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Chef and Graph Queries

題目大意:多次詢問保留編號在[L,R]之間的邊圖中的連通塊數量。1e5。 題解:固定右端點向左掃等價於求最大生成樹,那麼每條邊出現的時間是一個區間,維護這個區間的右端點+1(也就是其被擠掉的時間)即可。

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define Rep(i,v) rep(i,0,(int)v.size()-1)
#define lint long long
#define ull unsigned lint
#define db double
#define pb push_back
#define mp make_pair #define fir first #define sec second #define N 400010 #define INF (INT_MAX/10-10) #define inf (INT_MIN/10+10) #define gc getchar() #define debug(x) cerr<<#x<<"="<<x #define sp <<" " #define ln <<endl using namespace std; typedef pair<int,int> pii; typedef
set<int>::iterator sit; inline int inn() { int x,ch;while((ch=gc)<'0'||ch>'9'); x=ch^'0';while((ch=gc)>='0'&&ch<='9') x=(x<<1)+(x<<3)+(ch^'0');return x; } int ch[N][2],s[N],val[N],fa[N],pf[N],rev[N],nxt[N],P[N],u[N],v[N]; inline int gw(int x) { return
ch[fa[x]][1]==x; } inline int push_up(int x) { return s[x]=min(min(s[ch[x][0]],s[ch[x][1]]),val[x]); } inline int setc(int x,int y,int z) { if(!x) return fa[y]=0;ch[x][z]=y;if(y) fa[y]=x;return push_up(x); } inline int rotate(int x) { int y=fa[x],z=fa[y],a=gw(x),b=gw(y),c=ch[x][a^1]; return swap(pf[x],pf[y]),setc(y,c,a),setc(x,y,a^1),setc(z,x,b); } inline int push_down(int x) { if(!rev[x]) return 0; if(ch[x][0]) rev[ch[x][0]]^=1; if(ch[x][1]) rev[ch[x][1]]^=1; swap(ch[x][0],ch[x][1]),rev[x]=0; return 0; } inline int all_down(int x) { return (fa[x]?all_down(fa[x]):0),(rev[x]?push_down(x):0); } inline int splay(int x) { for(all_down(x);fa[x];rotate(x)) if(fa[fa[x]]) rotate(gw(x)==gw(fa[x])?fa[x]:x);return 0; } inline int expose(int x) { splay(x);int y=ch[x][1];if(!y) return 0; return pf[y]=x,ch[x][1]=fa[y]=0,push_up(x); } inline int splice(int x) { splay(x);int y=pf[x];if(!y) return 0; return pf[x]=0,expose(y),splay(y),setc(y,x,1),1; } inline int access(int x) { expose(x);while(splice(x));return 0; } inline int evert(int x) { return access(x),splay(x),rev[x]^=1; } inline int link(int x,int y) { return evert(x),evert(y),splay(x),splay(y),pf[x]=y; } inline int cut(int x,int y) { return evert(x),access(y),splay(x),ch[x][1]=fa[y]=0,push_up(x); } inline int grt(int x) { while(fa[x]) x=fa[x];return x; } inline int query(int x,int y) { evert(x),access(y),splay(x);return grt(y)==x?s[x]:0; } struct segment{ int s;segment *ch[2]; }*T[N]; int build(segment* &rt,int l,int r) { rt=new segment;int mid=(l+r)>>1;if(l==r) return rt->s=0; return build(rt->ch[0],l,mid),build(rt->ch[1],mid+1,r); } int update(segment* &x,segment* &y,int l,int r,int p) { x=new segment,x->ch[0]=y->ch[0],x->ch[1]=y->ch[1]; x->s=y->s+1;if(l==r) return 0;int mid=(l+r)>>1; if(p<=mid) update(x->ch[0],y->ch[0],l,mid,p); else update(x->ch[1],y->ch[1],mid+1,r,p);return 0; } int query(segment* &rt,int l,int r,int s,int t) { if(s<=l&&r<=t) return rt->s;int ans=0,mid=(l+r)>>1; if(s<=mid) ans+=query(rt->ch[0],l,mid,s,t); if(mid<t) ans+=query(rt->ch[1],mid+1,r,s,t); return ans; } int query(int a,int b,int l,int r,int s,int t) { return query(T[b],l,r,s,t)-query(T[a-1],l,r,s,t); } int main() { for(int Tcs=inn();Tcs;Tcs--) { int n=inn(),m=inn(),q=inn(); rep(i,1,m) u[i]=inn(),v[i]=inn(),nxt[i]=m+1,P[i]=i+n; rep(i,1,m) val[P[i]]=s[P[i]]=i;rep(i,0,n) val[i]=s[i]=INF; rep(i,1,n+m) ch[i][0]=ch[i][1]=fa[i]=pf[i]=rev[i]=0; rep(i,1,m) { if(u[i]==v[i]) { nxt[i]=1;continue; } int j=query(u[i],v[i]); if(j) cut(P[j],u[j]),cut(P[j],v[j]),nxt[j]=i; link(P[i],u[i]),link(P[i],v[i]); } // rep(i,1,m) debug(i)sp,debug(nxt[i])ln; build(T[0],1,m+1);rep(i,1,m) update(T[i],T[i-1],1,m+1,nxt[i]); for(int l,r;q;q--) l=inn(),r=inn(),printf("%d\n",n-query(l,r,1,m+1,r+1,m+1)); } return 0; }