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1 // Part 2 about finding a single tour for a board |
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2 //================================================ |
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3 |
2 type Pos = (Int, Int) |
4 // copy any function you need from file knight1.scala |
3 type Path = List[Pos] |
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4 |
5 |
5 def print_board(dim: Int, path: Path): Unit = { |
6 type Pos = (Int, Int) // a position on a chessboard |
6 println |
7 type Path = List[Pos] // a path...a list of positions |
7 for (i <- 0 until dim) { |
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8 for (j <- 0 until dim) { |
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9 print(f"${path.indexOf((i, j))}%3.0f ") |
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10 } |
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11 println |
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12 } |
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13 } |
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14 |
8 |
15 |
9 |
16 def add_pair(x: Pos)(y: Pos): Pos = |
10 //(2a) Implement a first-function that finds the first |
17 (x._1 + y._1, x._2 + y._2) |
11 // element, say x, in the list xs where f is not None. |
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12 // In that case return f(x), otherwise none. |
18 |
13 |
19 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
14 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = ... |
20 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
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21 |
15 |
22 def moves(x: Pos): List[Pos] = { |
16 //(2b) Implement a function that uses the first-function for |
23 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
17 // trying out onward moves, and searches recursively for an |
24 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
18 // *open* tour on a dim * dim-board. |
25 } |
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26 |
19 |
27 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
20 def first_tour(dim: Int, path: Path): Option[Path] = ... |
28 moves(x).filter(is_legal(dim, path)) |
21 |
29 |
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30 |
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31 |
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32 // non-circle tours |
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33 /* |
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34 def tour(dim: Int, path: List[Pos]): List[List[Pos]] = { |
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35 if (path.length == dim * dim) // && moves(n)(path.head).contains(path.last)) |
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36 List(path) |
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37 else |
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38 (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).flatten |
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39 } |
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40 */ |
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41 |
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42 def tour(dim: Int, path: Path): Int = { |
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43 if (path.length == dim * dim) 1 |
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44 else |
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45 (for (x <- legal_moves(dim, path, path.head) yield tour(dim, x::path))).sum |
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46 } |
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47 |
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48 |
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49 def dtour(dim: Int): List[List[Pos]] = { |
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50 var counter = 100000000 |
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51 |
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52 def etour(dim: Int, path: List[Pos]): List[List[Pos]] = { |
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53 counter = counter - 1 |
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54 if (counter <= 0) List() else |
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55 if (path.length == dim * dim) List(path) |
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56 else |
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57 (for (x <- legal_moves(dim, path, path.head)) yield etour(dim, x::path)).flatten |
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58 } |
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59 |
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60 (for (i <- (0 until dim).toList; |
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61 j <- (0 until dim).toList) yield etour(dim, List((i, j)))).flatten |
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62 } |
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63 |
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64 |
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65 |
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66 //val n = 8 |
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67 val n = 5 |
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68 println(s"number simple tours: n = $n") |
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69 |
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70 //println(etour(n, List((0, 0))).size) |
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71 |
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72 |
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73 |
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74 for (d <- 9 to 9) { |
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75 println(s"${d} x ${d} " + dtour(d).length) |
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76 } |
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77 |
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78 |
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