Size Balanced Tree

广州高中生发明的

 

代码

/***************************************** SBT.cpp** 2008-11-17 17:06:02 Fixed a bug in function SBT_Delete, it's now be test.* 2008-11-15 16:34:19 Give a new versin SBT_Delete that we don't need to using key-1.* Any problem contact [e-mail]* Copyright 2008 Yonggang Luo base on 巨菜逆铭*******************************************/#include <string.h>#include <iostream>typedef int32_t key_t;struct SBTNode { SBTNode *p,*ch[2]; ///ch[0]、ch[1]分别为左右孩子，p为双亲 size_t size; key_t key;///这里省略了卫星数据域 SBTNode(key_t _key,size_t _size);///构造函数：未考虑卫星数据}NULL_NODE(0,0);typedef SBTNode *SBTree;SBTree NULL_TREE = &NULL_NODE;SBTNode::SBTNode(key_t _key, size_t _size=1) { p=ch[0]=ch[1]= NULL_TREE; key=_key, size=_size;}bool cmp(key_t x, key_t y);//————SBT的旋转操作————inline void SBT_Rotate(SBTree &x, bool flag) { //flag: 0为将左子节点移到根, 1为将右子节点移到根 SBTree sub=x->ch[flag], &leaf = sub->ch[!flag]; x->ch[flag] = leaf; if (leaf!=NULL_TREE) leaf->p = x; /*设置双亲p*/ sub->p = x->p; /*设置双亲p*/ x->p = sub; /*设置双亲p*/ leaf = x; sub->size = x->size; x->size = x->ch[0]->size + x->ch[1]->size +1; x = sub;}//————SBT的维护操作————void SBT_Maintain(SBTree &T,bool flag) { if (T->ch[flag]->ch[!flag]->size > T->ch[!flag]->size) SBT_Rotate(T->ch[flag], !flag); else if (T->ch[flag]->ch[flag]->size <= T->ch[!flag]->size) return; SBT_Rotate(T, flag); SBT_Maintain(T->ch[0],0); //修复左子树 SBT_Maintain(T->ch[1],1); //修复右子树 SBT_Maintain(T,0); //修复整棵树 SBT_Maintain(T,1);}//————SBT的插入操作————void SBT_Insert(SBTree &T, SBTNode* x) { //将节点x插入树中 if (T!=NULL_TREE) { ++T->size; x->p =T; /*设置双亲p*/ SBT_Insert(T->ch[cmp(T->key, x->key)], x); SBT_Maintain(T, cmp(T->key, x->key)); /* here must be verify*/ } else T=x;}//————SBT的查找————SBTree &SBT_Search(SBTree *T, key_t key, int resize=0) { //在T中中寻找关键字为key的结点 //若能找到则返回指向它的指针，否则返回NULL_TREE while (*T!=NULL_TREE && (*T)->key!=key) { (*T)->size += resize; T=&((*T)->ch[cmp((*T)->key, key)]); } return *T;}//————SBT的极值————SBTree &SBT_Extremum(SBTree *T, bool maximum = true, int resize=0) { /*返回一棵树的极值 */ while ((*T)->ch[maximum]!=NULL_TREE) { (*T)->size += resize; T=&(*T)->ch[maximum]; } return *T;}/*删除一棵树的根节点，并返回被删节点*/SBTNode *SBT_Delete(SBTree &T){ --T->size; ///维护size int flag = T->ch[0]==NULL_TREE || T->ch[1]==NULL_TREE; SBTree *P = flag ? &T:&SBT_Extremum(&T->ch[1] , 0, -1); ///如果T有两棵子树，那么我们就先删T的后继 SBTree D=*P;///D用来保存 真正 被删的节点 *P=D->ch[D->ch[0]==NULL_TREE]; ///把被删节点设为此节点的其中一个儿子 if (*P!=NULL_TREE) (*P)->p = D->p; //设置双亲p if (flag) return D; ///如果 flag，则T是真正应当被删的节点，故直接返回D，否则继续处理D T->key = D->key;///简单替换 /*std::swap(T, D);///本质替换 memcpy(T, D, sizeof(*T)-sizeof(T->key)); //把关系复制过去 if (T->ch[0]!=NULL_TREE) T->ch[0]->p = T; //设置双亲p if (T->ch[1]!=NULL_TREE) T->ch[1]->p = T; //设置双亲p */ return D;}//————SBT的删除————SBTNode *SBT_Delete(SBTree &T, key_t key) { //如果树中没有一个这样的结点，则返回 NULL_TREE if (SBT_Search(&T, key) == NULL_TREE) return NULL_TREE; /*表示key不在树中**/ return SBT_Delete(SBT_Search(&T, key, -1)); /*RP 就是指向待删子树的指针*/}SBTree &SBT_Near(SBTree &T, key_t key, bool flag) { ///flag: 0 前驱 ; 1 后继 if (T==NULL_TREE) return T; if (key==T->key || cmp(T->key, key)==flag ) return SBT_Near(T->ch[flag],key, flag); SBTree &near=SBT_Near(T->ch[!flag],key, flag); return near!=NULL_TREE ? near:T;}//————SBT的选取第i个元素————SBTree SBT_Select(SBTree T, size_t i) { ///从树T中找到关键字第i的结点并返回其指针,从1开始计数，如果没有就返回NULL_TREE if (i > T->size) return NULL_TREE; size_t r = T->ch[0]->size+1; return i==r ? T:SBT_Select(T->ch[i>r], i>r?i-r:i);}//————SBT的给定节点是第几个元素————size_t SBT_Rank(SBTree T, key_t key) { ///此功能不完善，如果同一个key有两个不同的rank,那么返回值是其中的任意一个的rank。 ///可以考虑用二分法加 SBT_Select实现 ///若不存在此节点则返回0 if (T==NULL_TREE) return 0; if (key==T->key) return T->ch[0]->size+1; if (cmp(key, T->key)) return SBT_Rank(T->ch[0],key); size_t r=SBT_Rank(T->ch[1],key); return r==0?0:r+T->ch[0]->size+1;}inline void SBT_Free(SBTNode *t) { if (t!=NULL_TREE) delete t;}/**下面是一些测试代码**/bool cmp(key_t x, key_t y){ return x<y;}#include <stdlib.h>#include <time.h>int deep;size_t count;SBTree root=NULL_TREE;void SBT_Print(SBTree T, int d) { if (T==NULL_TREE) return; SBT_Print(T->ch[0], d+1); static size_t r; key_t value; printf("Rank = %d/n", r=SBT_Rank(root, T->key)); printf("value = %d/n", value = SBT_Select(root, r)->key); if (value!=T->key) { printf("Error!"); exit(1); } for (int i=0; i<d; ++i) printf(" "); printf("%d/n", T->key); if ( (T->ch[0]->p!=NULL_TREE && T->ch[0]->p!=T) || (T->ch[1]->p!=NULL_TREE && T->ch[1]->p!=T) ) { printf("Error parent!/n"); exit(0); } SBT_Print(T->ch[1], d+1);}void show() { if (root->p!=NULL_TREE) printf("Error!/n"); printf("The size of the tree is %d/n", root->size); printf("The tree is/n"); count = 0; SBT_Print(root,0); if (root->size != count) { printf("root->size = %u/n count = %u /n Error size!/n", root->size, count); } printf("End of the tree!/n/n");}int main() { srand(time(NULL)); size_t n=3000000; key_t x; freopen("output.txt","w",stdout);//#define READFILE#ifdef READFILE char order; freopen("input.txt","r",stdin); scanf("%d/n",&n); for (size_t i=0; i<n; ++i) { printf("i=%u/n", i); scanf("%c %d/n", &order, &x); printf("x=%d/n", x); if (order=='I') SBT_Insert(root, new SBTNode(x)); else SBT_Free(SBT_Delete(root, x)); show(); if (NULL_TREE->key !=0) printf("Error NULL"); }#else for (size_t i=0; i<n; ++i) { if (i%3==0) //printf("D %ld/n", x), SBT_Free(SBT_Delete(&root, x)); SBT_Free(SBT_Delete(root, x)); else //printf("I %ld/n",x = rand()),SBT_Insert(root, new SBTNode(x)); SBT_Insert(root, new SBTNode(x=rand())); //show(); if (NULL_TREE->key !=0) printf("Error NULL"); } // show(); SBTNode *pre, *suc; FILE* compare=fopen("compare.txt","w"); for (int i=0; i<32767; ++i) { pre = SBT_Near(root, i, 0); suc = SBT_Near(root, i, 1);// fprintf(compare,"pre=%d i=%d suc=%d/n",pre->key, i, suc->key); }#endif return 0;} 

 

 

 C++模板实现

#include <iostream>using namespace std;template<typename Type>struct SBNode{ int size; Type key; SBNode<Type>* lchild, *rchild; SBNode(){} SBNode( SBNode<Type>*l, SBNode<Type>*r, int s, Type k ): lchild(l), rchild(r), size(s), key(k) {}};template<typename Type>class SBTree{ private: SBNode<Type>* root; SBNode<Type>* _null; void left_rotate ( SBNode<Type>*& root ); void right_rotate( SBNode<Type>*& root ); void maintain( SBNode<Type>*& root, bool style ); void insert( SBNode<Type>*& root, Type key ); void erase ( SBNode<Type>*& root, Type key ); void clear ( SBNode<Type>* root ); void travel( SBNode<Type>* root ); public: SBTree (); ~SBTree(); void insert( Type key ); // 插入元素 void erase ( Type key ); // 删除元素 Type get_rank( int k ); // 获得第 k 个元素 Type get_min(); // 获得最小元素 Type get_max(); // 获得最大元素 void clear(); // 清空 void travel(); // 遍历 };template<typename Type>Type SBTree<Type>::get_rank( int k ){ SBNode<Type>* tmp= root; for( ;; ){ if( tmp->lchild->size> k ) tmp= tmp->lchild; else if( k> tmp->lchild->size ){ k-= tmp->lchild->size+ 1; tmp= tmp->rchild; } else break;} return tmp->key;}template<typename Type>void SBTree<Type>::clear( SBNode<Type>* root ){ if( root!= _null ){ clear( root->lchild ); clear( root->rchild ); delete root; }}template<typename Type>void SBTree<Type>::clear(){ clear(root); delete _null; }template<typename Type>void SBTree<Type>::travel( SBNode<Type>* root ){ if( root!= _null ){ travel( root->lchild ); cout << root->key << " "; travel( root->rchild ); }}template<typename Type>void SBTree<Type>::travel(){ travel( root ); }template<typename Type>Type SBTree<Type>::get_min(){ if( root== _null ) return Type(); SBNode<Type>* tmp= root; while( tmp->lchild!= _null ) tmp= tmp->lchild; return tmp->key;}template<typename Type>Type SBTree<Type>::get_max(){ if( root== _null ) return Type(); SBNode<Type>* tmp= root; while( tmp->rchild!= _null ) tmp= tmp->rchild; return tmp->key;}template<typename Type>void SBTree<Type>::erase( Type key ){ erase( root, key ); }template<typename Type>void SBTree<Type>::erase( SBNode<Type>*& root, Type key ){ if( root== _null ) return; root->size--; if( root->key== key ){ SBNode<Type>* tmp; if( root->lchild!= _null && root->rchild== _null ){ tmp= root; root= tmp->lchild; delete tmp; } else if( root->lchild== _null && root->rchild== _null ){ tmp= root; root= _null; delete tmp; } else { tmp= root->rchild; while( tmp->lchild!= _null ) tmp= tmp->lchild; root->key= tmp->key; erase( root->rchild, tmp->key );} } else if( key< root->key ) erase( root->lchild, key ); else erase( root->rchild, key );}template<typename Type>void SBTree<Type>::insert( SBNode<Type>*& root, Type key ){ if( root== _null ){ root= new SBNode<Type>( _null, _null, 1, key ); return; } root->size++; if( key< root->key ) insert( root->lchild, key ); else insert( root->rchild, key ); maintain( root, key>= root->key );}template<typename Type>void SBTree<Type>::insert( Type key ){ insert( root, key ); }template<typename Type>SBTree<Type>::SBTree(){ _null= new SBNode<Type>(); root= _null; root->lchild= root->rchild= _null; root->size= 0;}template<typename Type>SBTree<Type>::~SBTree(){ clear();}template<typename Type>void SBTree<Type>::left_rotate( SBNode<Type>*& root ){ SBNode<Type>* tmp= root->rchild; root->rchild= tmp->lchild; tmp->lchild= root; tmp->size= root->size; root->size= root->lchild->size+ root->rchild->size+ 1; root= tmp;}template<typename Type>void SBTree<Type>::right_rotate( SBNode<Type>*& root ){ SBNode<Type>* tmp= root->lchild; root->lchild= tmp->rchild; tmp->rchild= root; tmp->size= root->size; root->size= root->lchild->size+ root->rchild->size+ 1; root= tmp;}template<typename Type>void SBTree<Type>::maintain( SBNode<Type>*& root, bool style ){ if( root== _null ) return; if( !style ){ if( root->lchild->lchild->size> root->rchild->size ) right_rotate( root ); else if( root->lchild->rchild->size> root->rchild->size ){ left_rotate( root->lchild ); right_rotate( root ); }else return; } else { if( root->rchild->rchild->size> root->lchild->size ) left_rotate( root ); else if( root->rchild->lchild->size> root->lchild->size ){ right_rotate( root->rchild ); left_rotate( root ); }else return; } maintain(root->lchild, false); maintain(root->rchild, true); maintain(root, false); maintain(root, true);}