C++伸展树自顶向下实现

伸展树的三种旋转：单旋转，一字型旋转，之字形旋转

为了简化程序，将之字形旋转转变为如下旋转方式：

-SplayTree.h 代码：

/* * by: peige * 2015/11/29 */#ifndef __SPLAY_TREE_H__#define __SPLAY_TREE_H__#include <iostream>template <class T>struct SplayTreeNode {T key;// 关键字SplayTreeNode* left;// 左儿子SplayTreeNode* right;// 右儿子SplayTreeNode(const T& value = T(), SplayTreeNode* lt = NULL, SplayTreeNode* rt = NULL) :key(value), left(lt), right(rt) {}};template <class T, class Compare = std::less<T> >class SplayTree {private:SplayTreeNode<T>*mRoot;// 根节点CompareisLessThan;// Comparepublic:SplayTree();~SplayTree();void preOrder()const;// 前序遍历void inOrder()const;// 中序遍历void postOrder()const;// 后序遍历bool find(const T& key);T findMin();// 查找最小结点，返回键值T findMax();// 查找最大结点，返回键值void splay(const T& key);// 旋转key对应的结点为根节点void insert(const T& key);// 将结点(key为结点键值)插入到伸展树中void remove(const T& key);// 删除结点(key为结点键值)void destroy();// 销毁伸展树void print()const;// 打印伸展树private:void preOrder(SplayTreeNode<T>* node)const;void inOrder(SplayTreeNode<T>* node)const;void postOrder(SplayTreeNode<T>* node)const;bool find(SplayTreeNode<T>*& node, const T& key);T findMin(SplayTreeNode<T>*& node);T findMax(SplayTreeNode<T>*& node);// 旋转key对应的节点为根节点，并返回值为根节点void splay(SplayTreeNode<T>*& node, const T& key);void destroy(SplayTreeNode<T>*& node);void print(SplayTreeNode<T>* node, const T& key, const int& direction)const;void rotateWithLeftChild(SplayTreeNode<T>*& k1);// 左单旋void rotateWithRightChild(SplayTreeNode<T>*& k1);// 右单旋};// constructortemplate <class T, class Compare>SplayTree<T, Compare>::SplayTree() :mRoot(NULL) {}// destructortemplate <class T, class Compare>SplayTree<T, Compare>::~SplayTree() {destroy(mRoot);}/** * Internal method: splay * 整个伸展树中最重要的函数 * 对值为key的节点伸展,如果一项也没有找到， * 那么就要对访问路径上的最后的节点进行一次伸展(important) * 在insert,remove,findMax,findMin,find中都要进行伸展 */template <class T, class Compare>void SplayTree<T, Compare>::splay(SplayTreeNode<T>*& tree, const T& key) {if (NULL == tree) return;SplayTreeNode<T> header, *l, *r;header.left = header.right = NULL;l = r = &header;for (;;) {if (isLessThan(key, tree->key)) {// key is smaller than tree->keyif (NULL == tree->left)// 没找到break;if (isLessThan(key, tree->left->key)) {// 一字型rotateWithLeftChild(tree);// 左单旋if (NULL == tree->left)// 没找到break;}r->left = tree;// link rightr = tree;tree = tree->left;}else if (isLessThan(tree->key, key)) {// tree->key is smaller than keyif (NULL == tree->right)break;if (isLessThan(tree->right->key, key)) {// 一字型rotateWithRightChild(tree);if (NULL == tree->right)// 没找到break;}l->right = tree;// link leftl = tree;tree = tree->right;}elsebreak;}l->right = tree->left;r->left = tree->right;tree->left = header.right;tree->right = header.left;}// splaytemplate <class T, class Compare>void SplayTree<T, Compare>::splay(const T& key) {splay(mRoot, key);}// Internal method: rotateWithLeftChild(左单旋)template <class T, class Compare>void SplayTree<T, Compare>::rotateWithLeftChild(SplayTreeNode<T>*& k1) {SplayTreeNode<T>* k2 = k1->left;k1->left = k2->right;k2->right = k1;k1 = k2;}// Internal method: rotateWithRightChild(右单旋)template <class T, class Compare>void SplayTree<T, Compare>::rotateWithRightChild(SplayTreeNode<T>*& k1) {SplayTreeNode<T>* k2 = k1->right;k1->right = k2->left;k2->left = k1;k1 = k2;}/** * insert * 对值key进行伸展(树中可能已经含有有key值) * 旋转后1.如果mRoot->key就是key值(即本来就存在key),则return *       2.如果mRoot->key < key 则将mRoot和它的左子树放到newNode的左子树 *         将它的右子树放到newNode的右子树，将mRoot右子树置位空，再改变mRoot为newNode *       3.如果mRoot->key > key 和2差不多 */template <class T, class Compare>void SplayTree<T, Compare>::insert(const T& key) {if (NULL == mRoot) {mRoot = new SplayTreeNode<T>(key);return;}splay(key);if (isLessThan(key, mRoot->key)) {SplayTreeNode<T>* newNode = new SplayTreeNode<T>(key);newNode->left = mRoot->left;newNode->right = mRoot;mRoot->left = NULL;mRoot = newNode;}else if (isLessThan(mRoot->key, key)) {SplayTreeNode<T>* newNode = new SplayTreeNode<T>(key);newNode->right = mRoot->right;newNode->left = mRoot;mRoot->right = NULL;mRoot = newNode;}else {return;}}/** * remove * 对值key进行伸展(树中可能不存在key) * 1.如果mRoot->key != key(树中本来不存在key)，则return * 2.mRoot->key == key *    ⑴如果mRoot左子树为空，则mRoot指向右儿子，成为一棵新的树，再delete原来的根节点 *    ⑵如果mRoot左子树不为空，则对mRoot的左子树splay，将左子树中最大的key伸展到mRoot的左儿子 *      然后mRoot左儿子的右子树指向mRoot的右子树，此时mRoot的左儿子即可成为一个新的树，再delete原来的根节点 */template <class T,class Compare>void SplayTree<T, Compare>::remove(const T& key) {if (NULL == mRoot) return;SplayTreeNode<T>* delNode;splay(key);if (isLessThan(key, mRoot->key) || isLessThan(mRoot->key, key))return;if (mRoot->left == NULL) {delNode = mRoot;mRoot = mRoot->right;}else {delNode = mRoot;splay(mRoot->left, mRoot->key);// 把左子树中最大的元素伸展到根mRoot->left->right = mRoot->right;mRoot = mRoot->left;}delete delNode;}// findMintemplate <class T, class Compare>T SplayTree<T, Compare>::findMin() {return findMin(mRoot);}// Internal method: findMintemplate <class T, class Compare>T SplayTree<T, Compare>::findMin(SplayTreeNode<T>*& node) {if (NULL == node)throw std::runtime_error("can not find min in SplayTree.");SplayTreeNode<T>* min = node;while (NULL != min->left)min = min->left;T result = min->key;splay(node, result);return result;}// findMaxtemplate <class T, class Compare>T SplayTree<T, Compare>::findMax() {return findMax(mRoot);}// Internal method: findMaxtemplate <class T,class Compare>T SplayTree<T, Compare>::findMax(SplayTreeNode<T>*& node) {if (NULL == node)throw std::runtime_error("can not find max in SplayTree.");SplayTreeNode<T>* max = node;while (NULL != max->right)max = max->right;T result = max->key;splay(node, result);return result;}// findtemplate <class T, class Compare>bool SplayTree<T, Compare>::find(const T& key) {return find(mRoot, key);}// Internal method: findtemplate <class T, class Compare>bool SplayTree<T, Compare>::find(SplayTreeNode<T>*& node, const T& key) {splay(node, key);if (isLessThan(key, mRoot->key) || isLessThan(mRoot->key, key))return false;return true;}// 前序遍历：DLRtemplate <class T, class Compare>void SplayTree<T, Compare>::preOrder()const {preOrder(mRoot);}// Internal method: preOrdertemplate <class T, class Compare>void SplayTree<T, Compare>::preOrder(SplayTreeNode<T>* node)const {if (NULL == node) return;cout << node->key << " ";preOrder(node->left);preOrder(node->right);}// 中序遍历：LDRtemplate <class T, class Compare>void SplayTree<T, Compare>::inOrder()const {inOrder(mRoot);}// Internal method: inOrdertemplate <class T, class Compare>void SplayTree<T, Compare>::inOrder(SplayTreeNode<T>* node)const {if (NULL == node) return;inOrder(node->left);cout << node->key << " ";inOrder(node->right);}// 后序遍历：LRDtemplate <class T,class Compare>void SplayTree<T, Compare>::postOrder()const {postOrder(mRoot);}// Internal method: postOrdertemplate <class T, class Compare>void SplayTree<T, Compare>::postOrder(SplayTreeNode<T>* node)const {if (NULL == node) return;inOrder(node->left);inOrder(node->right);cout << node->key << " ";}// destroytemplate <class T, class Compare>void SplayTree<T, Compare>::destroy() {destroy(mRoot);}// Internal: destroytemplate <class T, class Compare>void SplayTree<T, Compare>::destroy(SplayTreeNode<T>*& node) {if (NULL == node) return;destroy(node->left);destroy(node->right);delete node;}// printtemplate <class T, class Compare>void SplayTree<T, Compare>::print()const {print(mRoot, T(), 0);}// Internal method: printtemplate <class T, class Compare>void SplayTree<T, Compare>::print(SplayTreeNode<T>* node, const T& key, const int& direction)const {if (NULL == node) return;if (node == mRoot)std::cout << node->key << " is the root" << std::endl;else {std::cout << node->key << " is " << key << "'s "<< ((direction == 1) ? "left" : "right") << " son" << std::endl;}print(node->left, node->key, 1);print(node->right, node->key, 2);}#endif

测试 -main.cpp

#include <iostream>#include "SplayTree.h"using namespace std;int main(){SplayTree<int>* pist = new SplayTree<int>;for (int i = 1; i <= 7; ++i)pist->insert(i);pist->print();cout << pist->find(1) << endl << endl;pist->print();cout << pist->find(8) << endl << endl;pist->print();cout << pist->findMin() << endl << endl;pist->print();cout << pist->findMax() << endl << endl;pist->destroy();return 0;}

测试2 -main.cpp

#include <iostream>#include "SplayTree.h"using namespace std;int main(){SplayTree<int>* pist = new SplayTree<int>;int n = 1;for (int i = 1; i <= 7; n += 2, ++i)pist->insert(n);pist->find(1);pist->print();cout << endl;pist->find(10);pist->print();pist->destroy();return 0;}