红黑树的插入删除-红黑树动态顺序统计

#include<iostream>#include <ctime>#include <limits>using namespace std;typedef struct rb_node{//带父节点的二叉树int value;rb_node *left,*right,*parent;bool rb;//rb=0表示结点,rb=1表示红结点int size;//存储左右子树大小和该结点之和}rb_node,*pRBNode;pRBNode nil;//所有结点的公共黑色结点，类似于NULLvoid binary_tree_left_rotation(pRBNode &pn,pRBNode y)//二叉搜索树左旋{pRBNode x=y->right;y->right=x->left;if(x->left!=nil){x->left->parent=y;}x->parent=y->parent;if(y->parent==nil){pn=x;}else if(y==y->parent->left){y->parent->left=x;}else{y->parent->right=x;}x->left=y;y->parent=x;x->size=y->size;//更新相应结点值y->size=y->left->size+y->right->size+1;}void binary_tree_right_rotation(pRBNode &pn,pRBNode x)//二叉搜索树右旋{pRBNode y=x->left;x->left=y->right;if(y->right!=nil){y->right->parent=x;}y->parent=x->parent;if(x->parent==nil){pn=y;}else if(x==x->parent->left){x->parent->left=y;}else{x->parent->right=y;}y->right=x;x->parent=y;y->size=x->size;//更新相应的size值x->size=x->left->size+x->right->size+1;}void rb_tree_insert_fixup(pRBNode &pn,pRBNode pz)//红黑结点修复{while(pz->parent->rb){//子结点父结点均为红结点pRBNode y;if(pz->parent==pz->parent->parent->left){//当前结点的父结点是当前结点父结点的父节点的左子树y=pz->parent->parent->right;if(y->rb){//堂叔为红结点,case onepz->parent->rb=0;pz->parent->parent->rb=1;y->rb=0;pz=pz->parent->parent;}else{if(pz==pz->parent->right){//case twopz=pz->parent;binary_tree_left_rotation(pn,pz);}pz->parent->rb=0;//case threepz->parent->parent->rb=1;binary_tree_right_rotation(pn,pz->parent->parent);}}else{//当前结点的父结点是当前结点父结点的父节点的右子树y=pz->parent->parent->left;if(y->rb){//堂叔结点是红色pz->parent->rb=0;pz->parent->parent->rb=1;y->rb=0;pz=pz->parent->parent;}else{if(pz==pz->parent->left){//case twopz=pz->parent;binary_tree_right_rotation(pn,pz);}pz->parent->rb=0;//case threepz->parent->parent->rb=1;binary_tree_left_rotation(pn,pz->parent->parent);}}pn->rb=0;}}void binary_tree_insert(pRBNode &pn,pRBNode pz){pRBNode x=pn;pRBNode y=nil;while (x!=nil){y=x;x->size++;//相应路径上的结点的子结点个数加1if(pz->value<=x->value){x=x->left;}else{x=x->right;}}if(y==nil){pn=pz;pn->rb=0;}else if(pz->value<=y->value){y->left=pz;}else{y->right=pz;}pz->parent=y;rb_tree_insert_fixup(pn,pz);//插入结点后可能会破坏红黑树的性质，}void build_binary_search_tree(pRBNode &pn,int n)//建立n个具有父节点的二叉搜索树{int value;pRBNode ptmp;//int a[10]={-2,-3,4,-3,-5,5,5,3,-3,0};for(int i=0;i<n;++i){value=rand()%101-50;ptmp=new rb_node;ptmp->left=nil;ptmp->right=nil;ptmp->parent=nil;ptmp->value=/*a[i]*/value;ptmp->rb=1;//红结点ptmp->size=1;cout<<value/*a[i]*/<<"\t";binary_tree_insert(pn,ptmp);}//cout<<endl;}void InOrder(pRBNode pn)//中序遍历{if(pn!=nil){InOrder(pn->left);cout<<pn->value<<"\t";InOrder(pn->right);}}pRBNode binary_tree_search(pRBNode pn,int key)//二叉搜索树查找{pRBNode pp=pn;while (pp !=nil && key != pp->value){if(key<pp->value){pp=pp->left;}else{pp=pp->right;}}return pp;}pRBNode binary_tree_maximum(pRBNode pn)//最大值{while (pn!=nil && pn->right!=nil){pn=pn->right;}return pn;}pRBNode binary_tree_minimux(pRBNode pn)//最小值{while(pn!=nil && pn->left!=nil){pn=pn->left;}return pn;}pRBNode binary_tree_successor(pRBNode pz)//后继结点{if(pz->right!=nil){return binary_tree_minimux(pz->right);}pRBNode p=pz->parent;//父亲节点while(p!=nil && pz==p->right){pz=p;p=p->parent;}return p;}pRBNode binary_tree_predecessor(pRBNode pz){if(pz->left!=nil){return binary_tree_maximum(pz->left);}pRBNode p=pz->parent;while(p!=nil && pz==p->left){pz=p;p=p->parent;}return p;}void rb_transplant(pRBNode &pn,pRBNode u,pRBNode v)//红黑树删除操作辅助程序{if(u->parent==nil){pn=v;}else if(u==u->parent->left){u->parent->left=v;}else{u->parent->right=v;}v->parent=u->parent;}void rb_delete_fixup(pRBNode &pn,pRBNode px)//红黑树 删除操作修正{while(px!=pn && 0==px->rb){pRBNode pw;//px的兄弟结点if(px==px->parent->left){//px为左子结点pw=px->parent->right;if(pw->rb){//兄弟结点为红色,case onepx->parent->rb=1;pw->rb=0;binary_tree_left_rotation(pn,px->parent);//左旋转pw=px->parent->right;}if(pw->left->rb==0 && pw->right->rb==0){//case twopw->rb=1;px=px->parent;}else{ if(pw->right->rb==0){//case threepw->left->rb=0;pw->rb=1;binary_tree_right_rotation(pn,pw);pw=px->parent->right;}pw->rb=px->parent->rb;px->parent->rb=0;pw->right->rb=0;binary_tree_left_rotation(pn,px->parent);px=pn;}}else{//px为右子结点pw=px->parent->left;if(pw->rb){px->parent->rb=1;pw->rb=0;binary_tree_right_rotation(pn,px->parent);pw=px->parent->left;}if(pw->left->rb==0 && pw->right->rb==0){pw->rb=1;px=px->parent;}else{if(pw->left->rb==0){pw->right->rb=0;pw->rb=1;binary_tree_left_rotation(pn,pw);pw=px->parent->left; }pw->rb=px->parent->rb;px->parent->rb=0;pw->left->rb=0;binary_tree_right_rotation(pn,px->parent);px=pn;}}}px->rb=0;}void rb_delete(pRBNode &pn,pRBNode pz){pRBNode py=pz;//py记录pz或者pz的后继bool y_org_color=py->rb;//记录删除结点的颜色pRBNode px;//px记录py的右结点if(pz->left==nil){px=py->right;rb_transplant(pn,pz,pz->right);}else if(pz->right==nil){px=py->left;rb_transplant(pn,pz,pz->left);}else{py=binary_tree_minimux(pz->right);//pz的后继px=py->right;//py的后继y_org_color=py->rb;if(py==pz->right){px->parent=py;}else{rb_transplant(pn,py,py->right);py->right=pz->right;py->right->parent=py;}rb_transplant(pn,pz,py);py->left=pz->left;py->left->parent=py;py->rb=pz->rb;}py=pz->parent;while (py!=nil){//更新结点的size值py->size--;py=py->parent;}delete pz;if(0==y_org_color){//被删除或者被调整为的内部结点为黑色rb_delete_fixup(pn,px);}}pRBNode os_select(pRBNode pn,int i)//选择红黑树中的第i个元素{int r=pn->left->size+1;if(r==i){return pn;}else if(i<r){return os_select(pn->left,i);}else{return os_select(pn->right,i-r);}}int os_rank(pRBNode pn,pRBNode pz)//求红黑树中pz的秩{int r=pz->left->size+1;while(pz!=pn){if(pz==pz->parent->right){r+=pz->parent->left->size+1;}pz=pz->parent;}return r;}int main(){srand((unsigned)time(NULL));int n=100;nil=new rb_node;nil->left=nil;nil->right=nil;nil->rb=0;//黑色nil->parent=nil;nil->value=numeric_limits<int>::min();nil->size=0;//nil结点大小为0pRBNode pn=nil;build_binary_search_tree(pn,n);cout<<endl;InOrder(pn);//中序排序cout<<"the "<<50<<"th value is : "<<os_select(pn,50)->value<<endl;pRBNode p;int key;for(int i=0;i<10;++i){key=rand()%101-50;cout<<endl<<"search key : "<<key;p=binary_tree_search(pn,key);//二叉搜索树查找if(p!=nil){cout<<" founded. ";cout<<"its rank is "<<os_rank(pn,p)<<endl;cout<<"successor is : "<<binary_tree_successor(p)->value<<endl;cout<<"predecessor is :"<<binary_tree_predecessor(p)->value<<endl;cout<<"node be deleted"<<endl;rb_delete(pn,p);//删除结点InOrder(pn);//中序排序}else{cout<<" not founded"<<endl;}cout<<endl;}p=binary_tree_maximum(pn);cout<<"maximum is : "<<p->value<<endl;p=binary_tree_minimux(pn);cout<<"minimum is : "<<p->value<<endl;cout<<"the "<<50<<"th value is : "<<os_select(pn,50)->value<<endl;}