+
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//import scala.concurrent._+
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//import scala.concurrent.duration._+
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//import ExecutionContext.Implicits.global+
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//import scala.language.postfixOps +
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+
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type Pos = (Int, Int)    // a position on a chessboard +
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type Path = List[Pos]    // a path...a list of positions+
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+
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def count_all_tours_urban(dim: Int) = {+
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  for (i <- (0 until dim).toList; +
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       j <- (0 until dim).toList) yield CW7a.count_tours(dim, List((i, j)))+
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}+
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+
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def add_pair_urban(x: Pos)(y: Pos): Pos = +
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  (x._1 + y._1, x._2 + y._2)+
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+
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def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = +
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  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)+
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+
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def moves_urban(x: Pos): List[Pos] = +
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  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),+
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       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))+
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+
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def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = +
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  moves_urban(x).filter(is_legal_urban(dim, path))+
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+
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def correct_urban(dim: Int)(p: Path): Boolean = p match {+
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  case Nil => true+
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  case x::Nil => true+
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  case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false+
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}+
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+
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+
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//lazy val f = Future {+
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  assert(count_all_tours_urban(1) == List(1))+
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  assert(count_all_tours_urban(2) == List(0, 0, 0, 0))+
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  assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))+
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  assert(count_all_tours_urban(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))+
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  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))+
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+
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  val ts = CW7a.enum_tours(5, List((0, 2)))+
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  assert(ts.map(correct_urban(5)).forall(_ == true) == true)+
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  assert(ts.length == 56)  +
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//}+
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+
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//Await.result(f, 360 second)+
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