1 import M4a._

     2 

     3 

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

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

     6 

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

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

     9 

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

    11   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    12 

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

    14   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    15        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))

    16 

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

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

    19 

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

    21   case Nil => true

    22   case x::Nil => true

    23   case x::y::p => 

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

    25 }

    26 

    27 

    28 val ts1_urban = first_tour(6, List((0, 0))).get

    29 assert(correct_urban(6)(ts1_urban) == true)

    30 

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

    32 assert(ts2_urban == None)