最小生成树之克鲁斯卡尔算法

关于最小生成树的经典算法一个是普里姆算法，另一个就是克鲁斯卡尔算法，在这里和大家一起讨论，有不对的地方希望大家多多指教，先上图

和普里姆算法用一个数组进行比较不同的是，克鲁斯卡尔算法用的是边进行比较，一条边的起始节点，终端 节点，和边的权值

再按权值的大小对边从小大到进行排序，而克鲁斯卡尔算法的核心思想是，要找到最小的生成树，那么就将边从小到大一条一条加进去，只要碰见加进去会出现回环就加，这样从小到大加的边所生成的树那么就一定是最小生成树，那么该算法的核心就是如何判断是否会出现回环，下面请看算法的java实现版

public class GraphKruskal {
   private Edge[] edges;
   private int edgeSize;
   public GraphKruskal(int edgeSize) {
      this.edgeSize = edgeSize;
      edges = new Edge[edgeSize];
   
   }
   public void miniSpanTreeKruskal(){
      int m,n,sum=0;
      int[] parent = new int[edgeSize];//神奇的数组，下标为起点，值为终点
      for(int i = 0 ;i<edgeSize;i++){
         parent[i] = 0;
      }
      for(int i = 0;i<edgeSize;i++){
         n = find(parent,edges[i].begin);
         m = find(parent,edges[i].end);
         if(n!=m){
            parent[n] = m;
            System.out.println("起始顶点："+edges[i].begin+"---结束顶点："+edges[i].end+"~权值："+edges[i].weight);
            sum+=edges[i].weight;
         }else{
            System.out.println("第"+i+"条边回环了");
         }
      }
      System.out.println("sum:"+sum);
   }
   
   
   /*这是最关键的一步，通过该find方法判断是否能够形成回环
    * 
    */
   public int find(int[] parent,int f){
      while(parent[f]>0){
         System.out.println("找到起点"+f);
         f = parent[f];
         System.out.println("找到终点:"+f);
      }
      return f;
   }
   public void createEdgeArray(){
      Edge edge0 = new Edge(4,7,7);
      Edge edge1 = new Edge(2,8,8);
      Edge edge2 = new Edge(0,1,10);
      Edge edge3 = new Edge(0,5,11);
      Edge edge4 = new Edge(1,8,12);
      Edge edge5 = new Edge(3,7,16);
      Edge edge6 = new Edge(1,6,16);
      Edge edge7 = new Edge(5,6,17);
      Edge edge8 = new Edge(1,2,18);
      Edge edge9 = new Edge(6,7,19);
      Edge edge10 = new Edge(3,4,20);
      Edge edge11 = new Edge(3,8,21);
      Edge edge12 = new Edge(2,3,22);
      Edge edge13 = new Edge(3,6,24);
      Edge edge14 = new Edge(4,5,26);
      edges[0] = edge0;
      edges[1] = edge1;
      edges[2] = edge2;
      edges[3] = edge3;
      edges[4] = edge4;
      edges[5] = edge5;
      edges[6] = edge6;
      edges[7] = edge7;
      edges[8] = edge8;
      edges[9] = edge9;
      edges[10] = edge10;
      edges[11] = edge11;
      edges[12] = edge12;
      edges[13] = edge13;
      edges[14] = edge14;
   }
   class Edge{
      private int begin;
      private int end;
      private int weight;
      public Edge(int begin, int end, int weight) {
         super();
         this.begin = begin;
         this.end = end;
         this.weight = weight;
      }
      public int getBegin() {
         return begin;
      }
      public void setBegin(int begin) {
         this.begin = begin;
      }
      public int getEnd() {
         return end;
      }
      public void setEnd(int end) {
         this.end = end;
      }
      public int getWeight() {
         return weight;
      }
      public void setWeight(int weight) {
         this.weight = weight;
      }
      
   }
   
   
   public static void main(String[]args){
      GraphKruskal graphKruskal = new GraphKruskal(15);
      graphKruskal.createEdgeArray();
      graphKruskal.miniSpanTreeKruskal();
   }
}