BST

BST终极版，已通过OJ的检验，应该没问题。

// Binary tree node implementation#include<iostream>using namespace std;template <typename E>class BSTNode{private:E it;        // The node's value;BSTNode* lc; // Pointer to left childBSTNode* rc; // Pointer to right child public:// Two constructors -- with and without initial valuesBSTNode(){ lc = rc = NULL; }BSTNode(E e, BSTNode* l = NULL, BSTNode* r = NULL){it = e; lc = l; rc = r;}~BSTNode(){}           // Destructor// Functions to set and return the valueE& element(){ return it; }void setElement(const E& e){ it = e; }// Functions to set and return the childreninline BSTNode* left() const { return lc; }void setLeft(BSTNode<E>* b){ lc = (BSTNode*)b; }inline BSTNode* right() const { return rc; }void setRight(BSTNode<E>* b){ rc = (BSTNode*)b; }// Return true if it is a leaf, false otherwisebool isLeaf(){ return lc == NULL && rc == NULL; }};// Binary Search Tree implementationtemplate <typename E>class BST{protected:BSTNode<E>* root;     // Root of the BSTint nodecount;        // Number of nodes in the BST// Private helper functionsvoid clearhelp(BSTNode<E>*);BSTNode<E>* inserthelp(BSTNode<E>*, const E&);BSTNode<E>* deletemin(BSTNode<E>*);BSTNode<E>* getmin(BSTNode<E>*);BSTNode<E>* removehelp(BSTNode<E>*, const E&);bool findhelp(BSTNode<E>*, const E&) const;void printhelp(BSTNode<E>*, int) const;void find_ith(BSTNode<E>* root, int& count, int dest, E& res) const;BSTNode<E>* delete_less_than(BSTNode<E>* root, const E& key);BSTNode<E>* delete_greater_than(BSTNode<E>* root, const E& key);BSTNode<E>* delete_interval(BSTNode<E>* root, const E& lkey, const E& hkey);int count(BSTNode<E>* root){if (root == NULL) return 0;else return 1 + count(root->left()) + count(root->right());}public:BST(){ root = NULL; nodecount = 0; }~BST(){ clearhelp(root); }void clear(){     // Reinitialize tree        clearhelp(root); root = NULL; nodecount = 0;}// Insert a record into the treevoid insert(const E& e){root = inserthelp(root, e);nodecount++;}// Remove a record from the treevoid remove(const E& e){if (findhelp(root, e)){            root = removehelp(root, e);            nodecount--;    }}// Remove and return the root nodeE removeAny(){assert(root != NULL);E tmp = root->element();root = removehelp(root, tmp);nodecount--;return tmp;}bool find(const E& e) const {return findhelp(root, e);}// Return the number of nodes in the treeint size(){ return nodecount; }void print() const {       // Print the contents of the BST        if (root == NULL) cout << "The BST is empty." << endl;        else printhelp(root, 0);}E find_ith(int th) const {E tmp;int count = 0;find_ith(root, count, th, tmp);return tmp;}void delete_less_than(const E& key){root = delete_less_than(root, key);}void delete_greater_than(const E& key){root = delete_greater_than(root, key);}void delete_interval(const E& lkey, const E& hkey){root = delete_interval(root, lkey, hkey);}int count(){return count(root);}};template <typename E>bool BST<E>::findhelp(BSTNode<E>* root, const E& e) const {if (root == NULL) return false;if (e < root->element()) return findhelp(root->left(), e);else if (e > root->element()) return findhelp(root->right(), e);else return true;}template <typename E>BSTNode<E>* BST<E>::inserthelp(BSTNode<E>* root, const E& e){if (root == NULL) return new BSTNode<E>(e);if (e < root->element()) root->setLeft(inserthelp(root->left(), e));else root->setRight(inserthelp(root->right(), e));return root;}template <typename E>BSTNode<E>* BST<E>::deletemin(BSTNode<E>* root){if (root->left() == NULL) return root->right();else{root->setLeft(deletemin(root->left()));return root;}}template <typename E>BSTNode<E>* BST<E>::getmin(BSTNode<E>* root){if (root->left() == NULL) return root;else return getmin(root->left());}template <typename E>BSTNode<E>* BST<E>::removehelp(BSTNode<E>* root, const E& e){if (root == NULL) return NULL;else if (e < root->element()) root->setLeft(removehelp(root->left(), e));    else if (e > root->element()) root->setRight(removehelp(root->right(), e));    else {    BSTNode<E>* tmp = root;    if (root->left() == NULL){    root = root->right();    delete tmp;    }    else if (root->right() == NULL){    root = root->left();    delete tmp;    }    else {    BSTNode<E>* tmp = getmin(root->right());    root->setElement(tmp->element());    root->setRight(deletemin(root->right()));    delete tmp;    }    }    return root;}template <typename E>void BST<E>::clearhelp(BSTNode<E>* root){if (root == NULL) return;clearhelp(root->left());clearhelp(root->right());delete root;}template <typename E>void BST<E>::printhelp(BSTNode<E>* root, int level) const {if (root == NULL) return;printhelp(root->left(), level + 1);for (int i = 0; i <= level; i++) cout << "  ";cout << "Level " << level << ": " << root->element() << endl;printhelp(root->right(), level + 1);}template <typename E>void BST<E>::find_ith(BSTNode<E>* root, int& count, int dest, E& res) const {if (root == NULL) return;if (count == dest) return;find_ith(root->left(), count, dest, res);if (count == dest) return;count++;if (count == dest) res = root->element();else find_ith(root->right(), count, dest, res);}template <typename E>BSTNode<E>* BST<E>::delete_less_than(BSTNode<E>* root, const E& key){if (root == NULL) return NULL;if (root->element() < key){clearhelp(root->left());BSTNode<E>* tmp = root;root = delete_less_than(root->right(), key);delete tmp;return root;}else {root->setLeft(delete_less_than(root->left(), key));return root;}}template <typename E>BSTNode<E>* BST<E>::delete_greater_than(BSTNode<E>* root, const E& key){if (root == NULL) return NULL;if (root->element() > key){clearhelp(root->right());BSTNode<E>* tmp = root;root = delete_greater_than(root->left(), key);delete tmp;return root;}else {root->setRight(delete_greater_than(root->right(), key));return root;}}template <typename E>BSTNode<E>* BST<E>::delete_interval(BSTNode<E>* root, const E& lkey, const E& hkey){if (root == NULL) return NULL;if (root->element() >= hkey) {root->setLeft(delete_interval(root->left(), lkey, hkey));return root;}else if (root->element() <= lkey){root->setRight(delete_interval(root->right(), lkey, hkey));return root;}else {BSTNode<E>* tmp = root;BSTNode<E>* tmp1 = delete_interval(root->left(), lkey, hkey);BSTNode<E>* tmp2 = delete_interval(root->right(), lkey, hkey);delete tmp;if (tmp1 == NULL && tmp2 == NULL) return NULL;else if (tmp1 == NULL && tmp2 != NULL) return tmp2;else if (tmp1 != NULL && tmp2 == NULL) return tmp1;else {BSTNode<E>* right_min = tmp2;while (right_min->left() != NULL) right_min = right_min->left();BSTNode<E>* new_root = new BSTNode<E>(right_min->element());tmp2 = removehelp(tmp2, new_root->element());new_root->setLeft(tmp1);new_root->setRight(tmp2);return new_root;}}}

相比起平衡树，BST的实现还是比较简单的，主要是运用递归的方法，实现二分查找，插入和删除（查找和插入也可以不用递归，用简单的循环实现）。若将BSTNode作为BST的内嵌类，实现起来更简单，代码更加简洁。