红黑树-逆序对

#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;}}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;}pRBNode os_successor(pRBNode pn,pRBNode pz,int i)//确定pz的第i个后继{int r=os_rank(pn,pz);r+=i;return os_select(pn,r);}int 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，return os_rank(pn,pz);}void random_data(int *a,int n)//生成乱序随机数{int tmp;int rnd;for(int i=0;i<n;++i){rnd=rand()%(n-i)+i;tmp=a[i];a[i]=a[rnd];a[rnd]=tmp;}}int build_binary_search_tree(pRBNode &pn,int n)//建立n个具有父节点的二叉搜索树{int invert_pair=0;int value;pRBNode ptmp;//int a[10]={-2,-3,4,-3,-5,5,5,3,-3,0};int *a=new int[n];for(int i=0;i<n;++i){a[i]=i;}random_data(a,n);//随机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];ptmp->rb=1;//红结点ptmp->size=1;cout<<a[i]<<"\t";invert_pair+=(i+1-binary_tree_insert(pn,ptmp));}cout<<endl;return invert_pair;}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;}int main(){srand((unsigned)time(NULL));int n=10;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;int inversions=build_binary_search_tree(pn,n);cout<<"inversions pairs is : "<<inversions<<endl;cout<<endl;InOrder(pn);//中序排序cout<<endl;pRBNode p;p=binary_tree_maximum(pn);cout<<"maximum is : "<<p->value<<endl;p=binary_tree_minimux(pn);cout<<"minimum is : "<<p->value<<endl;}