二叉搜索树(c++)

该版本翻译了算法导论中的伪代码。 水平有限，不足之处望指出。

#ifndef BST_H#define BST_Husing namespace std;template<class T>struct BstNode{BstNode(T k = 12, BstNode<T>* lt = NULL, BstNode<T> *rt = NULL, BstNode<T> *pt = NULL) :key(k), left(lt), right(rt), parent(pt){}T key;BstNode<T> *left;BstNode<T> *right;BstNode<T> *parent;};//二叉树 结点类template<class T>class BsTree{public:BsTree(){  }~BsTree(){ }void Destroy(BstNode<T>*&Node); //destroy a tree.void InOrder(BstNode<T> *&Node);//output the datas,from small to big;void CreateBst(BstNode<T>*&Tree);bool Search(BstNode<T> *&Node, T x);//search the exact data;BstNode<T> *Locate(BstNode<T>*Node, T x);//find address;BstNode<T> *MaxTree(BstNode<T> * &Node); //max,return *p;T OutputMax(BstNode<T> * Node);//max ,return value;BstNode<T> *MinTree(BstNode<T> * &Node);//min, return *p;T OutputMin(BstNode<T> * Node);//min return value;BstNode<T> *Successor(BstNode<T> *Node);//search the seuccessorbool Insert(BstNode<T>*&Node, T m);//insert value ;void  TransPlant(BstNode<T>*&Node, BstNode<T>*&x, BstNode<T>*&y);//定位1bool Delete(BstNode<T>*Node, BstNode<T>*&del);int Seq_Search(int *a, int n, int key);//顺序查找int Dichotomy(int *b, int n, int key);//二分查找private:BstNode<T>*root;};/*删除BST*/template<class T>void BsTree<T>::Destroy(BstNode<T>*&Node){if (Node != NULL){Destroy(Node->left);Destroy(Node->right);delete Node;}}/*删除BST*/template<class T>  //中序输出的实现void BsTree<T>::InOrder(BstNode<T> *&Node){if (Node == NULL) return;InOrder(Node->left);cout << " <" << Node->key << "> ";InOrder(Node->right);}template<class T> //查找指定的x,存在则Truebool BsTree<T>::Search(BstNode<T> *&Node, T x){if (Node == NULL) return NULL;if (Node->key == x)return true;if (Node->key > x)return Search(Node->left, x);else return Search(Node->right, x);}template<class T>BstNode<T>*BsTree<T>::Locate(BstNode<T>*Node, T x){ //if (Node == NULL) return NULL;if (Node->key == x)return Node;if (Node->key > x)return Locate(Node->left, x);else return Locate(Node->right, x);}template<class T>BstNode<T> *BsTree<T>::MaxTree(BstNode<T> * &Node){//返回地址，供其他函数调用while (Node->right != NULL)Node = Node->right;return Node;}template<class T>T BsTree<T>::OutputMax(BstNode<T> * Node){ //返回值while (Node->right != NULL)Node = Node->right;return Node->key;}template<class T>BstNode<T> *BsTree<T>::MinTree(BstNode<T> * &Node){//返回地址，供其他函数调用if (Node != NULL && Node->left != NULL)Node = Node->left;return Node;}template<class T>T BsTree<T>::OutputMin(BstNode<T> *Node){//返回值while (Node->left != NULL)Node = Node->left;return Node->key;}template<class T>BstNode<T> *BsTree<T>::Successor(BstNode<T> *Node){if (Node->right != NULL)return MinTree(Node->right);//如果结点的右子树非空，就返回右子树的分支中最小的关键值BstNode<T>*p = Node->parent;while (p != NULL && Node == p->right){Node = p;p = p->parent;}return p;}template<class T>bool BsTree<T>::Insert(BstNode<T>*&Node, T m){ //Node为根节点 算法导论中的做法BstNode<T> *y = NULL;BstNode<T> *x = Node;BstNode<T> *temp = NULL;while (x != NULL){y = x;if (m < x->key){x = x->left;//x->parent = y;}else{ x = x->right; } // x->parent = y; }}if (y == NULL)Node = new BstNode<T>(m);else if (m < y->key) {y->left = new BstNode<T>(m);y->left->parent = y;}else {y->right = new BstNode<T>(m);y->right->parent = y;}return true;}template<class T>void BsTree<T>::TransPlant(BstNode<T>*&Node, BstNode<T>*&x, BstNode<T>*&y){//用y替换结点x,并且更新Parent.// if (x->parent == NULL)//    Node.root = y;if (x == x->parent->left){x->parent->left = y;// y->parent = x->parent;//delete x;}else {// y->parent = x->parent;x->parent->right = y;//delete x;}// if (y == NULL);// y->parent = x->parent;}template<class T>bool BsTree<T>::Delete(BstNode<T>*Node, BstNode<T>*&del){BstNode<T>*p = NULL;if (del->left == NULL &&del->right == NULL) //删除叶结点{if (del == del->parent->left)  del->parent->left = NULL;else del->parent->right = NULL;delete del;return true;}if (del->left == NULL &&del->right != NULL)//左子树空{TransPlant(Node, del, del->right);return true;}else if (del->right == NULL && del->left != NULL)//右子树空{TransPlant(Node, del, del->left);return true;}else p = MinTree(del->right); //左右都不空if (p != NULL &&p->parent == del){TransPlant(Node, p, p->right);p->right = del->right;p->right->parent = p;return true;}else{TransPlant(Node, del, p);p->left = del->left;}return true;}template<class T >int BsTree<T>::Seq_Search(int *a, int n, int key){for (int i = 0; i < n; i++){if (a[i] == key)return i;}return 0;}template<class T>int BsTree<T>::Dichotomy(int *b, int n, int key){int start = 0, mid = 0, end = n;while (start <= end){mid = (start + end) / 2;if (b[mid] < key)start = mid + 1;else if (b[mid] > key)end = mid - 1;else return mid;}return -1;}<pre name="code" class="cpp">#include<iostream>#include"BST.h"#include<stdlib.h>#include<ctime>#include<time.h>using namespace std;int main(){BstNode<int>*Node = new BstNode<int>;BsTree<int> Tree;/****************//*制造随机数，插入树中*//****************/srand((unsigned)time(NULL));int A[100000];for (int i = 0; i != 100000; i++){A[i] = rand();Tree.Insert(Node, A[i]);}/****************//*制造随机数，插入树中 *//****************//****************//* 制造固定的数组，演示删除*//****************//*int B[13] = { 5, 25, 2, 9, 18, 30, 14, 20,13,16 ,19,21};for (int i = 0; i != 12; i++)Tree.Insert(Node,B[i]);*//****************//* 制造固定的数组，演示删除*//****************//*************/ /* 在二叉搜索树中 输出最小/大的值*/  /******************//*cout << "The minimal key is:" <<"<"<< Tree.OutputMin(Node)<<">" << endl;cout << "The max key is:" << "<"<<Tree.OutputMax(Node) <<">" <<endl;*//*************/ /*在二叉搜索树中 输出最小/大的值*/  /******************//****************/ /*查找一个数 是否存在在二叉搜索树中*/  /*********************//*int Num_exist = 0;cout << "Input the key value that you want to search." << endl;cin >> Num_exist;if (Tree.Search(Node, Num_exist))cout << Num_exist <<" "<< "exist." << endl;else cout << Num_exist << " isn't exist. " << endl;*//****************/ /*查找一个数 是否存在在二叉搜索树中*/  /*********************//****************/ /*删除*/  /*********************//*	BstNode<int>*Node_2 = Tree.Locate(Node,18); //创建一个新的结点 ,赋予他原结点Key=18的地址Tree.Delete(Node, Node_2);cout<<"After Delete 18 "<<endl;Tree.InOrder(Node); //中序输出（按从小到大的顺序输出) ;/****************/ /*删除*/  /*********************//***************/ // BST查找//***************/clock_t start_time_1 = clock();if (Tree.Locate(Node, 2))cout << "BST search succeed!" << endl;clock_t end_time_1 = clock();cout << "Binary Serach Tree search-->Running time is: " << static_cast<double>(end_time_1 - start_time_1) / CLOCKS_PER_SEC * 1000 << "ms" << endl;/**************////BST查找//***************/return 0;}