数据结构--二叉树的基本编码(原创)
先建立二叉树类的相关代码如下：
#include <iostream>
#include <math.h>
#include <stdlib.h>
using namespace std;
template <typename T>
struct bintreenode
{
T date;
bintreenode<T> *leftchild,*rightchild;
bintreenode()
{
leftchild = NULL;
rightchild = NULL;
}
bintreenode(T x, bintreenode<T> *l = NULL,bintreenode<T> *r = NULL)
{
date = x;
leftchild = l;
rightchild = r;
}
};
template <class T>
class binarytree
{
private:
bintreenode<T> *root;//根为非空节点，保存有数据
T refvalue;//标示空节点的字符
public:
friend istream& operator >> (istream&, binarytree<T>&);
friend ostream& operator << (ostream &out, binarytree<T> &tree)
{
out<<"二叉树前序遍历结果为："<<endl;
bintreenode<T> *p = tree.getroot();
tree.Traverse(p);
out<< endl;
return out;
}
binarytree()
{
root = NULL;
}
binarytree(T value)
{
refvalue = value;
root = NULL;
}
binarytree(const binarytree<T> &s);//复制构造函数
bintreenode<T>* copy(bintreenode<T>*);//复制函数
~binarytree(){destroy(root);}//析构函数
void destroy(bintreenode<T>*);//删除二叉树
bool IsEmpty(){return root == NULL ? true : false;}//判断是否为空树
void Createbintree(bintreenode<T>* &subtree);//创建二叉树
void Traverse(bintreenode<T>* subtree);//前序遍历
bintreenode<T>* getroot() const{ return root;}//取根节点
int size(bintreenode<T>* subtree)const;//计算节点个数
int height(bintreenode<T>* subtree)const;//求树的高度
int leaves(bintreenode<T>* subtree) const;//计算叶子节点个数
bintreenode<T>* parent(bintreenode<T>*, T);//求指定点的父节点
bintreenode<T>* find(bintreenode<T>* subtree,const T &t) const;//查找节点信息
bool equal(bintreenode<T>* t1,bintreenode<T>* t2)const;//判断两棵树是否相等
};
template<typename T>
istream& operator >> (istream& in,binarytree<T>& tree)
{
bintreenode<T> *p = tree.getroot();
tree.Createbintree(p);
return in;
}
/*
template<typename T>
ostream& operator<<(ostream& out, binarytree<T>& tree)
{
out<<"二叉树前序遍历结果为："<<endl;
bintreenode<T> *p = tree.getroot();
tree.Traverse(p);
out<< endl;
return out;
}
*/
template<typename T>
binarytree<T>::binarytree(const binarytree<T> &s)
{
root = copy(s.root);
}
template<typename T>
bintreenode<T>* binarytree<T>::copy(bintreenode<T>* orignode)
{
if(orignode == NULL)
return NULL;
bintreenode<T>* temp = new bintreenode<T>;
temp->date = orignode->date;
temp->leftchild = copy(orignode->leftchild);
temp->rightchild = copy(orignode->rightchild);
return temp;
}
template<typename T>
void binarytree<T>::destroy(bintreenode<T> * subtree)
{
if(subtree != NULL)
{
destroy(subtree->leftchild);
destroy(subtree->rightchild);
delete subtree;
}
}
template<typename T>
void binarytree<T>::Createbintree(bintreenode<T>* &subtree)
{
T item;
if(!cin.eof())
{
cin >> item;
if(item != refvalue)
{
subtree = new bintreenode<T>(item);
if(subtree == NULL)
{
cout << "储存分配出错！"<< endl;
exit(1);
}
if(root == NULL)
root = subtree;
Createbintree(subtree->leftchild);
Createbintree(subtree->rightchild);
}
else
subtree == NULL;
}
}
template<typename T>
void binarytree<T>::Traverse(bintreenode<T>* subtree)
{
if(subtree != NULL)
{
cout << subtree->date << " ";
Traverse(subtree->leftchild);
Traverse(subtree->rightchild);
}
}
template<typename T>
int binarytree<T>::size(bintreenode<T>* subtree)const
{
if(subtree == NULL)
return 0;
else
return 1 + size(subtree->leftchild) + size(subtree->rightchild);
}
template<typename T>
int binarytree<T>::height(bintreenode<T>* subtree)const
{
int dep1,dep2;
if(subtree == NULL)
return 0;
else
{
dep1 = height(subtree->leftchild);
dep2 = height(subtree->rightchild);
return dep1 > dep2 ? dep1+1 : dep2+1;
}
}
template<typename T>
int binarytree<T>::leaves(bintreenode<T> *subtree)const
{
if(subtree == NULL)
return 0;
else
{
if(subtree->leftchild == NULL && subtree->rightchild == NULL)
return 1;
else
return leaves(subtree->leftchild) + leaves(subtree->rightchild);
}
}
template<typename T>
bintreenode<T>* binarytree<T>::parent(bintreenode<T>* subtree, T current)
{
if(subtree == NULL)
return NULL;
if((subtree->leftchild != NULL && subtree->leftchild->date == current) || (subtree->rightchild != NULL &&subtree->rightchild->date == current))
return subtree;
bintreenode<T>* p;
if((p = parent(subtree->leftchild,current)) != NULL)
return p;
else
return parent(subtree->rightchild,current);
}
template<typename T>
bintreenode<T>* binarytree<T>::find(bintreenode<T>* subtree,const T &x)const
{
if(subtree == NULL)
return NULL;
if(subtree->date == x)
return subtree;
bintreenode<T>* p;
if((p = find(subtree->leftchild,x)) != NULL)
return p;
else
return find(subtree->rightchild,x);
}
//先处理都为空的情况为相等
//再处理只有一个为空的情况
//最后处理两个都不是空的时候的情况，子树的的判断
template<typename T>
bool binarytree<T>::equal(bintreenode<T>* t1, bintreenode<T>* t2)const
{
if(t1 == NULL && t2 == NULL)
return true;
else if(t1 == NULL || t2 == NULL)
return false;
else
{
if(t1->date == t2->date)
return true;
bool l_equal = equal(t1->leftchild,t2->leftchild);
bool r_equal = equal(t1->rightchild,t2->rightchild);
if(l_equal && r_equal)
return true;
else
return false;
}
}
再建立一个主文件如下：
#include <iostream>
#include "tree.h"
using namespace std;
int main()
{
binarytree<char> P('#');
binarytree<char> P1(P);
cout << "请按照前序遍历输入："<< endl;
bintreenode<char>* Q = P.getroot();
P.Createbintree(Q);
cout << "前序遍历为："<< endl;
P.Traverse(Q);
cout << endl <<"节点个数为：";
cout << P.size(Q) << endl;
cout << "树高度为：" << P.height(Q) << endl;
cout << "树种叶子数为：" << P.leaves(Q)<< endl;
/*
cout << "节点F的父节点为：";
bintreenode<char> *node = P.parent(Q,'A');
if(node != NULL)
cout << node->date;
else
cout <<"不存在父节点！";
cout << "查找信息为：" << P.find(Q,'G')->date << endl;
*/
if(P.equal(Q,Q))
cout << "xiangdeng"<<endl;
else
cout<<"bd"<< endl;
return 0;
}
在编码的过程中最容易出问题的是：查找指定元素的位置和父节点，还有两个二叉树是否相等的判断，在这三个函数中要用到递归的思想，在判断到找出准确位置时可以中断递归。但处理的过程不同，最主要还是要由清晰的思路和递归的思想。