1 // Part 2 about finding a single tour for a board |
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2 //================================================ |
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3 |
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4 type Pos = (Int, Int) // a position on a chessboard |
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5 type Path = List[Pos] // a path...a list of positions |
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6 |
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7 def print_board(dim: Int, path: Path): Unit = { |
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8 println |
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9 for (i <- 0 until dim) { |
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10 for (j <- 0 until dim) { |
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11 print(f"${path.reverse.indexOf((i, j))}%3.0f ") |
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12 } |
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13 println |
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14 } |
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15 } |
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16 |
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17 def add_pair(x: Pos)(y: Pos): Pos = |
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18 (x._1 + y._1, x._2 + y._2) |
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19 |
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20 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
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21 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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22 |
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23 def moves(x: Pos): List[Pos] = |
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24 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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25 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
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26 |
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27 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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28 moves(x).filter(is_legal(dim, path)) |
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29 |
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30 |
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31 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
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32 case Nil => None |
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33 case x::xs => { |
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34 val result = f(x) |
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35 if (result.isDefined) result else first(xs, f) |
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36 } |
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37 } |
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38 |
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39 first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
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40 first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
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41 |
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42 |
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43 |
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44 def first_tour(dim: Int, path: Path): Option[Path] = { |
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45 if (path.length == dim * dim) Some(path) |
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46 else |
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47 first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path)) |
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48 } |
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49 |
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50 /* |
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51 for (dim <- 1 to 8) { |
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52 val t = first_tour(dim, List((0, 0))) |
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53 println(s"${dim} x ${dim} " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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54 } |
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55 */ |
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56 |
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57 def add_pair_urban(x: Pos)(y: Pos): Pos = |
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58 (x._1 + y._1, x._2 + y._2) |
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59 |
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60 def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = |
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61 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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62 |
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63 def moves_urban(x: Pos): List[Pos] = |
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64 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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65 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair_urban(x)) |
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66 |
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67 def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = |
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68 moves_urban(x).filter(is_legal_urban(dim, path)) |
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69 |
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70 def correct_urban(dim: Int)(p: Path): Boolean = p match { |
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71 case Nil => true |
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72 case x::Nil => true |
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73 case x::y::p => |
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74 if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false |
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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 |
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80 val ts1 = first_tour(8, List((0, 0))).get |
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81 assert(correct_urban(8)(ts1) == true) |
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82 |
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83 val ts2 = first_tour(4, List((0, 0))) |
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84 assert(ts2 == None) |
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85 |
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86 print_board(8, first_tour(8, List((0, 0))).get) |
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87 |
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88 |
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