// Part 2 about finding a single tour for a board using the Warnsdorf Rule
//=========================================================================

// !!! Copy any function you need from file knight1.scala !!!
//
// If you need any auxiliary function, feel free to 
// implement it, but do not make any changes to the
// templates below.

type Pos = (Int, Int)    // a position on a chessboard 
type Path = List[Pos]    // a path...a list of positions


//(6) Complete the function that calculates a list of onward
//    moves like in (2) but orders them according to Warnsdorf’s 
//    rule. That means moves with the fewest legal onward moves 
//    should come first.


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


//(7) Complete the function that searches for a single *closed* 
//    tour using the ordered_moves function from (6). This
//    function will be tested on a 6 x 6 board. 


//def first_closed_tour_heuristic(dim: Int, path: Path) : Option[Path] = ...


//(8) Same as (7) but searches for *non-closed* tours. This 
//    version of the function will be called with dimensions of 
//    up to 30 * 30.

//def first_tour_heuristic(dim: Int, path: Path) : Option[Path] = ...