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1 // Part 2 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 M4b { // for preparing the jar |
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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 |
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10 // for measuring time in the JAR |
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11 def time_needed[T](code: => T) : T = { |
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12 val start = System.nanoTime() |
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13 val result = code |
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14 val end = System.nanoTime() |
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15 println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.") |
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16 result |
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17 } |
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18 |
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19 |
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20 def print_board(dim: Int, path: Path): Unit = { |
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21 println() |
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22 for (i <- 0 until dim) { |
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23 for (j <- 0 until dim) { |
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24 print(f"${path.reverse.indexOf((i, j))}%4.0f ") |
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25 } |
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26 println() |
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27 } |
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28 } |
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29 |
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30 def add_pair(x: Pos, y: Pos): Pos = |
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31 (x._1 + y._1, x._2 + y._2) |
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32 |
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33 def is_legal(dim: Int, path: Path, x: Pos): Boolean = |
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34 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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35 |
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36 def moves(x: Pos): List[Pos] = |
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37 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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38 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x, _)) |
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39 |
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40 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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41 moves(x).filter(is_legal(dim, path, _)) |
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42 |
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43 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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44 legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length) |
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45 |
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46 import scala.annotation.tailrec |
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47 |
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48 @tailrec |
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49 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
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50 case Nil => None |
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51 case x::xs => { |
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52 val result = f(x) |
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53 if (result.isDefined) result else first(xs, f) |
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54 } |
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55 } |
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56 |
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57 |
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58 def tfirst_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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59 if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path) |
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60 else |
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61 first(ordered_moves(dim, path, path.head), (x: Pos) => tfirst_closed_tour_heuristics(dim, x::path)) |
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62 } |
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63 |
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64 def first_closed_tour_heuristics(dim: Int, path: Path) = |
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65 time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path)) |
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66 |
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67 def first_closed_tour_heuristic(dim: Int, path: Path) = |
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68 time_needed(tfirst_closed_tour_heuristics(dim: Int, path: Path)) |
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69 |
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70 // heuristic cannot be used to search for closed tours on 7 x 7 an beyond |
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71 //for (dim <- 1 to 6) { |
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72 // val t = time_needed(0, first_closed_tour_heuristics(dim, List((dim / 2, dim / 2)))) |
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73 // println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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74 //} |
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75 |
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76 |
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77 def tfirst_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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78 if (path.length == dim * dim) Some(path) |
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79 else |
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80 first(ordered_moves(dim, path, path.head), (x: Pos) => tfirst_tour_heuristics(dim, x::path)) |
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81 } |
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82 |
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83 |
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84 def first_tour_heuristics(dim: Int, path: Path) = |
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85 time_needed(tfirst_tour_heuristics(dim: Int, path: Path)) |
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86 |
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87 def first_tour_heuristic(dim: Int, path: Path) = |
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88 time_needed(tfirst_tour_heuristics(dim: Int, path: Path)) |
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89 |
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90 // will be called with boards up to 30 x 30 |
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91 |
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92 |
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93 } |