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;

}