1 // Part 1 about finding and counting Knight's tours

     2 //==================================================

     3 

     4 object CW7a {

     5 

     6 type Pos = (Int, Int)    // a position on a chessboard 

     7 type Path = List[Pos]    // a path...a list of positions

     8 

     9 //(1a) Complete the function that tests whether the position 

    10 //     is inside the board and not yet element in the path.

    11 

    12 //def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = ...

    13 

    14 

    15 //(1b) Complete the function that calculates for a position 

    16 //     all legal onward moves that are not already in the path. 

    17 //     The moves should be ordered in a "clockwise" manner.

    18  

    19 //def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...

    20 

    21 

    22 //some test cases

    23 //

    24 //assert(legal_moves(8, Nil, (2,2)) == 

    25 //  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))

    26 //assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))

    27 //assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 

    28 //  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))

    29 //assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))

    30 

    31 

    32 //(1c) Complete the two recursive functions below. 

    33 //     They exhaustively search for knight's tours starting from the 

    34 //     given path. The first function counts all possible tours, 

    35 //     and the second collects all tours in a list of paths.

    36 

    37 //def count_tours(dim: Int, path: Path) : Int = ...

    38 

    39 //def enum_tours(dim: Int, path: Path) : List[Path] = ...

    40 

    41 

    42 }