最小生产树Prim和Kruskal

src/main/java/chapter9/mst/DisjSets.java

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+package chapter9.mst;
+
+/**
+ * 不相交集合
+ * @author wenlei
+ *
+ */
+public class DisjSets {
+	private Integer[] s;
+
+	public DisjSets(int numElements) {
+		s = new Integer[numElements];
+		for (int i = 0; i < s.length; i++) {
+			s[i]=-1;
+		}
+	}
+
+	/**
+	 * 采用按秩求并
+	 * @param root1 不相交集合1的根
+	 * @param root2 不相交集合2的根
+	 */
+	public void union(int root1, int root2) {
+		if(s[root2]<s[root1]){
+			s[root1]=root2;
+		}else{
+			if(s[root1]==s[root2]){
+				s[root1]--;
+			}
+			s[root2]=root1;
+		}
+	}
+
+	/**
+	 * 查找方式 ：路径压缩，没有错误检查 
+	 * @param x 要查找的元素
+	 * @return x所属集合的根的值
+	 */
+	public int find(int x) {
+		if (s[x] < 0) {
+			return x;
+		} else {
+			return s[x] = find(s[x]);
+		}
+	}
+
+	public Integer[] getS() {
+		return s;
+	}
+
+	public void setS(Integer[] s) {
+		this.s = s;
+	}
+
+}

src/main/java/chapter9/mst/Kruskal.java

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+package chapter9.mst;
+
+import java.util.ArrayList;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+import java.util.PriorityQueue;
+
+/**
+ * 利用不相交集，无向图的解决最小生成树
+ * 
+ * @author wenl
+ */
+public class Kruskal {
+	Map<Integer, Vertex> graph;
+
+public List<Edge> kruskal() {
+	List<Edge> result = new ArrayList<Edge>();
+	int vertexSize = graph.values().size();
+	int acceptedEdge = 0;
+	//以点的数量构建不相交集合
+	DisjSets disjSets = new DisjSets(vertexSize);
+	//以边的权构建堆
+	PriorityQueue<Edge> priorityQueue = new PriorityQueue<Edge>(getEdges());
+	while (acceptedEdge < vertexSize - 1&&!priorityQueue.isEmpty()) {
+		Edge e = priorityQueue.poll();
+		int disv = disjSets.find(e.vnum);
+		int disw = disjSets.find(e.wnum);
+		if (disv != disw) {
+			//两个顶点不在一颗树上，合并两个顶点
+				acceptedEdge++;
+				disjSets.union(disv, disw);
+				result.add(e);
+			}
+	}
+	return result;
+}
+
+	public Map<Integer, Vertex> getGraph() {
+		return graph;
+	}
+
+	public void setGraph(Map<Integer, Vertex> graph) {
+		this.graph = graph;
+	}
+
+	public List<Edge> getEdges() {
+		List<Edge> edges = new ArrayList<Edge>();
+		for (Vertex v : graph.values()) {
+			if (v.adj != null && !v.adj.isEmpty()) {
+				for (AdjVertex adjw : v.adj) {
+					Edge edge = new Edge(v.num, adjw.w.num, adjw.cvw);
+					edges.add(edge);
+				}
+			}
+		}
+		return edges;
+	}
+
+	public static class Edge implements Comparable<Edge> {
+		Integer vnum;// 从0开始
+		Integer wnum;
+		Integer cvw;
+
+		@Override
+		public String toString() {
+			return "Edge [vnum=" + vnum + ", wnum=" + wnum + ", cvw=" + cvw + "]";
+		}
+
+		public Edge(Integer vid, Integer wid, Integer cvw) {
+			this.vnum = vid;
+			this.wnum = wid;
+			this.cvw = cvw;
+		}
+
+		@Override
+		public int compareTo(Edge o) {
+			return this.cvw.compareTo(o.cvw);
+		}
+
+	}
+
+	public static class Vertex {
+		String name;
+		Integer num;
+		List<AdjVertex> adj;
+		boolean know;
+
+		public Vertex(String name, Integer num) {
+			this.name = name;
+			this.num = num;
+		}
+
+		public List<AdjVertex> getAdj() {
+			return adj;
+		}
+
+		public void setAdj(List<AdjVertex> adj) {
+			this.adj = adj;
+		}
+
+	}
+
+	public static class AdjVertex {
+		Vertex w;
+		public int cvw;// vw边的权
+
+		public AdjVertex(Vertex w, int cvw) {
+			super();
+			this.w = w;
+			this.cvw = cvw;
+		}
+
+		public Vertex getW() {
+			return w;
+		}
+
+		public void setW(Vertex w) {
+			this.w = w;
+		}
+
+		public int getCvw() {
+			return cvw;
+		}
+
+		public void setCvw(int cvw) {
+			this.cvw = cvw;
+		}
+
+	}
+
+	public static void main(String[] args) {
+		Map<Integer, Vertex> graph = new HashMap<Integer, Vertex>();
+		Vertex v1 = new Vertex("1", 0);
+		Vertex v20 = new Vertex("20", 1);
+		Vertex v21 = new Vertex("21", 2);
+		Vertex v22 = new Vertex("22", 3);
+		Vertex v30 = new Vertex("30", 4);
+		Vertex v31 = new Vertex("31", 5);
+		Vertex v32 = new Vertex("32", 6);
+		Vertex v4 = new Vertex("4", 7);
+		List<AdjVertex> adjV1 = new ArrayList<AdjVertex>();
+		adjV1.add(new AdjVertex(v20, 1));
+		adjV1.add(new AdjVertex(v21, 3));
+		adjV1.add(new AdjVertex(v22, 1));
+		v1.setAdj(adjV1);
+		List<AdjVertex> adjV20 = new ArrayList<AdjVertex>();
+		adjV20.add(new AdjVertex(v30, 1));
+		adjV20.add(new AdjVertex(v21, 1));
+		v20.setAdj(adjV20);
+		List<AdjVertex> adjV21 = new ArrayList<AdjVertex>();
+		adjV21.add(new AdjVertex(v31, 5));
+		v21.setAdj(adjV21);
+		List<AdjVertex> adjV22 = new ArrayList<AdjVertex>();
+		adjV22.add(new AdjVertex(v32, 2));
+		v22.setAdj(adjV22);
+		List<AdjVertex> adjV30 = new ArrayList<AdjVertex>();
+		List<AdjVertex> adjV31 = new ArrayList<AdjVertex>();
+		List<AdjVertex> adjV32 = new ArrayList<AdjVertex>();
+		adjV30.add(new AdjVertex(v31, 1));
+		adjV31.add(new AdjVertex(v4, 1));
+		adjV32.add(new AdjVertex(v31, 1));
+		v30.setAdj(adjV30);
+		v31.setAdj(adjV31);
+		v32.setAdj(adjV32);
+		//
+		graph.put(v1.num, v1);
+		graph.put(v20.num, v20);
+		graph.put(v21.num, v21);
+		graph.put(v22.num, v22);
+		graph.put(v30.num, v30);
+		graph.put(v31.num, v31);
+		graph.put(v32.num, v32);
+		graph.put(v4.num, v4);
+		Kruskal kruskal = new Kruskal();
+		kruskal.setGraph(graph);
+		PriorityQueue<Edge> priorityQueue = new PriorityQueue<Edge>(kruskal.getEdges());
+		while (!priorityQueue.isEmpty()) {
+			Edge e=priorityQueue.poll();
+			System.out.println(graph.get(e.vnum).name + ":" + graph.get(e.wnum).name + " weight:" + e.cvw);
+		}
+		System.out.println("================================================");
+		List<Edge> edge = kruskal.kruskal();
+		System.out.println("================================================");
+		for (Edge e : edge) {
+			System.out.println(graph.get(e.vnum).name + ":" + graph.get(e.wnum).name + " weight:" + e.cvw);
+		}
+	}
+}