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 adressint leve;             //levelQuefh<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 adressQuefs<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"Tree.h"
#include<iostream>
using namespace std;
int main()
{//是否进入程序int uscho;   bool flag = true;//uscho：user choice的缩写cout << "敬告;请您务必按提示要求操作，如果您进行了规定以外的操作，由此造成的一切后果，将全部由您个人承担，程序开发者概不负责！" << endl;cout << "是否进入程序？进入请按1，否则按0;" << endl;cin >> uscho;if (uscho == 0) return 0;//用户选择类型while (flag){cout << "请选择您所要创建树的数据类型，输入类型前的数字进行选择;" << endl;cout << "1.整型  2.浮点  3.字符" << endl;cin >> uscho;if (uscho != 1 && uscho != 2 && uscho != 3){cout << "您的输入有误！重新输入请按1，退出请按0：" << endl;cin >> uscho;if (uscho == 0)return 0;else  flag = false;}if (flag) flag = false;else flag = true;}switch (uscho){case 1:{Tree<int> tree_int;tree_int.Operate();break;}case 2:{Tree<float> tree_float;tree_float.Operate();break;}case 3:{Tree<char> tree_char;tree_char.Operate();break;}default:cout << "您的输入有误！" << endl;break;}return 0;
}Ⅳ.结语：代码已经过测试，在VS2013上成功运行！发此文有两大目的：1.和大家交流经验，供需要的人参考。2.在下菜鸟，代码中难免有不妥之处，恳求大神批评指正。您的批评就是在下提高的起点，对于您的批评，在下将不胜感激！