avl树
2011-11-08 00:27
316 查看
#include<time.h>
#include<iostream>
#include<stack>
using namespace std;
template<class E>
struct AVLNode
{
int bf; //ÆœºâÒò×Ó balance factor
AVLNode *leftchild; //leftchild
AVLNode *rightchild; //rightchild
E data;
AVLNode(E el){ data=el;bf=0;leftchild=NULL;rightchild=NULL;};
};
template<class E>
class AVLTree
{
public:
AVLTree():root(NULL){}; //construtor
bool Insert(E el); //insert new node
bool Remove(E el); //remove the node
void output(ostream &out); //output the AVLTree by inorder
private:
AVLNode<E> *root; //root of avl Tree
void RotateL(AVLNode<E> *&ptr); //rotation left
void RotateR(AVLNode<E> *&ptr); //rotation right
void RotateLR(AVLNode<E> *&ptr); //rotation left right
void RotateRL(AVLNode<E> *&ptr); //rotation right left
void Traverse(AVLNode<E> *ptr,ostream &out); //traverse the tree inorder
};
//remove a node
//@param
//el the key of the node to be removed
//if the node is removed successfully ,return true,else return false
template<class E>
bool AVLTree<E>::Remove(E el)
{
AVLNode<E> *pr=NULL,*p=root,*q,*ppr;
int d,dd=0;
stack<AVLNode<E> *>st;
while(p!=NULL) //Ñ°ÕÒÉŸ³ýλÖÃ
{
if(el==p->data)break; //ÕÒµœµÈÓÚkµÄœáµã Í£Ö¹ËÑË÷
pr=p;
st.push(pr); //ÓÃÕ»ŒÇÒä²éÕÒ·Ÿ¶
if(el<p->data)p=p->leftchild;
else p=p->rightchild;
}
if(p==NULL) return false; //ÎŽÕÒµœ±»ÉŸœáµã£¬ÉŸ³ýʧ°Ü
if(p->leftchild!=NULL&&p->rightchild!=NULL) //±»ÉŸœáµãÓÐÁœžö×ÓÅ®
{
pr=p;
st.push(pr);
q=p->leftchild; //ÔÚp×ö×ÖÊýÕÒpµÄÖ±œÓÇ°Çý
while(q->rightchild!=NULL)
{
pr=q;
st.push(pr);
q=q->rightchild;
}
p->data=q->data;
p=q;
}
if(p->leftchild!=NULL)q=p->leftchild;
else q=p->rightchild;
if(pr==NULL)root=q;
else
{
if(pr->leftchild==p)pr->leftchild=q;
else pr->rightchild=q;
while(st.empty()==false) //ÖØÐÂÆœºâ»¯
{
pr=st.top();
st.pop();
if(pr->rightchild==q)pr->bf--;
else pr->bf++;
if(st.empty()==false)
{
ppr=st.top();
dd=(ppr->leftchild==pr)?-1:1;
}
else dd=0; //Õ»¿Õ Ðýתºó²»ÓÃÓëÉϲãÁŽœÓ
if(pr->bf==1||pr->bf==-1)break;
if(pr->bf!=0) //|bf|=2
{
if(pr->bf<0)
{
d=-1;
q=pr->leftchild;
}
else
{
d=1;
q=pr->rightchild;
}
if(q->bf==0)
{
if(d==-1)
{
RotateR(pr);
pr->bf=1;
pr->leftchild->bf=-1;
}
else
{
RotateL(pr);
pr->bf=-1;
pr->rightchild->bf=1;
}
break;
}
if(q->bf==d) //ÁœœÚµãÆœºâÒò×ÓͬºÅ
{
if(d==-1) RotateR(pr);
else RotateL(pr);
}
else //ÁœÆœºâÒò×Ó·ŽºÅ
{
if(d==-1)RotateLR(pr);
else RotateRL(pr);
}
if(dd==-1)ppr->leftchild=pr;
else if(dd==1)ppr->rightchild=pr;
}
q=pr;
}
if(st.empty()==true)root=pr;
}
delete p;
return true;
}
//output the AVLTree inorder
//@param
//out the ostream
template<class E>
void AVLTree<E>::output(ostream &out)
{
out<<"Inorder traversal of AVL Tree.\n";
Traverse(root,out);
out<<endl;
}
//Traverse the AVLTree inorder
//@param
//ptr the root of tree
//out the ostream
template<class E>
void AVLTree<E>::Traverse(AVLNode<E> *ptr,ostream &out)
{
if(ptr==NULL)return;
Traverse(ptr->leftchild,out);
out<<ptr->data<<" ";
Traverse(ptr->rightchild,out);
}
//insert new node into the AVLTree
//@param el new element to insert
//if insert successfully ,return true,else return false
template<class E>
bool AVLTree<E>::Insert(E el)
{
AVLNode<E> *pr=NULL,*p=root,*q;
stack<AVLNode<E> *> st;
while(p!=NULL)
{ //Ñ°ÕÒ²åÈëλÖÃ
if(el==p->data) return false; //ÕÒµœµÈÓÚelµÄœáµã£¬²»²åÈë
pr=p;
st.push(pr);
if(el<p->data)p=p->leftchild;
else p=p->rightchild;
}
p=new AVLNode<E>(el); //ŽŽœšÒ»žöÐÂœáµã£¬data=el,bf=0;
if(p==NULL)
{
cerr<<"ŽæŽ¢¿ÕŒä²»×ã!"<<endl;
exit(1);
}
if(pr==NULL)
{
root=p; //¿ÕÊ÷£¬ÐÂœáµã³ÉΪžùœáµã
return true;
}
if(el<pr->data) pr->leftchild=p; //²åÈëÐÂœáµã
else pr->rightchild=p;
while(st.empty()==false)
{ //ÖØÐÂÆœºâ»¯
pr=st.top();
st.pop();
if(p==pr->leftchild) pr->bf--;
else pr->bf++;
if(pr->bf==0)break; //²åÈëÖ®ºóÆœºâ Í˳ö
if(pr->bf==1||pr->bf==-1) //|bf|=1 ÔòŒÌÐøÏòÉÏÕÒ²»ÆœºâµÄœáµã
p=pr;
else //|bf|=2,Ôòµ÷Õû
{
int d=(pr->bf<0)?-1:1; //ÉÏÃæœáµãµÄ·ûºÅ
if(p->bf==d) //ÁœžöœáµãÆœºâÒò×ÓͬºÅ£¬µ¥Ðý
{
if(d==-1) RotateR(pr);
else RotateL(pr);
}
else
{
if(d==-1) RotateLR(pr);
else RotateRL(pr);
}
break; //²»ÔÙÏòÉϵ÷Õû
}
}
if(st.empty()) root=pr; //µ÷ÕûµœÊ÷µÄžùœÚµã
else
{
q=st.top();
if(q->data>pr->data)q->leftchild=pr;
else q->rightchild=pr;
}
return true;
}
//rotation left right
//@param
//ptr the root of the tree to be rotated
template<class E>
void AVLTree<E>::RotateLR(AVLNode<E> *&ptr)
{
AVLNode<E> *subR=ptr,*subL=subR->leftchild;
ptr=subL->rightchild;
subL->rightchild=ptr->leftchild;
subR->leftchild=ptr->rightchild;
ptr->leftchild=subL;
ptr->rightchild=subR;
if(ptr->bf<=0)subL->bf=0;
else subL->bf=-1;
if(ptr->bf==-1)subR->bf=1;
else subR->bf=0;
ptr->bf=0;
}
//rotation right left
//@param
//ptr the root of the tree to be rotated
template <class E>
void AVLTree<E>::RotateRL(AVLNode<E> *&ptr)
{
AVLNode<E> *subL=ptr,*subR=subL->rightchild;
ptr=subR->leftchild;
subL->rightchild=ptr->leftchild;
subR->leftchild=ptr->rightchild;
ptr->leftchild=subL;
ptr->rightchild=subR;
if(ptr->bf>=0)subR->bf=0;
else subR->bf=1;
if(ptr->bf==1)subL->bf=-1;
else subL->bf=0;
ptr->bf=0;
}
//rotation left
//@param
//ptr the root of the tree to be rotated
template<class E>
void AVLTree<E>::RotateL(AVLNode<E> *&ptr)
{
AVLNode<E> *subL=ptr;
ptr=subL->rightchild;
subL->rightchild=ptr->leftchild;
ptr->leftchild=subL;
ptr->bf=subL->bf=0;
}
//rotation right
//@param
//ptr the root of the tree to be rotated
template<class E>
void AVLTree<E>::RotateR(AVLNode<E> *&ptr)
{
AVLNode<E> *subR=ptr;
ptr=subR->leftchild;
subR->leftchild=ptr->rightchild;
ptr->rightchild=subR;
subR->bf=0;
ptr->bf=0;
}
int _tmain(int argc, _TCHAR* argv[])
{
int n;
srand(unsigned int(time(0)));
n=rand()%5+5;
int *arr=new int
;
for(int i=0;i<n;i++)
{
arr[i]=rand()%100;
cout<<arr[i]<<" ";
}
cout<<endl;
AVLTree<int> myAVLTree;
for(int i=0;i<n;i++)
{
myAVLTree.Insert(arr[i]);
}
myAVLTree.output(cout);
myAVLTree.Remove(arr[0]);
myAVLTree.output(cout);
myAVLTree.Remove(arr[n-1]);
myAVLTree.output(cout);
myAVLTree.Remove(arr[n/2]);
myAVLTree.output(cout);
return 0;
}
内容来自用户分享和网络整理，不保证内容的准确性，如有侵权内容，可联系管理员处理 
相关文章推荐