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1 // Main Part 4 about finding Knight's tours |
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2 //========================================== |
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3 |
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4 |
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5 object M4a { |
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6 |
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7 // If you need any auxiliary functions, feel free to |
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8 // implement them, but do not make any changes to the |
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9 // templates below. Also have a look whether the functions |
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10 // at the end of the file are of any help. |
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11 |
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12 |
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13 |
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14 type Pos = (Int, Int) // a position on a chessboard |
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15 type Path = List[Pos] // a path...a list of positions |
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16 |
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17 //(1) Complete the function that tests whether the position x |
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18 // is inside the board and not yet element in the path. |
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19 |
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20 def is_legal(dim: Int, path: Path, x: Pos) : Boolean = ??? |
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21 |
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22 |
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23 |
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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] = ??? |
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29 |
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30 |
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31 //some testcases |
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32 // |
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33 //assert(legal_moves(8, Nil, (2,2)) == |
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34 // List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4))) |
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35 //assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6))) |
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36 //assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == |
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37 // List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))) |
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38 //assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))) |
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39 |
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40 |
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41 //(3) Complete the two recursive functions below. |
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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 = ??? |
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47 |
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48 def enum_tours(dim: Int, path: Path) : List[Path] = ??? |
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49 |
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50 |
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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] = ??? |
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57 |
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58 |
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59 // testcases |
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60 // |
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61 //def foo(x: (Int, Int)) = if (x._1 > 3) Some(List(x)) else None |
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62 // |
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63 //first(List((1, 0),(2, 0),(3, 0),(4, 0)), foo) // Some(List((4,0))) |
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64 //first(List((1, 0),(2, 0),(3, 0)), foo) // None |
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65 |
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66 |
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67 //(5) Implement a function that uses the first-function from (4) for |
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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] = ??? |
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72 |
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73 |
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74 |
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75 /* Helper functions |
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76 |
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77 |
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78 // for measuring time |
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79 def time_needed[T](code: => T) : T = { |
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80 val start = System.nanoTime() |
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81 val result = code |
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82 val end = System.nanoTime() |
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83 println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.") |
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84 result |
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85 } |
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86 |
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87 // can be called for example with |
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88 // |
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89 // time_needed(count_tours(dim, List((0, 0)))) |
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90 // |
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91 // in order to print out the time that is needed for |
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92 // running count_tours |
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93 |
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94 |
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95 // for printing a board |
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96 def print_board(dim: Int, path: Path): Unit = { |
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97 println() |
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98 for (i <- 0 until dim) { |
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99 for (j <- 0 until dim) { |
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100 print(f"${path.reverse.indexOf((j, dim - i - 1))}%3.0f ") |
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101 } |
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102 println() |
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103 } |
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104 } |
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105 |
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106 |
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107 */ |
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108 |
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109 } |