// Part 3 about finding a single tour using the Warnsdorf Rule
//=============================================================

// copy any function you need from files knight1.scala and
// knight2.scala

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

//(3a) Complete the function that calculates a list of onward
// moves like in (1b) but orders them according to the 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] = ..

//(3b) Complete the function that searches for a single *closed* 
// tour using the ordered moves function.

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

//(3c) Same as (3b) but searches for *open* tours.

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