1 // Part 3 about finding a single tour using the Warnsdorf Rule |
1 // Part 3 about finding a single tour using the Warnsdorf Rule |
2 //============================================================= |
2 //============================================================= |
3 |
3 |
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4 // copy any function you need from files knight1.scala and |
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5 // knight2.scala |
4 |
6 |
5 type Pos = (Int, Int) |
7 type Pos = (Int, Int) // a position on a chessboard |
6 type Path = List[Pos] |
8 type Path = List[Pos] // a path...a list of positions |
7 |
9 |
8 def print_board(dim: Int, path: Path): Unit = { |
10 //(3a) Complete the function that calculates a list of onward |
9 println |
11 // moves like in (1b) but orders them according to the Warnsdorf’s |
10 for (i <- 0 until dim) { |
12 // rule. That means moves with the fewest legal onward moves |
11 for (j <- 0 until dim) { |
13 // should come first. |
12 print(f"${path.reverse.indexOf((i, j))}%3.0f ") |
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13 } |
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14 println |
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15 } |
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16 } |
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17 |
14 |
18 def add_pair(x: Pos)(y: Pos): Pos = |
15 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = .. |
19 (x._1 + y._1, x._2 + y._2) |
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20 |
16 |
21 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
17 //(3b) Complete the function that searches for a single *closed* |
22 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
18 // tour using the ordered moves function. |
23 |
19 |
24 def moves(x: Pos): List[Pos] = |
20 def first_closed_tour_heuristic(dim: Int, path: Path): Option[Path] = ... |
25 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
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26 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
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27 |
21 |
28 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
22 //(3c) Same as (3b) but searches for *open* tours. |
29 moves(x).filter(is_legal(dim, path)) |
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30 |
23 |
31 def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
24 def first_tour_heuristic(dim: Int, path: Path): Option[Path] = ... |
32 legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length) |
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33 |
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34 |
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35 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
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36 case Nil => None |
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37 case x::xs => { |
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38 val result = f(x) |
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39 if (result.isDefined) result else first(xs, f) |
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40 } |
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41 } |
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42 |
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43 |
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44 def first_closed_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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45 if (path.length == dim * dim && moves(path.head).contains(path.last)) Some(path) |
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46 else |
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47 first(ordered_moves(dim, path, path.head), (x: Pos) => first_closed_tour_heuristics(dim, x::path)) |
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48 } |
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49 |
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50 for (dim <- 1 to 6) { |
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51 val t = first_closed_tour_heuristics(dim, List((dim / 2, dim / 2))) |
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52 println(s"${dim} x ${dim} closed: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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53 } |
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54 |
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55 |
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56 def first_tour_heuristics(dim: Int, path: Path): Option[Path] = { |
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57 if (path.length == dim * dim) Some(path) |
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58 else |
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59 first(ordered_moves(dim, path, path.head), (x: Pos) => first_tour_heuristics(dim, x::path)) |
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60 } |
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61 |
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62 for (dim <- 1 to 50) { |
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63 val t = first_tour_heuristics(dim, List((dim / 2, dim / 2))) |
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64 println(s"${dim} x ${dim}: " + (if (t == None) "" else { print_board(dim, t.get) ; "" })) |
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65 } |
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