// Core Part about finding a single tour for a board using the

// Warnsdorf Rule

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

object M4b {

// !!! Copy any function you need from file knight1.scala !!!

//

// If you need any auxiliary functions, feel free to 

// implement them, 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

// ADD YOUR CODE BELOW

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

//(6) 

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

//(7) 

def first_closed_tour_heuristics(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_heuristics(dim: Int, path: Path) : Option[Path] = ???

}