最小乘积生成树 - Timeismoney（BZOJ2395）

Analysis

学习ing
最小乘积生成树

Code

/*
	created by xly
*/
#include<bits/stdc++.h>
#define in red()
#define re register
using namespace std;
inline int red(){
	char ch;int f=1,res=0;
	while((ch=getchar())<'0'||ch>'9') if(ch=='-') f=-1;
	while(ch>='0'&&ch<='9'){
		res=(res<<1)+(res<<3)+(ch^48);
		ch=getchar();
	}
	return f==1?res:-res;
}
const int N=205,M=10009;
struct EDGE{
	int u,v,c,t,w;
	void read(){u=in;v=in;c=in;t=in;}
	bool operator <(const EDGE &a){	return w<a.w;}
}edge[M];
struct POINT{
	int x,y;
	POINT(int _x=0,int _y=0):x(_x),y(_y){}
	POINT operator -(const POINT &a){
		POINT c;
		c.x=x-a.x;c.y=y-a.y;
		return c;
	}
}minc,mint,ans;
int cross(POINT a,POINT b){
	return a.x*b.y-a.y*b.x;
}
int n,m,fa[N];
inline int getfa(int x){return x==fa[x]?x:fa[x]=getfa(fa[x]);}
inline POINT Kruscal(){
	for(re int i=0;i<=n;++i) fa[i]=i;
	int t=0;
	POINT now;
	for(re int i=1;i<=m;++i){
		int u=getfa(edge[i].u),v=getfa(edge[i].v);
		if(u!=v){
			fa[u]=v;
			now.x+=edge[i].c;
			now.y+=edge[i].t;
			t++;
			if(t==n-1) break;
		}
	}
	long long ANS=ans.x*1ll*ans.y,NOW=now.x*1ll*now.y;
	if(ANS>NOW||(ANS==NOW&&ans.x>now.x)) ans=now;
	return now;
}
void work(POINT a,POINT b){
	for(re int i=1;i<=m;++i) edge[i].w=edge[i].t*(b.x-a.x)-edge[i].c*(b.y-a.y);
	sort(edge+1,edge+m+1);
	POINT c=Kruscal();
	if(cross(b-a,c-a)>=0) return;
	work(a,c);
	work(c,b);
}
int main(){
	n=in;m=in;
	ans.x=1e9;ans.y=1e9;
	for(re int i=1;i<=m;++i) edge[i].read();
	for(re int i=1;i<=m;++i) edge[i].w=edge[i].c;
	sort(edge+1,edge+m+1);
	minc=Kruscal();
	for(re int i=1;i<=m;++i) edge[i].w=edge[i].t;
	sort(edge+1,edge+m+1);
	mint=Kruscal();
	work(minc,mint);
	printf("%d %d",ans.x,ans.y);
	return 0;
}