P5385 [Cnoi2019]须臾幻境(LCT+主席树，思维题)

题目

P5385 [Cnoi2019]须臾幻境

做法

考虑一条边\((u,v)\)是否\([L,R]\)中的贡献：\([L,R]\)中第一条位于\(u,v\)链的边，则减少了一个联通块

实现：\(LCT\)维护最小边，产生环则删除最小边，再替换\((\)和这题差不多\()\)

得出删除序列，建好主席树，直接查询\([L,R]\)中小于\(L\)的数量即可

Code

#include<bits/stdc++.h>
typedef int LL;
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;
}
const LL maxn=1e6+9,inf=0x3f3f3f3f;
LL n,m,q,seed;
LL ear[maxn];
namespace LCT{
	struct node{
		LL u,v;
	}e[maxn];
	LL son[maxn][2],fa[maxn],mi[maxn],mi_n[maxn],val[maxn],sta[maxn],r[maxn];
	inline LL Notroot(LL x){
		return son[fa[x]][0]==x || son[fa[x]][1]==x;
	}
	inline void Update(LL x){
		LL lt(son[x][0]),rt(son[x][1]);
		mi[x]=std::min(mi[lt],mi[rt]);
		if(mi[x]==mi[lt]){
			mi_n[x]=mi_n[lt];
		}else{
			mi_n[x]=mi_n[rt];
		}
		if(val[x]<=mi[x]){
			mi[x]=val[x]; mi_n[x]=x;
		}
	}
	inline void Pushr(LL x){
		std::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;
		son[y][lz]=son[x][lz^1]; fa[son[y][lz]]=y;
		son[x][lz^1]=y; fa[y]=x;fa[x]=z;
		Update(y); Update(x);
	}
	inline void Splay(LL x){
		LL y(x),tot(0);
		sta[++tot]=y;
		while(Notroot(y)) sta[++tot]=y=fa[y];
		while(tot) Pushdown(sta[tot--]);
		while(Notroot(x)){
			y=fa[x];
			if(Notroot(y)){
				LL z(fa[y]);
				if((son[y][0]==x)^(son[z][0]==y)) Rotate(x); else Rotate(y);
			}Rotate(x);
		}
	}
	inline void Access(LL x){
		for(LL y=0;x;y=x,x=fa[x]){
			Splay(x); son[x][1]=y; 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 LL Query(LL x,LL y){
		Split(x,y); return mi_n[y];
	}
	inline LL Find(LL x){
		Access(x); Splay(x);
		while(son[x][0]){
			Pushdown(x); x=son[x][0];
		}Splay(x);
		return x;
	}
	inline void Cut(LL x,LL y){
		Split(x,y); son[y][0]=fa[x]=0; Update(y);//这里也可不更新，因为在查询时整条链都会更新
	}
	inline void Link(LL x,LL y){
		Makeroot(x); fa[x]=y;
	}
	inline void Solve(){
		for(LL i=0;i<=n;++i) val[i]=mi[i]=inf,mi_n[i]=i;
		LL tot=n;
		for(LL i=1;i<=m;++i){
			LL u(Read()),v(Read());
			e[i]=(node){u,v};
			if(u==v){
				ear[i]=i; continue;
			}else if(Find(u)==Find(v)){
				LL t(Query(u,v)),x(val[t]); ear[i]=x;
				Cut(e[x].u,t); Cut(e[x].v,t);
			}
			++tot; mi[tot]=val[tot]=i; mi_n[tot]=tot;
			Link(u,tot); Link(v,tot);
		}
	}
}
namespace Sgt{
	LL nod;
	LL size[maxn*20],son[maxn*20][2],root[maxn];
	void Update(LL pre,LL &now,LL l,LL r,LL v){
		now=++nod; size[now]=size[pre]+1;
		if(l==r) return;
		LL mid(l+r>>1);
		if(v<=mid){
			Update(son[pre][0],son[now][0],l,mid,v);
			son[now][1]=son[pre][1];
		}else{
			Update(son[pre][1],son[now][1],mid+1,r,v);
			son[now][0]=son[pre][0];
		}
	}
	LL Query(LL pre,LL now,LL l,LL r,LL v){
		if(l==r) return size[now]-size[pre];
		LL mid(l+r>>1);
		if(mid<v) return Query(son[pre][1],son[now][1],mid+1,r,v)+size[son[now][0]]-size[son[pre][0]];
		else return Query(son[pre][0],son[now][0],l,mid,v);
	}
	inline void Solve(){
		for(LL i=1;i<=m;++i) Update(root[i-1],root[i],0,m,ear[i]);
		LL lst(0);
		while(q--){
			LL l(Read()),r(Read());
			if(seed>0)
			    l=1ll*(l+1ll*seed*lst%m)%m+1,
				r=1ll*(r+1ll*seed*lst%m)%m+1;
			if(l>r) std::swap(l,r);
			printf("%d\n",lst=n-Query(root[l-1],root[r],0,m,l-1));
		}
	}
}
int main(){
	n=Read(); m=Read(); q=Read(); seed=Read();
	LCT::Solve();
	Sgt::Solve();
	return 0;
}