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

//==================================================

object CW7a {

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

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

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

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

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

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

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

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

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

//some test cases

//

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

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

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

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

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

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

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

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

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

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

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

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

}