Ⅰ.说明：

    1.采用左孩子右兄弟的方式，转化为二叉树来实现。

    2.树的后根遍历与二叉树的中根遍历即有联系又有区别，请读者注意分析体会。

Ⅱ.功能：

    1.创建树并写入数据

    2.先根遍历树

    3.计算树高

    4.后根遍历树

    5.层次遍历树

    6.搜索数据域为某值的结点

    7.删除数据域为某值的结点及其子树

    8.销毁树

Ⅲ.代码：

//.h文件

#ifndef TREE_H
#define TREE_H

#include<iostream>
#include<iomanip>
using namespace std;

template<typename T>       //树结点
struct Node            
{
    T data;
    Node<T> *left, *right;
    Node(const T& item);
};

template<typename T>        //树结点初始化
Node<T>::Node(const T& item)  
{
    data = item;
    left = NULL;
    right = NULL;
}

template<typename T>      //辅助队列，计算树高 Quefh：queue for high    
struct Quefh
{
    Node<T>* nodrs;       //node's adress
    int leve;             //level
    Quefh<T>* hnext;
    Quefh(Node<T>* nds, int lel, Quefh<T>* hnxt);
};

template<typename T>        //Quefh构造函数
Quefh<T>::Quefh(Node<T>* nds, int lel, Quefh<T>* hnxt)
{
    nodrs = nds;
    leve = lel;
    hnext = hnxt;
}

template<typename T>        //辅助队列，查找结点 Quefs：queue for search
struct Quefs                //此队列同时用于层次遍历   
{
    Node<T>* snodrs;        //Quefs::node's adress
    Quefs<T>* snext;
    Quefs(Node<T>* snds, Quefs<T>* snxt);
};

template<typename T>          //Quefs构造函数
Quefs<T>::Quefs(Node<T>* snds, Quefs<T>* snxt)
{
    snodrs = snds;
    snext = snxt;
}

template<typename T>           //辅助队列，删除结点 Quefd：queue for delete
struct Quefd                   //此队列同时在后根遍历中做临时堆栈
{
    T ddata;
    Quefd<T>* dnext;
    Quefd(const T& ddt, Quefd<T>* dnxt);
};

template<typename T>           //Quefd构造函数
Quefd<T>::Quefd(const T& ddt, Quefd<T>* dnxt)
{
    ddata = ddt;
    dnext = dnxt;
}

template<typename T>           //树类
class Tree
{
private:
    Node<T>* root;
    Quefh<T> *hhead, *htail;
    Quefs<T> *shead, *stail;
    Quefd<T> *dhead, *dtail,*top;
    int size;
    int hsize;
    int ssize;
    int dsize;
public:
    Tree();
    ~Tree();
    void Operate();
private:
    Node<T>* Creat(Node<T>* &rt);
    void Destory(Node <T>* t);
    void Addqh(Node<T>* pn, int levl);
    void Addqs(Node<T>* spn);  
    void Addqd(const T& dedata);
    void Outqh(Node<T>* &pn, int &levl);
    Node<T>* Outqs();
    void Delqh();
    void Delqs();
    void Delqd();
    int Couhg(Node<T>* t);
    Node<T>* GetFather(Node<T>* t, Node<T>* p);
    void Search(Node<T>* t, const T& item, bool& sign);
    void Del(Node<T>* t);
    void D_ShowAll(Quefd<T>* dheader);
    void FiRoTra(Node<T>* rt, int& ct);
    void MiRoTra(Node<T>* rt, int& ct);
    void LeveTra(Node<T>* t);
    void ShowAll(Quefs<T>* header);
    Node<T>* Push(Node<T>* t);
    void PopAll(int& ct);
};

template<typename T>           //类构造函数
Tree<T>::Tree()
{
    root = NULL;
    hhead = NULL;
    htail = NULL;
    shead = NULL;
    stail = NULL;
    dhead = NULL;
    dtail = NULL;
    top = NULL;
    size = 0;
    hsize = 0;
    ssize = 0;
    dsize = 0;
}

template<typename T>          //类析构函数
Tree<T>::~Tree()
{
    Destory(root);
}

template<typename T>             //Quefh入队一个结点
void Tree<T>::Addqh(Node<T>* pn, int levl)
{
    if (!hhead){ hhead = htail = new Quefh<T>(pn, levl, NULL); hsize = 1; }
    else
    {
        htail->hnext = new Quefh<T>(pn, levl, NULL);
        htail = htail->hnext;
        hsize++;
    }
}

template<typename T>             //Quefh出队一个结点
void Tree<T>::Outqh(Node<T>* &pn, int &levl)
{
    pn = hhead->nodrs;              
    levl = hhead->leve;
    Quefh<T>* itemph;
    itemph = hhead;
    hhead = hhead->hnext;
    delete itemph;
    hsize--;
}

template<typename T>           //清空队列Quefh
void Tree<T>::Delqh()
{
    while (hhead)
    {
        Quefh<T>* itemphd;
        itemphd = hhead; hhead = hhead->hnext; delete itemphd;
    }
}

template<typename T>             //Quefs入队一个结点
void Tree<T>::Addqs(Node<T>* spn)
{
    if (!shead){ shead = stail = new Quefs<T>(spn, NULL); ssize = 1; }
    else
    {
        stail->snext = new Quefs<T>(spn, NULL);
        stail = stail->snext;
        ssize++;
    }
}

template<typename T>             //Quefs出队一个结点
Node<T>* Tree<T>::Outqs()
{
    Node<T>* pn;
    pn = shead->snodrs;
    Quefs<T>* itemps;
    itemps = shead;
    shead = shead->snext;
    delete itemps;
    ssize--;
    return pn;
}

template<typename T>               //输出队列Quefs内全部元素
void Tree<T>::ShowAll(Quefs<T>* header)
{
    Quefs<T>* p = header;
    for (int i = 1; i <= ssize; i++)
    {
        cout << p->snodrs << "  ";
        if (i % 5 == 0)cout << endl;
        p = p->snext;
    }
    cout << endl;
}

template<typename T>           //清空队列Quefs
void Tree<T>::Delqs()
{
    Quefs<T>* itempsd;
    while(shead){ itempsd = shead; shead = shead->snext; delete itempsd; }
}

template<typename T>             //Quefd入队一个结点
void Tree<T>::Addqd(const T& dedata)
{
    if (!dhead){ dhead = dtail = new Quefd<T>(dedata, NULL); dsize = 1; }
    else
    {
        dtail->dnext = new Quefd<T>(dedata, NULL);
        dtail = dtail->dnext;
        dsize++;
    }
}

template<typename T>               //输出队列Quefd内全部元素
void Tree<T>::D_ShowAll(Quefd<T>* dheader)
{
    Quefd<T>* dp = dheader;
    for (int i = 1; i <= dsize; i++)
    {
        cout << setiosflags(ios::left);
        cout << setw(10) << dp->ddata;
        if (i % 5 == 0)cout << endl;
        dp = dp->dnext;
    }
    cout << endl;
}

template<typename T>           //利用结构体Quefd构造的临时堆栈的入队操作
Node<T>* Tree<T>::Push(Node<T>* t)
{
    while (!t->right)
    {
        top = new Quefd<T>(t->data, top);
        t = t->left;
    }
    return t;
}

template<typename T>            //一次性弹出队列中所有元素
void Tree<T>::PopAll(int& ct)
{
    while (top)
    {
        cout << setiosflags(ios::left);
        cout << setw(10) << top->ddata;
        ct++;
        if (ct % 5 == 0)cout << endl;
        Quefd<T>* itemp4;
        itemp4 = top; top = top->dnext; delete itemp4;
    }
}
template<typename T>           //清空队列Quefs
void Tree<T>::Delqd()
{
    Quefd<T>* itempdd;
    while (dhead){ itempdd = dhead; dhead = dhead->dnext; delete itempdd; }
}

template<typename T>          //创建树
Node<T>* Tree<T>::Creat(Node<T>* &rt)   
{
    int choice; bool flag;
    if (size > 0)
    {
        cout << "是否继续创建子树？是请按1，否请按0：" << endl;
        cin >> choice;
        flag = true;
    }
    if (size == 0)
    {
        cout << "请输入根结点数据;" << endl;
        T data; cin >> data;
        rt = new Node<T>(data);
        if (!rt){ cout << "根结点创建失败！" << endl; return NULL; }
        size++;
        flag = false;
        cout << "根结点创建成功！" << endl;
        cout << "目前树中共有结点" << size << "个。" << endl;
    }
    if (flag)
    {
        if (choice == 0)return 0;
        else
        {
            cout << "请输入子结点数据;" << endl;
            T data; cin >> data;
            rt = new Node<T>(data);
            if (!rt){ cout << "子结点创建失败！" << endl; return NULL; }
            size++;
            cout << "子结点创建成功！" << endl;
            cout << "目前树中共有结点" << size << "个。" << endl;
        }
    }
    Creat(rt->left);
    Creat(rt->right);
    return root;
}

template<typename T>              //先根递归遍历 FiRoTra是first root traversal的缩写
void Tree<T>::FiRoTra(Node<T>* rt, int& ct)
{
    if (rt)
    {
        cout << setiosflags(ios::left);
        cout << setw(10) << rt->data;
        ct++;
        if (ct % 5 == 0)
            cout << endl;
        FiRoTra(rt->left, ct);
        FiRoTra(rt->right, ct);
    }
}

template<typename T>              //中根递归遍历 MiRoTra是middle root traversal的缩写 这里用来进行树的后根遍历
void Tree<T>::MiRoTra(Node<T>* rt, int& ct)
{
    if (rt)
    {
        MiRoTra(rt->left, ct);
        cout << setiosflags(ios::left);
        cout << setw(10) << rt->data;
        ct++;
        if (ct % 5 == 0)
            cout << endl;
        MiRoTra(rt->right, ct);
    }
}

template<typename T>               //层次遍历 LeveTra是level traversal的缩写
void Tree<T>::LeveTra(Node<T>* t)
{
    int count=0;
    Node<T>* pt;
    Addqs(t);
    while (ssize>0)
    {
        pt = Outqs();
        count++;
        cout << setiosflags(ios::left);
        cout << setw(10) << pt->data;
        if (count % 5 == 0)cout << endl;
        pt = pt->left;
        while (pt)
        {
            Addqs(pt);
            pt = pt->right;
        }
    }
}
template<typename T>          //计算树高
int Tree<T>::Couhg(Node<T>* t)
{
    int level = 0, lev, max = 0;
    Node<T>* pt;
    Addqh(t, level);
    while (hsize>0)
    {
        Outqh(pt, lev);
        level = lev + 1;
        if (max < lev)max = lev;
        while (pt)
        {
            if (pt->left)Addqh(pt->left, level);
            pt = pt->right;
        }
    }
    hhead = htail = NULL;
    return max;
}

template<typename T>            //搜索数据域为某值的结点
void Tree<T>::Search(Node<T>* t, const T& item, bool& sign)
{
    if (t)
    {
        Search(t->left, item, sign);
        Search(t->right, item, sign);
        if (t->data == item){ sign = true; Addqs(t); }
    }
}

template<typename T>                         //得到某结点（以地址为关键值）的父结点的地址
Node<T>* Tree<T>::GetFather(Node<T>* t, Node<T>* p)
{
    Node<T>* q;
    if (t == NULL)return NULL;
    if (t->left == p || t->right == p)return t;
    q = GetFather(t->left, p);
    if (q != NULL)return q;
    else return GetFather(t->right, p);
}

template<typename T>             //在树中删除以某结点为根的树
void Tree<T>::Del(Node<T>* t)
{
    if (t != NULL)
    {
        Del(t->left);
        Del(t->right);
        Addqd(t->data);
        delete t;
        size--;
    }
}

template<typename T>           //销毁树
void Tree<T>::Destory(Node<T>* t)
{
    if (t != NULL)
    {
        Destory(t->left);
        Destory(t->right);
        delete t;
        size--;
    }
}

template <typename T>
void Tree<T>::Operate()
{
    bool flager = true;
    while (flager)
    {
        cout << "请您选择操作（输入操作前的数字进行选择）：" << endl;
        cout << "1.创建树并写入数据" << endl;
        cout << "2.先根遍历树" << endl;
        cout << "3.计算树高" << endl;
        cout << "4.后根遍历树" << endl;
        cout << "5.层次遍历树" << endl;
        cout << "6.搜索数据域为某值的结点" << endl;
        cout << "7.删除数据域为某值的结点及其子树" << endl;
        cout << "8.销毁树" << endl;
        int choice;
        cin >> choice;
        switch (choice)
        {
        //由用户创建树
        case 1:
        {
                  if (root){ cout << "树已经创建，无需再建！若想新建，请您先销毁旧树！" << endl; break; }
                  Creat(root);
                  cout << "树创建完成！" << endl;
                  cout << "此树中共有结点" << size << "个！" << endl;
                  break;
        }
        //先根遍历树
        case 2:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法执行遍历操作，请您先创建树！" << endl; break; }
                  int counter2 = 0;
                  FiRoTra(root, counter2);
                  cout << endl;
                  break;
        }
        //计算树高    
        case 3:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法计算树高，请您先创建树！" << endl; break; }
                  int high;
                  high= Couhg(root);     
                  cout << "树的高度为：" <<high<< endl;
                  break;
        }
        //后根遍历树
        case 4:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法执行遍历操作，请您先创建树！" << endl; break; }
                  Node<T>* pt4 = Push(root);
                  int counter4 = 0;
                  MiRoTra(pt4, counter4);
                  PopAll(counter4);
                  cout << endl;
                  break;
        }
        //层次遍历树
        case 5:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法执行遍历操作，请您先创建树！" << endl; break; }              
                  LeveTra(root);
                  cout << endl;
                  shead = stail = NULL;
                  break;
        }
        //搜索数据域为某值的结点    
        case 6:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法执行搜索操作，请您先创建树！" << endl; break; }
                  cout << "请您输入数据域的值;" << endl;
                  T indata;  cin >> indata;
                  bool flag = false;
                  Search(root, indata, flag);
                  if (!flag){ cout << "该树中没有数据域为" << indata << "的结点！" << endl; break; }
                  else cout << "该树中数据域为" << indata << "的结点共有" << ssize << "个。" << endl;
                  cout << "是否输出这些结点的地址？是请按1，否则按0：" << endl;
                  int choice6; cin >> choice6;
                  if (choice6 == 1)    ShowAll(shead);
                  Delqs(); shead = stail = NULL; ssize = 0;
                  break;
        }
        //删除数据域为某值的结点及其子树
        case 7:
        {
                  if (!root){ cout << "树还未创建或已被销毁，无法执行删除操作，请您先创建树！" << endl; break; }
                  T data7; bool flag7 = false; bool sign7 = true; int choice7;
                  cout << "请您输入结点数据的值：" << endl;
                  cin >> data7;
                  Search(root, data7, flag7);
                  if (!flag7){ cout << "目前树中无数据域为" << data7 << "的结点！" << endl;  break; }
                  while (sign7)
                  {
                      Node<T> *p7, *fp7;
                      Quefs<T> *item7;
                      p7 = shead->snodrs;
                      item7 = shead; shead = shead->snext; delete item7; ssize--;
                      if (p7 == root)
                      {
                          cout << "数据域为" << data7 << "的结点为根结点，若执行删除操作将会销毁整棵树！" << endl;
                          cout << "是否确定执行删除操作？确定请按1，取消请按0：" << endl;
                          cin >> choice7;
                          if (choice7 == 0){ Delqs(); shead = stail = NULL; ssize = 0; goto mark7; }
                          else
                          {
                              Destory(p7); root = NULL; size = 0;
                              cout << "删除成功！同时整棵树也被销毁！" << endl;
                              Delqs(); shead = stail = NULL; ssize = 0;
                              goto mark7;
                          }
                      }
                      fp7 = GetFather(root, p7);
                      if (p7->right)               //其实这两个if可以合成一个，但考虑到程序的可读性，分开来写
                      {
                          if (fp7->left == p7)fp7->left = p7->right;
                          if (fp7->right == p7) fp7->right = p7->right;
                          p7->right = NULL;
                      }
                      if (!p7->right)
                      {
                          if (fp7->left == p7)fp7->left = NULL;
                          if (fp7->right == p7)fp7->right = NULL;
                      }
                      Del(p7);
                      cout << "删除成功！" << endl;
                      if (ssize == 0){ cout << "此时树中已无数据域为" << data7 << "的结点及其子树！" << endl; sign7 = false; }
                      if (ssize > 0){ cout << "但此时树中数据域为" << data7 << "的结点还有" << ssize << "个！" << endl; }
                      cout << "此次共删除结点" << dsize << "个，" << "目前树中还有结点" << size << "个。" << endl;
                      cout << "是否显示被删除的各结点的值？是请按1，否则请按0：" << endl;
                      cin >> choice7;
                      if (choice7 == 1)D_ShowAll(dhead);
                      Delqd(); dhead = dtail = NULL; dsize = 0;
                      if (ssize > 0)
                      {
                          cout << "是否继续删除数据域为" << data7 << "的结点及其子树？是请按1，否则按0：" << endl;
                          cin >> choice7;
                          if (choice7 == 0)sign7 = false;
                      }
                  }
                  Delqs(); shead = stail = NULL; ssize = 0;
              mark7:break;
        }
        
        //销毁树
        case 8:
        {
                  if (!root){ cout << "树还未创建或已被销毁！" << endl; break; }
                  cout << "您确定销毁该树吗？确定请按1，取消请按0：" << endl;
                  int choice8; cin >> choice8;
                  if (choice8 == 0)break;
                  else Destory(root);
                  root = NULL;
                  size = 0;
                  cout << "树已销毁！" << endl;
                  break;
        }
            //处理用户的错误输入    
        default:
        {
                   cout << "您的输入有误，无法进行操作！" << endl;
                   break;
        }

        }//switch结束
        //控制循环
        cout << "是否继续？继续请按1，退出请按0：" << endl;
        int ifgoon;
        cin >> ifgoon;
        if (ifgoon == 0)flager = false;
    }//while结束
}

#endif

//.cpp文件

#include 
                       
                    
                    
 
                      




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