7 // If you need any auxiliary functions, feel free to |
7 // If you need any auxiliary functions, feel free to |
8 // implement them, but do not make any changes to the |
8 // implement them, but do not make any changes to the |
9 // templates below. Also have a look whether the functions |
9 // templates below. Also have a look whether the functions |
10 // at the end of the file are of any help. |
10 // at the end of the file are of any help. |
11 |
11 |
12 |
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13 |
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14 type Pos = (Int, Int) // a position on a chessboard |
12 type Pos = (Int, Int) // a position on a chessboard |
15 type Path = List[Pos] // a path...a list of positions |
13 type Path = List[Pos] // a path...a list of positions |
16 |
14 |
17 //(1) Complete the function that tests whether the position x |
15 // ADD YOUR CODE BELOW |
18 // is inside the board and not yet element in the path. |
16 //====================== |
19 |
17 |
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18 |
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19 |
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20 //(1) |
20 def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ??? |
21 def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ??? |
21 |
22 |
22 |
23 |
23 |
24 //(2) |
24 //(2) Complete the function that calculates for a position x |
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25 // all legal onward moves that are not already in the path. |
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26 // The moves should be ordered in a "clockwise" manner. |
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27 |
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28 def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ??? |
25 def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ??? |
29 |
26 |
30 |
27 |
31 //some testcases |
28 //some testcases |
32 // |
29 // |
36 //assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == |
33 //assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == |
37 // List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))) |
34 // List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))) |
38 //assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))) |
35 //assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))) |
39 |
36 |
40 |
37 |
41 //(3) Complete the two recursive functions below. |
38 // (3) |
42 // They exhaustively search for knight's tours starting from the |
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43 // given path. The first function counts all possible tours, |
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44 // and the second collects all tours in a list of paths. |
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45 |
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46 def count_tours(dim: Int, path: Path) : Int = ??? |
39 def count_tours(dim: Int, path: Path) : Int = ??? |
47 |
40 |
48 def enum_tours(dim: Int, path: Path) : List[Path] = ??? |
41 def enum_tours(dim: Int, path: Path) : List[Path] = ??? |
49 |
42 |
50 |
43 // (4) |
51 //(4) Implement a first-function that finds the first |
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52 // element, say x, in the list xs where f is not None. |
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53 // In that case Return f(x), otherwise None. If possible, |
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54 // calculate f(x) only once. |
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55 |
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56 def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = ??? |
44 def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = ??? |
57 |
45 |
58 |
46 |
59 // testcases |
47 // testcases |
60 // |
48 // |
62 // |
50 // |
63 //first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) // Some(List((4,0))) |
51 //first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) // Some(List((4,0))) |
64 //first(List((1, 0),(2, 0),(3, 0)), foo) // None |
52 //first(List((1, 0),(2, 0),(3, 0)), foo) // None |
65 |
53 |
66 |
54 |
67 //(5) Implement a function that uses the first-function from (4) for |
55 //(5) |
68 // trying out onward moves, and searches recursively for a |
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69 // knight tour on a dim * dim-board. |
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70 |
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71 def first_tour(dim: Int, path: Path) : Option[Path] = ??? |
56 def first_tour(dim: Int, path: Path) : Option[Path] = ??? |
72 |
57 |
73 |
58 |
74 |
59 |
75 /* Helper functions |
60 /* Helper functions |