题目
做法
这题是动态维护树的重心,连边后找到两棵树的重心拉一条链(性质:新重心在链上),然后暴力爬
要注意:
1.是找重心的过程中要先把旋转标记放下来,因为(Splay(x)),这个操作只把(x)到根节点的跟上旋有关标记放下来
而找重心过程中跟整个链有关
2.并查集的时候记得把(z)也改变一下,不然会死循环,卡了好久(emmm)
My complete code
#include<cstdio>
#include<iostream>
#include<cstring>
#include<string>
#include<algorithm>
using namespace std;
typedef int LL;
const LL maxn=200000,inf=0x3f3f3f3f;
inline LL Read(){
LL x(0),f(1);char c=getchar();
while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
while(c>='0'&&c<='9')x=(x<<3)+(x<<1)+c-'0',c=getchar();
return x*f;
}
LL n,m,Xor;
LL son[maxn][2],fa[maxn],sta[maxn],f[maxn],isum[maxn],sum[maxn],r[maxn];
inline void Update(LL x){
sum[x]=sum[son[x][0]]+sum[son[x][1]]+isum[x]+1;
}
inline bool Notroot(LL x){
return son[fa[x]][0]==x||son[fa[x]][1]==x;
}
inline void Pushr(LL x){
swap(son[x][0],son[x][1]),r[x]^=1;
}
inline void Pushdown(LL x){
if(r[x]){
if(son[x][0]) Pushr(son[x][0]);
if(son[x][1]) Pushr(son[x][1]);
r[x]=0;
}
}
inline void Rotate(LL x){
LL y(fa[x]),z(fa[y]),lz(son[y][1]==x);
if(Notroot(y)) son[z][son[z][1]==y]=x;fa[x]=z;
son[y][lz]=son[x][lz^1];
if(son[y][lz]) fa[son[y][lz]]=y;
son[x][lz^1]=y; fa[y]=x;
Update(y),Update(x);
}
inline void Splay(LL x){
LL y(x),top(0);sta[++top]=y;
while(Notroot(y)) sta[++top]=y=fa[y];
while(top) Pushdown(sta[top--]);
while(Notroot(x)){
y=fa[x];
if(Notroot(y)){
LL z(fa[y]);
if(((son[y][1]==x)^(son[z][1]==y))==0) Rotate(y);
else Rotate(x);
}Rotate(x);
}
}
inline void Access(LL x){
for(LL y=0;x;y=x,x=fa[x]){
Splay(x),isum[x]+=sum[son[x][1]];
son[x][1]=y;isum[x]-=sum[son[x][1]];
Update(x);
}
}
inline void Makeroot(LL x){
Access(x),Splay(x),Pushr(x);
}
inline void Split(LL x,LL y){
Makeroot(x),Access(y),Splay(y);
}
inline void Link(LL x,LL y){
Makeroot(x),Access(y),Splay(y);
fa[x]=y;
isum[y]+=sum[x];
Update(y);
}
LL Get_fa(LL x){
return f[x]=(f[x]==x?x:Get_fa(f[x]));
}
inline LL Get_w(LL x){
LL ji=sum[x]&1,M=sum[x]>>1,lsum(0),rsum(0),new_w(inf),nowl,nowr;
while(x){
Pushdown(x);
nowl=sum[son[x][0]]+lsum,nowr=sum[son[x][1]]+rsum;
if(nowl<=M&&nowr<=M){
if(ji){
new_w=x;
break;
}else
new_w=min(new_w,x);
}
if(nowl<nowr){
lsum+=sum[son[x][0]]+isum[x]+1;
x=son[x][1];
}else{
rsum+=sum[son[x][1]]+isum[x]+1;
x=son[x][0];
}
}
Splay(new_w);
return new_w;
}
int main(){
n=Read(),m=Read();
for(LL i=1;i<=n;++i)
sum[i]=1,f[i]=i,Xor^=i;
while(m--){
char s[100];
scanf(" %s",s);
if(s[0]=='X') printf("%d
",Xor);
else if(s[0]=='Q'){
LL x(Read());
printf("%d
",Get_fa(x));
}else{
LL x(Read()),y(Read());
Link(x,y);
Split(x=Get_fa(x),y=Get_fa(y));
LL z=Get_w(y);
f[x]=f[y]=f[z]=z;
Xor^=x^y^z;
}
}return 0;
}