Splay
求一个数的前驱后继和排名和第k大的数
普通平衡树
#include<algorithm>
#include<iostream>
#include<cstring>
#include<iomanip>
#include<sstream>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<cmath>
#include<stack>
#include<set>
#include<map>
#define rep(i,x,n) for(int i=x;i<=n;i++)
#define per(i,n,x) for(int i=n;i>=x;i--)
#define sz(a) int(a.size())
#define rson mid+1,r,p<<1|1
#define pii pair<int,int>
#define lson l,mid,p<<1
#define ll long long
#define pb push_back
#define mp make_pair
#define se second
#define fi first
using namespace std;
const double eps=1e-8;
const int mod=1e9+7;
const int N=1e5+10;
const int inf=1e9;
int n,m;
int rt,tot,ch[N][2],sz[N],val[N],fa[N],cnt[N];
struct Splay{
void maintain(int x){
sz[x]=sz[ch[x][0]]+sz[ch[x][1]]+cnt[x];
}
bool get(int x){
return x==ch[fa[x]][1];
}
void clear(int x){
ch[x][0]=ch[x][1]=fa[x]=val[x]=sz[x]=cnt[x]=0;
}
void rotate(int x){
int y=fa[x],z=fa[y],chk=get(x);
ch[y][chk]=ch[x][chk^1];
fa[ch[x][chk^1]]=y;
ch[x][chk^1]=y;
fa[y]=x;
fa[x]=z;
if(z) ch[z][ y==ch[z][1] ]=x;
maintain(x);
maintain(y);
}
void splay(int x,int goal=0){
for(int f;(f=fa[x])!=goal;rotate(x)){
if(fa[f]!=goal) rotate(get(x)==get(f)?f:x);
}
if(goal==0) rt=x;
}
void ins(int k){
if(!rt){
val[++tot]=k;
cnt[tot]++;
rt=tot;
maintain(rt);
return;
}
int cnr=rt,f=0;
while(1){
if(val[cnr]==k){
cnt[cnr]++;
maintain(cnr);
maintain(f);
splay(cnr);
break;
}
f=cnr;
cnr=ch[cnr][val[cnr]<k];
if(!cnr){
val[++tot]=k;
cnt[tot]++;
fa[tot]=f;
ch[f][val[f]<k]=tot;
maintain(tot);
maintain(f);
splay(tot);
break;
}
}
}
int rk(int k){
int res=0,cnr=rt;
while(1){
if(k<val[cnr]){
cnr=ch[cnr][0];
}else{
res+=sz[ch[cnr][0]];
if(k==val[cnr]){
splay(cnr);
return res+1;
}
res+=cnt[cnr];
cnr=ch[cnr][1];
}
}
}
int kth(int k){
int cnr=rt;
while(1){
if(ch[cnr][0]&&sz[ch[cnr][0]]>=k){
cnr=ch[cnr][0];
}else{
k-=cnt[cnr]+sz[ch[cnr][0]];
if(k<=0){
splay(cnr);
return val[cnr];
}
cnr=ch[cnr][1];
}
}
}
int pre(){
int cnr=ch[rt][0];
while(ch[cnr][1]) cnr=ch[cnr][1];
splay(cnr);
return cnr;
}
int nxt(){
int cnr=ch[rt][1];
while(ch[cnr][0]) cnr=ch[cnr][0];
splay(cnr);
return cnr;
}
void del(int k){
rk(k);
if(cnt[rt]>1){
cnt[rt]--;
maintain(rt);
return;
}
if(!ch[rt][0]&&!ch[rt][1]){
clear(rt);
rt=0;
return;
}
if(!ch[rt][0]){
int cnr=rt;
rt=ch[rt][1];
fa[rt]=0;
clear(cnr);
return;
}
if(!ch[rt][1]){
int cnr=rt;
rt=ch[rt][0];
fa[rt]=0;
clear(cnr);
return;
}
int cnr=rt,x=pre();
splay(x);
fa[ch[cnr][1]]=x;
ch[x][1]=ch[cnr][1];
clear(cnr);
maintain(rt);
}
}S;
int main(){
//ios::sync_with_stdio(false);
//freopen("in","r",stdin);
scanf("%d",&n);
rep(i,1,n){
int opt,x;
scanf("%d%d",&opt,&x);
if(opt==1){
S.ins(x);
}else if(opt==2){
S.del(x);
}else if(opt==3){
S.ins(x);
printf("%d\n",S.rk(x));
S.del(x);
}else if(opt==4){
printf("%d\n",S.kth(x));
}else if(opt==5){
S.ins(x);
printf("%d\n",val[S.pre()]);
S.del(x);
}else{
S.ins(x);
printf("%d\n",val[S.nxt()]);
S.del(x);
}
}
return 0;
}
区间翻转
文艺平衡树
#include<algorithm>
#include<iostream>
#include<cstring>
#include<iomanip>
#include<sstream>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<cmath>
#include<stack>
#include<set>
#include<map>
#define rep(i,x,n) for(int i=x;i<=n;i++)
#define per(i,n,x) for(int i=n;i>=x;i--)
#define sz(a) int(a.size())
#define rson mid+1,r,p<<1|1
#define pii pair<int,int>
#define lson l,mid,p<<1
#define ll long long
#define pb push_back
#define mp make_pair
#define se second
#define fi first
using namespace std;
const double eps=1e-8;
const int mod=1e9+7;
const int N=1e5+10;
const int inf=1e9;
int n,m;
int rt,tot,ch[N][2],sz[N],val[N],fa[N],cnt[N],tag[N];
struct Splay{
void maintain(int x){
sz[x]=sz[ch[x][0]]+sz[ch[x][1]]+cnt[x];
}
bool get(int x){
return x==ch[fa[x]][1];
}
void clear(int x){
ch[x][0]=ch[x][1]=fa[x]=val[x]=sz[x]=cnt[x]=0;
}
void pd(int x){
if(x&&tag[x]){
tag[ch[x][0]]^=1;
tag[ch[x][1]]^=1;
swap(ch[x][0],ch[x][1]);
tag[x]=0;
}
}
void rotate(int x){
int y=fa[x],z=fa[y],chk=get(x);
pd(x),pd(y);
ch[y][chk]=ch[x][chk^1];
fa[ch[x][chk^1]]=y;
ch[x][chk^1]=y;
fa[y]=x;
fa[x]=z;
if(z) ch[z][ y==ch[z][1] ]=x;
maintain(y);
maintain(x);
}
void splay(int x,int goal=0){
for(int f;(f=fa[x])!=goal;rotate(x)){
if(fa[f]!=goal) rotate(get(x)==get(f)?f:x);
}
if(goal==0) rt=x;
}
void ins(int k){
if(!rt){
val[++tot]=k;
cnt[tot]++;
rt=tot;
maintain(rt);
return;
}
int cnr=rt,f=0;
while(1){
if(val[cnr]==k){
cnt[cnr]++;
maintain(cnr);
maintain(f);
splay(cnr);
break;
}
f=cnr;
cnr=ch[cnr][val[cnr]<k];
if(!cnr){
val[++tot]=k;
cnt[tot]++;
fa[tot]=f;
ch[f][val[f]<k]=tot;
maintain(tot);
maintain(f);
splay(tot);
break;
}
}
}
int kth(int k){
int cnr=rt;
while(1){
pd(cnr);
if(ch[cnr][0]&&sz[ch[cnr][0]]>=k){
cnr=ch[cnr][0];
}else{
k-=cnt[cnr]+sz[ch[cnr][0]];
if(k<=0){
return cnr;
}
cnr=ch[cnr][1];
}
}
}
void reverse(int x,int y){
int l=kth(x-1),r=kth(y+1);
splay(l,0);
splay(r,l);
int pos=ch[rt][1];
pos=ch[pos][0];
tag[pos]^=1;
}
void dfs(int x){
pd(x);
if(ch[x][0]) dfs(ch[x][0]);
if(val[x]!=inf&&val[x]!=-inf){
printf("%d ",val[x]);
}
if(ch[x][1]) dfs(ch[x][1]);
}
}S;
int main(){
//ios::sync_with_stdio(false);
//freopen("in","r",stdin);
scanf("%d%d",&n,&m);
S.ins(-inf);
rep(i,1,n) S.ins(i);
S.ins(inf);
rep(i,1,m){
int l,r;
scanf("%d%d",&l,&r);
S.reverse(l+1,r+1);
}
S.dfs(rt);
return 0;
}
