Kruskal算法求解最小生成树的Java实现

假设一个无向图共有V（V>1）个顶点，E条边，那么它的最小生成树（如果有的话）有V个顶点，V-1条边。Krusal算法在求解最小生成树的过程中就是不断地选出一条权重最小的边，如果将这条边插入到目前的最小生成树（此时尚未最终形成）中不形成环路，则将其插入，否则再选择次小边重复以上过程，直到最后最小生成树中有V-1条边，则最小生成树求解成功，否则，原图中不包含最小生成树。

下面是《算法导论》一书中的一个Krusal算法求解最小生成树过程的一个例子。

以下是具体的Java代码实现

package Kruskal;
/**
 * 边
 * @author sdu20
 *
 */
public class Edge {

	private int v1;
	private int v2;
	private int weight;
	
	/**
	 * 为查找最小边专门所设
	 * @param weight
	 */
	public Edge(int weight){
		this.v1 = -1;
		this.v2 = -1;
		this.weight = weight;
	}
	
	public Edge(int v1,int v2,int weight){
		this.v1 = v1;
		this.v2 = v2;
		this.weight = weight;
	}
	
	public int getV1(){
		return v1;
	}
	
	public int getV2(){
		return v2;
	}
	
	public int getWeight(){
		return weight;
	}
	
	public String toString(){
		String str = "[ "+v1+" , "+v2+" , "+weight+" ]";
		return str;
	}
	
	public boolean equals(Edge edge){
		boolean equal = this.v1==edge.getV1() && this.v2==edge.getV2() && this.weight==edge.getWeight()
				|| this.v1==edge.getV2() && this.v2==edge.getV1() && this.weight==edge.getWeight();
		return equal;
	}
}

package Kruskal;

import java.util.*;

public class Graph {

	private int vNum;
	private int edgeNum;
	private LinkedList[] edgeLinks;
	private LinkedList T;	//入选的边集
	private LinkedList[] kindLists;	//用于区分是否形成环
	
	public Graph(int vNum){
		this.vNum = vNum;
		this.edgeNum = 0;
		edgeLinks = new LinkedList[vNum];
		for(int i = 0;i();
		}
	}
	
	public void insertEdge(Edge edge){
		int v1 = edge.getV1();
		int v2 = edge.getV2();
		edgeLinks[v1].add(edge);
		Edge edge2 = new Edge(v2,v1,edge.getWeight());
		edgeLinks[v2].add(edge2);
		edgeNum++;
	}
	
	public void deleteEdge(Edge edge){
		int v1 = edge.getV1();
		int v2 = edge.getV2();
		edgeLinks[v1].remove(edge);
		
		for(int i = 0;i list = (LinkedList) edgeLinks[i].clone();
			System.out.print(i+" : [");
			while(!list.isEmpty()){
				Edge edge = list.pop();
				System.out.print(edge.getV2()+"("+edge.getWeight()+")"+"  ");
			}
			System.out.println("]");
		}
	}
	
	/**
	 * Kruskal算法实现
	 */
	public void Kruskal(){
		
		T = new LinkedList<>();
		kindLists = new LinkedList[vNum];
		for(int i = 0;i();
			int num = i;
			kindLists[i].add(num);
		}
		
		while(edgeNum>0 && T.size()!=vNum-1){
			Edge edge = this.getMinEdge();
			this.deleteEdge(edge);
			int v1 = edge.getV1();
			int v2 = edge.getV2();
			
			int containsV1 = -1;
			int containsV2 = -1;
			for(int i = 0;i list = (LinkedList) kindLists[i].clone();
				if(list.contains(v1)){
					containsV1 = i;
				}
				if(list.contains(v2)){
					containsV2 = i;
				}
			}
			
			if(containsV1 != containsV2){
				T.add(edge);
				while(!kindLists[containsV2].isEmpty()){
					kindLists[containsV1].add(kindLists[containsV2].pop());
				}		
			}
		}
				
		if(T.size() == vNum-1){
			System.out.println("求最小生成树成功");
			int sumWeight = 0;
			LinkedList TT = (LinkedList) T.clone();
			while(!TT.isEmpty()){
				Edge ee = TT.pop();
				sumWeight += ee.getWeight();
				System.out.println(ee.toString());				
			}
			System.out.println("最小生成树权重之和为： "+sumWeight);
		}else{
			System.out.println("没有最小生成树");
		}
	}
	
	
	
	public Edge getMinEdge(){
		
		Edge minEdge = new Edge(10000);
				
		for(int i = 0;i list = (LinkedList) edgeLinks[i].clone();
			while(!list.isEmpty()){
				Edge edge = list.pop();
				if(minEdge.getWeight()>edge.getWeight()){
					minEdge = edge;
				}
			}
		}		

		if(minEdge.getWeight()==10000)
			return null;
		return minEdge;
	}
	
}

package Kruskal;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		bookGraph();
		//randomGraph();
	}
	
	public static void bookGraph(){
		
		Graph graph = new Graph(9);
		Edge[] edges = new Edge[14];
		
		edges[0] = new Edge(0,1,4);
		edges[1] = new Edge(0,7,8);
		edges[2] = new Edge(1,2,8);
		edges[3] = new Edge(1,7,11);
		edges[4] = new Edge(2,3,7);
		edges[5] = new Edge(2,5,4);
		edges[6] = new Edge(2,8,2);
		edges[7] = new Edge(3,4,9);
		edges[8] = new Edge(3,5,14);
		edges[9] = new Edge(4,5,10);
		edges[10] = new Edge(5,6,2);
		edges[11] = new Edge(6,7,1);
		edges[12] = new Edge(6,8,6);
		edges[13] = new Edge(7,8,7);
		
		for(int i = 0;i<14;i++){
			graph.insertEdge(edges[i]);
		}
		
		graph.bianli();
		graph.Kruskal();
	}
	
	/**
	 * 100个点，1000条边，权重为1~100的随机数
	 */
	public static void randomGraph(){
		Graph graph = new Graph(100);
		
		for(int i = 0;i<1000;){
			
			int preV = (int)(Math.random()*100);
            int folV = (int)(Math.random()*100);
            int weight = (int)(Math.random()*100+1);
            if(preV != folV){
            	Edge edge = new Edge(preV,folV,weight);
            	try{
            		graph.insertEdge(edge);
            		i++;
            	}catch(Exception e){
            		continue;
            	}
            }
		}
		
		graph.bianli();
		graph.Kruskal();
	}

}

运行截图如下

该测试用例即为前面所给的例子。