1 

     2 import scala.concurrent._

     3 import scala.concurrent.duration._

     4 import ExecutionContext.Implicits.global

     5 import scala.language.postfixOps 

     6 

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

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

     9 

    10 def count_all_tours_urban(dim: Int) = {

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

    12        j <- (0 until dim).toList) yield CW7a.count_tours(dim, List((i, j)))

    13 }

    14 

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

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

    17 

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

    19   0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

    20 

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

    22   List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

    23        (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))

    24 

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

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

    27 

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

    29   case Nil => true

    30   case x::Nil => true

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

    32 }

    33 

    34 

    35 lazy val f = Future {

    36   assert(count_all_tours_urban(1) == List(1))

    37   assert(count_all_tours_urban(2) == List(0, 0, 0, 0))

    38   assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))

    39   assert(count_all_tours_urban(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))

    40   assert(count_all_tours_urban(5) == List(304, 0, 56, 0, 304, 0, 56, 0, 56, 0, 56, 0, 64, 0, 56, 0, 56, 0, 56, 0, 304, 0, 56, 0, 304))

    41 

    42   val ts = CW7a.enum_tours(5, List((0, 2)))

    43   assert(ts.map(correct_urban(5)).forall(_ == true) == true)

    44   assert(ts.length == 56)  

    45 }

    46 

    47 Await.result(f, 360 second)