二叉树首先要有树节点
template<class T>
class BinaryNode
{
public:
T element;
BinaryNode *left;
BinaryNode *right; public:
BinaryNode(T passelement);
~BinaryNode();
}; template<class T>
BinaryNode<T>::BinaryNode(T passelement)
{
this->element=passelement;
this->left=NULL;
this->right=NULL;
} template<class T>
BinaryNode<T>::~BinaryNode()
{
}
二叉树对象则比较复杂
template<class T>
class BinarySearchTree
{
private:
BinaryNode<T> *m_proot;
public:
const T findMin() const;//获取最小值
const T findMax() const;//获取最大值
bool contains(const T& xele) const;//判断是否包含
void makeEmpty();//清空二叉树
void insert(const T& xele);//插入
void remove(const T& xele);//删除
void inordertrav();//中序遍历
void toDoublelist();//转化为双向链表
void printDoublelist();//打印双向链表
public://构造与析构函数
BinarySearchTree();
BinarySearchTree(const BinarySearchTree& bst);
~BinarySearchTree();
private://全部用于递归调用
void makeEmpty(BinaryNode<T>* &t);
const T findMin(BinaryNode<T>* &t);
void remove(const T& xele, BinaryNode<T>* &t);
void insert(const T& xele, BinaryNode<T>* &t);
void inordertrav(BinaryNode<T>* &t);
void toDoublelist(BinaryNode<T>* &t);
BinaryNode<T>* getlLeftTail(BinaryNode<T>* &t);//获取左子树的最大节点
BinaryNode<T>* getlRightHead(BinaryNode<T>* &t);//获取右子树的最小节点
};
具体函数实现如下：
1.判断是否包含：
template<class T>
bool BinarySearchTree<T>::contains(const T& xele) const
{
BinaryNode<T>* pcurrent = m_proot;
while (true)
{
if (pcurrent == NULL)//指针为空
{
return false;
}
else if (xele < pcurrent->element)
pcurrent = pcurrent->left;
else if (xele > pcurrent->element)
pcurrent = pcurrent->right;
else
{
pcurrent = NULL;
return true;
}
} }
2.返回最小值：
template<class T>
const T BinarySearchTree<T>::findMin() const
{
BinaryNode<T>* m_pcurrent = m_proot;
while (m_pcurrent->left != NULL)
{
m_pcurrent = m_pcurrent->left;
}
return m_pcurrent->element;
}
或：
template<class T>
const T BinarySearchTree<T>::findMin(BinaryNode<T>* &t)
{
if (t == NULL)
return NULL;
if (t->left == NULL)
return t->element;
else
return findMin(t->left); }
template<class T>
const T BinarySearchTree<T>::findMin()
{
findMin(m_proot);
}
3.返回最大值：
template<class T>
const T BinarySearchTree<T>::findMax() const
{
BinaryNode<T>* m_pcurrent = m_proot;
while (m_pcurrent->right != NULL)
{
m_pcurrent = m_pcurrent->right;
}
return m_pcurrent->element;
}
4.清空：
template<class T>
void BinarySearchTree<T>::makeEmpty(BinaryNode<T>* &t)
{
if (t!=NULL)
{
makeEmpty(t->left);
makeEmpty(t->right);
delete t;
}
t = NULL;
}
template<class T>
void BinarySearchTree<T>::makeEmpty()
{
makeEmpty(m_proot);
}
5.插入：
template<class T>
void BinarySearchTree<T>::insert(const T& xele, BinaryNode<T>* &t)
{
if (t == NULL)
t = new BinaryNode<T>(xele);
else if (xele < t->element)
return insert(xele, t->left);
else if (xele > t->element)
return insert(xele, t->right);
else
;
}
template<class T>
void BinarySearchTree<T>::insert(const T& xele)
{
insert(xele, m_proot);
}
6.删除:
template<class T>
void BinarySearchTree<T>::remove(const T& xele, BinaryNode<T>* &t)
{
if (t == NULL)
return;
else if (xele < t->element)
remove(xele, t->left);
else if (xele > t->element)
remove(xele, t->right);
else
{
if (t->left != NULL&&t->right != NULL)
{
t->element = findMin(t->right);
remove(t->element, t->right);
}
else
{
BinaryNode<T>* oldNode = t;
t = (t->left != NULL) ? t->left : t->right;
delete oldNode;
}
}
}
template<class T>
void BinarySearchTree<T>::remove(const T& xele)
{
remove(xele, m_proot);
}
7.中序遍历：
template<class T>
void BinarySearchTree<T>::inordertrav()
{
inordertrav(m_proot);
}
template<class T>
void BinarySearchTree<T>::inordertrav(BinaryNode<T>* &t)//参数是根节点
{
if (NULL == t)
return;
if (NULL != t->left)
inordertrav(t->left);
cout << t->element << "," << endl;
if (NULL != t->right)
inordertrav(t->right);
}
8.转换为双向链表，需要注意的是：不能使用中序遍历的方法去实现转换，这样会引起指针异常；转换后以前操作二叉树的函数全部失效
template<class T>
BinaryNode<T>* BinarySearchTree<T>::getlLeftTail(BinaryNode<T>* &t)
{
BinaryNode<T>* pC = t;
while (true)
if (NULL != pC->right)
pC = pC->right;
else
break;
return pC;
}
template<class T>
BinaryNode<T>* BinarySearchTree<T>::getlRightHead(BinaryNode<T>* &t)
{
BinaryNode<T>* pC = t;
while (true)
if (NULL != pC->left)
pC = pC->left;
else
break;
return pC;
}
template<class T>
void BinarySearchTree<T>::toDoublelist()
{
toDoublelist(m_proot);
}
template<class T>
void BinarySearchTree<T>::toDoublelist(BinaryNode<T>* &t)
{ if (NULL == t)
return;
if (NULL != t->left)
{
BinaryNode<T>* listtail = getlLeftTail(t->left);//先记录下来要与根节点的左指针相连的。
toDoublelist(t->left);
listtail->right = t;
t->left = listtail;
} /*这个方法会出现问题
//不为空
if (NULL != m_plist)
{
t->left = m_plist;
m_plist->right = t;
}
else//为空表示使双向链表的头
{
m_phead = t;
}
//为下一次连接做准备
m_plist = t; cout << m_plist->element << ",";*/ if (NULL != t->right)
{
BinaryNode<T>* listhead = getlRightHead(t->right);
toDoublelist(t->right);
listhead->left = t;
t->right = listhead; } }
9.打印链表：
template<class T>
void BinarySearchTree<T>::printDoublelist()
{
BinaryNode<T>* phead = m_proot;
while (true)
{
if (phead->left != NULL)
phead = phead->left;
else
break;
}
while (phead->right!=NULL)
{
cout << phead->element << ",";
phead = phead->right;
}
cout << phead->element;
}