1 |
1 |
2 type Pos = (Int, Int) // a position on a chessboard |
2 //type Pos = (Int, Int) // a position on a chessboard |
3 type Path = List[Pos] // a path...a list of positions |
3 //type Path = List[Pos] // a path...a list of positions |
4 |
4 |
5 def count_all_tours_urban(dim: Int) = { |
5 def count_all_tours_urban(dim: Int) = { |
6 for (i <- (0 until dim).toList; |
6 for (i <- (0 until dim).toList; |
7 j <- (0 until dim).toList) yield count_tours(dim, List((i, j))) |
7 j <- (0 until dim).toList) yield count_tours(dim, List((i, j))) |
8 } |
8 } |
9 |
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10 def add_pair_urban(x: Pos)(y: Pos): Pos = |
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11 (x._1 + y._1, x._2 + y._2) |
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12 |
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13 def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = |
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14 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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15 |
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16 def moves_urban(x: Pos): List[Pos] = |
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17 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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18 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair_urban(x)) |
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19 |
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20 def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = |
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21 moves_urban(x).filter(is_legal_urban(dim, path)) |
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22 |
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23 def correct_urban(dim: Int)(p: Path): Boolean = p match { |
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24 case Nil => true |
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25 case x::Nil => true |
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26 case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false |
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27 } |
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28 |
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29 |
9 |
30 |
10 |
31 assert(count_all_tours_urban(1) == List(1)) |
11 assert(count_all_tours_urban(1) == List(1)) |
32 assert(count_all_tours_urban(2) == List(0, 0, 0, 0)) |
12 assert(count_all_tours_urban(2) == List(0, 0, 0, 0)) |
33 assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0)) |
13 assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0)) |