2-3-4树实现

//==================2-3-4树的异常处理类========================= #ifndef TWO_THREE_FOUR_TREE_EXCEPTION_H_ #define TWO_THREE_FOUR_TREE_EXCEPTION_H_ #include<string> #include<stdexcept> class TtfTreeException:public std::logic_error { public: TtfTreeException(const std::string &message="") :std::logic_error(message.c_str()) {} }; #endif

//===================two_three_four_tree_item.h===================== #ifndef TWO_THREE_FOUR_TREE_ITEM_H_ #define TWO_THREE_FOUR_TREE_ITEM_H_ template<class ValT,class KeyT> class Item { public: Item() {} Item(ValT &_val,KeyT &_key) :val(_val),key(_key) {} KeyT getKey()const { return key; } ValT getVal()const { return val; } void set(ValT &_val,KeyT &_key) { val=_val; key=_key; } private: ValT val; KeyT key; }; #endif

//====================two_three_four_tree_node.h========================= // 2-3-4树的节点， #ifndef TWO_THREE_FOUR_TREE_NODE_H_ #define TWO_THREE_FOUR_TREE_NODE_H_ template<class ItemT,class KeyT> class TtfTree; template<class ItemT,class KeyT> class Node { private: enum {SIZE=3}; //定义一个含有3个ItemT元素的数组，用于存放数据 ItemT item[SIZE]; //定义一个含有4个节点指针元素的数组，用于存放子树 Node *childPtr[SIZE+1]; //当前节点中数据项的数目； int size; Node(ItemT &_item,Node *fchildPtr,Node *lchildPtr) { item[0]=_item; childPtr[0]=fchildPtr; childPtr[1]=lchildPtr; size=1; childPtr[2]=childPtr[3]=NULL; } friend class TtfTree<ItemT,KeyT>; }; #endif

//======================two_three_four_tree.h========================= //2-3-4树的主体文件 #ifndef TWO_THREE_FOUR_TREE_H_ #define TWO_THREE_FOUR_TREE_H_ #include"two_three_four_tree_exception.h" #include"two_three_four_tree_node.h" template<class ItemT,class KeyT> class TtfTree { public: //默认构造函数 TtfTree(); //复制构造函数 TtfTree(TtfTree &ttftree); ~TtfTree(); bool empty()const; void insert(ItemT &_item)throw(TtfTreeException); void remove(KeyT &_key)throw(TtfTreeException); //遍历2-3-4树 void traverse(void (*visit)(ItemT _item)); //检索2-3-4树 void retrieve(KeyT &_key,ItemT &_item)throw(TtfTreeException); protected: void insertNode(Node<ItemT,KeyT>*&treePtr,ItemT &_item)throw(TtfTreeException); void removeNode(Node<ItemT,KeyT>*&treePtr,KeyT &_key,int &pos)throw(TtfTreeException); void traverseNode(Node<ItemT,KeyT>*&treePtr,void (*visit)(ItemT _item)); void retrieveNode(Node<ItemT,KeyT>*&treePtr,KeyT &_key,ItemT &_item)throw(TtfTreeException); void copy(Node<ItemT,KeyT>*&treePtr,Node<ItemT,KeyT> *&oldPtr)throw(TtfTreeException); void destroy(Node<ItemT,KeyT>*&treePtr); // get the index of the childPtr the next child should retrieve int getIndex(Node<ItemT,KeyT>*&treePtr,KeyT &_key)const; //get the index of the item whose searchkey equal to _key; int getEqual(Node<ItemT,KeyT>*&treePtr,KeyT &_key)const; //分解具有三项数据的节点 void spliteNode(Node<ItemT,KeyT>*&treePtr,int n)throw(TtfTreeException); //修复只含有一个数据项的节点，使其包含2或3项 void repairNode(Node<ItemT,KeyT>*&treePtr,int n); //判断是否为根 bool isRoot(Node<ItemT,KeyT>*&treePtr); private: Node<ItemT,KeyT> *root; }; #endif

//==================two_three_four_tree.cpp========================= // 2-3-4树的实现文件 #include<cstddef> #include"two_three_four_tree.h" template<class ItemT,class KeyT> TtfTree<ItemT,KeyT>::TtfTree() { root=NULL; } template<class ItemT,class KeyT> TtfTree<ItemT,KeyT>::TtfTree(TtfTree &ttftree) { copy(root,ttftree.root); } template<class ItemT,class KeyT> TtfTree<ItemT,KeyT>::~TtfTree() { destroy(root); } template<class ItemT,class KeyT> bool TtfTree<ItemT,KeyT>::empty()const { return root==NULL; } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::insert(ItemT &_item)throw(TtfTreeException) { if(empty()) { root=new Node<ItemT,KeyT>(_item,NULL,NULL); if(root==NULL) throw TtfTreeException("allocate memory failded !"); } else { if(root->size==3) { Node<ItemT,KeyT> *tempPtr= new Node<ItemT,KeyT>(root->item[2],root->childPtr[2],root->childPtr[3]); if(tempPtr==NULL) throw TtfTreeException("allocate memory failed !"); root->childPtr[2]=root->childPtr[3]=NULL; Node<ItemT,KeyT> *tranPtr= new Node<ItemT,KeyT>(root->item[1],root,tempPtr); if(tranPtr==NULL) throw TtfTreeException("allocate memory failed !"); root->size=1; root=tranPtr; } try{ insertNode(root,_item); }catch(TtfTreeException &e) { throw; } } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::remove(KeyT &_key)throw(TtfTreeException) { if(empty()) throw TtfTreeException("empty tree !"); try{ int index=-1; removeNode(root,_key,index); }catch(TtfTreeException &e) { throw; } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::traverse(void (*visit)(ItemT _item)) { traverseNode(root,visit); } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::retrieve(KeyT &_key,ItemT &_item)throw(TtfTreeException) { if(empty()) throw TtfTreeException("empty tree !"); try{ retrieveNode(root,_key,_item); }catch(TtfTreeException &e) { throw; } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::insertNode(Node<ItemT,KeyT>*&treePtr,ItemT &_item)throw(TtfTreeException) { if(treePtr->childPtr[0]==NULL) { int index=getIndex(treePtr,_item.getKey()); for(int i=treePtr->size;i>index;i--) treePtr->item[i]=treePtr->item[i-1]; treePtr->item[index]=_item; (treePtr->size)++; } else { int index=getIndex(treePtr,_item.getKey()); if(treePtr->childPtr[index]->size==3) { try{ spliteNode(treePtr,index); }catch(TtfTreeException &e) { throw; } } //重新获取下一步要检索的孩子指针 index=getIndex(treePtr,_item.getKey()); insertNode(treePtr->childPtr[index],_item); } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::removeNode(Node<ItemT,KeyT> *&treePtr,KeyT &_key,int &pos)throw(TtfTreeException) { pos=getEqual(treePtr,_key); if(pos==-1) { if(treePtr->childPtr[0]==NULL) throw TtfTreeException("key item not exist !"); pos=getIndex(treePtr,_key); if(treePtr->childPtr[pos]->size==1) repairNode(treePtr,pos); pos=getIndex(treePtr,_key); removeNode(treePtr->childPtr[pos],_key,pos); } else { Node<ItemT,KeyT>*tempPtr=treePtr->childPtr[pos+1]; if(tempPtr==NULL) { for(int i=pos;i<treePtr->size-1;i++) treePtr->item[i]=treePtr->item[i+1]; (treePtr->size)--; } else { while(tempPtr->childPtr[0]!=NULL) tempPtr=tempPtr->childPtr[0]; treePtr->item[pos]=tempPtr->item[0]; KeyT newkey=tempPtr->item[0].getKey(); removeNode(treePtr->childPtr[pos+1],newkey,pos); } } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::traverseNode(Node<ItemT,KeyT> *&treePtr,void (*visit)(ItemT _item)) { if(treePtr!=NULL) { int i=0; for(i=0;i<treePtr->size;i++) { traverseNode(treePtr->childPtr[i],visit); visit(treePtr->item[i]); } traverseNode(treePtr->childPtr[i],visit); } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::retrieveNode(Node<ItemT,KeyT>*&treePtr,KeyT &_key,ItemT &_item)throw(TtfTreeException) { int pos=getEqual(treePtr,_key); if(pos==-1) { if(treePtr->childPtr[0]==NULL) throw TtfTreeException("key item not exist !"); pos=getIndex(treePtr,_key); retrieveNode(treePtr->childPtr[pos],_key,_item); } else { _item=treePtr->item[pos]; } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::copy(Node<ItemT,KeyT>*&treePtr,Node<ItemT,KeyT>*&oldPtr)throw(TtfTreeException) { if(oldPtr!=NULL) { treePtr=new Node<ItemT,KeyT>(oldPtr->item[0],NULL,NULL); if(treePtr==NULL) throw TtfTreeException("allocate memory failed !"); treePtr->size=oldPtr->size; int i=0; for(i=0;i<oldPtr->size;i++) { copy(treePtr->childPtr[i],oldPtr->childPtr[i]); treePtr->item[i]=oldPtr->item[i]; } copy(treePtr->childPtr[i],oldPtr->childPtr[i]); } } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::destroy(Node<ItemT,KeyT>*&treePtr) { if(treePtr!=NULL) { for(int i=0;i<=treePtr->size;i++) { destroy(treePtr->childPtr[i]); } delete treePtr; treePtr=NULL; } } template<class ItemT,class KeyT> int TtfTree<ItemT,KeyT>::getIndex(Node<ItemT,KeyT> *&treePtr,KeyT &_key)const { int i=0; while((i<treePtr->size)&&(treePtr->item[i].getKey()<_key)) i++; return i; } template<class ItemT,class KeyT> int TtfTree<ItemT,KeyT>::getEqual(Node<ItemT,KeyT> *&treePtr,KeyT &_key)const { int i=0; while((i<treePtr->size)&&(treePtr->item[i].getKey()!=_key)) i++; if(i>=treePtr->size) return -1; else return i; } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::spliteNode(Node<ItemT,KeyT>*&treePtr,int n)throw(TtfTreeException) { Node<ItemT,KeyT> *tempPtr=treePtr->childPtr[n]; Node<ItemT,KeyT> *tranPtr= new Node<ItemT,KeyT>(tempPtr->item[2],tempPtr->childPtr[2],tempPtr->childPtr[3]); if(tranPtr==NULL) throw TtfTreeException("allocate memory failed !"); tempPtr->childPtr[2]=tempPtr->childPtr[3]=NULL; tempPtr->size=1; int i=0; for(i=treePtr->size;i>n;i--) { treePtr->item[i]=treePtr->item[i-1]; treePtr->childPtr[i+1]=treePtr->childPtr[i]; } treePtr->item[i]=tempPtr->item[1]; treePtr->childPtr[i+1]=tranPtr; (treePtr->size)++; } template<class ItemT,class KeyT> void TtfTree<ItemT,KeyT>::repairNode(Node<ItemT,KeyT>*&treePtr,int n) { if(n==treePtr->size) n=n-1; if((treePtr->childPtr[n]->size==1)&&(treePtr->childPtr[n+1]->size==1)) { //合并treePtr->childPtr[n]和treePtr->childPtr[n+1]项 treePtr->childPtr[n]->item[1]=treePtr->item[n]; treePtr->childPtr[n]->item[2]=treePtr->childPtr[n+1]->item[0]; treePtr->childPtr[n]->childPtr[2]=treePtr->childPtr[n+1]->childPtr[0]; treePtr->childPtr[n]->childPtr[3]=treePtr->childPtr[n+1]->childPtr[1]; treePtr->childPtr[n+1]->childPtr[0]=treePtr->childPtr[n+1]->childPtr[1]=NULL; treePtr->childPtr[n]->size=3; (treePtr->size)--; delete treePtr->childPtr[n+1]; treePtr->childPtr[n+1]=NULL; if(isRoot(treePtr)&&(treePtr->size==1)) { Node<ItemT,KeyT>*tempPtr=treePtr; treePtr=treePtr->childPtr[n]; tempPtr->childPtr[n]=NULL; delete tempPtr; } else { int i=0; for(i=n;i<treePtr->size-1;i++) { treePtr->item[i]=treePtr->item[i+1]; treePtr->childPtr[i+1]=treePtr->childPtr[i+2]; } treePtr->childPtr[i+1]=NULL; } } else if(treePtr->childPtr[n]->size==1) { treePtr->childPtr[n]->item[1]=treePtr->item[n]; treePtr->childPtr[n]->childPtr[2]=treePtr->childPtr[n+1]->childPtr[0]; (treePtr->childPtr[n]->size)++; treePtr->item[n]=treePtr->childPtr[n+1]->item[0]; int numb=treePtr->childPtr[n+1]->size; int i=0; for(i=0;i<numb-1;i++) { treePtr->childPtr[n+1]->item[i]=treePtr->childPtr[n+1]->item[i+1]; treePtr->childPtr[n+1]->childPtr[i]=treePtr->childPtr[n+1]->childPtr[i+1]; } treePtr->childPtr[n+1]->childPtr[i]=treePtr->childPtr[n+1]->childPtr[numb]; treePtr->childPtr[n+1]->childPtr[numb]=NULL; (treePtr->childPtr[n+1]->size)++; } else { treePtr->childPtr[n+1]->item[1]=treePtr->childPtr[n+1]->item[0]; treePtr->childPtr[n+1]->item[0]=treePtr->item[n]; for(int i=2;i>0;i--) treePtr->childPtr[n+1]->childPtr[i]=treePtr->childPtr[n+1]->childPtr[i-1]; int numb=treePtr->childPtr[n]->size; treePtr->childPtr[n+1]->childPtr[0]=treePtr->childPtr[n]->childPtr[numb]; (treePtr->childPtr[n+1]->size)++; treePtr->item[n]=treePtr->childPtr[n]->item[numb-1]; treePtr->childPtr[n]->childPtr[numb]=NULL; (treePtr->childPtr[n]->size)--; } } template<class ItemT,class KeyT> bool TtfTree<ItemT,KeyT>::isRoot(Node<ItemT,KeyT>*&treePtr) { return &treePtr==&root; }

//================测试程序======================== #include<iostream> #include<string> #include<ctime> #include<cstdlib> #include"two_three_four_tree_item.h" #include"two_three_four_tree.h" #include"two_three_four_tree.cpp" using namespace std; void display(Item<string,string> _item); int main() { srand(time(0)); TtfTree<Item<string,string>,string> atree; Item<string,string> newitem; string thekey,theval; cout<<"creating avl tree atree with 100 datas !"<<endl; for(int i=0;i<100;i++) { for(int j=0;j<10;j++) { thekey=thekey+char(rand()%26+'a'); theval=theval+char(rand()%10+'0'); } newitem.set(theval,thekey); try{ atree.insert(newitem); thekey.clear(); theval.clear(); }catch(TtfTreeException &e) { cout<<e.what()<<endl; } } cout<<"the data in atree are :"<<endl; atree.traverse(display); cout<<"traverse the tree atree over !"<<endl; cout<<"enter the key word of the item (q to quit ):"<<endl; Item<string,string> aitem; string keyword; cin>>keyword; while(keyword!="q") { try{ atree.retrieve(keyword,aitem); display(aitem); }catch(TtfTreeException &e) { cout<<e.what()<<endl; } cout<<"enter other one key (q to quit): "<<endl; cin>>keyword; } cout<<"enter the key word of the item you want to delete (q to quit):"<<endl; cin>>keyword; while(keyword!="q") { try{ atree.remove(keyword); }catch(TtfTreeException &e) { cout<<e.what()<<endl; } cout<<"enter other one key (s to stop):"<<endl; cin>>keyword; } cout<<"create a tree same as atree !"<<endl; TtfTree<Item<string,string>,string> btree(atree); cout<<"the date in btree :"<<endl; btree.traverse(display); cout<<"over !"<<endl; return 0; } void display(Item<string,string> _item) { cout<< _item.getKey()<<'\t'<<_item.getVal()<<endl; }