hdu 4081 最小生成树+树形dp

思路：直接先求一下最小生成树，然后用树形dp来求最优值。也就是两遍dfs。

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#define Maxn 2010
using namespace std;
struct Edge{
    int u,v;
    double c;
    int operator <(const Edge &temp) const
    {
        return c<temp.c;
    }
}p[1000010];
struct PP{
    int u,v,next;
    double val;
}edge[Maxn*2];
struct Point{
    double x,y;
}city[Maxn];
int set[Maxn],e,vi[10010],num[Maxn],head[Maxn],road[Maxn],Max[Maxn],lMax[Maxn];
double ans,S;
int find(int x)
{
    if(x!=set[x])
        set[x]=find(set[x]);
    return set[x];
}
int merg(int a,int b)
{
    int x,y;
    x=find(a);
    y=find(b);
    if(x==y)
        return 0;
    set[x]=y;
    return 1;
}
void add(int u,int v,double val)
{
    edge[e].u=u,edge[e].v=v,edge[e].val=val,edge[e].next=head[u],head[u]=e++;
    edge[e].u=v,edge[e].v=u,edge[e].val=val,edge[e].next=head[v],head[v]=e++;
    memset(Max,0,sizeof(Max));
}
double DIS(Point a,Point b)
{
   return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
void init()
{
    for(int i=0;i<Maxn;i++)
        set[i]=i,num[i]=0;
    memset(head,-1,sizeof(head));
    memset(vi,0,sizeof(vi));
    memset(road,0,sizeof(road));
    e=0;
}
void dfs(int u)
{
    int i,v;
    vi[u]=1;
    Max[u]=lMax[u]=num[u];
    for(i=head[u];i!=-1;i=edge[i].next){
        v=edge[i].v;
        if(vi[v]) continue;
        dfs(v);
        if(Max[v]>Max[u]){
            lMax[u]=Max[u];
            Max[u]=Max[v];
            road[u]=v;
        }
        else if(Max[v]>lMax[u]){
            lMax[u]=Max[v];
        }
    }
}
void predfs(int u,int sum)
{
    int i,v;
    vi[u]=1;
    double a,b;
    for(i=head[u];i!=-1;i=edge[i].next){
        v=edge[i].v;
        if(vi[v]) continue;
        if(road[u]==v) a=max(lMax[u],sum);
        else a=max(sum,Max[u]);
        a+=Max[v];
        b=S-edge[i].val;
        if(a/b>ans){
            ans=a/b;
        }
        if(road[u]==v) predfs(v,max(lMax[u],sum));
        else predfs(v,max(Max[u],sum));
    }
}
int main()
{
    int t,n,m,i,j,x,y,c;
    scanf("%d",&t);
    while(t--)
    {
        init();
        scanf("%d",&n);
        for(i=1;i<=n;i++)
            scanf("%lf%lf%d",&city[i].x,&city[i].y,&num[i]);
        int cnt=0;
        for(i=1;i<=n;i++){
            for(j=i+1;j<=n;j++){
                p[++cnt].u=i,p[cnt].v=j,p[cnt].c=DIS(city[i],city[j]);
            }
        }
        sort(p+1,p+1+cnt);
        int cc=0;
        double temp=0;
        int lis[Maxn];
        for(i=1;i<=cnt;i++){
            if(merg(p[i].u,p[i].v)){
                temp+=p[i].c;
                lis[++cc]=i;
            }
            if(cc==n-1)
                break;
        }
        for(i=1;i<=cc;i++){
            add(p[lis[i]].u,p[lis[i]].v,p[lis[i]].c);
        }
        S=temp;
        ans=0;
        dfs(1);
        memset(vi,0,sizeof(vi));
        predfs(1,0);
        printf("%.2lf\n",ans);
    }
    return 0;
}