Extending Set of Points[CF1140F][並查集]

題目

Luogu

思路

沒什麼可說的，線段樹分治，觀察是單點查詢和區間修改就能統一處理詢問
將點視爲行和列的連接，那麼就能和題目中擴展操作符合
注意這裏方案數是並查集內的 $cntx*cnty$ ，並查集帶撤回
以前打Atcoder最後一道題就是這個套路…沒見過，然後就把它記着了

代碼

#include<map>
#include<set>
#include<stack>
#include<queue>
#include<cmath>
#include<cstring>
#include<climits>
#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define LL long long
//#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)
//char buf[(1 << 21) + 1], *p1 = buf, *p2 = buf;
inline LL read() {
	bool f=0;LL x=0;char c=getchar();
	while(c<'0'||'9'<c){if(c==EOF)exit(0);if(c=='-')f=1;c=getchar();}
	while('0'<=c&&c<='9') x=(x<<3)+(x<<1)+(c^48),c=getchar();
	return !f?x:-x;
}
#define lch (rt<<1)
#define rch (rt<<1|1)
#define MAXN 600000
#define mp make_pair
#define INF 0x3f3f3f3f
#define pii pair<int,int>
vector<pii > tree[5*MAXN+5];
void Insert(int rt,int L,int R,int qL,int qR,pii x){
	if(qL<=L&&R<=qR){
		tree[rt].push_back(x);
		return ;
	}
	int Mid=(L+R)>>1;
	if(qL<=Mid)
		Insert(lch,L,Mid,qL,qR,x);
	if(Mid+1<=qR)
		Insert(rch,Mid+1,R,qL,qR,x);
	return ;
}
struct node{
	int u,v,dep,sizx,sizy;
}Stk[MAXN+5];
LL ans[MAXN+5],sum;
int tp,fa[MAXN+5],dep[MAXN+5],sizx[MAXN+5],sizy[MAXN+5];
int Find(int u){return fa[u]==u?u:Find(fa[u]);}
LL Cal(int u){return 1ll*sizx[u]*sizy[u];}
void Merge(int u,int v){
	u=Find(u),v=Find(v);
	if(u==v) return ;
	if(dep[u]<dep[v])
		swap(u,v);
	Stk[++tp]=(node){u,v,dep[u],sizx[u],sizy[u]};
	if(dep[u]==dep[v])
		dep[u]++;
	sum-=Cal(u)+Cal(v);
	fa[v]=u,sizx[u]+=sizx[v],sizy[u]+=sizy[v];
	sum+=Cal(u);
	return ;
}
void Restore(int ntp){
	while(tp>ntp){
		int u=Stk[tp].u,v=Stk[tp].v;
		sum-=Cal(u);
		fa[v]=v,dep[u]=Stk[tp].dep;
		sizx[u]=Stk[tp].sizx,sizy[u]=Stk[tp].sizy;
		sum+=Cal(u)+Cal(v),tp--;
	}
	return ;
}
void DFS(int rt,int L,int R){
	int ntp=tp;
	for(int i=0;i<(int)tree[rt].size();i++){
		int u=tree[rt][i].first,v=tree[rt][i].second;
		Merge(u,v);
	}
	if(L==R){
		ans[L]=sum;
		Restore(ntp);
		return ;
	}
	int Mid=(L+R)>>1;
	DFS(lch,L,Mid),DFS(rch,Mid+1,R);
	Restore(ntp);
	return ;
}
map<pii,int>Map;
int main(){
	int n=read();
	for(int i=1;i<=n;i++)
		fa[i]=i,sizx[i]=1;
	for(int i=n+1;i<=2*n;i++)
		fa[i]=i,sizy[i]=1;
	for(int i=1;i<=n;i++){
		int u=read(),v=n+read();
		if(Map[mp(u,v)])
			Insert(1,1,n,Map[mp(u,v)],i-1,mp(u,v)),Map.erase(mp(u,v));
		else Map[mp(u,v)]=i;
	}
	for(map<pii,int>::iterator it=Map.begin();it!=Map.end();it++)
		Insert(1,1,n,it->second,n,it->first);
	DFS(1,1,n);
	for(int i=1;i<=n;i++)
		printf("%lld ",ans[i]);
	return 0;
}