Binary Search Tree的实现 C++版

// 定义二叉检索树类template <typename Key >class BST{private:BSTNode<Key >* root;int nodecount;void clearhelp(BSTNode<Key >*);BSTNode<Key>* inserthelp(BSTNode<Key >*, const Key&);BSTNode<Key>* deletemin(BSTNode<Key >*);BSTNode<Key>* getmin(BSTNode<Key >*);BSTNode<Key>* removehelp(BSTNode<Key >*, const Key&);Key findhelp(BSTNode<Key >*, const Key&) const;void printhelp(BSTNode<Key >*, int) const;void preodhelper(BSTNode<Key >*) const;void inodhelper(BSTNode<Key >*) const;void postodhelper(BSTNode<Key >*) const;Key sumvalue(BSTNode<Key>*);public:BST() {root = NULL; nodecount = 0;}~BST() { clearhelp(root); }void clear(){clearhelp(root);root = NULL;nodecount = 0;}void insert(const Key& k){root = inserthelp(root, k);nodecount ++;}Key remove(const Key& k){Key temp = findhelp(root, k);if(temp != NULL){root = removehelp(root, k);nodecount --;}return temp;}Key removeAny(){if(root != NULL){Key temp = root->key();root = removehelp(root, root->key());nodecount --;return temp;}elsereturn NULL;}Key find(const Key& k) const{return findhelp(root, k);}int size(){return nodecount;}void print() const{if(root == NULL)cout << "The BST is empty." << endl;elseprinthelp(root, 0);}void preorder(){preodhelper(root);}void inorder(){inodhelper(root);}void postorder(){postodhelper(root);}Key sum(){return sumvalue(root);}};template <typename Key >Key BST<Key>::findhelp(BSTNode<Key >* root, const Key& k) const{if(root == NULL)return NULL;if(k < root->key())return findhelp(root->left(), k);else if(k > root->key())return findhelp(root->right(), k);elsereturn root->key();}template <typename Key >BSTNode<Key>* BST<Key>::inserthelp(BSTNode<Key >* root, const Key& k){if(root == NULL)return new BSTNode<Key >(k, NULL, NULL);if(k < root->key())root->setLeft(inserthelp(root->left(), k));elseroot->setRight(inserthelp(root->right(), k));return root;}template <typename Key >BSTNode<Key >* BST<Key >::deletemin(BSTNode<Key >* root){if(root->left() == NULL)return root->right();else{root->setLeft(deletemin(root->left()));return root;}}template <typename Key >BSTNode<Key >* BST<Key >::getmin(BSTNode<Key >* root){if(root->left() == NULL)return root;elsereturn getmin(root->left());}template <typename Key >BSTNode<Key >* BST<Key >::removehelp(BSTNode<Key >* root, const Key& k){if(root == NULL)return NULL;else if(k < root->key())root -> setLeft(removehelp(root->left(), k));else if(k > root->key())root -> setRight(removehelp(root->right(), k));else{BSTNode<Key >* temp =root;if( root->left() == NULL){root = root->right();delete temp;}else if(root->right() == NULL){root = root->left();delete temp;}else{BSTNode<Key >* temp = getmin(root->right());root->setkey(temp->key());root->setKey(temp->key());root->setRight(deletemin(rt->right()));delete temp;}}return root;}template <typename Key >void BST<Key >::clearhelp(BSTNode<Key >* root){if(root == NULL)return ;clearhelp(root->left());clearhelp(root->right());delete root;}template <typename Key >void BST<Key >::printhelp(BSTNode<Key >* root, int level) const{if(root == NULL)return ;printhelp(root->left(), level+1);for(int i = 0; i<level; i++)cout << " ";cout << root->key() << "\n";printhelp(root->right(), level+1);}// 递归，前序遍历template <typename Key >void BST<Key>::preodhelper(BSTNode<Key >* rt) const{if(rt == NULL)return ;cout << rt->key() << " ";preodhelper(rt->left());preodhelper(rt->right());}// 递归，中序遍历template <typename Key >void BST<Key>::inodhelper(BSTNode<Key >* rt) const{if(rt == NULL)return ;inodhelper(rt->left());cout << rt->key() << " ";inodhelper(rt->right());}// 递归，后序遍历template <typename Key >void BST<Key>::postodhelper(BSTNode<Key >* rt) const{if(rt == NULL)return ;postodhelper(rt->left());postodhelper(rt->right());cout << rt->key() << " ";}// 一棵在结点上存放整型数值的数，递归计算所有结点的数值之和template <typename Key>Key BST<Key>::sumvalue(BSTNode<Key>* rt){if (rt == NULL)return 0;if ((rt->left() == NULL)&&(rt->right() == NULL))return rt->key();else{return rt->key() + sumvalue(rt->left()) + sumvalue(rt->right());}}

#include <iostream>using namespace std;// 测试用主程序int main(){int a[] = {15,20,25,18,16,5,7};int len = sizeof(a) / sizeof(a[0]);// 创建二叉检索树BST<int> myBST;for(int count = 0; count < len; count++){myBST.insert(a[count]);}// 打印二叉检索树myBST.print();// 前序遍历myBST.preorder();cout << endl;// 中序遍历myBST.inorder();cout << endl;// 后序遍历myBST.postorder();cout << endl;// 打印树的所有结点的数值之和cout << "The sum of each node's value is: " << myBST.sum() << endl;return 0;}