二叉树的查找、二叉树高度、二叉树获得双亲结点、构造二叉树、二叉树的广义表表示法、二叉树的插入删除、二叉树的非递归实现

二叉树的查找：

#include<iostream>#include"DoubleNode.h"     //双链表结点类#include"SeqStack.h"           //顺序栈#include"LinkedStack.h"       //链式栈#include"SeqQueue.h"          //顺序循环队列using namespace std;template <class T>class BinaryTree    // 二叉树类{public:DoubleNode<T> *root;  //指向根结点BinaryTree();   //构造空二叉树BinaryTree(T prelist [],int n);  //标明空子树的先根序列构造一棵二叉树BinaryTree(T prelist [],T inlist [],int n);  //先根和中根序列构造二叉树~BinaryTree();bool IsEmpty();  //判断是否是空二叉树int Count();   //返回结点个数int Height();   //返回二叉树的高度DoubleNode<T> *Search(T value); //查找首次出现值为value的结点DoubleNode<T> *GetParent(DoubleNode<T> *node);  //返回node结点的双亲结点void preRoot();  //先根次序遍历二叉树void midRoot();  //中根次序遍历二叉树void postRoot();  //后根次序遍历二叉树DoubleNode<T> *Insert(DoubleNode<T> *p, T value,bool priorChild = true);//插入value作为P结点的孩子void Remove(DoubleNode<T> * p,bool priorChild = true);  //删除p结点的左或右子树void PrintGList();  //以广义表输出二叉树void preRootTraverse();  // 先根次序遍历二叉树的非递归算法void midRootTraverse();  // 中根次序遍历二叉树的非递归算法void LevelOrder();  //按层次遍历二叉树private:void Destroy (DoubleNode<T> *p);  //撤销二叉树int Count(DoubleNode<T> *p);  //返回以P结点为根的子树结点个数int Height(DoubleNode<T> *p);  //返回以P结点为根的子树结点的高度DoubleNode<T>*Search (DoubleNode<T> *p, T value);  //在以p为根的子树中查找首次出现的值为value的结点DoublenNode<T> *GetParent (DoubleNode<T> *p, DoubleNode<T> *node);  // p为根的子树中查找并返回首次出现的值为value的结点void preRoot(DoubleNode<T> *p);  //先跟次序遍历以p结点为根的子树void midtRoot(DoubleNode<T> *p);  //中根次序遍历以p结点为根的子树void postRoot(DoubleNode<T> *p);  //后根次序遍历以P结点为根的子树DoubleNode<T> *creat(T prelist[],int n,int &i);   //以标明空子树的先根遍历序列创建子树DoubleNode<T> *creat(T prelist[],T inlist[],int preStart, int inStart,int n); //以先根和中根序列创建一棵子树void PrintGList (DoubleNode<T> *p);  //以广义表表示输出以p结点为根的子树};template <class T>BinaryTree<T>::BinaryTree()  //构造空二叉树{   this->root =NULL;}template<class T>BinaryTree<T>::~BinaryTree(){  cout<<"撤销二叉树：";  Destroy(this->root);  cout<<endl;}template<class T>void BinaryTree<T>::Destroy(DoubleNode<T> *p){   if(p!=NULL)   {  Destroy (p->prior);  Destroy (p->next);  cout<<p->data<<" ";  // 显示撤销结点的次序  delete p;   }}template<class T>bool BinaryTree<T>::IsEmpty(){  return this->root==NULL;}template <class T>int BinaryTree<T>::Count(){   return Count(this->root);}template<class T>int BinaryTree<T>::Count(DoubleNode<T> *p){  if(p==NULL)      return 0;  else return 1+Count(p->prior)+Count(p->next);}template <class T>void BinaryTree<T>::preRoot(){  cout<<"先根次序遍历二叉树";  preRoot(this->root);  cout<<endl;}template<class T>void BinaryTree<T>::preRoot(DoubleNode<T> *p){   if(p!=NULL)   {     cout<<p->data<<" ";preRoot(p->prior);preRoot(p->next);   }}template <class T>void BinaryTree<T>::midRoot(){  cout<<"中根次序遍历二叉树";  midRoot(this->root);  cout<<endl;}template<class T>void BinaryTree<T>::midtRoot(DoubleNode<T> *p){   if(p!=NULL)   {  midRoot(p->prior);  cout<<p->data<<" ";  midRoot(p->next);   }}template<class T>void BinaryTree<T>::postRoot(){   cout<<"后根次序遍历二叉树";   postRoot(this->root);   cout<<endl;}template<class T>void BinaryTree<T>::postRoot(DoubleNode<T> *p){   if(p!=NULL)   {  postRoot(p->prior);  postRoot(p->next);  cout<<p->data<<" ";   }}

计算二叉树高度：

二叉树的高是一棵较高的一棵子树的高度加1，因此计算二叉树高度必须采用后根次序遍历，首先分别计算出左右子树高度，再计算当前结点为根的子树的高度

template <class T>int BinaryTree<T> ::Height()//返回二叉树的高度{return Height(this->root);}template<class T>int BinaryTree<T>::Height(DoubleNode<T> *p){    if(p!=NULL){  int lh = Height(p->prior);  int rh = Height(p->next);  return (lh>=rh)?lh+1:rh+1;}return 0;}

查找：

template <class T>DoubleNode<T> *BinaryTree<T>::Search(T value){    return BinaryTree(this->root,value);}template <class T>DoubleNode <T> *BinaryTree<T>::Search(DoubleNode<T> *p, T value)   //先根次序遍历查找值为value的结点，返回首次出现结点的指针，若未找到返回NULL{     DoubleNode<T> *find = NULL;if(p!=NULL){    if(p->data == value)return p;find = Search(p->prior,value);if(find == NULL)find = Search(p->next,value);}return find;}

二叉树的双亲结点：

template<class T>DoubleNode<T> *BinaryTree<T>::GetParent(DoubleNode<T> *node){if(this->root == NULL||node==NULL||node==this->root)return NULL;return GetParent(this->root,node);}template<class T>DoubleNode<T> * BinaryTree<T>::GetParent(DoubleNode<T> *p, DoubleNode<T> *node){   DoubleNode<T> *find =NULL;   if(p!=NULL)   {      if(p->prior == node|| p->next == node) return p; find = GetParent(p->prior,node); if(find ==NULL) find =GetParent(p->next,node);   }   return find;}

构造二叉树：

template <class T>BinaryTree<T>::BinaryTree(T prelist[], T inlist[], int n){   this->root = creat(parlist,inlist,0,0,n);}template <class T>DoubleNode<T> *BinaryTree<T>::creat(T prelist[], T inlist[], int preStart, int inStart, int n)                        //以先根和中根序列创建一颗子树，子树根结点是prelist[i],返回根结点指{   DoubleNode<T> *p = NULL;   if(n>0)   {      T elem = prelist[preStart];  //根结点值 p = new DoubleNode<T> (elem);  //创建结点 int i= 0; while(i<n && elem !=inlist[inStart+i])  //在中根序列中查找根值所在的位置 i++; p->prior = create(prelist,inlist,preStart+1,inStart,i)  //创建左子树 p->next  = create(prelist,inlist,preStart+i+1,inStart+i+1,n-1-i);  //创建右子树  }   return p;}template <class T>BinaryTre<T>::BinaryTree(T prelist [],int n)  //标明空子树的先根序列构造二叉树{   int i = 0;   this->root = create(prelist,n,i);}template <class T>DoubleNode<T> * BinaryTree<T>::create(T prelist[], int n, int &i)  //以标明空子树的先根次序遍历序列创建一颗子树，子树根结点是prelist[i],返回根结点指针{    DoubleNode<T> *p =NULL;if(i<n){ T elem = prelist[i]; i++; if(elem!=NULL) {     p = new DoubleNode<T> (elem);  //创建结点 p->prior = create(prelist, n , i); // 创建左子树 p->next = create(prelist,n,i);   //创建右子树 }}return p;}

二叉树的广义表表示法：

template <class T>void BinaryTree<T>::PrintGList()  //以广义表输出二叉树{    PrintGlist(this -> root);cout<<endl;}template<class T>void BinaryTree<T>::PrintGList(DoubleNode<T> *p){   if(p==NULL)  cout<<"^";   else   {      cout<<p->data; if(p->prior!=NULL||p->next != NULL) {      cout<<"(";  PrintGlist(p->prior);  cout<<",";  PrintGlist(p->next);  cout<<")"; }   }}

插入：

template <class T>DoubleNode<T> *BinaryTree<T>::Insert(DoubleNode<T> *p, T value, bool priorChild )  //插入value作为P结点的孩子{   DoubleNode<T> *q = NULL;   if(p!=NULL)  if(priorChild)  {     q = new DoubleNode<T> (value,p->prior,NULL); p->prior = q;  }  else  {    q = new DoubleNode<T> (value,NULL,p->next);p->next = q;  }  return q;}删除：template <class T>void BinaryTree<T>::Remove(DoubleNode<T> *p, bool priorChild){   if(p!=NULL)  if(priorChild)  {    Destroy(p->prior);  //撤销左子树p->prior = NULL;  }  else  {    Destroy (p->next);  // 撤销右子树p->next = NULL;  }}

二叉树的非递归实现：

template <class T>void BinaryTree<T>::preRootTraverse()  //先根次序遍历二叉树的非递归算法{   cout<<"先根次序遍历的非递归";   SeqStack<DoubleNode<T> *> stack;  // 创建一个空栈   DoubleNode<T> * p = this ->root;   while(p!=NULL||!stack.isEmpty())  //p非空或栈非空时  if(p!=NULL)  {    cout<<p->data<<" "; // 访问结点stack.push(p);  // p结点入栈p = p->prior;// 进入左子树  }  else  {     p=stack.pop(); p = p->next;  }  cout<<endl;}template <class T>void BinaryTree<T>::midRootTraverse(){  cout<<"中根次序遍历的非递归";  LinkedStack<DoubleNode<T> *> stack;  //创建一个空栈  DoubleNode<T> *p =this->root;  while(p!=NULL||!stack.isEmpty())  //p非空或栈非空树 if(p!=NULL) {   stack.push(p);p = p->prior; } else {   p = stack.pop();cout<<p->data<<" ";p = p->next; } cout<<endl;}template<class T>void BinaryTree<T>::LevelOrder()  //按层次遍历二叉树{  cout<<"层次遍历： ";  SeqQueue<DoubleNode<T> *>que;  DoubleNode<T> *p = this->root;  while(p!=NULL)  {    cout<<p->data<<" ";if(p->prior!=NULL)    que.enqueue(p->prior);if(p->next!=NULL)que.enqueue(p->next);if(!que.isEmpty())p = que.dequeue();elsep = NULL;  }  cout<<endl;}