图的存储，搜索，遍历，广度优先算法和深度优先算法，最小生成树-Java实现

1）用邻接矩阵方式进行图的存储。如果一个图有n个节点，则可以用n*n的二维数组来存储图中的各个节点关系。

对上面图中各个节点分别编号，ABCDEF分别设置为012345。那么AB AC AD 关系可以转换为01 02 03， BC BE BF 可以转换为12 14 15， EF可以转换为45。换句话所，我们将各个节点关系存储在一个n*n的二位数组中，数组下标分别对应A-F，有关系的两个节点，在数组中用1表示，否则用0表示。这上图关系可以用6*6数组表示为：

2）深度优先进行图的遍历以及将图转换为最小生成树

深度优先的原则是从根节点开始，依次寻找后继的第一个子节点，直到没有后继为止。然后回到根节点，寻找根的第二个子节点，然后再依次寻找他的后继，直到没有后继为止。以此类推，直到所有节点都被遍历为止。实现深度优先遍历，有一个回朔的过程，所以需要用栈这种数据结构。

3）广度优先进行图的遍历以及将图转换为最小生成树

广度优先原则是从根节点开始，先将根的所有后继找出来，然后依次将所有后继的后继再找出来。以此类推，直到所有元素节点都被遍历。实现广度优先，是一个顺序过程，所以这里需要用到队列或者链表这种数据结构。

下面是代码实现:

 package org.lyk.impl;
 
 import java.util.ArrayList;
 import java.util.Queue;
 import java.util.Stack;
 
 public class Graph
 {
     private class Node
     {
         private boolean wasVisited;
         private char data;
 
         public Node(char data)
         {
             this.data = data;
             this.wasVisited= false;
         }
     }
 
     private Node[] nodes;
     private int[][] adjMetrix;
     private int maxSize;
     private int index;
     public Graph()
     {
         this.maxSize = 6;
         this.index = 0;
         this.nodes= new Node[this.maxSize];
         this.adjMetrix = new int[this.maxSize][this.maxSize];
     }
 
     /**
      * 增加节点
      * @param data
      * @throws Exception
      */
     public void add(char data) throws Exception
     {
         if(this.index >= this.maxSize)
         {
             throw new Exception("数组已满");
         }
         else
         {
             this.nodes[index++]= new Node(data);
         }
     }
 
     /**
      * 设置图中各个节点关系
      * @param x
      * @param y
      * @throws Exception
      */
     public void setRelation(int x,int y) throws Exception
     {
         if(x < this.maxSize && y < this.maxSize)
         {
             this.adjMetrix[x][y] = 1;
             this.adjMetrix[y][x] = 1;
         }
         else
         {
             throw new Exception("下标错误!");
         }
     }
 
     /**
      * 广度优先对图进行遍历
      * @param x
      * @throws Exception
      */
     public void showBreathFirst(int x) throws Exception
     {
         if(x >= 0 && x < this.index)
         {
             java.util.List<Integer> list = new java.util.ArrayList<>();
             int current = 0;
             list.add(x);
             this.nodes[list.get(current)].wasVisited = true;
             while(current < list.size())
             {
                 System.out.println(this.nodes[list.get(current)].data); 
 
                 int nextSuccessor = this.getNextSuccessor(list.get(current));
                 while(nextSuccessor != -1)
                 {
                     list.add(nextSuccessor);
                     this.nodes[nextSuccessor].wasVisited = true;
                     nextSuccessor = this.getNextSuccessor(list.get(current));
                 }
                 current++;
             }
 
             this.resetNodes();
         }
         else
         {
             throw new Exception("下标越界");
         }
     }
 
     /**
      * 深度优先对图进行遍历
      * @param x
      * @throws Exception
      */
     public void showDeepFirst(int x) throws Exception
     {
         if(x < this.index && x >= 0)
         {
             Stack<Integer> stack = new Stack<>();
             stack.push(x);
             System.out.println(this.nodes[x].data);
             this.nodes[x].wasVisited = true;
             while(!stack.isEmpty())
             {
                 int temp = stack.peek();
                 int nextSuccessor = this.getNextSuccessor(temp);
                 if(nextSuccessor == -1)
                 {
                     stack.pop();
                 }
                 else
                 {
                     stack.push(nextSuccessor);
                     System.out.println(this.nodes[nextSuccessor].data);
                     this.nodes[nextSuccessor].wasVisited = true;
                 }
             }
             this.resetNodes();
         }
         else
         {
             throw new Exception("下标错误");
         }
 
     }
 
     /**
      * 广度优先-最小生成树
      * @param x
      * @throws Exception
      */
     public void toMSTBreathFirst(int x ) throws Exception
     {
         if(x >= 0 && x < this.index)
         {
             java.util.List<Integer> list = new java.util.ArrayList();
             int current = 0;
             list.add(x);
             this.nodes[list.get(current)].wasVisited = true;
             while(current < this.index)
             {
                 int successor = this.getNextSuccessor(list.get(current));
                 while(successor != -1)
                 {
                     list.add(successor);
                     System.out.println(this.nodes[list.get(current)].data + "->" + this.nodes[successor].data);
                     this.nodes[successor].wasVisited = true;
                     successor = this.getNextSuccessor(list.get(current));
                 }
                 current++;
             }
         }
         else
         {
             throw new Exception("下标错误");
         }
     }
 
     /**
      * 深度优先求最小生成树
      * @param x
      * @throws Exception
      */
     public void toMSTDeepFirst(int x) throws Exception
     {
         if(x < this.index && x >=0)
         {
             Stack<Integer> stack = new Stack<Integer>();
             stack.push(x);
             this.nodes[x].wasVisited = true;
             while(!stack.isEmpty())
             {
                 int current = stack.peek();
                 int nextSuccessor = this.getNextSuccessor(current);
                 if(nextSuccessor == -1)
                 {
                     stack.pop();
                 }
                 else
                 {
                     stack.push(nextSuccessor);
                     this.nodes[nextSuccessor].wasVisited = true;
                     System.out.print(this.nodes[current].data);
                     System.out.print("-");
                     System.out.print(this.nodes[nextSuccessor].data);
                     System.out.print(" ");
                 }
             }
 
             this.resetNodes();
         }
         else
         {
             throw new Exception("下标错误");
         }
     }
 
     private int getNextSuccessor(int x)
     {
         for(int i = 0; i <this.maxSize; i++)
         {
             if(this.adjMetrix[x][i] != 0 && this.nodes[i].wasVisited == false)
             {
                 return i;
             }
         }
         return -1;
     }
 
     private void resetNodes()
     {
         for(int i = 0; i < this.index; i++)
         {
             this.nodes[i].wasVisited = false;
         }
     }
 }

Graph