1 // Part 3 about finding a single tour using the Warnsdorf Rule |
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2 //============================================================= |
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3 |
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4 object CW7c { |
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5 |
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6 type Pos = (Int, Int) |
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7 type Path = List[Pos] |
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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((i, j))}%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 def moves(x: Pos): List[Pos] = |
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26 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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27 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
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28 |
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29 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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30 moves(x).filter(is_legal(dim, path)) |
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31 |
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32 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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33 legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length) |
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34 |
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35 |
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36 import scala.annotation.tailrec |
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37 |
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38 @tailrec |
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39 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
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40 case Nil => None |
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41 case x::xs => { |
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42 val result = f(x) |
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43 if (result.isDefined) result else first(xs, f) |
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44 } |
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45 } |
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46 |
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47 |
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48 def first_closed_tour_heuristic(dim: Int, path: Path): Option[Path] = { |
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49 if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path) |
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50 else |
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51 first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristic(dim, x::path)) |
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52 } |
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53 |
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54 /* |
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55 for (dim <- 1 to 6) { |
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56 val t = first_closed_tour_heuristic(dim, List((dim / 2, dim / 2))) |
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57 println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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58 }*/ |
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59 |
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60 |
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61 def first_tour_heuristic(dim: Int, path: Path): Option[Path] = { |
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62 |
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63 @tailrec |
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64 def aux(dim: Int, path: Path, moves: List[Pos]): Option[Path] = |
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65 if (path.length == dim * dim) Some(path) |
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66 else |
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67 moves match { |
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68 case Nil => None |
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69 case x::xs => { |
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70 val r = first_tour_heuristic(dim, x::path) |
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71 if (r.isDefined) r else aux(dim, path, xs) |
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72 } |
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73 } |
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74 |
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75 aux(dim, path, ordered_moves(dim, path, path.head)) |
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76 } |
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77 |
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78 /* |
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79 def first_tour_heuristic(dim: Int, path: Path): Option[Path] = { |
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80 if (path.length == dim * dim) Some(path) |
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81 else |
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82 first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristic(dim, x::path)) |
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83 } |
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84 */ |
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85 |
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86 /* |
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87 for (dim <- 1 to 50) { |
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88 val t = first_tour_heuristic(dim, List((dim / 2, dim / 2))) |
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89 println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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90 } |
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91 */ |
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92 |
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93 } |
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94 |
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95 |
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96 //CW7c.first_tour_heuristic(50, List((0,0))).get |
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