二叉查找树

-BinarySearchTree.h

#ifndef __BINARY_SEARCH_TREE_H__#define __BINARY_SEARCH_TREE_H__#include <iostream>

#include <string>template <class Object, class Comparator = std::less<Object> >class BinarySearchTree {public:BinarySearchTree();BinarySearchTree(const BinarySearchTree& rhs);~BinarySearchTree();const Object& findMin()const;const Object& findMax()const;bool contains(const Object& x)const;bool isEmpty()const { return NULL == root; }void printTree()const;void makeEmpty();void insert(const Object& x);void remove(const Object& x);const BinarySearchTree& operator=(const BinarySearchTree& rhs);private:struct BinaryNode {Object element;BinaryNode* left;BinaryNode* right;BinaryNode(const Object& theElement, BinaryNode* lt, BinaryNode* rt) :element(theElement), left(lt), right(rt) {}};BinaryNode* root;Comparator isLessThan;BinaryNode* findMin(BinaryNode* t)const;BinaryNode* findMax(BinaryNode* t)const;bool contains(const Object& x, BinaryNode* t)const;void printTree(BinaryNode* t)const;void insert(const Object& x, BinaryNode*& t)const;void remove(const Object& x, BinaryNode*& t)const;void makeEmpty(BinaryNode*& t);BinaryNode* clone(BinaryNode* t)const;};// constructortemplate <class Object, class Comparator>BinarySearchTree<Object, Comparator>::BinarySearchTree() {root = NULL;}// copy constructortemplate <class Object, class Comparator>BinarySearchTree<Object, Comparator>::BinarySearchTree(const BinarySearchTree& rhs) {root = rhs.clone(rhs.root);}// destructortemplate <class Object, class Comparator>BinarySearchTree<Object, Comparator>::~BinarySearchTree() {makeEmpty();}/** * Returns true if x is found in the tree */template <class Object, class Comparator>bool BinarySearchTree<Object, Comparator>::contains(const Object& x)const {return contains(x, root);}/** * Internal method to test if an item is in a subtree * x is item to search for * t is the node that roots the subtree  */template <class Object, class Comparator>bool BinarySearchTree<Object, Comparator>::contains(const Object& x, BinaryNode* t)const {if (t == NULL)return false;else if (isLessThan(x, t->element))return contains(x, t->left);else if (isLessThan(t->element, x))return contains(x, t->right);elsereturn true;// Match}/** * Insert x into the tree; duplicates are ignored */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::insert(const Object& x) {insert(x, root);}/** * Internal method to insert into a subtree * x is the item to insert * t is the node that roots the subtree * Set the new root of the subtree */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::insert(const Object& x, BinaryNode*& t)const {//root = new BinaryNode(2, NULL, NULL);if (t == NULL)t = new BinaryNode(x, NULL, NULL);else if (isLessThan(x, t->element))insert(x, t->left);else if (isLessThan(t->element, x))insert(x, t->right);elsereturn;}/*** Return the smallest item*/template <class Object, class Comparator>const Object& BinarySearchTree<Object, Comparator>::findMin()const {BinaryNode* node = findMin(root);if (NULL == node) throw out_of_range("BinarySearchTree is empty.");else return node->element;}/** * Internal method to find the smallest item in a subtree t. * Return node containing the smallest item */template <class Object, class Comparator>typename BinarySearchTree<Object, Comparator>::BinaryNode*BinarySearchTree<Object, Comparator>::findMin(BinaryNode* t)const {if (t == NULL)return NULL;else if (t->left == NULL)return t;return findMin(t->left);}/*** Return the largest item*/template <class Object, class Comparator>const Object& BinarySearchTree<Object, Comparator>::findMax()const {BinaryNode* node = findMax(root);if (NULL == node) throw out_of_range("BinarySearchTree is empty.");else return node->element;}/** * Internal method to find the largest item in a subtree t. * Return node containing the largest item */template <class Object, class Comparator>typename BinarySearchTree<Object, Comparator>::BinaryNode*BinarySearchTree<Object, Comparator>::findMax(BinaryNode* t)const {if (t == NULL)return NULL;else if (t->right == NULL)return t;return findMax(t->right);}/** * Remove x from the tree */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::remove(const Object& x) {remove(x, root);}/** * Internal method to remove from a subtree * x is the item to remove * t is the node that roots the subtree * Set the new root of the subtree */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::remove(const Object& x, BinaryNode*& t)const {if (NULL == t)return;else if (isLessThan(x, t->element))remove(x, t->left);else if (isLessThan(t->element, x))remove(x, t->right);else if (NULL != t->left && NULL != t->right) {// there are both left son and right son// 用结点t的右子树的最小结点来替代t// 再递归调用从t的右子数中删除t->element这个结点t->element = findMin(t->right)->element;remove(t->element, t->right);}else {BinaryNode* oldNode = t;t = (t->left != NULL) ? t->left : t->right;delete oldNode;}}// makeEmptytemplate <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::makeEmpty() {makeEmpty(root);}/** * Internal method to make subtree empty */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::makeEmpty(BinaryNode*& t) {if (t != NULL) {makeEmpty(t->left);makeEmpty(t->right);delete t;}t = NULL;}/** * Deep Copy */template <class Object, class Comparator>const BinarySearchTree<Object, Comparator>& BinarySearchTree<Object, Comparator>::operator=(const BinarySearchTree<Object, Comparator>& rhs) {if (this != &rhs) {this->makeEmpty();this->root = rhs.clone(rhs.root);}return *this;}/** * Internal method to clone subtree  */template <class Object, class Comparator>typename BinarySearchTree<Object, Comparator>::BinaryNode* BinarySearchTree<Object, Comparator>::clone(BinaryNode* t)const {if (t == NULL) return NULL;else return new BinaryNode(t->element, clone(t->left), clone(t->right));}/** * Print the subtree */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::printTree()const {printTree(root);}/**  * Internal method to print the subtree */template <class Object, class Comparator>void BinarySearchTree<Object, Comparator>::printTree(BinaryNode* t)const {if (t == NULL) return;printTree(t->left);printTree(t->right);std::cout << t->element << " ";}#endif

-main.cpp

#include "BinarySearchTree.h"using namespace std;void printTree(BinarySearchTree<int>& ibst, string s);int main(){BinarySearchTree<int> ibst;ibst.insert(6);ibst.insert(2);ibst.insert(1);ibst.insert(8);ibst.insert(7);ibst.insert(100);BinarySearchTree<int> ibst2(ibst);printTree(ibst2, "ibst2");ibst.remove(7);ibst.remove(100);BinarySearchTree<int> ibst3 = ibst;printTree(ibst3, "ibst3");ibst.insert(4);ibst.insert(3);printTree(ibst, "ibst");if (ibst.contains(6)) cout << "ibst contains 6" << endl;else cout << "ibst doesn't contain 6" << endl;if (ibst.contains(10)) cout << "ibst contains 10" << endl;else cout << "ibst doesn't contain 10" << endl;if (!ibst.isEmpty()) cout << "ibst isn't empty" << endl;else cout << "ibst is empty" << endl;ibst.makeEmpty();if (!ibst.isEmpty()) cout << "ibst isn't empty" << endl;else cout << "ibst is empty" << endl;system("pause");return 0;}void printTree(BinarySearchTree<int>& ibst, string s) {cout << s << ": ";ibst.printTree();cout << endl;cout << s << ".max: " << ibst.findMax()<< "  " << s << ".min: " << ibst.findMin();cout << endl << endl;}