算法导论 第12章 二叉搜索树 C++实现

chapter12.h

#ifndef CHAPTER12_H#define CHAPTER12_H#include<iostream>#include<vector>#include<exception>//binary search tree node//供二叉搜索树使用的节点类class bstree;class node{public:node(int k,node* p=NULL,node* l=NULL,node* r=NULL):key(k),parent(p),left(l),right(r){}//声明为友元类，bstree可以使用node的private成员friend class bstree;private://键值int key;//父节点node* parent;//左儿子node* left;//右儿子node* right;};//binary search tree//二叉搜索树类class bstree{public://二叉搜索树的默认构造函数bstree():root(NULL){}//析构函数~bstree(){clear(root);}//由析构函数调用的clear函数void clear(node* x);//构造函数，由vector<int>构造二叉搜索数bstree(const std::vector<int>& a);//中序遍历，从根root开始void inorder_tree_walk()const;//中序遍历，从x开始void inorder_tree_walk(node* x) const;//以x为根的子树中搜索key的节点，node* search_tree(node* x,int key) const;//以root为根搜索key的节点，node* search_tree(int key)const;//以x为根的子树中迭代搜索key的节点，node* iterative_search_tree(node* x,int key) const;//以root为根迭代搜索key的节点，node* iterative_search_tree(int key) const;//以x为根的子树中搜索最大key的节点，node* tree_maximum(node* x) const;//以root为根的树中搜索最大key的节点，node* tree_maximum()const;//以x为根的子树中搜索最小key的节点，node* tree_minimum(node* x) const;//以root为根的树中搜索最小key的节点，node* tree_minimum()const;//结点x的后继node* tree_successor(node* x)const;//结点x的前驱node* tree_predecessor(node* x)const;//在树中插入节点zvoid tree_insert(node* z);//将以u为根节点的子树变换为以v为根节点的子树void transplant(node* u,node* v );//删除节点zvoid tree_delete(node* z);private://根节点rootnode* root;};bstree::bstree(const std::vector<int>& a){root=NULL;for(int i=0;i<a.size();i++){node* p=new node(a[i]);if(p==NULL){std::runtime_error("bad allocate !");exit(0);}tree_insert(new node(a[i]));}root->parent=NULL;}void bstree::clear(node* x){while(x!=NULL){clear(x->left);clear(x->right);//释放内存node* tmp=x;x=NULL;delete tmp;}}void bstree::inorder_tree_walk(node* x) const{if(x!=NULL){inorder_tree_walk(x->left);std::cout<<x->key<<" ";inorder_tree_walk(x->right);}}void bstree::inorder_tree_walk()const{inorder_tree_walk(root);std::cout<<std::endl;}node* bstree::search_tree(node* x,int k)const{if(x==NULL||x->key==k)return x;if(k<x->key)return search_tree(x->left,k);elsereturn search_tree(x->right,k);}node* bstree::search_tree(int key)const{node* p=search_tree(root,key);if(p!=NULL)std::cout<<"find key "<<p->key<<std::endl;elsestd::cout<<"no find key "<<key<<std::endl;return p;}node* bstree::iterative_search_tree(node* x,int k) const{while(x!=NULL&&k!=x->key)if(k<x->key)x=x->left;else x=x->right;return x;}node* bstree::iterative_search_tree(int key) const{node* p=iterative_search_tree(root,key);if(p!=NULL)std::cout<<"find key "<<p->key<<std::endl;elsestd::cout<<"no find key "<<key<<std::endl;return p;}node* bstree::tree_maximum(node* x)const{while(x->right!=NULL)x=x->right;return x;}node* bstree::tree_maximum()const{node* p=tree_maximum(root);std::cout<<"tree maximum:"<<p->key<<std::endl;return p;}node* bstree::tree_minimum(node* x) const{while(x->left!=NULL)x=x->left;return x;}node* bstree::tree_minimum()const{node* p=tree_minimum(root);std::cout<<"tree minimum:"<<p->key<<std::endl;return p;}node* bstree::tree_successor(node* x) const{if(x->right!=NULL)return tree_minimum(x->right);node* y=x->parent;while(y!=NULL&&x==y->right){x=y;y=y->parent;}//std::cout<<"tree successor:"<<y->key<<std::endl;return y;}node* bstree::tree_predecessor(node* x)const{if(x->left!=NULL)return tree_maximum(x->left);node* y=x->parent;while(y!=NULL&&x==y->left){x=y;y=y->parent;}//std::cout<<"tree predecessor:"<<y->key<<std::endl;return y;}void bstree::tree_insert(node* z){node* y=NULL;node* x=root;while(x!=NULL){y=x;if(x->key>=z->key)x=x->left;elsex=x->right;}z->parent=y;if(y==NULL)root=z;else if(z->key<y->key)y->left=z;else y->right=z;}void bstree::transplant(node* u ,node* v ){if(u->parent==NULL)root=v;else if(u==u->parent->left)u->parent->left=v;else u->parent->right=v;if(v!=NULL)v->parent=u->parent;}void bstree::tree_delete(node* z){if(z->left==NULL)transplant(z,z->right);else if(z->right==NULL)transplant(z,z->left);else{node* y=tree_minimum(z->right);if(y->parent!=z){transplant(y,y->right);y->right=z->right;y->right->parent=y;}transplant(z,y);y->left=z->left;y->left->parent=y;}node* tmp=z;z=NULL;delete tmp;}#endif

chapter12_test.cpp

#include"chapter12.h"void main(){int array[]={15,6,18,3,7,17,20,2,4,13,9};std::vector<int> vec(array,array+sizeof(array)/sizeof(int));bstree bst(vec);bst.inorder_tree_walk();node* p1=bst.search_tree(6);node* p2=bst.iterative_search_tree(7);bst.tree_maximum();bst.tree_minimum();node* p3=bst.tree_successor(p1);node* p4=bst.tree_predecessor(p1);node* p5=bst.tree_successor(p2);node* p6=bst.tree_predecessor(p2);node* p_new1=new node(14);node* p_new2=new node(19);bst.tree_insert(p_new1);bst.tree_insert(p_new2);bst.tree_delete(p_new1);bst.tree_delete(p_new2);bst.tree_delete(p1);bst.tree_delete(p2);}