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;
}