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1 // Part 1 about finding and counting Knight's tours |
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2 //================================================== |
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3 |
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4 object CW7a { |
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5 |
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6 type Pos = (Int, Int) // a position on a chessboard |
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7 type Path = List[Pos] // a path...a list of positions |
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8 |
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9 def print_board(dim: Int, path: Path): Unit = { |
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10 println |
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11 for (i <- 0 until dim) { |
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12 for (j <- 0 until dim) { |
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13 print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ") |
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14 } |
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15 println |
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16 } |
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17 } |
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18 |
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19 def add_pair(x: Pos)(y: Pos): Pos = |
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20 (x._1 + y._1, x._2 + y._2) |
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21 |
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22 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
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23 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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24 |
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25 assert(is_legal(8, Nil)((3,4)) == true) |
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26 assert(is_legal(8, List((4,1), (1,0)))((4,1)) == false) |
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27 assert(is_legal(2, Nil)((0,0)) == true) |
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28 |
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29 |
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30 |
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31 def moves(x: Pos): List[Pos] = |
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32 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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33 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
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34 |
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35 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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36 moves(x).filter(is_legal(dim, path)) |
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37 |
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38 def count_tours(dim: Int, path: Path): Int = { |
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39 if (path.length == dim * dim) 1 |
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40 else |
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41 (for (x <- legal_moves(dim, path, path.head)) yield count_tours(dim, x::path)).sum |
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42 } |
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43 |
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44 def enum_tours(dim: Int, path: Path): List[Path] = { |
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45 if (path.length == dim * dim) List(path) |
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46 else |
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47 (for (x <- legal_moves(dim, path, path.head)) yield enum_tours(dim, x::path)).flatten |
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48 } |
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49 |
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50 def count_all_tours(dim: Int) = { |
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51 for (i <- (0 until dim).toList; |
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52 j <- (0 until dim).toList) yield count_tours(dim, List((i, j))) |
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53 } |
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54 |
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55 def enum_all_tours(dim: Int): List[Path] = { |
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56 (for (i <- (0 until dim).toList; |
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57 j <- (0 until dim).toList) yield enum_tours(dim, List((i, j)))).flatten |
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58 } |
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59 |
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60 /* |
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61 for (dim <- 1 to 5) { |
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62 println(s"${dim} x ${dim} " + count_tours(dim, List((0, 0)))) |
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63 } |
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64 |
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65 for (dim <- 1 to 5) { |
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66 println(s"${dim} x ${dim} " + count_all_tours(dim)) |
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67 } |
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68 |
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69 for (dim <- 1 to 5) { |
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70 val ts = enum_tours(dim, List((0, 0))) |
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71 println(s"${dim} x ${dim} ") |
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72 if (ts != Nil) { |
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73 print_board(dim, ts.head) |
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74 println(ts.head) |
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75 } |
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76 } |
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77 */ |
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78 |
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79 } |