数据结构与算法(C#完成)系列---树(一)

       数据结构与算法(C#实现)系列---树(一)

                                          Heavenkiller(原创)

首先我们给树下一个定义：

树是一个有限的、非空的结点集，

T={r} or T1 or T2 or…or Tn

它具有下列性质：

1．集合指定的结点r叫做树的根结点

2．其余的结点可以划分成n个子集，T1,T2,…Tn(n>=0),其中每一个子集都是一棵树。

树的其它定义如度，叶子，高等就请大家查阅别的资料吧，到处都有的。

树的主要性质一个就是遍历，分为深度遍历和广度遍历

在这里分别实现为DepthFirstTravesal()和WidthFirstTravesal()

其中深度遍历又分为前序遍历、中序遍历、和后序遍历

这是是采用适配器技术实现的。

using System;

using System.Collections;

namespace DataStructure

{

     /// <summary>

     /// Tree 的摘要说明。

     /// when traverse, traversaltype can't be changed,or throw a  exception

     /// 支持枚举、比较、深度复制

     /// </summary>

     public abstract class Tree:IEnumerable,IComparable

     {

         public Tree()

         {

              //

              // TODO: 在此处添加构造函数逻辑

              //

         }

         protected Queue keyqueue=new Queue();//仅仅用于枚举时存放数据，不参与Equals实现中的比较

         protected TraversalType traversaltype=TraversalType.Breadth;// choose a traversal  type,and  DepthFirst is default

         //protected uint degree=0;//degree of the tree, init  it as 0

         //protected uint height=0;//height of the tree, init it as 0

         //枚举不同的遍历类型

         public enum TraversalType

         {

              Breadth=1,//广度遍历

              PreDepth=2,//前序遍历

              InDepth=3,//中序遍历

              PostDepth=4//后序遍历

         };

         //public virtual abstract object  Key{}

         public abstract Tree this[uint _index]{get;set;}//if I only use get, can I change it later?

         public  abstract object Key{get;}

         public  abstract uint Degree{get;}

         //public  abstract uint Height{get;}

         public  void SetTraversalType(TraversalType _type){traversaltype=_type;}//set a traversal a type, if it's not set manually, DepthFirst will be chosen in default

         public  abstract bool IsEmpty();// property takes the place of IsEmpty()

         public  abstract bool IsLeaf();

         //Only Visit, needn't queue

         public virtual void DepthFirstTraversal(IPrePostVisitor _vis)//middle depthfirst traversal

         {

              //通过_vis使用不同的访问者来进行前序、后序、中序遍历

              if(!IsEmpty())

              {

                   _vis.PreVisit(this.Key);

                   if( this.Degree>=1 )

                   {

                       if( this.Degree>=2)

                       {

                            for(uint i=0;i<(this.Degree-1);i++)//

                            {

                                 this[i].DepthFirstTraversal(_vis);//recursive call

                                 //_vis.Visit(this.Key);

                            }

                       }

                       this[this.Degree-1].DepthFirstTraversal(_vis);

                   }

                   _vis.PostVisit(this.Key);

              }

         }

         public virtual void BreadthFirstTraversal(IVisitor _vis)//breadth first traversal

         {

              Queue tmpQueue=new Queue();//used to help BreadthFirstTraversal

              //this.keyqueue=new Queue();//store keys

              if(!this.IsEmpty())

                   tmpQueue.Enqueue(this);//enqueue the root node at first

              while(tmpQueue.Count!=0)//until the number of the queue is zero

              {

                   Tree headTree=(Tree)tmpQueue.Dequeue();

                   //this.keyqueue.Enqueue(headTree.Key);

                   _vis.Visit(headTree.Key);

                   for(uint i=0;i<headTree.Degree;i++)

                   {

                       Tree childTree=headTree[i];

                       if(!childTree.IsEmpty())

                            tmpQueue.Enqueue(childTree);

                   }

              }

         }

         //------------------------------------------------end------------------------------------

         //内部成员类 用于提供不同遍历类型的访问者

         public class PreOrder:IPrePostVisitor

         {

              private IVisitor visitor;

              public PreOrder(IVisitor _vis){visitor=_vis;}

              #region IPrePostVisitor 成员

              public void PreVisit(object _obj)

              {

                   // TODO:  添加 PreOrder.PreVisit 实现

                   this.visitor.Visit(_obj);

              }

              public void Visit(object _obj)

              {

                   // TODO:  添加 PreOrder.Visit 实现

              }

              public void PostVisit(object _obj)

              {

                   // TODO:  添加 PreOrder.PostVisitor 实现

              }

              #endregion

         }