【HDU 4081】 Qin Shi Huang's National Road System

Solution

要求最大的A/B，贪心的想就是A最大，B，最小
考虑B最小，就求最小生成树
A最大怎么办？只能枚举边，那么便不再生成树上怎么办？次小生成树！f[i][j]表示树上i到j的边上的最大值，则ans=max{ans，A/(B-f[i][j])}

CODE

#include<bits/stdc++.h>
using namespace std;
const int MAXN=1010;
int fa[MAXN],rank[MAXN],Head[MAXN];
int nume,tot,n;
bool flag[MAXN*MAXN];
double f[MAXN][MAXN],sum,ans;

struct node{
    int x,y,p;
}a[MAXN];
struct Edge{
    int u,v;
    double d;
    int p;
}e[MAXN*MAXN];
struct EDGE{
    int next,v;
    double d;
}edge[MAXN*2];


inline double distance(int x1,int y1,int x2,int y2)
{
    return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
bool cmp(const Edge &x,const Edge &y)
{
    return x.d<y.d;
}
int getfa(int x)
{
    if (x==fa[x]) return fa[x];
    fa[x]=getfa(fa[x]);
    return fa[x];
}
bool Union(int x,int y)
{
    x=getfa(x); y=getfa(y);
    if (x==y) return false;
    if (rank[x]>rank[y]) fa[y]=x;
    else fa[x]=y,rank[y]++;
    return true;
}
void addedge(int x,int y,double z)
{
    edge[++tot]=(EDGE){Head[x],y,z};
    Head[x]=tot;
    edge[++tot]=(EDGE){Head[y],x,z};
    Head[y]=tot;
    sum+=z;
}
void dfs(int u,int pre,int root)
{
    for (int i=Head[u];i;i=edge[i].next)
    {
        int v=edge[i].v;
        if (v==pre) continue;
        double d=edge[i].d;
        f[root][v]=max(f[root][u],d);
        dfs(v,u,root);
    }
}
int main()
{
    int T;
    scanf("%d",&T);
    while (T--)
    {
        scanf("%d",&n);
        memset(Head,0,sizeof(Head));
        memset(f,0,sizeof(f));
        memset(flag,false,sizeof(flag));
        for (int i=1;i<=n;i++) fa[i]=i,rank[i]=0;
        nume=tot=sum=ans=0;
        for (int i=1;i<=n;i++) 
            scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].p);
        for (int i=1;i<=n;i++)
            for (int j=i+1;j<=n;j++)
                e[++nume]=(Edge){i,j,distance(a[i].x,a[i].y,a[j].x,a[j].y),a[i].p+a[j].p};
        sort(e+1,e+1+nume,cmp);
        for (int i=1;i<=nume && tot<2*(n-1);i++)
            if (Union(e[i].u,e[i].v)) 
                addedge(e[i].u,e[i].v,e[i].d),flag[i]=true;
        for (int i=1;i<=n;i++) dfs(i,0,i);     
        for (int i=1;i<=nume;i++)
            if (flag[i]) ans=max(ans,e[i].p/(sum-e[i].d));
            else ans=max(ans,e[i].p/(sum-f[e[i].u][e[i].v]));
        printf("%.2lf\n",ans);
    }
    //system("pause");
    return 0;
}