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 M4c { // 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 tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match { |
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50 case Nil => None |
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51 case (path::rest) => |
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52 if (path.length == dim * dim) Some(path) |
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53 else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest) |
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54 } |
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55 |
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56 def ttour_on_mega_board(dim: Int, path: Path): Option[Path] = |
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57 tour_on_mega_board_aux(dim, List(path)) |
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58 |
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59 |
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60 def tour_on_mega_board(dim: Int, path: Path) = |
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61 time_needed(ttour_on_mega_board(dim: Int, path: Path)) |
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62 |
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63 |
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64 // testcases |
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65 //print_board(70, tour_on_mega_board(70, List((0, 0))).get) |
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66 |
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67 |
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68 } |
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69 |
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70 |
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71 //val dim = 66 //75 |
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72 M4c.print_board(30, M4c.tour_on_mega_board(30, List((0, 0))).get) |
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73 M4c.print_board(66, M4c.tour_on_mega_board(66, List((0, 0))).get) |
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