Red-Black Tree
https://www.cnblogs.com/skywang12345/p/3245399.html
#include<bits/stdc++.h>
using namespace std;
enum Col{red,black};
struct node{
node *fa,*lson,*rson;
int val;
Col col;
int sz;
node(int _val=0,node *tmp=nullptr):fa(tmp),lson(tmp),rson(tmp),val(_val),col(black),sz(0){}
}tmp;
class Red_Black_Tree{
private:
node *root,*nodeNull;
void Clear(node *x){
if(x==nodeNull)return;
Clear(x->lson),Clear(x->rson);
delete x;
}
void Clear_nodeNull(){
nodeNull->fa=nodeNull->lson=nodeNull->rson=nodeNull;
nodeNull->val=0,nodeNull->col=black,nodeNull->sz=0;
}
public:
Red_Black_Tree(){
nodeNull=&tmp;
Clear_nodeNull();
root=nodeNull;
}
~Red_Black_Tree(){Clear(root);}
private:
void pushup(node *x){
if(x==nodeNull)return;
x->sz=x->lson->sz+x->rson->sz+1;
}
void R_Rotate(node *x){
node *y=x->lson;
node *f=x->fa;
y->fa=f;
if(f==nodeNull)root=y;
else f->lson==x?f->lson=y:f->rson=y;
x->lson=y->rson;
if(y->rson!=nodeNull)y->rson->fa=x;
y->rson=x,x->fa=y;
pushup(x),pushup(y);
}
void L_Rotate(node *x){
node *y=x->rson;
node *f=x->fa;
y->fa=f;
if(f==nodeNull)root=y;
else f->lson==x?f->lson=y:f->rson=y;
x->rson=y->lson;
if(y->lson!=nodeNull)y->lson->fa=x;
y->lson=x,x->fa=y;
pushup(x),pushup(y);
}
public:
void Check_DFS(node *x){
if(x==nodeNull)return;
// if(x->sz!=x->lson->sz+x->rson->sz+1){
// cout<<"!!!!!!!!!!!!!!"<<" "<<x->sz<<" "<<x->lson->sz<<" "<<x->rson->sz<<endl;
// cout<<nodeNull->sz<<" "<<nodeNull->lson->sz<<" "<<nodeNull->rson->sz<<endl;
// exit(0);
// }
// printf("%d %d %d %s fa:%d sz:%d\n",x->val,x->lson->val,x->rson->val,x->col==black?"Black":"Red",x->fa->val,x->sz);
Check_DFS(x->lson),Check_DFS(x->rson);
}
void Check(){
cout<<"!!!!!!"<<endl;
// printf("%d %d %d %s fa:%d sz:%d\n",nodeNull->val,nodeNull->lson->val,nodeNull->rson->val,nodeNull->col==black?"Black":"Red",nodeNull->fa->val,nodeNull->sz);
Check_DFS(root);
}
void Insert(int val){
node *x=root,*y=nodeNull;
while(x!=nodeNull){
x->sz++;
y=x;
x=(val<x->val)?x->lson:x->rson;
}
node *z=new node(val,nodeNull);
z->sz=1;
if(y==nodeNull){
root=z;
z->col=black;
}
else {
z->fa=y,val<y->val?y->lson=z:y->rson=z;
z->col=red;
}
Insert_Fixup(z);//消除相连的两个红色节点以维护红黑树的性质
}
void Insert_Fixup(node *x){
while(x->fa->col==red){
if(x->fa==x->fa->fa->lson){
// cout<<"$1"<<endl;
node *y=x->fa->fa->rson;
if(y->col==red){//直接换色，不旋转
x->fa->col=black,y->col=black;
x->fa->fa->col=red;
x=x->fa->fa;
//往上跳，继续进入循环
}
else {
if(x==x->fa->rson){//LR
x=x->fa;
L_Rotate(x);//此次旋转把LR变成了LL，且根到底下任意一点x的路径上的黑点数不变
}
//LL
x->fa->col=black,x->fa->fa->col=red;
R_Rotate(x->fa->fa);//进行一次旋转，并换色
//不管是LL还是LR，进行一次后红黑树的性质就以完全满足，接下来就直接break掉了
}
}
else {//swap(l,r)
// cout<<"$2"<<endl;
node *y=x->fa->fa->lson;
if(y->col==red){//直接换色，不旋转
x->fa->col=black,y->col=black;
x->fa->fa->col=red;
x=x->fa->fa;
//往上跳，继续进入循环
}
else {
if(x==x->fa->lson){//RL
x=x->fa;
R_Rotate(x);//此次旋转把RL变成了RR，且根到底下任意一点x的路径上的黑点数不变
}
//RR
x->fa->col=black,x->fa->fa->col=red;
L_Rotate(x->fa->fa);//进行一次旋转，并换色
//不管是RR还是RL，进行一次后红黑树的性质就以完全满足，接下来就直接break掉了
}
}
}
root->col=black;
}
node* successor(node *x){
x=x->rson;
while(x->lson!=nodeNull)x=x->lson;
return x;
}
void update_sz(node *x){
if(x==nodeNull)return;
while(x!=nodeNull)x->sz--,x=x->fa;
}
void Delete(node *x){
node *y,*z;
if(x->lson==nodeNull||x->rson==nodeNull)y=x;
else y=successor(x),x->val=y->val;//改为删x的后继节点
//y为此时要删的点，保证y至多只有一个儿子
update_sz(y);
z=(y->lson!=nodeNull)?y->lson:y->rson;
z->fa=y->fa;
if(y->fa==nodeNull)root=z;
else (y->fa->lson==y)?y->fa->lson=z:y->fa->rson=z;
if(y->col==black)Delete_Fixup(z);
delete y;
}
void Delete_Fixup(node *x){
//先给x额外添加一个黑的属性 此时x为 黑+黑，通过不断转移直至 x为 黑+红 or x为根,然后只需把x改为 黑 即可
while(x!=root&&x->col==black){
if(x->fa->lson==x){
node *y=x->fa->rson;
if(y->col==red){//Case1
y->col=black,x->fa->col=red;
L_Rotate(x->fa);
y=x->fa->rson;
}
//经过Case1，一定会变成Case2,3,4
if(y->lson->col==black&&y->rson->col==black){//Case2
y->col=red;
x=x->fa;
}
else {
if(y->rson->col==black){//Case3
y->lson->col=black,y->col=red;
R_Rotate(y);
y=x->fa->rson;
}
//经过Case3，一定会变成Case4
//以下是Case4
y->col=x->fa->col,x->fa->col=black,y->rson->col=black;
L_Rotate(x->fa);
x=root;
}
}
else {//swap(l,r)
node *y=x->fa->lson;
if(y->col==red){//Case1
y->col=black,x->fa->col=red;
R_Rotate(x->fa);
y=x->fa->lson;
}
//经过Case1，一定会变成Case2,3,4
if(y->rson->col==black&&y->lson->col==black){//Case2
y->col=red;
x=x->fa;
}
else {
if(y->lson->col==black){//Case3
y->rson->col=black,y->col=red;
L_Rotate(y);
y=x->fa->lson;
}
//经过Case3，一定会变成Case4
//以下是Case4
y->col=x->fa->col,x->fa->col=black,y->lson->col=black;
R_Rotate(x->fa);
x=root;
}
}
}
x->col=black;
}
node* Find(int val){
node *x=root;
while(x!=nodeNull){
if(val==x->val)return x;
else if(val<x->val)x=x->lson;
else x=x->rson;
}
return nodeNull;
}
int Find_rank(int val){
node *x=root;
int ans=0;
while(x!=nodeNull){
if(val>x->val)ans+=x->lson->sz+1,x=x->rson;
else x=x->lson;
}
return ans+1;
}
int Find_val(int rnk){
node *x=root;
while(x!=nodeNull){
if(rnk==x->lson->sz+1)return x->val;
else if(rnk<=x->lson->sz)x=x->lson;
else rnk-=(x->lson->sz+1),x=x->rson;
}
return -1;
}
int Find_pre(int val){
node *x=root;
int ans=-1;
while(x!=nodeNull){
if(val>x->val)ans=x->val,x=x->rson;
else x=x->lson;
}
return ans;
}
int Find_next(int val){
node *x=root;
int ans=-1;
while(x!=nodeNull){
if(val<x->val)ans=x->val,x=x->lson;
else x=x->rson;
}
return ans;
}
void Delete(int val){
node *x=Find(val);
Delete(x);
}
}T;
int main(){
int n,op,x;
scanf("%d",&n);
for(int i=1;i<=n;i++){
scanf("%d%d",&op,&x);
if(op==1)T.Insert(x);
if(op==2)T.Delete(x);
if(op==3)printf("%d\n",T.Find_rank(x));
if(op==4)printf("%d\n",T.Find_val(x));
if(op==5)printf("%d\n",T.Find_pre(x));
if(op==6)printf("%d\n",T.Find_next(x));
// T.Check();
}
return 0;
}
}
