數據結構與算法(C#實現)系列---樹(一)

                                          Heavenkiller(原創)

首先我們給樹下一個定義：

樹是一個有限的、非空的結點集，

T={r} or T1 or T2 or…or Tn

它具有下列性質：

1．集合指定的結點r叫做樹的根結點

2．其余的結點可以劃分成n個子集，T1,T2,…Tn(n>=0),其中每一個子集都是一棵樹。

樹的其它定義如度，葉子，高等就請大家查閱別的資料吧，到處都有的。

樹的主要性質一個就是遍歷，分為深度遍歷和廣度遍歷

在這里分別實現為DepthFirstTravesal()和WidthFirstTravesal()

其中深度遍歷又分為前序遍歷、中序遍歷、和后序遍歷

這是是采用適配器技術實現的。

using System;

using System.Collections;

namespace DataStructure

{

     /// <summary>

     /// Tree 的摘要說明。

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

     /// 支持枚舉、比較、深度復制

     /// </summary>

     public abstract class Tree:IEnumerable,IComparable

     {

         public Tree()

         {

              //

              // TODO: 在此處添加構造函數邏輯

              //

         }

         protected Queue keyqueue=new Queue();//僅僅用于枚舉時存放數據，不參與Equals實現中的比較

         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

         //枚舉不同的遍歷類型

         public enum TraversalType

         {

              Breadth=1,//廣度遍歷

              PreDepth=2,//前序遍歷

              InDepth=3,//中序遍歷

              PostDepth=4//后序遍歷

         };

         //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

         {

              //通過_vis使用不同的訪問者來進行前序、后序、中序遍歷

              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------------------------------------

         //內部成員類 用于提供不同遍歷類型的訪問者

         public class PreOrder:IPrePostVisitor

         {

              private IVisitor visitor;

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

              #region IPrePostVisitor 成員

              public void PreVisit(object _obj)

              {

                   // TODO:  添加 PreOrder.PreVisit 實現

                   this.visitor.Visit(_obj);

              }

              public void Visit(object _obj)

              {

                   // TODO:  添加 PreOrder.Visit 實現

              }

              public void PostVisit(object _obj)

              {

                   // TODO:  添加 PreOrder.PostVisitor 實現

              }

              #endregion

         }