【Codeforces #1137 F】—Matches Are Not a Child's Play（LCT）

传送门

初始设根为$n$
考虑对于每个点
如果一个子树最大值大于自己，就把向那个子树的边设成重链
这样每条重链都是连续删除的一段
设个标号为链底的值
$Compare$直接$2$次$when$就可以了
$when$只需要查询所有标号小于当前链的和以及链底的一段的$size$
而修改一个点之后它到根一定是最后的一段，而且是从原来的根到当前这个点
和$makeroot$操作一样

然后就完了

#include<bits/stdc++.h>
using namespace std;
const int RLEN=1<<20|1;
inline char gc(){
    static char ibuf[RLEN],*ib,*ob;
    (ob==ib)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
    return (ob==ib)?EOF:*ib++;
}
inline int read(){
    char ch=gc();
    int res=0,f=1;
    while(!isdigit(ch))f^=ch=='-',ch=gc();
    while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
    return f?res:-res;
}
inline int readchar(char *s){
	char ch=gc();int top=0;
	while(!isalpha(ch))ch=gc();
	while(isalpha(ch))s[top++]=ch,ch=gc();
	return top;
}
#define ll long long
#define re register
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
#define cs const
#define bg begin
#define poly vector<int>
inline void chemx(int &a,int b){a<b?a=b:0;}
inline void chemn(int &a,int b){a>b?a=b:0;}
cs int N=200005;
namespace Tr{
	cs int N=400000;
	int tr[N+5];
	#define lb(x) (x&(-x))
	inline void update(int p,int k){
		for(;p<=N;p+=lb(p))tr[p]+=k;
	}
	inline int query(int p,int res=0){
		for(;p;p-=lb(p))res+=tr[p];return res;
	}
}
int n,m,val[N],tot;
vector<int> e[N];
char s[N];
namespace Lct{
	int son[N][2],fa[N],rev[N],siz[N];
	#define lc(u) son[u][0]
	#define rc(u) son[u][1]
	inline bool isrt(int u){
		return fa[u]?(lc(fa[u])!=u&&rc(fa[u])!=u):1;
	}
	inline bool isrc(int u){
		return rc(fa[u])==u;
	}
	inline void pushnow(int u){
		swap(lc(u),rc(u)),rev[u]^=1;
	}
	inline void pushdown(int u){
		if(lc(u))val[lc(u)]=val[u];
		if(rc(u))val[rc(u)]=val[u];
		if(!rev[u])return;
		if(lc(u))pushnow(lc(u));
		if(rc(u))pushnow(rc(u));
		rev[u]=0;
	}
	inline void pushup(int u){
		siz[u]=1;
		if(lc(u))siz[u]+=siz[lc(u)];
		if(rc(u))siz[u]+=siz[rc(u)];
	}
	inline void rotate(int v){
		int u=fa[v],z=fa[u];
		int t=isrc(v);
		if(!isrt(u))son[z][isrc(u)]=v;
		fa[v]=z;
		fa[son[v][t^1]]=u;
		son[u][t]=son[v][t^1];
		fa[u]=v,son[v][t^1]=u;
		pushup(u),pushup(v);
	}
	int stk[N],top;
	inline void splay(int u){
		stk[top=1]=u;
		for(int v=u;!isrt(v);v=fa[v])stk[++top]=fa[v];
		for(int i=top;i;i--)pushdown(stk[i]);
		while(!isrt(u)){
			if(!isrt(fa[u]))
			isrc(u)==isrc(fa[u])?rotate(fa[u]):rotate(u);
			rotate(u);
		}
	}
	inline void access(int u){
		for(int v=0;u;v=u,u=fa[u]){
			splay(u),rc(u)=0,pushup(u);
			Tr::update(val[u],-siz[u]);
			Tr::update(tot,siz[u]);
			rc(u)=v;
			pushup(u);
		}
	}
	inline void makert(int u){
		access(u),splay(u),pushnow(u);
	}
	inline void update(int u){
		tot++,makert(u),val[u]=tot;
	}
	inline int query(int u){
		splay(u);
		return Tr::query(val[u])-siz[lc(u)];
	}
}
void dfs(int u,int fa){
	int mx=0,son=0;val[u]=u;
	for(int &v:e[u]){
		if(v==fa)continue;
		dfs(v,u);if(val[v]>mx)mx=val[v],son=v;
		Lct::fa[v]=u;
	}
	if(mx>val[u])Lct::rc(u)=son,val[u]=mx;
	Lct::pushup(u),Tr::update(val[u],1);
}
int main(){
	tot=n=read(),m=read();
	for(int i=1;i<n;i++){
		int u=read(),v=read();
		e[u].pb(v),e[v].pb(u);
	}
	dfs(n,0);
	while(m--){
		int len=readchar(s),u=read();
		if(s[0]=='u'){
			Lct::update(u);
		}
		else if(s[0]=='w'){
			cout<<Lct::query(u)<<'\n';
		}
		else{
			int v=read();
			cout<<(Lct::query(u)>Lct::query(v)?v:u)<<'\n';
		}
	}
}