编程练习——伸展树(SplayTree)

最新推荐文章于 2021-02-13 15:40:51 发布

iteye_2449

最新推荐文章于 2021-02-13 15:40:51 发布

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文章标签：编程 Apache 数据结构 Blog

本文介绍了伸展树(Splay Tree)的基本概念及其实现细节，包括插入、删除和查找操作的具体步骤，并探讨了其适用场景。伸展树是一种自调整的二叉查找树，适用于查询结果概率非平均的情况。

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 伸展树用于查询结果的概率非平均情况，即起初假设某些要查询的信息偏多，有些信息几乎无人问津。对于平均访问概率来说，使用SplayTree实现并不是一个明智的选择。

 可能会用到此数据结构的程序：词典或者多维搜索树，还有连接/切除树（link/cut tree）（这个树是用于网络优化问题包括最大流和最小代价）

 
 /*
*createbychicochen
*date:2008/10/02
 */ 
 template<classT> 
 classSplayTree:publicBinaryTree<T> 
{
 public: 
 explicitSplayTree(T&data):BinaryTree(data) 
{
}
 explicitSplayTree(TreeNode<T>*root):BinaryTree(root) 
{
}
~SplayTree()
{
}
 public: 
 voidinsertNode(T&data) 
{
 if(NULL==this->head) 
{
 this->head=newTreeNode<T>(data); 
 return; 
}
 splay(this->head,data); 
 if(this->head->data>data) 
{
 //ABA  
 // /\-> /\  
 //CDCB  
 //\  
 //D  
 TreeNode<T>*node=newTreeNode<T>(data); 
 node->left=this->head->left; 
 node->right=this->head; 
 this->head->left=NULL; 
 this->head=node; 
}
 elseif(this->head->data<data) 
{
 //ABA  
 // /\-> /\  
 //CDBD  
 // /  
 // C  
 TreeNode<T>*node=newTreeNode<T>(data); 
 node->right=this->head->right; 
 node->left=this->head; 
 this->head->right=NULL; 
 this->head=node; 
}
 else 
{
 //insertthesamekey  
 //throwexception  
 throw"thesamekey"; 
}
}
 //usethedataaskeytosplaythetree  
 //thenwecangetthestructuresofthetreelikethefollowing:  
 //(1)A(2)A  
 // \ /\  
 // BCB  
 //thedifferencebetweenthetwostructuresiswhethertheroothasleftchild  
 //Incase(1),wecansimpliymaketherootrightchildinsteadtheroot.  
 //Incase(2),weshouldsplaytherootleftsubtreeandthenitwillbe  
 //changedlikecase(1),andwemakethesplayedleftsubtreerootinstead  
 //theroot.  
 voiddeleteNode(T&data) 
{
 if(NULL==this->head) 
{
 return; 
}
 splay(this->head,data); 
 if(this->head->data!=data) 
{
 //notfoundthekeytodelete  
 return; 
}
TreeNode<T>*newRoot;
 if(NULL==this->head->left) 
{
 newRoot=this->head->right; 
}
 else 
{
 newRoot=this->head->left; 
splay(newRoot,data);
 newRoot->right=this->head->right; 
}
 deletethis->head; 
 this->head=newRoot; 
}
TreeNode<T>*searchNode(T&data)
{
 if(NULL==this->head) 
{
 returnNULL; 
}
 splay(this->head,data); 
 if(this->head->data==data) 
{
 returnthis->head; 
}
 returnNULL; 
}
 private: 
 //usetop-downsplaymethod,  
 //youshouldmakethesuitablefinalstep  
 //accordingtothesituation,suchas"insert","delete","search".  
 //Andwhat'sthetop-downmethod?  
 //nowweshouldaddLeftMaxRootasLandRightMinRootasR  
 //1.LAR2.LAR3.LAR  
 // // /  
 // BB B  
 // /\  
 //CC  
 //  
 //1.->LBR2.->LCR3.LCR  
 //// \/  
 //A B BA  
 //\  
 // A  
 //butincase3.wecansimplifiedcase3rotateas  
 //3.LBR  
 // \ /  
 // CA  
 //andwemustintegratetheLeftMaxRootandRightMinRoottogether,  
 //thenwehavefinalsteptodothis.AndLislefttree,andRisrighttree.  
 //LARA  
 ///\-> /\  
 //BCLR  
 // \/  
 // BC  
 voidsplay(TreeNode<T>*&subRoot,T&data) 
{
 if(NULL==subRoot) 
{
 return; 
}
TreeNode<T>*leftRoot;
TreeNode<T>*rightRoot;
 //heresomecodeusestaticmember,ifyoupromiseyouhavesync-control  
 //oryoudon'tusethiscodeinthreadorprocess,youcouldchoosestatic  
 //membertoaccelerateyourprogram.  
 //Itmeansthefollowingcodeisthread-safe.  
TreeNode<T>head(data);
leftRoot=rightRoot=&head;
 while(true) 
{
 if(data<subRoot->data) 
{
 if(NULL==subRoot->left) 
{
 break; 
}
 elseif(data<subRoot->left->data) 
{
 //Leftrotate  
TreeNode<T>*tempLeft=subRoot->left;
subRoot->left=tempLeft->right;
tempLeft->right=subRoot;
subRoot=tempLeft;
}
 else 
{
 //donothing  
}
 //splitthetreewithrightroot  
 if(NULL==subRoot->left) 
 break; 
rightRoot->left=subRoot;
rightRoot=subRoot;
subRoot=subRoot->left;
}
 elseif(data>subRoot->data) 
{
 if(NULL==subRoot->right) 
{
 //neednottorotate  
 break; 
}
 elseif(data>subRoot->right->data) 
{
 //rightrotate  
TreeNode<T>*tempRight=subRoot->right;
subRoot->right=tempRight->left;
tempRight->left=subRoot;
subRoot=tempRight;
}
 else 
{
 //donothing  
}
 //splitthetreebyleftroot  
 if(NULL==subRoot->right) 
 break; 
leftRoot->right=subRoot;
leftRoot=subRoot;
subRoot=subRoot->right;
}
 else 
{
 //thesamekey  
 break; 
}
}
 //thefinalstep  
 //wehavefindthelastnode,antthenweshould  
 //integratetheleftroot,therightrootandtherootintoOnetree.  
 //head.rightisleftroot  
 //head.leftisrightroot  
leftRoot->right=subRoot->left;
rightRoot->left=subRoot->right;
subRoot->left=head.right;
subRoot->right=head.left;
}
};