java数据结构和算法------图(最小生成树Kruskal)

  1 package iYou.neugle.graph;
  2
  3 import java.util.Set;
  4 import java.util.TreeSet;
  5
  6 //创建图过程的代码在图的那篇博文中，此处直接使用
  7 public class Kruskal {
  8     private MyGraph1 graph;
  9     private int[] a;// 并查集使用数组(存储前置节点)
 10     private Set<Edge> edgeSet = new TreeSet<>();// 边的集合按w的升序排序
 11
 12     class Edge implements Comparable<Object> {
 13         public int start;// 开始边
 14         public int end;// 结束边
 15         public int w;// 权值
 16
 17         // 将边的集合进行w的升序排序
 18         @Override
 19         public int compareTo(Object o) {
 20             if (o instanceof Edge) {
 21                 Edge edge = (Edge) o;
 22                 if (this.w >= edge.w) {
 23                     return 1;
 24                 } else {
 25                     return -1;
 26                 }
 27             }
 28             return 0;
 29         }
 30     }
 31
 32     // 并查集
 33     // 首先初始化各个节点
 34     private void MakeSet(int n) {
 35         for (int i = 0; i < n; i++) {
 36             a[i] = i;
 37         }
 38     }
 39
 40     // 查找根节点
 41     private int Find(int n) {
 42         if (a[n] == n) {
 43             return n;
 44         } else {
 45             return Find(a[n]);
 46         }
 47     }
 48
 49     // 合并节点
 50     private void UnionSet(int x, int y) {
 51         if (a[x] != a[y]) {
 52             a[this.Find(y)] = this.Find(x);
 53         }
 54     }
 55
 56     public Kruskal(MyGraph1 graph) {
 57         this.graph = graph;
 58         a = new int[this.graph.getGraph().maxNum];
 59     }
 60
 61     // 初始化edgeSet集合
 62     private void Init() {
 63         // 如果为无向图
 64         if (this.graph.getGraph().type == 0) {
 65             for (int i = 0; i < this.graph.getGraph().maxNum; i++) {
 66                 for (int j = 0; j < i; j++) {
 67                     Function(j, i);
 68                 }
 69             }
 70         }
 71         // 如果为有向图
 72         else {
 73             for (int i = 0; i < this.graph.getGraph().maxNum; i++) {
 74                 for (int j = 0; j < this.graph.getGraph().maxNum; j++) {
 75                     Function(i, j);
 76                 }
 77             }
 78         }
 79     }
 80
 81     // 功能函数
 82     private void Function(int i, int j) {
 83         int w = this.graph.getGraph().edge[i][j];
 84         if (w != 0) {
 85             Edge edge = new Edge();
 86             edge.start = i;
 87             edge.end = j;
 88             edge.w = w;
 89             this.edgeSet.add(edge);
 90         }
 91     }
 92
 93     public void KruskalCore() {
 94         this.Init();
 95         int maxNum = this.graph.getGraph().maxNum;
 96         // 初始化a
 97         this.MakeSet(maxNum);
 98         Edge[] edgeArr = this.edgeSet.toArray(new Edge[] {});
 99         int sum = edgeArr[0].w;
100         // 合并一条边的两个节点
101         this.UnionSet(edgeArr[0].start, edgeArr[0].end);
102         System.out.println("最小生成树为--------");
103         System.out
104                 .println((edgeArr[0].start + 1) + "->" + (edgeArr[0].end + 1));
105         // 通过并查集进行判断是否该条边生成回路
106         int n = 1;
107         for (int i = 1; i < edgeArr.length && n < maxNum; i++) {
108             if (this.Find(edgeArr[i].start) != this.Find(edgeArr[i].end)) {
109                 this.UnionSet(edgeArr[i].start, edgeArr[i].end);
110                 System.out.println((edgeArr[i].start + 1) + "->"
111                         + (edgeArr[i].end + 1));
112                 sum += edgeArr[i].w;
113             }
114             n++;
115         }
116         System.out.println("----------------");
117         System.out.println("最小生成树的权值为: " + sum);
118     }
119
120     public static void main(String[] args) {
121         MyGraph1 graph = new MyGraph1(5, 0);
122         graph.CreateMaxtrixGraph(1, 2, 2);
123         graph.CreateMaxtrixGraph(1, 3, 5);
124         graph.CreateMaxtrixGraph(1, 5, 3);
125         graph.CreateMaxtrixGraph(2, 4, 4);
126         graph.CreateMaxtrixGraph(3, 5, 5);
127         graph.CreateMaxtrixGraph(4, 5, 2);
128         graph.OutPutMaxtrixGraph();
129         Kruskal kruskal = new Kruskal(graph);
130         kruskal.KruskalCore();
131     }
132 }

  1 2 3 4 5
1 0 2 5 0 3
2 2 0 0 4 0
3 5 0 0 0 5
4 0 4 0 0 2
5 3 0 5 2 0
最小生成树为--------
1->2
4->5
1->5
1->3
----------------
最小生成树的权值为: 12