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"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！