, 0)), 40, x => x._1 < 5).get)

    51 

    52 

    53 }