[Function add]

1.Prim MST algorithm.

Author: Seanforfun

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

@@ -0,0 +1,43 @@
+package ca.mcmaster.chapter.four.graph.mstree;
+
+import edu.princeton.cs.algs4.IndexMinPQ;
+
+public class PrimMst implements MST {
+	private Edge[] edgeTo;
+	private double[] distTo;
+	private boolean[] marked;
+	private IndexMinPQ<Double> pq;
+	public PrimMst(EdgeWeightedGraph g) {
+		edgeTo = new Edge[g.V()];
+		distTo = new double[g.V()];
+		marked = new boolean[g.V()];
+		for(int i = 0; i < g.V(); i++){
+			distTo[i] = Double.POSITIVE_INFINITY;
+		}
+		pq = new IndexMinPQ<Double>(g.V());
+		distTo[0] = 0.0d;
+		while(!pq.isEmpty())
+			visit(g, pq.delMin());
+	}
+	private void visit(EdgeWeightedGraph g, int v){	//当前的顶点不在最小树中
+		marked[v] = true;
+		for(Edge e : g.adj(v)){	//遍历连接这个顶点的所有边
+			int w = e.other(v);		//找到这些边中除了v的另一个顶点
+			if(marked[w]) continue;	//v-w已经在树中，失效
+			if(e.weight() < distTo[w]){	//判断是不是可以替代
+				edgeTo[w] = e;
+				distTo[w] = e.weight();
+				if(pq.contains(w)) pq.change(w, distTo[w]);
+				else pq.insert(w, distTo[w]);
+			}
+		}
+	}
+	@Override
+	public Iterable<Edge> edges() {
+		return null;
+	}
+	@Override
+	public double weight() {
+		return 0;
+	}
+}

DataStructrue/Graph/MinimumSpanningTrees.md

@@ -141,6 +141,7 @@ public interface MST {
 ![Prim轨迹](https://i.imgur.com/mURZUQo.jpg)
 
 * Prim实现类
+	* LazyPrim
 ```Java
 public class LazyPrimMST implements MST {
 	private final EdgeWeightedGraph g;
@@ -188,4 +189,39 @@ public class LazyPrimMST implements MST {
 		System.out.println("Weight: " + mst.weight());
 	}
 }
+```
+	* 即时Prim
+	![即时Prim](https://i.imgur.com/2WX62dl.jpg)
+```Java
+public class PrimMst implements MST {
+	private Edge[] edgeTo;
+	private double[] distTo;
+	private boolean[] marked;
+	private IndexMinPQ<Double> pq;
+	public PrimMst(EdgeWeightedGraph g) {
+		edgeTo = new Edge[g.V()];
+		distTo = new double[g.V()];
+		marked = new boolean[g.V()];
+		for(int i = 0; i < g.V(); i++){
+			distTo[i] = Double.POSITIVE_INFINITY;
+		}
+		pq = new IndexMinPQ<Double>(g.V());
+		distTo[0] = 0.0d;
+		while(!pq.isEmpty())	//一定会访问到所有的顶点
+			visit(g, pq.delMin());	//将所有的有效横切边从队列中读取出来。
+	}
+	private void visit(EdgeWeightedGraph g, int v){	//当前的顶点不在最小树中
+		marked[v] = true;
+		for(Edge e : g.adj(v)){	//遍历连接这个顶点的所有边
+			int w = e.other(v);		//找到这些边中除了v的另一个顶点
+			if(marked[w]) continue;	//v-w已经在树中，失效
+			if(e.weight() < distTo[w]){	//判断是不是可以替代
+				edgeTo[w] = e;
+				distTo[w] = e.weight();
+				if(pq.contains(w)) pq.change(w, distTo[w]);
+				else pq.insert(w, distTo[w]);
+			}
+		}
+	}
+}
 ```

DataStructrue/Graph/PrimMst.java

@@ -0,0 +1,43 @@
+package ca.mcmaster.chapter.four.graph.mstree;
+
+import edu.princeton.cs.algs4.IndexMinPQ;
+
+public class PrimMst implements MST {
+	private Edge[] edgeTo;
+	private double[] distTo;
+	private boolean[] marked;
+	private IndexMinPQ<Double> pq;
+	public PrimMst(EdgeWeightedGraph g) {
+		edgeTo = new Edge[g.V()];
+		distTo = new double[g.V()];
+		marked = new boolean[g.V()];
+		for(int i = 0; i < g.V(); i++){
+			distTo[i] = Double.POSITIVE_INFINITY;
+		}
+		pq = new IndexMinPQ<Double>(g.V());
+		distTo[0] = 0.0d;
+		while(!pq.isEmpty())
+			visit(g, pq.delMin());
+	}
+	private void visit(EdgeWeightedGraph g, int v){	//当前的顶点不在最小树中
+		marked[v] = true;
+		for(Edge e : g.adj(v)){	//遍历连接这个顶点的所有边
+			int w = e.other(v);		//找到这些边中除了v的另一个顶点
+			if(marked[w]) continue;	//v-w已经在树中，失效
+			if(e.weight() < distTo[w]){	//判断是不是可以替代
+				edgeTo[w] = e;
+				distTo[w] = e.weight();
+				if(pq.contains(w)) pq.change(w, distTo[w]);
+				else pq.insert(w, distTo[w]);
+			}
+		}
+	}
+	@Override
+	public Iterable<Edge> edges() {
+		return null;
+	}
+	@Override
+	public double weight() {
+		return 0;
+	}
+}