/**
  * The Hamilton class contains static methods to find Hamiltonian circuits in Graph objects.
  * This class cannot be instantiated.
  * <BR>THIS CLASS SHOULD BE MODIFIED 
  * @author Sophie Quigley
  * @author PUT YOUR NAMES HERE
  * 
  */
public class Hamilton {

    /**
    * Stops class from being instantiated.
    */
    private Hamilton() {}
    
    /**
     * graph for which a Hamiltonian circuit is sought
     */
    private static Graph g = null;

    /**
     * Total number of vertices in graph
     */
    private static int totalV;

    /**
     * Hamiltonian circuit being built
     */
    private static Walk hamiltonian = null;
       
    /**
     * Finds a Hamiltonian circuit in graph if there is one.
     * <br> DO NOT MODIFY THE METHOD SIGNATURE AND RETURN TYPE OF THIS METHOD
     * @param graph graph for which a Hamiltonian circuit is sought
     * @return A Hamiltonian circuit for the graph if there is one, or null otherwise.
     */
    public static Walk getHamiltonian(Graph graph) {

        // Store static information
        g = graph;
        totalV = g.getTotalVertices();
        hamiltonian = new Walk(totalV+1);
        
        // Continue the Implementation
    }

    /**
     * Finds a Hamiltonian circuit in graph if there is one.
     * @param vertex current vertex in the circuit
     * @param totalvisited total number of vertices visited so far in the graph
     * @return true if a Hamiltonian path for the graph has been found 
     * starting at the current vertex and returning to the first vertex in the walk
     */
    
    private static boolean foundHamiltonian(int vertex, int totalvisited) {
    }
    
}