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

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

     7 

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

     9   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    10 

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

    12   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    13        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))

    14 

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

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

    17 

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

    19   case Nil => true

    20   case x::Nil => true

    21   case x::y::p => 

    22     if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false

    23 }

    24 

    25 

    26 val ts1_urban = first_tour(8, List((0, 0))).get

    27 assert(correct_urban(8)(ts1_urban) == true)

    28 

    29 val ts2_urban = first_tour(4, List((0, 0)))

    30 assert(ts2_urban == None)