1 

     2 type Pos = (Int, Int)    // a position on a chessboard 

     3 type Path = List[Pos]    // a path...a list of positions

     4 

     5 def count_all_tours_urban(dim: Int) = {

     6   for (i <- (0 until dim).toList; 

     7        j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))

     8 }

     9 

    10 def add_pair_urban(x: Pos)(y: Pos): Pos = 

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

    12 

    13 def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 

    14   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    15 

    16 def moves_urban(x: Pos): List[Pos] = 

    17   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    18        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))

    19 

    20 def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 

    21   moves_urban(x).filter(is_legal_urban(dim, path))

    22 

    23 def correct_urban(dim: Int)(p: Path): Boolean = p match {

    24   case Nil => true

    25   case x::Nil => true

    26   case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false

    27 }

    28 

    29 

    30 

    31 val ts_urban = enum_tours(5, List((0, 2)))

    32 assert(ts_urban.map(correct_urban(5)).forall(_ == true) == true)

    33 assert(ts_urban.length == 56)