Algorithme de KRUSKAL

/*
Kruskal's algorithm finds a minimum spanning tree for a connected weighted graph.
The program below uses a hard-coded example.
You can change this to match your problem by changing the edges in the graph.
The program uses 3 classes.
    The Kruskal class contains the main method.
    The Edge class represents an edge.
    The KruskalEdges class contains the edges determined by the Kruskal algorithm.
*/

import java.util.TreeSet;
import java.util.Vector;
import java.util.HashSet;

class Edge implements Comparable<Edge>
{
    String vertexA, vertexB;
    int weight;

    public Edge(String vertexA, String vertexB, int weight)
    {
        this.vertexA = vertexA;
        this.vertexB = vertexB;
        this.weight = weight;
    }
    public String getVertexA()
    {
        return vertexA;
    }
    public String getVertexB()
    {
        return vertexB;
    }
    public int getWeight()
    {
        return weight;
    }
    @Override
    public String toString()
    {
        return "(" + vertexA + ", " + vertexB + ") : Weight = " + weight;
    }
    public int compareTo(Edge edge)
    {
    	//== is not compared so that duplicate values are not eliminated. 
    	return (this.weight < edge.weight) ? -1: 1;
    }
}

class KruskalEdges
{
    Vector<HashSet<String>> vertexGroups = new Vector<HashSet<String>>();
    TreeSet<Edge> kruskalEdges = new TreeSet<Edge>();

    public TreeSet<Edge> getEdges()
    {
        return kruskalEdges;
    }
    HashSet<String> getVertexGroup(String vertex)
    {
        for (HashSet<String> vertexGroup : vertexGroups) {
            if (vertexGroup.contains(vertex)) {
                return vertexGroup;
            }
        }
        return null;
    }

    /**
     * The edge to be inserted has 2 vertices - A and B
     * We maintain a vector that contains groups of vertices.
     * We first check if either A or B exists in any group
     * If neither A nor B exists in any group
     *     We create a new group containing both the vertices.
     * If one of the vertices exists in a group and the other does not
     *     We add the vertex that does not exist to the group of the other vertex
     * If both vertices exist in different groups
     *     We merge the two groups into one
     * All of the above scenarios mean that the edge is a valid Kruskal edge
     * In that scenario, we will add the edge to the Kruskal edges    
     * However, if both vertices exist in the same group
     *     We do not consider the edge as a valid Kruskal edge
     */
    public void insertEdge(Edge edge)
    {
        String vertexA = edge.getVertexA();
        String vertexB = edge.getVertexB();

        HashSet<String> vertexGroupA = getVertexGroup(vertexA);
        HashSet<String> vertexGroupB = getVertexGroup(vertexB);

        if (vertexGroupA == null) {
            kruskalEdges.add(edge);
            if (vertexGroupB == null) {
                HashSet<String> htNewVertexGroup = new HashSet<String>();
                htNewVertexGroup.add(vertexA);
                htNewVertexGroup.add(vertexB);
                vertexGroups.add(htNewVertexGroup);
            }
            else {
                vertexGroupB.add(vertexA);        	
            }
        }
        else {
            if (vertexGroupB == null) {
                vertexGroupA.add(vertexB);
                kruskalEdges.add(edge);
            }
            else if (vertexGroupA != vertexGroupB) {
                vertexGroupA.addAll(vertexGroupB);
                vertexGroups.remove(vertexGroupB);
                kruskalEdges.add(edge);
            }
        }
    }
}

public class Kruskal
{
    public static void main(String[] args)
    {
        //TreeSet is used to sort the edges before passing to the algorithm
        TreeSet<Edge> edges = new TreeSet<Edge>();

        //Sample problem - replace these values with your problem set
        edges.add(new Edge("0", "1", 2)); 
        edges.add(new Edge("0", "3", 1)); 
        edges.add(new Edge("1", "2", 3)); 
        edges.add(new Edge("2", "3", 5)); 
        edges.add(new Edge("2", "4", 7)); 
        edges.add(new Edge("3", "4", 6)); 
        edges.add(new Edge("4", "5", 4));

        System.out.println("Graph");
        KruskalEdges vv = new KruskalEdges();

        for (Edge edge : edges) {
            System.out.println(edge);
            vv.insertEdge(edge);
        }

        System.out.println("Kruskal algorithm");
        int total = 0;
        for (Edge edge : vv.getEdges()) {
            System.out.println(edge);
            total += edge.getWeight();
        }
        System.out.println("Total weight is " + total);
    }
}