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[Function add]
1.Add the function of DirectEdge and EdgeWeightDigraph.
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Diff for: ‎Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/spt/DirectedEdge.java

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package ca.mcmaster.chapter.four.graph.spt;
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public class DirectedEdge {
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private final int v; //边的起始点
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private final int w; //边的指向
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private final double weight; //有向边的权重
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public DirectedEdge(int v, int w, double weight){
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this.v = v;
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this.w = w;
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this.weight = weight;
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}
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public double weight(){ return weight; }
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public int from(){ return this.v; }
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public int to(){ return this.w; }
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@Override
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public String toString() {
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return String.format("%d -> %d %.2f", v, w, weight);
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}
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}

Diff for: ‎Algorithm(4th_Edition)/src/ca/mcmaster/chapter/four/graph/spt/EdgeWeightedDigraph.java

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package ca.mcmaster.chapter.four.graph.spt;
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import java.io.FileInputStream;
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import java.util.Scanner;
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import ca.mcmaster.chapter.one.bag.Bag;
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import ca.mcmaster.chapter.one.bag.ListBag;
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public class EdgeWeightedDigraph {
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private final int V; //Number of vertex.
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private int E; //Number of edges.
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private Bag<DirectedEdge>[] adj; //Adjacency list
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(int V){
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this.V = V;
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this.E = 0;
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for(int i = 0; i < V; i++)
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adj[i] = new ListBag<>();
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}
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(FileInputStream in) {
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Scanner s = null;
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s = new Scanner(in);
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this.V = s.nextInt();
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this.E = s.nextInt();
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for (int i = 0; i < V; i++)
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adj[i] = new ListBag<DirectedEdge>();
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for(int i = 0; i < E; i ++){
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int v = s.nextInt();
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int w = s.nextInt();
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double weight = s.nextDouble();
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addEdge(v, w, weight);
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}
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s.close();
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}
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public int V() { return this.V; }
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public int E() { return this.E; }
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public void addEdge(int v, int w, double weight) {
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adj[v].add(new DirectedEdge(v, w, weight));
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this.E ++;
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}
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public Iterable<DirectedEdge> adj(int v) {
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return adj[v];
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}
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public void display() {
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for(int i = 0; i < V; i++){
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StringBuilder sb = new StringBuilder(i + ": ");
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for(DirectedEdge e : adj[i]){
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sb.append(e.to() + "|");
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}
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System.out.println(sb.toString());
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}
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}
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}

Diff for: ‎DataStructrue/Graph/DirectedEdge.java

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package ca.mcmaster.chapter.four.graph.spt;
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public class DirectedEdge {
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private final int v; //边的起始点
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private final int w; //边的指向
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private final double weight; //有向边的权重
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public DirectedEdge(int v, int w, double weight){
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this.v = v;
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this.w = w;
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this.weight = weight;
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}
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public double weight(){ return weight; }
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public int from(){ return this.v; }
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public int to(){ return this.w; }
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@Override
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public String toString() {
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return String.format("%d -> %d %.2f", v, w, weight);
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}
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}

Diff for: ‎DataStructrue/Graph/EdgeWeightedDigraph.java

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package ca.mcmaster.chapter.four.graph.spt;
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import java.io.FileInputStream;
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import java.util.Scanner;
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import ca.mcmaster.chapter.one.bag.Bag;
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import ca.mcmaster.chapter.one.bag.ListBag;
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public class EdgeWeightedDigraph {
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private final int V; //Number of vertex.
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private int E; //Number of edges.
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private Bag<DirectedEdge>[] adj; //Adjacency list
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(int V){
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this.V = V;
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this.E = 0;
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for(int i = 0; i < V; i++)
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adj[i] = new ListBag<>();
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}
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(FileInputStream in) {
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Scanner s = null;
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s = new Scanner(in);
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this.V = s.nextInt();
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this.E = s.nextInt();
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for (int i = 0; i < V; i++)
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adj[i] = new ListBag<DirectedEdge>();
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for(int i = 0; i < E; i ++){
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int v = s.nextInt();
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int w = s.nextInt();
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double weight = s.nextDouble();
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addEdge(v, w, weight);
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}
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s.close();
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}
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public int V() { return this.V; }
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public int E() { return this.E; }
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public void addEdge(int v, int w, double weight) {
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adj[v].add(new DirectedEdge(v, w, weight));
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this.E ++;
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}
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public Iterable<DirectedEdge> adj(int v) {
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return adj[v];
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}
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public void display() {
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for(int i = 0; i < V; i++){
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StringBuilder sb = new StringBuilder(i + ": ");
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for(DirectedEdge e : adj[i]){
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sb.append(e.to() + "|");
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}
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System.out.println(sb.toString());
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}
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}
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}

Diff for: ‎DataStructrue/Graph/ShortestPath.md

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# Shortest Path
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> 找到从一个顶点到达另一个顶点的成本的最小路径。
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> 在一幅加权有向图中，从顶点s到顶点t的最短路径是从所有从s到t的路径中最小权重者。
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### 最短路径的性质
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1. 路径是有向的。最短路径需要考虑到各边的方向。
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2. 权重不一定等价距离，和最小树相似，可以理解为成本的最小值。
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3. 并不是所有顶点都是可达的。为了简化问题，我们的样图都是强连通的（从每个顶点到另一个顶点都是可达的）。
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4. 负权重会使问题更复杂，我们假设边的权重都是正的。
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5. 最短路径一般都是简单的。忽略构成环的零权重边。
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6. 最短路径不一定是唯一的。
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7. 可能存在平行边或自环。
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### 最短路径树（Shortest Path Tree）
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> 给定一幅加权有向图和一个顶点s，以s为起点的一棵最短路径树是图的一幅子图，它包含s和从s可到达的所有顶点。这棵树的根节点为s，树的每条路径都是有向图中的一条最短路径。
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#### Directed Edge 有向边对象
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```Java
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public class DirectedEdge {
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private final int v; //边的起始点
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private final int w; //边的指向
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private final double weight; //有向边的权重
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public DirectedEdge(int v, int w, double weight){
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this.v = v;
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this.w = w;
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this.weight = weight;
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}
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public double weight(){ return weight; }
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public int from(){ return this.v; }
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public int to(){ return this.w; }
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@Override
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public String toString() {
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return String.format("%d -> %d %.2f", v, w, weight);
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}
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}
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```
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#### EdgeWeightDigraph 加权有向图
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```Java
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public class EdgeWeightedDigraph {
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private final int V; //Number of vertex.
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private int E; //Number of edges.
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private Bag<DirectedEdge>[] adj; //Adjacency list
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(int V){
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this.V = V;
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this.E = 0;
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for(int i = 0; i < V; i++)
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adj[i] = new ListBag<>();
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}
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@SuppressWarnings("unchecked")
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public EdgeWeightedDigraph(FileInputStream in) {
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Scanner s = null;
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s = new Scanner(in);
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this.V = s.nextInt();
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this.E = s.nextInt();
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adj = (Bag<DirectedEdge>[])new Bag[V];
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for (int i = 0; i < V; i++)
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adj[i] = new ListBag<DirectedEdge>();
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for(int i = 0; i < E; i ++){
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int v = s.nextInt();
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int w = s.nextInt();
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double weight = s.nextDouble();
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addEdge(v, w, weight);
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}
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s.close();
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}
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public int V() { return this.V; }
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public int E() { return this.E; }
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public void addEdge(int v, int w, double weight) {
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adj[v].add(new DirectedEdge(v, w, weight));
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this.E ++;
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}
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public Iterable<DirectedEdge> adj(int v) {
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return adj[v];
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}
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public void display() {
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for(int i = 0; i < V; i++){
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StringBuilder sb = new StringBuilder(i + ": ");
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for(DirectedEdge e : adj[i]){
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sb.append(e.to() + "|");
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}
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System.out.println(sb.toString());
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}
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}
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}
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```

Diff for: ‎README.md

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1. [Undirected Graph](https://github.com/Seanforfun/Algorithm/blob/master/DataStructrue/Graph/UndirectedGraph.md)
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2. [Directed Graph](https://github.com/Seanforfun/Algorithm/blob/master/DataStructrue/Graph/DirectedGraph.md)
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3. [Minimun Spanning Trees](https://github.com/Seanforfun/Algorithm/blob/master/DataStructrue/Graph/MinimumSpanningTrees.md)
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4. [Shortest Path](https://github.com/Seanforfun/Algorithm/blob/master/DataStructrue/Graph/ShortestPath.md)
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## LeetCode
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This part I listed my [leetcode solutions](https://github.com/Seanforfun/Algorithm/tree/master/leetcode).

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