C#实现二叉树--二叉链表结构

二叉树的简单介绍

关于二叉树的介绍请看这里 ：

二叉树的简单介绍 http://www.cnblogs.com/JiYF/p/7048785.html

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二叉链表存储结构：

二叉树的链式存储结构是指，用链表来表示一棵二叉树，即用链来指示元素的逻辑关系。

通常的方法是链表中每个结点由三个域组成，数据域和左右指针域，左右指针分别用来给出该结点左孩子和右孩子所在的链结点的存储地址。其结点结构为：

  其中，data域存放某结点的数据信息；lchild与rchild分别存放指向左孩子和右孩子的指针，当左孩子或右孩子不存在时，相应指针域值为空（用符号∧或NULL表示）。利用这样的结点结构表示的二叉树的链式存储结构被称为二叉链表，如图5-8所示。  

C#实现代码

二叉树的节点类：

Binary Tree

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace DataStructure
{
    /// <summary>
    /// 二叉链表结点类
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public  class TreeNode<T>
    {
        private T data;               //数据域
        private TreeNode<T> lChild;   //左孩子   树中一个结点的子树的根结点称为这个结点的孩子
        private TreeNode<T> rChild;   //右孩子

        public TreeNode(T val, TreeNode<T> lp, TreeNode<T> rp)
        {
            data = val;
            lChild = lp;
            rChild = rp;
        }

        public TreeNode(TreeNode<T> lp, TreeNode<T> rp)
        {
            data = default(T);
            lChild = lp;
            rChild = rp;
        }

        public TreeNode(T val)
        {
            data = val;
            lChild = null;
            rChild = null;
        }

        public TreeNode()
        {
            data = default(T);
            lChild = null;
            rChild = null;
        }

        public T Data
        {
            get { return data; }
            set { data = value; }
        }

        public TreeNode<T> LChild
        {
            get { return lChild; }
            set { lChild = value; }
        }

        public TreeNode<T> RChild
        {
            get { return rChild; }
            set { rChild = value; }
        }

    }

定义索引文件结点的数据类型

 /// <summary>
    /// 定义索引文件结点的数据类型
    /// </summary>
    public struct indexnode
    {
        int key;         //键
        int offset;      //位置
        public indexnode(int key, int offset)
        {
            this.key = key;
            this.offset = offset;
        }

        //键属性
        public int Key
        {
            get { return key; }
            set { key = value; }
        }
        //位置属性
        public int Offset
        {
            get { return offset; }
            set { offset = value; }
        }


    }


    public class LinkBinaryTree<T>
    {
        private TreeNode<T> head;       //头引用

        public TreeNode<T> Head
        {
            get { return head; }
            set { head = value; }
        }

        public LinkBinaryTree()
        {
            head = null;
        }

        public LinkBinaryTree(T val)
        {
            TreeNode<T> p = new TreeNode<T>(val);
            head = p;
        }

        public LinkBinaryTree(T val, TreeNode<T> lp, TreeNode<T> rp)
        {
            TreeNode<T> p = new TreeNode<T>(val, lp, rp);
            head = p;
        }

        //判断是否是空二叉树
        public bool IsEmpty()
        {
            if (head == null)
                return true;
            else
                return false;
        }

        //获取根结点
        public TreeNode<T> Root()
        {
            return head;
        }

        //获取结点的左孩子结点
        public TreeNode<T> GetLChild(TreeNode<T> p)
        {
            return p.LChild;
        }

        public TreeNode<T> GetRChild(TreeNode<T> p)
        {
            return p.RChild;
        }

        //将结点p的左子树插入值为val的新结点，原来的左子树称为新结点的左子树
        public void InsertL(T val, TreeNode<T> p)
        {
            TreeNode<T> tmp = new TreeNode<T>(val);
            tmp.LChild = p.LChild;
            p.LChild = tmp;
        }

        //将结点p的右子树插入值为val的新结点，原来的右子树称为新节点的右子树
        public void InsertR(T val, TreeNode<T> p)
        {
            TreeNode<T> tmp = new TreeNode<T>(val);
            tmp.RChild = p.RChild;
            p.RChild = tmp;
        }

        //若p非空 删除p的左子树
        public TreeNode<T> DeleteL(TreeNode<T> p)
        {
            if ((p == null) || (p.LChild == null))
                return null;
            TreeNode<T> tmp = p.LChild;
            p.LChild = null;
            return tmp;
        }

        //若p非空 删除p的右子树
        public TreeNode<T> DeleteR(TreeNode<T> p)
        {
            if ((p == null) || (p.RChild == null))
                return null;
            TreeNode<T> tmp = p.RChild;
            p.RChild = null;
            return tmp;
        }

        //编写算法 在二叉树中查找值为value的结点

        public TreeNode<T> Search(TreeNode<T> root, T value)
        {
            TreeNode<T> p = root;
            if (p == null)
                return null;
            if (!p.Data.Equals(value))
                return p;
            if (p.LChild != null)
            {
                return Search(p.LChild, value);
            }
            if (p.RChild != null)
            {
                return Search(p.RChild, value);
            }
            return null;
        }

        //判断是否是叶子结点
        public bool IsLeaf(TreeNode<T> p)
        {
            if ((p != null) && (p.RChild == null) && (p.LChild == null))
                return true;
            else
                return false;
        }


        //中序遍历
        //遍历根结点的左子树->根结点->遍历根结点的右子树 
        public void inorder(TreeNode<T> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                inorder(ptr.LChild);
                Console.WriteLine(ptr.Data + " ");
                inorder(ptr.RChild);
            }
        }


        //先序遍历
        //根结点->遍历根结点的左子树->遍历根结点的右子树 
        public void preorder(TreeNode<T> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                Console.WriteLine(ptr.Data + " ");
                preorder(ptr.LChild);
                preorder(ptr.RChild);
            }
        }


        //后序遍历
        //遍历根结点的左子树->遍历根结点的右子树->根结点
        public void postorder(TreeNode<T> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                postorder(ptr.LChild);
                postorder(ptr.RChild);
                Console.WriteLine(ptr.Data + "");
            }
        }


        //层次遍历
        //引入队列 
        public void LevelOrder(TreeNode<T> root)
        {
            if (root == null)
            {
                return;
            }
            CSeqQueue<TreeNode<T>> sq = new CSeqQueue<TreeNode<T>>(50);
            sq.EnQueue(root);
            while (!sq.IsEmpty())
            {
                //结点出队
                TreeNode<T> tmp = sq.DeQueue();
                //处理当前结点
                Console.WriteLine("{0}", tmp);
                //将当前结点的左孩子结点入队
                if (tmp.LChild != null)
                {
                    sq.EnQueue(tmp.LChild);
                }
                if (tmp.RChild != null)
                {
                    sq.EnQueue(tmp.RChild);
                }
            }
        }
    }

二叉搜索树：结点的左子节点的值永远小于该结点的值，而右子结点的值永远大于该结点的值 称为二叉搜索树

/// <summary>
    /// 二叉搜索树：结点的左子节点的值永远小于该结点的值，而右子结点的值永远大于该结点的值 称为二叉搜索树
    /// </summary>
    public class LinkBinarySearchTree : LinkBinaryTree<indexnode>
    {
        //定义增加结点的方法
        public void insert(indexnode element)
        {
            TreeNode<indexnode> tmp, parent = null, currentNode = null;
            //调用FIND方法
            find(element, ref parent, ref currentNode);
            if (currentNode != null)
            {
                Console.WriteLine("Duplicates words not allowed");
                return;
            }
            else
            {
                //创建结点
                tmp = new TreeNode<indexnode>(element);
                if (parent == null)
                    Head = tmp;
                else
                {
                    if (element.Key < parent.Data.Key)
                        parent.LChild = tmp;
                    else
                        parent.RChild = tmp;
                }
            }
        }

        //定义父结点
        public void find(indexnode element, ref TreeNode<indexnode> parent, ref TreeNode<indexnode> currentNode)
        {
            currentNode = Head;
            parent = null;
            while ((currentNode != null) && (currentNode.Data.Key.ToString() != element.Key.ToString()) && (currentNode.Data.Offset .ToString() != element.Offset .ToString()))//
            {
                parent = currentNode;
                if (element.Key < currentNode.Data.Key)
                    currentNode = currentNode.LChild;
                else
                    currentNode = currentNode.RChild;
            }
        }

        //定位结点
        public void find(int key)
        {
            TreeNode<indexnode> currentNode = Head;
            while ((currentNode != null) && (currentNode.Data.Key.ToString () != key.ToString ()))
            {
                Console.WriteLine(currentNode.Data.Offset.ToString());
                if (key < currentNode.Data.Key)
                    currentNode = currentNode.LChild;
                else
                    currentNode = currentNode.RChild;
            }
        }

        //中序遍历
        //遍历根结点的左子树->根结点->遍历根结点的右子树 
        public void inorderS(TreeNode<indexnode> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                inorderS(ptr.LChild);
                Console.WriteLine(ptr.Data.Key  + " ");
                inorderS(ptr.RChild);
            }
        }


        //先序遍历
        //根结点->遍历根结点的左子树->遍历根结点的右子树 
        public void preorderS(TreeNode<indexnode> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                Console.WriteLine(ptr.Data.Key  + " ");
                preorderS(ptr.LChild);
                preorderS(ptr.RChild);
            }
        }


        //后序遍历
        //遍历根结点的左子树->遍历根结点的右子树->根结点
        public void postorderS(TreeNode<indexnode> ptr)
        {
            if (IsEmpty())
            {
                Console.WriteLine("Tree is Empty !");
                return;
            }
            if (ptr != null)
            {
                postorderS(ptr.LChild);
                postorderS(ptr.RChild);
                Console.WriteLine(ptr.Data.Key + "");
            }
        }
    }


    /// <summary>
    /// 循环顺序队列
    /// </summary>
    /// <typeparam name="T"></typeparam>
    class CSeqQueue<T>
    {
        private int maxsize;       //循环顺序队列的容量
        private T[] data;          //数组，用于存储循环顺序队列中的数据元素
        private int front;         //指示最近一个已经离开队列的元素所占有的位置 循环顺序队列的对头
        private int rear;          //指示最近一个进入队列的元素的位置           循环顺序队列的队尾

        public T this[int index]
        {
            get { return data[index]; }
            set { data[index] = value; }
        }

        //容量属性
        public int Maxsize
        {
            get { return maxsize; }
            set { maxsize = value; }
        }

        //对头指示器属性
        public int Front
        {
            get { return front; }
            set { front = value; }
        }

        //队尾指示器属性
        public int Rear
        {
            get { return rear; }
            set { rear = value; }
        }

        public CSeqQueue()
        {

        }

        public CSeqQueue(int size)
        {
            data = new T[size];
            maxsize = size;
            front = rear = -1;
        }

        //判断循环顺序队列是否为满
        public bool IsFull()
        {
            if ((front == -1 && rear == maxsize - 1) || (rear + 1) % maxsize == front)
                return true;
            else
                return false;
        }

        //清空循环顺序列表
        public void Clear()
        {
            front = rear = -1;
        }

        //判断循环顺序队列是否为空
        public bool IsEmpty()
        {
            if (front == rear)
                return true;
            else
                return false;
        }

        //入队操作
        public void EnQueue(T elem)
        {
            if (IsFull())
            {
                Console.WriteLine("Queue is Full !");
                return;
            }
            rear = (rear + 1) % maxsize;
            data[rear] = elem;
        }

        //出队操作
        public T DeQueue()
        {
            if (IsEmpty())
            {
                Console.WriteLine("Queue is Empty !");
                return default(T);
            }
            front = (front + 1) % maxsize;
            return data[front];
        }

        //获取对头数据元素
        public T GetFront()
        {
            if (IsEmpty())
            {
                Console.WriteLine("Queue is Empty !");
                return default(T);
            }
            return data[(front + 1) % maxsize];//front从-1开始
        }

        //求循环顺序队列的长度
        public int GetLength()
        {
            return (rear - front + maxsize) % maxsize;
        }
    }