4 object CW7b { |
4 object CW7b { |
5 |
5 |
6 type Pos = (Int, Int) // a position on a chessboard |
6 type Pos = (Int, Int) // a position on a chessboard |
7 type Path = List[Pos] // a path...a list of positions |
7 type Path = List[Pos] // a path...a list of positions |
8 |
8 |
9 def print_board(dim: Int, path: Path): Unit = { |
9 def print_board(dim: Int, path: Path) : Unit = { |
10 println |
10 println |
11 for (i <- 0 until dim) { |
11 for (i <- 0 until dim) { |
12 for (j <- 0 until dim) { |
12 for (j <- 0 until dim) { |
13 print(f"${path.reverse.indexOf((i, j))}%3.0f ") |
13 print(f"${path.reverse.indexOf((i, j))}%3.0f ") |
14 } |
14 } |
15 println |
15 println |
16 } |
16 } |
17 } |
17 } |
18 |
18 |
19 def add_pair(x: Pos)(y: Pos): Pos = |
19 def add_pair(x: Pos)(y: Pos) : Pos = |
20 (x._1 + y._1, x._2 + y._2) |
20 (x._1 + y._1, x._2 + y._2) |
21 |
21 |
22 def is_legal(dim: Int, path: Path)(x: Pos): Boolean = |
22 def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = |
23 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
23 0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x) |
24 |
24 |
25 def moves(x: Pos): List[Pos] = |
25 def moves(x: Pos) : List[Pos] = |
26 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
26 List(( 1, 2),( 2, 1),( 2, -1),( 1, -2), |
27 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
27 (-1, -2),(-2, -1),(-2, 1),(-1, 2)).map(add_pair(x)) |
28 |
28 |
29 def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = |
29 def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = |
30 moves(x).filter(is_legal(dim, path)) |
30 moves(x).filter(is_legal(dim, path)) |
31 |
31 |
32 |
32 |
33 def first(xs: List[Pos], f: Pos => Option[Path]): Option[Path] = xs match { |
33 def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = xs match { |
34 case Nil => None |
34 case Nil => None |
35 case x::xs => { |
35 case x::xs => { |
36 val result = f(x) |
36 val result = f(x) |
37 if (result.isDefined) result else first(xs, f) |
37 if (result.isDefined) result else first(xs, f) |
38 } |
38 } |
39 } |
39 } |
40 |
40 |
41 //first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
41 //first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
42 //first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
42 //first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None)) |
43 |
43 |
44 def first_tour(dim: Int, path: Path): Option[Path] = { |
44 def first_tour(dim: Int, path: Path) : Option[Path] = { |
45 if (path.length == dim * dim) Some(path) |
45 if (path.length == dim * dim) Some(path) |
46 else |
46 else |
47 first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path)) |
47 first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path)) |
48 } |
48 } |
49 |
49 |