[Function add]

1.Add Prim algorithm for finding minimum spanning tree.

Author: Seanforfun

Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/mstree/EdgeWeightedGraph.java

@@ -61,7 +61,7 @@ public Iterable<Edge> edges(){
 		return res;
 	}
 	public static void main(String[] args) throws FileNotFoundException {
-		FileInputStream is = new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/mstree/tinyEWG.txt"));
+		FileInputStream is = new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/mstree/mediumEWG.txt"));
 		EdgeWeightedGraph graph = new EdgeWeightedGraph(is);
 		Iterable<Edge> edges = graph.edges();
 		for(Edge e : edges)

Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/mstree/LazyPrimMST.java

@@ -0,0 +1,55 @@
+package ca.mcmaster.chapter.four.graph.mstree;
+
+import java.io.File;
+import java.io.FileInputStream;
+import java.io.FileNotFoundException;
+import java.util.LinkedList;
+import java.util.PriorityQueue;
+import java.util.Queue;
+
+public class LazyPrimMST implements MST {
+	private final EdgeWeightedGraph g;
+	private PriorityQueue<Edge> pq;
+	private Queue<Edge> mst;	//minimum spanning tree
+	private final boolean[] marked;	//If current vertex is in the tree
+	public LazyPrimMST(EdgeWeightedGraph g){
+		this.g = g;
+		marked = new boolean[g.V()];
+		pq = new PriorityQueue<>();
+		mst = new LinkedList<Edge>();
+		visit(g, 0);
+		while(!pq.isEmpty()){
+			Edge edge = pq.poll();	//get the smallest edge from the graph
+			int v = edge.either(); int w = edge.other(v);
+			if(marked[v] && marked[w]) continue;	//both vertexs are in the mst
+			mst.offer(edge);
+			if(!marked[v]) visit(g, v);
+			if(!marked[w]) visit(g, w);
+		}
+	}
+	@Override
+	public Iterable<Edge> edges() {
+		return mst;
+	}
+	@Override
+	public double weight() {
+		double res = 0d;
+		for(Edge e : mst)
+			res += e.weight();
+		return res;
+	}
+	private void visit(EdgeWeightedGraph g, int v){
+		marked[v] = true;
+		for(Edge e : g.adj(v))
+			if(!marked[e.other(v)]) pq.add(e);
+	}
+	public static void main(String[] args) throws FileNotFoundException {
+		FileInputStream is = new FileInputStream(new File("src/ca/mcmaster/chapter/four/graph/mstree/mediumEWG.txt"));
+		EdgeWeightedGraph graph = new EdgeWeightedGraph(is);
+		LazyPrimMST mst = new LazyPrimMST(graph);
+		Iterable<Edge> edges = mst.edges();
+		for(Edge e : edges)
+			System.out.println(e.toString());
+		System.out.println("Weight: " + mst.weight());
+	}
+}

Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/mstree/MST.java

@@ -0,0 +1,14 @@
+package ca.mcmaster.chapter.four.graph.mstree;
+
+public interface MST {
+	/**
+	 * @Description: Find the edges on the minimum spanning tree.
+	 * @return
+	 */
+	public Iterable<Edge> edges();
+	/**
+	 * @Description: Return the total weight of the tree.
+	 * @return
+	 */
+	public double weight();
+}