P14442 [JOISC 2013] 礼物 / Presents

\(i\to a_i\) 连边，形成基环树森林。

无论是环还是树，答案上界为 \(\sum_i b_i\cdot \max\{c_{a_i},d_{a_i}\}\)，每条边未取到较大时的代价为 \(b_i\cdot |c_{a_i}-d_{a_i}|\)，按代价降序排序贪心取一定不劣。

所以扩展域并查集维护每个点的颜色关系即可。

#include<bits/stdc++.h>
#define fin(x) freopen(#x".in","r",stdin)
#define fout(x) freopen(#x".out","w",stdout)
#define fr(x) fin(x),fout(x);
#define Fr(x,y) fin(x),fout(y)
#define INPUT(_1,_2,FILE,...) FILE
#define IO(...) INPUT(__VA_ARGS__,Fr,fr)(__VA_ARGS__)
using namespace std;
#define mp make_pair
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
#define cfast ios::sync_with_stdio(false);cin.tie(0),cout.tie(0)
#define ll long long
#define ull unsigned long long
#define intz(x,y) memset((x),(y),sizeof((x)))
char *p1,*p2,buf[100000];
#define nc() (p1==p2 && (p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++)
#define tup(x) array<int,(x)>
inline ll read(){
    ll x=0,f=1;char ch=nc();
    while(ch<48||ch>57){if(ch=='-')f=-1;ch=nc();}
    while(ch>=48&&ch<=57)x=x*10+ch-48,ch=nc();
   	return x*f;
}
//void write(int x){cout<<x<<' ';}
//void write(pii x){cout<<"P("<<x.fi<<','<<x.se<<")\n";}
//void write(vector<auto>x){for(auto i:x)write(i);cout<<'\n';}
//void write(auto *a,int l,int r){for(int i=l;i<=r;i++)write(a[i]);cout<<'\n';}
inline ll lowbit(ll x){return x&-x;}
inline int pcount(ll x){
	for(int i=0,res=0;;res+=(x>>i)&1,i++)
		if(i>60)return res;
}

//struct mt{
//	ll v;
//	mt(){v=0;}
//	mt(int x){this->v=x;}
//	inline mt operator+(mt x){return {(v+x.v)%mod};}
//	inline mt operator-(mt x){return {(v+mod-x.v)%mod};}
//	inline mt operator*(mt x){return {1ll*v*x.v%mod};}
//};
//inline void add(mt &x,mt y){x=x+y;}
//mt qp(mt x,int y){mt res(1);for(;y;x=x*x,y>>=1)if(y&1)res=res*x;return res;}
const int N=1e6+5;
#define int ll
struct edge{int u,v,w,x,y;};
vector<edge>E;
int a[N],b[N],c[N],d[N],f[N<<1];
int find(int x){return x==f[x]?x:f[x]=find(f[x]);}
inline void UesugiErii(){
	int n,ans=0;cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i]>>b[i]>>c[i]>>d[i];
	for(int i=1;i<=n;i++)
		E.pb(edge{i,a[i],b[i]*max(c[a[i]],d[a[i]]),b[i]*abs(c[a[i]]-d[a[i]])}),
		ans+=E.back().w;
	sort(E.begin(),E.end(),[](edge x,edge y){return x.x>y.x;});
	for(int i=1;i<=n<<1;i++)f[i]=i;
	for(edge i:E){
		if(c[i.v]>d[i.v]){
			if(find(i.u)==find(i.v+n))ans-=i.x;
			else f[find(i.u)]=find(i.v),f[find(i.u+n)]=find(i.v+n);
		}else{
			if(find(i.u)==find(i.v))ans-=i.x;
			else f[find(i.u)]=find(i.v+n),f[find(i.u+n)]=find(i.v);
		}
	}
	cout<<ans;
}
signed main(){
	//IO();//cfast;
	int _=1;//cin>>_;
	for(;_;_--)UesugiErii();
	return 0;
}