算法导论P151 二叉查找树

// 头文件 BSTree.h

#ifndef _H_BSTREE_H_#define _H_BSTREE_H_#include <iostream>#include <stdio.h>#include <stdlib.h>#include <time.h>using namespace std;typedef struct BSTreeNode{struct BSTreeNode* m_pLeft; // 左孩子struct BSTreeNode* m_pRight; // 右孩子struct BSTreeNode* m_pParent; // 父亲节点int m_nValue;BSTreeNode(int val):m_pLeft(NULL), m_pRight(NULL), m_pParent(NULL),m_nValue(val){};}BSTree;// 输出数组元素void printArr(int* arr, int len);// 随机生成数组数据void randArr(int* arr, int len, int maxVal);// func proto// 函数名后面带_v2的均为非递归实现// 向二叉查找树插入元素valvoid insert2BSTree(BSTree* &root, BSTree* pParent, int val);void insert2BSTree_v2(BSTree* &root, int val);// 中序遍历二叉查找树void inorderBSTree(BSTree* &root);// 查找元素,返回该节点的指针BSTree* searchBSTree(BSTree* &root, int val);BSTree* searchBSTree_v2(BSTree* &root, int val);// 删除某一节点bool removeFromBSTree(BSTree* &root, int val);// 清空二叉查找树void emptyBSTree(BSTree* &root);// 找到最下节点BSTree* findMin(BSTree* &root);BSTree* findMin_v2(BSTree* &root);// 找到最大节点BSTree* findMax(BSTree* &root);BSTree* findMax_v2(BSTree* &root);// 找到元素的后继节点BSTree* findSuccessor(BSTree* &root, int val);// 找到元素的前驱节点BSTree* findPredecessor(BSTree* &root, int val);#endif

 

// cpp文件 BSTree.cpp

 

#include "BSTree.h"// 输出数组元素void printArr(int* arr, int len){for (int i = 0; i < len; i++){printf("%d ", *(arr+i));}}// 随机生成数组数据void randArr(int* arr, int len, int maxVal){srand((int)time(0));for (int i = 0; i < len; i++){*(arr+i) = rand() % maxVal;}}// 向二叉查找树插入元素valvoid insert2BSTree(BSTree* &root,BSTree* pParent,int val){if (root == NULL){root = new BSTreeNode(val);root->m_pParent = pParent;if (!root){printf("error: alloc failed, exit!!/n");return;}}// root != NULLelse if (val <= root->m_nValue){insert2BSTree(root->m_pLeft, root, val);}else if (val >= root->m_nValue){insert2BSTree(root->m_pRight, root, val);}}// 插入的非递归版本void insert2BSTree_v2(BSTree* &root, int val){if (root == NULL) // 空树{root = new BSTreeNode(val);return;}BSTree* pChild = root;BSTree* pParent = NULL;while(pChild != NULL){pParent = pChild; // 保存父节点if (val > pChild->m_nValue){pChild = pChild->m_pRight;}else{pChild = pChild->m_pLeft;}}BSTreeNode* node = new BSTreeNode(val);node->m_pParent = pParent; // 父节点if (pParent->m_nValue < node->m_nValue){pParent->m_pRight = node; // 右孩子}else{pParent->m_pLeft = node; // 左孩子}}// 中序遍历二叉查找树void inorderBSTree(BSTree* &root){if (root != NULL){inorderBSTree(root->m_pLeft);cout << root->m_nValue << " ";inorderBSTree(root->m_pRight);}}// 查找元素,返回该节点的指针BSTree* searchBSTree(BSTree* &root, int val){if (!root){return NULL;}else{if (root->m_nValue == val){return root;}else if (val < root->m_nValue){return searchBSTree(root->m_pLeft, val);}else // val > root->m_nValue{return searchBSTree(root->m_pRight, val);}}}BSTree* searchBSTree_v2(BSTree* &root, int val){if (root){// 否则从树跟开始BSTree* pRoot = root;while(pRoot != NULL) // 当前节点不为空{if (val == pRoot->m_nValue){return pRoot; // 直接返回}if (val < pRoot->m_nValue){pRoot = pRoot->m_pLeft;}else{pRoot = pRoot->m_pRight;}}}return NULL;}// 清空二叉查找树, 先根遍历void emptyBSTree(BSTree* &root){if (root){emptyBSTree(root->m_pLeft);emptyBSTree(root->m_pRight);cout << root->m_nValue << " ";delete root;}root = NULL;}// 删除某一节点bool removeFromBSTree(BSTree* &root, int val){BSTree* pCurr = NULL;pCurr =searchBSTree_v2(root, val); // 找到当前元素位置if (!pCurr){return false;}BSTree* pSuccessor = NULL;if (pCurr->m_pLeft == NULL || pCurr->m_pRight == NULL) // 有一个或者无孩子, pSuccessor指向被删节点{pSuccessor = pCurr;}else // 有俩孩子，pSuccessor指向被删节点后继,后继为右子树最左节点，最多一个右孩子{pSuccessor = findSuccessor(root, pCurr->m_nValue);}// pChild指向pSuccessor的非空儿子，pSuccessor最多一个儿子BSTree* pChild = NULL;if (pSuccessor->m_pLeft != NULL) // 后继有左孩子{pChild = pSuccessor->m_pLeft;}else{pChild = pSuccessor->m_pRight;}if (pChild != NULL) // pSuccessor有孩子,修改指针，删除pSuccessor{pChild->m_pParent = pSuccessor->m_pParent;}if (pSuccessor->m_pParent == NULL) // pSuccessor为根{root = pChild; // 删除根后更新根}else{if (pSuccessor == pSuccessor->m_pParent->m_pLeft) // pSuccessor 为左孩子{pSuccessor->m_pParent->m_pLeft = pChild;}else // pSuccessor 为右孩子{pSuccessor->m_pParent->m_pRight = pChild;}}if (pSuccessor != pCurr) // pCurr的后继就是要被删除的结点(pCurr有俩孩子),拷贝数据{pCurr->m_nValue = pSuccessor->m_nValue;}// 删除后继 pSuccessordelete pSuccessor;return true;}// 找到最下节点BSTree* findMin(BSTree* &root){if (!root){return NULL;}if (root->m_pLeft == NULL){return root;}else{return findMin(root->m_pLeft);}}BSTree* findMin_v2(BSTree* &root){BSTree* pRoot = root;while (pRoot->m_pLeft != NULL){pRoot = pRoot->m_pLeft;}return pRoot;}// 找到最大节点BSTree* findMax(BSTree* &root){if (!root){return NULL;}if (root->m_pRight == NULL){return root;}else{return findMax(root->m_pRight);}}BSTree* findMax_v2(BSTree* &root){BSTree* pRoot = root;while (pRoot->m_pRight != NULL){pRoot = pRoot->m_pRight;}return pRoot;}// 找到元素的后继节点BSTree* findSuccessor(BSTree* &root, int val){BSTree* pCurr = searchBSTree_v2(root, val); // 找到当前元素位置if (!pCurr){return NULL;}if (pCurr->m_pRight) //有右子树{return findMin_v2(pCurr->m_pRight); // 右子树的最小}// 无右子树，从当前节点开始向上查找，// 直到遇到某个是其父节点的左儿子的节点为止BSTree* pParent = NULL;pParent = pCurr->m_pParent;while(pParent != NULL && pCurr == pParent->m_pRight){pCurr = pParent;pParent = pCurr->m_pParent; // 向上走}return pParent;}// 找到元素的前驱节点BSTree* findPredecessor(BSTree* &root, int val){BSTree* pCurr = searchBSTree_v2(root, val); // 找到当前元素位置if (!pCurr){return NULL;}if (pCurr->m_pLeft) //有左子树{return findMax_v2(pCurr->m_pLeft); // 左子树的最大}// 无左子树，从当前节点开始向上查找，// 直到遇到某个是其父节点的右儿子的节点为止BSTree* pParent = NULL;pParent = pCurr->m_pParent;while(pParent != NULL && pCurr == pParent->m_pLeft){pCurr = pParent;pParent = pCurr->m_pParent; // 向上走}return pParent;}

 

// 测试文件 mainEntry.cpp

// copyright by Kennie.D.John#include "BSTree.h"int main(int argc, char* argv[]){cout << "hello, i am Kennie" << endl;int len = 20;int* arr = new int[len];randArr(arr, len, 100);cout << "source array data: " << endl;printArr(arr, len);// test func insert2BSTreeBSTree* root = NULL;for (int i = 0; i < len; i++){insert2BSTree(root, NULL, arr[i]);//insert2BSTree_v2(root, arr[i]);}cout << endl;cout << "inorder BSTree: " << endl;inorderBSTree(root);// test func searchBSTreeBSTree* toBeFound = NULL;int valToBeFound = 63;//toBeFound = searchBSTree(root, valToBeFound);toBeFound = searchBSTree_v2(root, valToBeFound);if (toBeFound != NULL){cout << endl;cout << toBeFound->m_nValue << "found " << endl;}else{cout << endl;cout << valToBeFound << " not found" << endl;}// test func findMinBSTree* minNode = NULL;//minNode = findMin(root);minNode = findMin_v2(root);cout << endl;cout << "min val: " << minNode->m_nValue << endl;// test func findMaxBSTree* maxNode = NULL;//maxNode = findMax(root);maxNode = findMax_v2(root);cout << endl;cout << "max val: " << maxNode->m_nValue << endl;// test func findSuccessor and findPredecessorBSTree* pSuccessor = NULL;BSTree* pPredecessor = NULL;int toBeInserted = 49;insert2BSTree_v2(root, toBeInserted);cout << endl;cout << "inorder BSTree: " << endl;inorderBSTree(root);pSuccessor = findSuccessor(root, toBeInserted);pPredecessor = findPredecessor(root, toBeInserted);if (pPredecessor != NULL){cout << endl;cout << toBeInserted << "'s predecessor is " << pPredecessor->m_nValue << endl;}else{cout << endl;cout << " no successor" << endl;}if (pSuccessor != NULL){cout << endl;cout << toBeInserted << "'s successor is " << pSuccessor->m_nValue << endl;}else{cout << endl;cout << " no successor" << endl;}// test func removeFromBSTreebool isRemoved = false;int toBeRemoved = root->m_nValue;isRemoved = removeFromBSTree(root, toBeRemoved);if (isRemoved){cout << endl;cout << "after removed " << toBeRemoved << endl;inorderBSTree(root);}else{cout << endl;cout << "nothing removed " << endl;}// test func emptyBSTreecout << endl;cout << "empty BSTree " << endl;emptyBSTree(root);cout << endl;delete arr;arr = NULL;return 0;}

 

// 运行结果