1 import scala.util._ |
1 |
2 type Pos = (Int, Int) |
2 type Pos = (Int, Int) |
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3 type Path = List[Pos] |
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4 |
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5 def print_board(dim: Int, path: Path): Unit = { |
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6 println |
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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 |
3 |
15 |
4 def add_pair(x: Pos)(y: Pos): Pos = |
16 def add_pair(x: Pos)(y: Pos): Pos = |
5 (x._1 + y._1, x._2 + y._2) |
17 (x._1 + y._1, x._2 + y._2) |
6 |
18 |
7 def is_legal(dim: Int, path: List[Pos])(x: Pos): Boolean = |
19 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
8 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
20 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
9 |
21 |
10 def moves(x: Pos): List[Pos] = { |
22 def moves(x: Pos): List[Pos] = { |
11 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
23 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
12 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
24 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
13 } |
25 } |
14 |
26 |
15 def legal_moves(dim: Int, path: List[Pos], x: Pos): List[Pos] = { |
27 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
16 moves(x).filter(is_legal(dim, path)) |
28 moves(x).filter(is_legal(dim, path)) |
17 } |
29 |
18 |
30 |
19 |
31 |
20 // non-circle tours |
32 // non-circle tours |
21 /* |
33 /* |
22 def tour(dim: Int, path: List[Pos]): List[List[Pos]] = { |
34 def tour(dim: Int, path: List[Pos]): List[List[Pos]] = { |
25 else |
37 else |
26 (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).flatten |
38 (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).flatten |
27 } |
39 } |
28 */ |
40 */ |
29 |
41 |
30 def tour(dim: Int, path: List[Pos]): Int = { |
42 def tour(dim: Int, path: Path): Int = { |
31 if (path.length == dim * dim) 1 |
43 if (path.length == dim * dim) 1 |
32 else |
44 else |
33 (for (x <- legal_moves(dim, path, path.head).par) yield tour(dim, x::path)).sum |
45 (for (x <- legal_moves(dim, path, path.head) yield tour(dim, x::path))).sum |
34 } |
46 } |
35 |
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 |
36 //val n = 8 |
66 //val n = 8 |
37 val n = 6 |
67 val n = 5 |
38 println(s"number simple tours: n = $n") |
68 println(s"number simple tours: n = $n") |
39 |
69 |
40 println(tour(n, List((0, 0)))) |
70 //println(etour(n, List((0, 0))).size) |
41 |
71 |
42 /* |
72 |
43 for (d <- 1 to 6) { |
73 |
44 println(s"${d} x ${d} " + (for (i <- 0 until d; j <- 0 until d) yield tour(d, List((i, j)))).sum) |
74 for (d <- 9 to 9) { |
45 } |
75 println(s"${d} x ${d} " + dtour(d).length) |
46 */ |
76 } |
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77 |
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78 |