【最小乘积生成树】bzoj2395[Balkan 2011]Timeismoney

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 using namespace std;
 5 int res;
 6 char c;
 7 inline int Get()
 8 {
 9     res=0;c=‘*‘;
10     while(c<‘0‘||c>‘9‘)c=getchar();
11     while(c>=‘0‘&&c<=‘9‘){res=res*10+(c-‘0‘);c=getchar();}
12     return res;
13 }
14 struct Edge{int u,v,c,t,w;void read(){u=Get();v=Get();c=Get();t=Get();}};
15 struct Point{int x,y;Point(const int &A,const int &B){x=A;y=B;}Point(){}};
16 typedef Point Vector;
17 typedef long long LL;
18 Vector operator - (const Point &a,const Point &b){return Vector(a.x-b.x,a.y-b.y);}
19 int Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}
20 bool operator < (const Edge &a,const Edge &b){return a.w<b.w;}
21 Edge edges[10001];
22 int n,m,rank[201],fa[201];
23 Point ans=Point(1000000000,1000000000),minc,mint;
24 inline void init()
25 {
26     memset(rank,0,sizeof(rank));
27     for(int i=0;i<n;i++)
28       fa[i]=i;
29 }
30 int findroot(int x) 
31 {
32     if(fa[x]==x)
33       return x;
34     int t=findroot(fa[x]);
35     fa[x]=t;
36     return t;
37 }
38 inline void Union(int U,int V)
39 {
40     if(rank[U]<rank[V])
41       fa[U]=V;
42     else
43       {
44         fa[V]=U;
45         if(rank[U]==rank[V])
46           rank[U]++;
47       }
48 }
49 inline Point Kruscal()
50 {
51     int tot=0;
52     Point now=Point(0,0);
53     init();
54     for(int i=1;i<=m;i++)
55       {
56           int U=findroot(edges[i].u),V=findroot(edges[i].v);
57           if(U!=V)
58             {
59                 Union(U,V);
60                 tot++;
61                 now.x+=edges[i].c;
62                 now.y+=edges[i].t;
63                 if(tot==n-1)
64                   break;
65             }
66       }
67     LL Ans=(LL)ans.x*ans.y,Now=(LL)now.x*now.y;
68     if( Ans>Now || (Ans==Now&&now.x<ans.x) )
69       ans=now;
70     return now;
71 }
72 void Work(Point A,Point B)
73 {
74     for(int i=1;i<=m;i++)
75       edges[i].w=edges[i].t*(B.x-A.x)+edges[i].c*(A.y-B.y);
76     sort(edges+1,edges+m+1);
77     Point C=Kruscal();
78     if(Cross(B-A,C-A)>=0)
79       return;
80     Work(A,C);
81     Work(C,B);
82 }
83 int main()
84 {
85     scanf("%d%d",&n,&m);
86     for(int i=1;i<=m;i++)
87       edges[i].read();
88     for(int i=1;i<=m;i++)
89       edges[i].w=edges[i].c;
90     sort(edges+1,edges+m+1);
91     minc=Kruscal();
92     for(int i=1;i<=m;i++)
93       edges[i].w=edges[i].t;
94     sort(edges+1,edges+m+1);
95     mint=Kruscal();
96     Work(minc,mint);
97     printf("%d %d\n",ans.x,ans.y);
98     return 0;
99 }