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 |
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5 type Pos = (Int, Int) |
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6 type Path = List[Pos] |
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7 |
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8 // for measuring time |
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9 def time_needed[T](n: Int, code: => T) : T = { |
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10 val start = System.nanoTime() |
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11 for (i <- 0 until n) code |
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12 val result = code |
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13 val end = System.nanoTime() |
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14 println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.") |
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15 result |
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16 } |
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17 |
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18 def print_board(dim: Int, path: Path): Unit = { |
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19 println |
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20 for (i <- 0 until dim) { |
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21 for (j <- 0 until dim) { |
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22 print(f"${path.reverse.indexOf((i, j))}%4.0f ") |
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23 } |
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24 println |
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25 } |
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26 } |
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27 |
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28 def add_pair(x: Pos, y: Pos): Pos = |
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29 (x._1 + y._1, x._2 + y._2) |
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30 |
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31 def is_legal(dim: Int, path: Path, x: Pos): Boolean = |
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32 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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33 |
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34 def moves(x: Pos): List[Pos] = |
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35 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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36 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x, _)) |
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37 |
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38 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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39 moves(x).filter(is_legal(dim, path, _)) |
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40 |
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41 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
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42 legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length) |
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43 |
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44 import scala.annotation.tailrec |
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45 |
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46 @tailrec |
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47 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
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48 case Nil => None |
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49 case x::xs => { |
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50 val result = f(x) |
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51 if (result.isDefined) result else first(xs, f) |
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52 } |
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53 } |
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54 |
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55 |
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56 //def first[A, B](xs: List[A], f: A => Option[B]): Option[B] = |
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57 // xs.flatMap(f(_)).headOption |
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58 |
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59 |
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60 def first_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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61 if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path) |
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62 else |
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63 first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristics(dim, x::path)) |
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64 } |
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65 |
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66 // heuristic cannot be used to search for closed tours on 7 x 7 |
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67 for (dim <- 1 to 6) { |
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68 val t = time_needed(0, first_closed_tour_heuristics(dim, List((dim / 2, dim / 2)))) |
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69 println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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70 } |
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71 |
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72 |
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73 //@tailrec |
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74 /* |
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75 def first_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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76 |
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77 @tailrec |
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78 def aux(dim: Int, path: Path, moves: List[Pos]): Option[Path] = |
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79 if (path.length == dim * dim) Some(path) |
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80 else |
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81 moves match { |
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82 case Nil => None |
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83 case x::xs => { |
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84 val r = first_tour_heuristics(dim, x::path) |
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85 if (r.isDefined) r else aux(dim, path, xs) |
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86 } |
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87 } |
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88 |
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89 aux(dim, path, ordered_moves(dim, path, path.head)) |
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90 } |
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91 */ |
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92 |
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93 @tailrec |
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94 def tour_on_mega_board(dim: Int, paths: List[Path]): Option[Path] = paths match { |
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95 case Nil => None |
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96 case (path::rest) => |
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97 if (path.length == dim * dim) Some(path) |
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98 else tour_on_mega_board(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest) |
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99 } |
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100 |
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101 |
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102 |
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103 /* |
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104 def first_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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105 if (path.length == dim * dim) Some(path) |
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106 else |
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107 for (p <- ordered_moves(dim, path, path.head)) |
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108 val r = first_tour_heuristics(dim, x::path) |
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109 //first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path)) |
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110 ordered_moves(dim, path, path.head).view.flatMap((x: Pos) => first_tour_heuristics(dim, x::path)).headOption |
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111 } |
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112 */ |
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113 |
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114 /* |
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115 for (dim <- 1 to 50) { |
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116 val t = first_tour_heuristics(dim, List((dim / 2, dim / 2))) |
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117 println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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118 } |
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119 */ |
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120 |
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121 val dim = 70 |
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122 println(s"${dim} x ${dim}:") |
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123 print_board(dim, time_needed(0, tour_on_mega_board(dim, List(List((0, 0)))).get)) |
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124 |
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