十六、图的遍历（深度，广度）

1. 深度优先搜索介绍

图的深度优先搜索(Depth First Search)，和树的先序遍历比较类似。

它的思想：假设初始状态是图中所有顶点均未被访问，则从某个顶点v出发，首先访问该顶点，然后依次从它的各个未被访问的邻接点出发深度优先搜索遍历图，直至图中所有和v有路径相通的顶点都被访问到。 若此时尚有其他顶点未被访问到，则另选一个未被访问的顶点作起始点，重复上述过程，直至图中所有顶点都被访问到为止。

显然，深度优先搜索是一个递归的过程。

2. 深度优先搜索图解

2.1 无向图的深度优先搜索

下面以"无向图"为例，来对深度优先搜索进行演示。

对上面的图G1进行深度优先遍历，从顶点A开始。

第1步：访问A。 
第2步：访问(A的邻接点)C。 
    在第1步访问A之后，接下来应该访问的是A的邻接点，即"C,D,F"中的一个。但在本文的实现中，顶点ABCDEFG是按照顺序存储，C在"D和F"的前面，因此，先访问C。 
第3步：访问(C的邻接点)B。 
    在第2步访问C之后，接下来应该访问C的邻接点，即"B和D"中一个(A已经被访问过，就不算在内)。而由于B在D之前，先访问B。 
第4步：访问(C的邻接点)D。 
    在第3步访问了C的邻接点B之后，B没有未被访问的邻接点；因此，返回到访问C的另一个邻接点D。 
第5步：访问(A的邻接点)F。 
    前面已经访问了A，并且访问完了"A的邻接点B的所有邻接点(包括递归的邻接点在内)"；因此，此时返回到访问A的另一个邻接点F。 
第6步：访问(F的邻接点)G。 
第7步：访问(G的邻接点)E。

因此访问顺序是：A -> C -> B -> D -> F -> G -> E

邻接矩阵：

class StackX
{
    private  int maxSize ;
    private int[] st;
    private int top;
    
    public StackX(int s)
    {
        maxSize = s;
        st = new int[maxSize];
        top = -1;
    }
    public void push(int j)
    {
        st[++top] = j;
    }
    public int pop()
    {
        return st[top--];
    }
    public  int peek()
    {
        return st[top];
    }
    public boolean isEmpty()
    {
        return (top==-1);
    }
}

class Vertex
{
    public char label;
    public boolean wasVisited;
    public Vertex(char lab)
    {
        label = lab;
        wasVisited = false;
    }
}

class UDGraph
{
    private final int MAX_VERTS = 20;
    private Vertex vertexList[];
    private int adjMat[][];
    private int nVerts;
    private StackX theStack;
    
    public UDGraph()
    {//无向图
        vertexList = new Vertex[MAX_VERTS];
        adjMat = new int[MAX_VERTS][MAX_VERTS];
        nVerts = 0;
        for(int i=0;i<MAX_VERTS;i++)
            for(int j=0;j<MAX_VERTS;j++)
                adjMat[i][j] = 0;
        theStack = new StackX(MAX_VERTS);
    }
    
    public void addVertex(char lab)
    {
        vertexList[nVerts++] = new Vertex(lab);
    }
    
    public void addEdge(int start,int end)
    {
        adjMat[start][end] = 1;
        adjMat[end][start] = 1;//无向图
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    public void dfs() 
    {
        vertexList[0].wasVisited = true;
        displayVertex(0);
        theStack.push(0);
        while(!theStack.isEmpty())
        {
            int v = getAdjUnvisitedVertex(theStack.peek());
            if(v == -1)
                theStack.pop();
            else
　　　　　　  {
                vertexList[v].wasVisited = true;
                displayVertex(v);
                theStack.push(v);
            }
        }
        for(int j=0;j<nVerts;j++)
            vertexList[j].wasVisited = false;
    }
    
    public int getAdjUnvisitedVertex(int v)
    {
        for(int j=0;j<nVerts;j++)
            if(adjMat[v][j]==1 && vertexList[j].wasVisited==false)
                return j;
        return -1;
    }

}
public class MatrixUDG_DFS
{
    public static void main(String[] args) 
    {
          UDGraph theGraph = new UDGraph();
          theGraph.addVertex('A');    // 0  (start for mst)
          theGraph.addVertex('B');    // 1
          theGraph.addVertex('C');    // 2
          theGraph.addVertex('D');    // 3
          theGraph.addVertex('E');    // 4

          theGraph.addEdge(0, 1);     // AB
          theGraph.addEdge(0, 2);     // AC
          theGraph.addEdge(0, 3);     // AD
          theGraph.addEdge(0, 4);     // AE
          theGraph.addEdge(1, 2);     // BC
          theGraph.addEdge(1, 3);     // BD
          theGraph.addEdge(1, 4);     // BE
          theGraph.addEdge(2, 3);     // CD
          theGraph.addEdge(2, 4);     // CE
          theGraph.addEdge(3, 4);     // DE

          System.out.println("dbs");
          theGraph.dfs();
    }
}

邻接链表： 

import java.util.ArrayList;
class StackX
{
    private  int maxSize ;
    private Vertex[] st;
    private int top;
    
    public StackX(int s)
    {
        maxSize = s;
        st = new Vertex[maxSize];
        top = -1;
    }
    public void push(Vertex vertex)
    {
        st[++top] = vertex;
    }
    public Vertex pop()
    {
        return st[top--];
    }
    public  Vertex peek()
    {
        return st[top];
    }
    public boolean isEmpty()
    {
        return (top==-1);
    }
}


class Vertex
{
    public char label;
    public boolean wasVisited;
    public Edge firstEdge;
    
    public Vertex(char lab)
    {
        this.label = lab;
        this.wasVisited = false;
        firstEdge = null;
    }
}

class Edge
{
    public int dest;
    public Edge nextEdge;
    public Edge(int dest)
    {
        this.dest= dest;
        nextEdge = null;
    }
}

class UDGraph
{
    private final int MAX_VERTS = 20;//图的最大顶点数
    private int nVerts = 0;//当前顶点数
    private Vertex vertexList[];//顶点链表
    private StackX theStack;
    private ArrayList<Vertex> dfs;
    
    public UDGraph()
    {
        vertexList = new Vertex[MAX_VERTS];    
        theStack = new StackX(20);
        dfs = new ArrayList<Vertex>();
    }
    
    public void addVertex(Vertex vertex)
    {
        //vertex.indexId = nVerts;
        vertexList[nVerts++] = vertex;
    }
    
    public void addEdge(int start,int end)
    {
        Edge startEdge = new Edge(start);
        Edge endEdge = new Edge(end);
        Edge edge2 = vertexList[start].firstEdge;
        if(edge2==null)
        {
            vertexList[start].firstEdge = endEdge;
        }else
　　　　  {
            while(edge2.nextEdge!=null)
                edge2 = edge2.nextEdge;
            edge2.nextEdge = endEdge;
         }
        Edge edge3 = vertexList[end].firstEdge;
        if(edge3==null)
        {
            vertexList[end].firstEdge = startEdge;
        }else
         {
            while(edge3.nextEdge!=null)
                edge3 = edge3.nextEdge;
            edge3.nextEdge = startEdge;
         }
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    //返回顶点v的一个邻接点并且是未访问过的
    public Vertex getAdjUnvisitedVertex(Vertex vertex)
    {
        Edge currentEdge = vertex.firstEdge;
        while(currentEdge != null )
　　　　 {
            if(!vertexList[currentEdge.dest].wasVisited)
                return vertexList[currentEdge.dest];
            currentEdge = currentEdge.nextEdge;
        }

        return null;
    }
    
    public void dfs()
    {
        vertexList[0].wasVisited = true;
        dfs.add(vertexList[0]);
        theStack.push(vertexList[0]);
        Vertex vertex;
        while(!theStack.isEmpty())
　　　　 {
            vertex = getAdjUnvisitedVertex(theStack.peek());
            if(vertex == null)
                theStack.pop();
            else
　　　　　　  {
                vertex.wasVisited = true;
                dfs.add(vertex);
                theStack.push(vertex);
            }
        }
        
        //遍历完成，清楚所有访问标志位
        for(int i=0;i<nVerts;i++)
            vertexList[i].wasVisited = false;
    }
    
    public void displayDFS()
　　{
        for(int i=0;i<dfs.size();i++)
            System.out.print(dfs.get(i).label);
        System.out.println("");
    }   
}

public class ListUDG_DFS2 
{
    public static void main(String[] args) 
    {
        UDGraph theGraph = new UDGraph();
        theGraph.addVertex(new Vertex('A'));
        theGraph.addVertex(new Vertex('B'));
        theGraph.addVertex(new Vertex('C'));
        theGraph.addVertex(new Vertex('D'));
        theGraph.addVertex(new Vertex('E'));
        theGraph.addVertex(new Vertex('F'));
        theGraph.addVertex(new Vertex('G'));
        
        theGraph.addEdge(0, 1); //AB
        theGraph.addEdge(0, 2); //AC
        theGraph.addEdge(0, 3); //AD
        theGraph.addEdge(1, 4); //BE
        theGraph.addEdge(2, 5); //CF
        theGraph.addEdge(3, 4); //DE
        theGraph.addEdge(1, 6); //BG
        theGraph.addEdge(3, 5);

        System.out.println("dbs");
        theGraph.dfs();
        theGraph.displayDFS();
    }
}

2.2 有向图的深度优先搜索

下面以"有向图"为例，来对深度优先搜索进行演示。

对上面的图G2进行深度优先遍历，从顶点A开始。

第1步：访问A。 
第2步：访问B。 
    在访问了A之后，接下来应该访问的是A的出边的另一个顶点，即顶点B。 
第3步：访问C。 
    在访问了B之后，接下来应该访问的是B的出边的另一个顶点，即顶点C,E,F。在本文实现的图中，顶点ABCDEFG按照顺序存储，因此先访问C。 
第4步：访问E。 
    接下来访问C的出边的另一个顶点，即顶点E。 
第5步：访问D。 
    接下来访问E的出边的另一个顶点，即顶点B,D。顶点B已经被访问过，因此访问顶点D。 
第6步：访问F。 
    接下应该回溯"访问A的出边的另一个顶点F"。 
第7步：访问G。

因此访问顺序是：A -> B -> C -> E -> D -> F -> G

邻接矩阵：

class StackX
{
    private  int maxSize ;
    private int[] st;
    private int top;
    
    public StackX(int s)
    {
        maxSize = s;
        st = new int[maxSize];
        top = -1;
    }
    public void push(int j)
    {
        st[++top] = j;
    }
    public int pop()
    {
        return st[top--];
    }
    public  int peek()
    {
        return st[top];
    }
    public boolean isEmpty()
    {
        return (top==-1);
    }
}

class Vertex
{
    public char label;
    public boolean wasVisited;
    public Vertex(char lab)
    {
        label = lab;
        wasVisited = false;
    }
}

class DGraph
{
    private final int MAX_VERTS = 20;
    private Vertex vertexList[];
    private int adjMat[][];
    private int nVerts;
    private StackX theStack;
    
    public DGraph()
    {
        vertexList = new Vertex[MAX_VERTS];
        adjMat = new int[MAX_VERTS][MAX_VERTS];
        nVerts = 0;
        for(int i=0;i<MAX_VERTS;i++)
            for(int j=0;j<MAX_VERTS;j++)
                adjMat[i][j] = 0;
        theStack = new StackX(MAX_VERTS);
    }
    
    public void addVertex(char lab)
    {
        vertexList[nVerts++] = new Vertex(lab);
    }
    
    public void addEdge(int start,int end)
    {
        adjMat[start][end] = 1;
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    public void dfs()
    {
        vertexList[0].wasVisited = true;
        displayVertex(0);
        theStack.push(0);
        while(!theStack.isEmpty())
        {
            int v = getAdjUnvisitedVertex(theStack.peek());
            if(v == -1)
                theStack.pop();
            else
            {
                vertexList[v].wasVisited = true;
                displayVertex(v);
                theStack.push(v);
            }
        }
        for(int j=0;j<nVerts;j++)
            vertexList[j].wasVisited = false;
    }
    
    public int getAdjUnvisitedVertex(int v)
    {
        for(int j=0;j<nVerts;j++)
            if(adjMat[v][j]==1 && vertexList[j].wasVisited==false)
                return j;
        return -1;
    }

}
public class MatrixDG_DFS 
{
    public static void main(String[] args) 
    {
          DGraph theGraph = new DGraph();
          theGraph.addVertex('A');    // 0  (start for mst)
          theGraph.addVertex('B');    // 1
          theGraph.addVertex('C');    // 2
          theGraph.addVertex('D');    // 3
          theGraph.addVertex('E');    // 4

          theGraph.addEdge(0, 1);     // AB
          theGraph.addEdge(0, 2);     // AC
          theGraph.addEdge(1, 3);     // BD
          theGraph.addEdge(1, 4);     // BE
          theGraph.addEdge(2, 3);     // CD
          theGraph.addEdge(4, 2);

          System.out.println("dbs");
          theGraph.dfs();
    }
}

邻接链表 ：

import java.util.ArrayList;
class StackX
{
    private  int maxSize ;
    private Vertex[] st;
    private int top;
    
    public StackX(int s)
    {
        maxSize = s;
        st = new Vertex[maxSize];
        top = -1;
    }
    public void push(Vertex vertex)
    {
        st[++top] = vertex;
    }
    public Vertex pop()
    {
        return st[top--];
    }
    public  Vertex peek()
    {
        return st[top];
    }
    public boolean isEmpty()
    {
        return (top==-1);
    }
}


class Vertex
{
    public char label;
    public boolean wasVisited;
    public Edge firstEdge;
    
    public Vertex(char lab)
    {
        this.label = lab;
        this.wasVisited = false;
        firstEdge = null;
    }
}

class Edge
{
    public int dest;
    public Edge nextEdge;
    public Edge(int dest)
    {
        this.dest= dest;
        nextEdge = null;
    }
}

class DGraph
{
    private final int MAX_VERTS = 20;//图的最大顶点数
    private int nVerts = 0;//当前顶点数
    private Vertex vertexList[];//顶点链表
    private StackX theStack;
    private ArrayList<Vertex> dfs;
    
    public DGraph()
    {
        vertexList = new Vertex[MAX_VERTS];    
        theStack = new StackX(20);
        dfs = new ArrayList<Vertex>();
    }
    
    public void addVertex(Vertex vertex)
    {
        //vertex.indexId = nVerts;
        vertexList[nVerts++] = vertex;
    }
    
    public void addEdge(int start,int end)
    {
        Edge endEdge = new Edge(end);
        Edge currentEdge = vertexList[start].firstEdge;
        if(currentEdge==null)
        {
            vertexList[start].firstEdge = endEdge;
        }else
　　　　  {
            while(currentEdge.nextEdge!=null)
                currentEdge = currentEdge.nextEdge;
            currentEdge.nextEdge = endEdge;
        }
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    //返回顶点v的一个邻接点并且是未访问过的
    public Vertex getAdjUnvisitedVertex(Vertex vertex)
    {
        Edge currentEdge = vertex.firstEdge;
        while(currentEdge != null )
        {
            if(!vertexList[currentEdge.dest].wasVisited)
                return vertexList[currentEdge.dest];
            currentEdge = currentEdge.nextEdge;
        }
        return null;
    }
    
    public void dfs()
    {
        vertexList[0].wasVisited = true;
        dfs.add(vertexList[0]);
        theStack.push(vertexList[0]);
        Vertex vertex;
        while(!theStack.isEmpty())
        {
            vertex = getAdjUnvisitedVertex(theStack.peek());
            if(vertex == null)
                theStack.pop();
            else
　　　　　　　{
                vertex.wasVisited = true;
                dfs.add(vertex);
                theStack.push(vertex);
            }
        }
        
        //遍历完成，清楚所有访问标志位
        for(int i=0;i<nVerts;i++)
            vertexList[i].wasVisited = false;
    }
    
    public void displayDFS()
    {
        for(int i=0;i<dfs.size();i++)
            System.out.print(dfs.get(i).label);
        System.out.println("");
    }
    
}

public class ListDG_DFS 
{
    public static void main(String[] args) 
    {
        DGraph theGraph = new DGraph();
        theGraph.addVertex(new Vertex('A'));
        theGraph.addVertex(new Vertex('B'));
        theGraph.addVertex(new Vertex('C'));
        theGraph.addVertex(new Vertex('D'));
        theGraph.addVertex(new Vertex('E'));
        theGraph.addVertex(new Vertex('F'));
        theGraph.addVertex(new Vertex('G'));
        
        theGraph.addEdge(0, 1); //AB
        theGraph.addEdge(0, 2); //AC
        theGraph.addEdge(0, 3); //AD
        theGraph.addEdge(1, 4); //BE
        theGraph.addEdge(2, 5); //CF
        theGraph.addEdge(3, 4); //DE
        theGraph.addEdge(1, 6); //BG
        theGraph.addEdge(3, 5); //DF

        System.out.println("dbs");
        theGraph.dfs();
        theGraph.displayDFS();
    }
}

广度优先搜索的图文介绍

1. 广度优先搜索介绍

广度优先搜索算法(Breadth First Search)，又称为"宽度优先搜索"或"横向优先搜索"，简称BFS。

它的思想是：从图中某顶点v出发，在访问了v之后依次访问v的各个未曾访问过的邻接点，然后分别从这些邻接点出发依次访问它们的邻接点，并使得“先被访问的顶点的邻接点先于后被访问的顶点的邻接点被访问，直至图中所有已被访问的顶点的邻接点都被访问到。如果此时图中尚有顶点未被访问，则需要另选一个未曾被访问过的顶点作为新的起始点，重复上述过程，直至图中所有顶点都被访问到为止。

换句话说，广度优先搜索遍历图的过程是以v为起点，由近至远，依次访问和v有路径相通且路径长度为1,2...的顶点。

2. 广度优先搜索图解

2.1 无向图的广度优先搜索

下面以"无向图"为例，来对广度优先搜索进行演示。还是以上面的图G1为例进行说明。

第1步：访问A。 
第2步：依次访问C,D,F。 
    在访问了A之后，接下来访问A的邻接点。前面已经说过，在本文实现中，顶点ABCDEFG按照顺序存储的，C在"D和F"的前面，因此，先访问C。再访问完C之后，再依次访问D,F。 
第3步：依次访问B,G。 
    在第2步访问完C,D,F之后，再依次访问它们的邻接点。首先访问C的邻接点B，再访问F的邻接点G。 
第4步：访问E。 
    在第3步访问完B,G之后，再依次访问它们的邻接点。只有G有邻接点E，因此访问G的邻接点E。

因此访问顺序是：A -> C -> D -> F -> B -> G -> E

邻接矩阵：

class Queue
{
   private final  int maxSize;
   private int[] queArray;
   private int front;
   private int rear;

   public Queue(int s)  
   {
      maxSize = s;
      queArray = new int[maxSize];
      front = rear = 0;
    }

   public boolean insert(int j) 
   {
      if(isFull())     
         return false;
      else
      {
            queArray[rear] = j;
            rear=(rear+1)%maxSize;
             return true;
       }        
   }

   public int remove()   
   {
      if(isEmpty())
          return -1;
      else
      {
          int value = queArray[front];
          front = (front+1)%maxSize;
           return value;
       }
   }

   public int peekFront() 
   {
      if(!isEmpty())
          return queArray[front];
      else
          return -1;
   }

   public boolean isEmpty()  
   {
       return (front==rear);
   }

   public boolean isFull()  
   {
       return (front==(rear+1)%maxSize);
   }
}  


class Vertex
{
    public char label;
    public boolean wasVisited;
    public Vertex(char lab)
    {
        label = lab;
        wasVisited = false;
    }
}

class UDGraph
{
    private final int MAX_VERTS = 20;
    private Vertex vertexList[];
    private int adjMat[][];
    private int nVerts;
    private Queue theQueue;
    
    public UDGraph()
    {
        vertexList = new Vertex[MAX_VERTS];
        adjMat = new int[MAX_VERTS][MAX_VERTS];
        nVerts = 0;
        for(int i=0;i<MAX_VERTS;i++)
            for(int j=0;j<MAX_VERTS;j++)
                adjMat[i][j] = 0;
        theQueue = new Queue(MAX_VERTS);
    }
    
    public void addVertex(char lab)
    {
        vertexList[nVerts++] = new Vertex(lab);
    }
    
    public void addEdge(int start,int end)
    {
        adjMat[start][end] = 1;
        adjMat[end][start] = 1;//无向图
    }
    
    public void displayVertex(int v){
        System.out.println(vertexList[v].label);
    }
    
    public void bfs(){
         vertexList[0].wasVisited = true;
         displayVertex(0);
         theQueue.insert(0);
         int v2;
         while(!theQueue.isEmpty())
         {
             int v1 = theQueue.remove();
             while((v2 = getAdjUnvisitedVertex(v1)) != -1)
             {
                 vertexList[v2].wasVisited = true;
                 displayVertex(v2);
                 theQueue.insert(v2);
             }
         }
         for(int j=0;j<nVerts;j++)
             vertexList[j].wasVisited = false;
    }
    
    
    
    public int getAdjUnvisitedVertex(int v)
    {
        for(int j=0;j<nVerts;j++)
            if(adjMat[v][j]==1 && vertexList[j].wasVisited==false)
                return j;
        return -1;
    }

}
public class MatrixUDG_BFS 
{
    public static void main(String[] args) 
    {
          UDGraph theGraph = new UDGraph();
          theGraph.addVertex('A');    // 0  (start for mst)
          theGraph.addVertex('B');    // 1
          theGraph.addVertex('C');    // 2
          theGraph.addVertex('D');    // 3
          theGraph.addVertex('E');    // 4

          theGraph.addEdge(0, 1);     // AB
          theGraph.addEdge(0, 2);     // AC
          theGraph.addEdge(1, 3);     // BD
          theGraph.addEdge(1, 4);     // BE
          theGraph.addEdge(2, 3);     // CD
          theGraph.addEdge(4, 2);
          
          theGraph.bfs();
          System.out.println();
    }
}

邻接链表：

import java.util.ArrayList;
class Queue
{
   private final  int maxSize;
   private Vertex[] queArray;
   private int front;
   private int rear;

   public Queue(int s)  
   {
      maxSize = s;
      queArray = new Vertex[maxSize];
      front = rear = 0;
    }

   public boolean insert(Vertex vertex) 
   {
      if(isFull())     
         return false;
      else
      {
            queArray[rear] = vertex;
            rear=(rear+1)%maxSize;
             return true;
       }        
   }

   public Vertex remove()   
   {
      if(isEmpty())
          return null;
      else
      {
          Vertex vertex = queArray[front];
          front = (front+1)%maxSize;
           return vertex;
       }
   }

   public Vertex peekFront() 
   {
       if(!isEmpty())
           return queArray[front];
       else
           return null;
   }

   public boolean isEmpty()  
   {
       return (front==rear);
   }

   public boolean isFull()  
   {
       return (front==(rear+1)%maxSize);
   }
}  

class Vertex
{
    public char label;
    public boolean wasVisited;
    public Edge firstEdge;
    
    public Vertex(char lab)
    {
        this.label = lab;
        this.wasVisited = false;
        firstEdge = null;
    }
}

class Edge
{
    public int dest;
    public Edge nextEdge;
    public Edge(int dest)
    {
        this.dest= dest;
        nextEdge = null;
    }
}

class UDGraph
{
    private final int MAX_VERTS = 20;//图的最大顶点数
    private int nVerts = 0;//当前顶点数
    private Vertex vertexList[];//顶点链表
    private Queue theQueue;
    private ArrayList<Vertex> bfsList;
    
    public UDGraph()
    {
        vertexList = new Vertex[MAX_VERTS];    
        theQueue = new Queue(MAX_VERTS);
        bfsList = new ArrayList<Vertex>();
    }
    
    public void addVertex(Vertex vertex)
    {
        //vertex.indexId = nVerts;
        vertexList[nVerts++] = vertex;
    }
    
    public void addEdge(int start,int end)
    {
        Edge startEdge = new Edge(start);
        Edge endEdge = new Edge(end);
        Edge edge2 = vertexList[start].firstEdge;
        if(edge2==null)
        {
            vertexList[start].firstEdge = endEdge;
        }else
　　　　　{
            while(edge2.nextEdge!=null)
                edge2 = edge2.nextEdge;
            edge2.nextEdge = endEdge;
         }
        Edge edge3 = vertexList[end].firstEdge;
        if(edge3==null)
　　     {
            vertexList[end].firstEdge = startEdge;
        }else
         {
            while(edge3.nextEdge!=null)
                edge3 = edge3.nextEdge;
            edge3.nextEdge = startEdge;
         }
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    //返回顶点v的一个邻接点并且是未访问过的
    public Vertex getAdjUnvisitedVertex(Vertex vertex)
    {
        Edge currentEdge = vertex.firstEdge;
        while(currentEdge != null )
        {
            if(!vertexList[currentEdge.dest].wasVisited)
                return vertexList[currentEdge.dest];
            currentEdge = currentEdge.nextEdge;
        }
        return null;
    }
    
    public void bfs()
    {
        vertexList[0].wasVisited = true;
        bfsList.add(vertexList[0]);
         theQueue.insert(vertexList[0]);
         Vertex vertex2;
         while(!theQueue.isEmpty())
         {
             Vertex vertex1 = theQueue.remove();
             while((vertex2 = getAdjUnvisitedVertex(vertex1)) != null)
             {
                 vertex2.wasVisited = true;
                 bfsList.add(vertex2);
                 theQueue.insert(vertex2);
             }
         }
            
         //遍历完成，清楚所有访问标志位
         for(int j=0;j<nVerts;j++)
             vertexList[j].wasVisited = false;
    }
        
    public void displayBFS()
    {
        for(int i=0;i<bfsList.size();i++)
            System.out.print(bfsList.get(i).label);
        System.out.println("");
    }    
}

public class ListUDG_BFS 
{
    public static void main(String[] args) 
    {
        UDGraph theGraph = new UDGraph();
        theGraph.addVertex(new Vertex('A'));
        theGraph.addVertex(new Vertex('B'));
        theGraph.addVertex(new Vertex('C'));
        theGraph.addVertex(new Vertex('D'));
        theGraph.addVertex(new Vertex('E'));
        theGraph.addVertex(new Vertex('F'));
        theGraph.addVertex(new Vertex('G'));
        
        theGraph.addEdge(0, 1);//AB
        theGraph.addEdge(0, 3);//AD
        theGraph.addEdge(1, 4);//BE
        theGraph.addEdge(2, 5);//CF
        theGraph.addEdge(3, 4);//DE
        theGraph.addEdge(1, 6);//BG
        theGraph.addEdge(3, 5);//DF

        System.out.println("bfs");
        theGraph.bfs();
        theGraph.displayBFS();
    }
}

2.2 有向图的广度优先搜索

下面以"有向图"为例，来对广度优先搜索进行演示。还是以上面的图G2为例进行说明。

第1步：访问A。 
第2步：访问B。 
第3步：依次访问C,E,F。 
    在访问了B之后，接下来访问B的出边的另一个顶点，即C,E,F。前面已经说过，在本文实现中，顶点ABCDEFG按照顺序存储的，因此会先访问C，再依次访问E,F。 
第4步：依次访问D,G。 
    在访问完C,E,F之后，再依次访问它们的出边的另一个顶点。还是按照C,E,F的顺序访问，C的已经全部访问过了，那么就只剩下E,F；先访问E的邻接点D，再访问F的邻接点G。

因此访问顺序是：A -> B -> C -> E -> F -> D -> G

class Queue
{
   private final  int maxSize;
   private int[] queArray;
   private int front;
   private int rear;

   public Queue(int s)  
   {
      maxSize = s;
      queArray = new int[maxSize];
      front = rear = 0;
    }

   public boolean insert(int j) 
   {
      if(isFull())     
         return false;
      else
      {
            queArray[rear] = j;
            rear=(rear+1)%maxSize;
             return true;
       }        
   }

   public int remove()   
   {
      if(isEmpty())
          return -1;
      else
      {
          int value = queArray[front];
          front = (front+1)%maxSize;
           return value;
       }
   }

   public int peekFront() 
   {
       if(!isEmpty())
           return queArray[front];
       else
           return -1;
   }

   public boolean isEmpty()  
   {
       return (front==rear);
   }

   public boolean isFull()  
   {
       return (front==(rear+1)%maxSize);
   }
} 


class Vertex
{
    public char label;
    public boolean wasVisited;
    public Vertex(char lab)
    {
        label = lab;
        wasVisited = false;
    }
}

class DGraph
{
    private final int MAX_VERTS = 20;
    private Vertex vertexList[];
    private int adjMat[][];
    private int nVerts;
    private Queue theQueue;
    
    public DGraph()
    {
        vertexList = new Vertex[MAX_VERTS];
        adjMat = new int[MAX_VERTS][MAX_VERTS];
        nVerts = 0;
        for(int i=0;i<MAX_VERTS;i++)
            for(int j=0;j<MAX_VERTS;j++)
                adjMat[i][j] = 0;
        theQueue = new Queue(MAX_VERTS);
    }
    
    public void addVertex(char lab)
    {
        vertexList[nVerts++] = new Vertex(lab);
    }
    
    public void addEdge(int start,int end)
    {
        adjMat[start][end] = 1;    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }

    public void bfs()
    {
        vertexList[0].wasVisited = true;
        displayVertex(0);
         theQueue.insert(0);
         int v2;
         while(!theQueue.isEmpty())
         {
             int v1 = theQueue.remove();
             while((v2 = getAdjUnvisitedVertex(v1)) != -1)
             {
                 vertexList[v2].wasVisited = true;
                 displayVertex(v2);
                 theQueue.insert(v2);
             }
         }
         for(int j=0;j<nVerts;j++)
             vertexList[j].wasVisited = false;
    }

    public int getAdjUnvisitedVertex(int v)
    {
        for(int j=0;j<nVerts;j++)
            if(adjMat[v][j]==1 && vertexList[j].wasVisited==false)
                return j;
        return -1;
    }
}
public class MatrixDG_BFS 
{
    public static void main(String[] args) 
    {
          DGraph theGraph = new DGraph();
          theGraph.addVertex('A');    // 0  (start for mst)
          theGraph.addVertex('B');    // 1
          theGraph.addVertex('C');    // 2
          theGraph.addVertex('D');    // 3
          theGraph.addVertex('E');    // 4

          theGraph.addEdge(0, 1);     // AB
          theGraph.addEdge(0, 2);     // AC
          theGraph.addEdge(1, 3);     // BD
          theGraph.addEdge(1, 4);     // BE
          theGraph.addEdge(2, 3);     // CD
          theGraph.addEdge(4, 2);
          
          theGraph.bfs();
          System.out.println();
    }
}

邻接链表：

import java.util.ArrayList;
class Queue
{
   private final  int maxSize;
   private Vertex[] queArray;
   private int front;
   private int rear;

   public Queue(int s)  
   {
      maxSize = s;
      queArray = new Vertex[maxSize];
      front = rear = 0;
    }

   public boolean insert(Vertex vertex) 
   {
      if(isFull())     
         return false;
      else
      {
            queArray[rear] = vertex;
            rear=(rear+1)%maxSize;
             return true;
       }        
   }

   public Vertex remove()   
   {
      if(isEmpty())
          return null;
      else
      {
          Vertex vertex = queArray[front];
          front = (front+1)%maxSize;
           return vertex;
       }
   }

   public Vertex peekFront() 
   {
       if(!isEmpty())
           return queArray[front];
       else
           return null;
   }

   public boolean isEmpty()  
   {
       return (front==rear);
   }

   public boolean isFull()  
   {
       return (front==(rear+1)%maxSize);
   }
}  

class Vertex
{
    public char label;
    public boolean wasVisited;
    public Edge firstEdge;
    
    public Vertex(char lab)
    {
        this.label = lab;
        this.wasVisited = false;
        firstEdge = null;
    }
}

class Edge
{
    public int dest;
    public Edge nextEdge;
    public Edge(int dest)
    {
        this.dest= dest;
        nextEdge = null;
    }
}

class DGraph
{
    private final int MAX_VERTS = 20;//图的最大顶点数
    private int nVerts = 0;//当前顶点数
    private Vertex vertexList[];//顶点链表
    private Queue theQueue;
    private ArrayList<Vertex> bfsList;
    
    public DGraph()
    {
        vertexList = new Vertex[MAX_VERTS];    
        theQueue = new Queue(MAX_VERTS);
        bfsList = new ArrayList<Vertex>();
    }
    
    public void addVertex(Vertex vertex)
    {
        //vertex.indexId = nVerts;
        vertexList[nVerts++] = vertex;
    }
    
    public void addEdge(int start,int end)
    {
        Edge endEdge = new Edge(end);
        Edge currentEdge = vertexList[start].firstEdge;
        if(currentEdge==null)
        {
            vertexList[start].firstEdge = endEdge;
        }else
         {
            while(currentEdge.nextEdge!=null)
                currentEdge = currentEdge.nextEdge;
            currentEdge.nextEdge = endEdge;
        }
    }
    
    public void displayVertex(int v)
    {
        System.out.println(vertexList[v].label);
    }
    
    //返回顶点v的一个邻接点并且是未访问过的
    public Vertex getAdjUnvisitedVertex(Vertex vertex)
    {
        Edge currentEdge = vertex.firstEdge;
        while(currentEdge != null )
        {
            if(!vertexList[currentEdge.dest].wasVisited)
                return vertexList[currentEdge.dest];
            currentEdge = currentEdge.nextEdge;
        }
        return null;
    }
    
    public void bfs()
    {
        vertexList[0].wasVisited = true;
        bfsList.add(vertexList[0]);
         theQueue.insert(vertexList[0]);
         Vertex vertex2;
         while(!theQueue.isEmpty())
         {
             Vertex vertex1 = theQueue.remove();
             while((vertex2 = getAdjUnvisitedVertex(vertex1)) != null)
             {
                 vertex2.wasVisited = true;
                 bfsList.add(vertex2);
                 theQueue.insert(vertex2);
             }
         }
            
         //遍历完成，清楚所有访问标志位
         for(int j=0;j<nVerts;j++)
             vertexList[j].wasVisited = false;
    }
        
    public void displayBFS()
    {
        for(int i=0;i<bfsList.size();i++)
            System.out.print(bfsList.get(i).label);
        System.out.println("");
    }    
}

public class ListDG_BFS 
{
    public static void main(String[] args) 
　　{
        DGraph theGraph = new DGraph();
        theGraph.addVertex(new Vertex('A'));
        theGraph.addVertex(new Vertex('B'));
        theGraph.addVertex(new Vertex('C'));
        theGraph.addVertex(new Vertex('D'));
        theGraph.addVertex(new Vertex('E'));
        theGraph.addVertex(new Vertex('F'));
        theGraph.addVertex(new Vertex('G'));
        
        theGraph.addEdge(0, 1);//AB
        theGraph.addEdge(0, 2);//AC
        theGraph.addEdge(0, 3);//AD
        theGraph.addEdge(1, 4);//BE
        theGraph.addEdge(2, 5);//CF
        theGraph.addEdge(3, 4);//DE
        theGraph.addEdge(1, 6);//BG
        theGraph.addEdge(3, 5);//DF

        System.out.println("bfs");
        theGraph.bfs();
        theGraph.displayBFS();
    }
}