// 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] = ...