poj2728

最优比率生成树

#include<iostream>
#include<cmath>
#include<iomanip>
#include<string.h>
const int MAX=1005;
const int inf=0x7fffffff;
using namespace std;
int n;
double x[MAX],y[MAX],z[MAX],cost[MAX][MAX],dist[MAX][MAX],ans;
double prim(double mid)
{
    double dis[MAX];
    bool visit[MAX];
    double mini;
    ans=0;
    memset(visit,true,sizeof(visit));
    int i,j,num;
    for(i=2;i<=n;i++) dis[i]=cost[1][i]-dist[1][i]*mid;
    for(i=2;i<=n;i++)
    {
        mini=inf;
        for(j=2;j<=n;j++)
            if(visit[j]&&mini>dis[j])
            {
                num=j;
                mini=dis[j];
            }
        visit[num]=false;
        ans+=mini;
        for(j=2;j<=n;j++)
            if(visit[j]&&dis[j]>cost[num][j]-dist[num][j]*mid)
            dis[j]=cost[num][j]-dist[num][j]*mid;
    }
    return ans;
}
double fun(int i,int j)
{
    return sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]));
}
int main()
{
    int i,j;
    double t;
    cout<<setiosflags(ios::fixed)<<setprecision(3);
    while(cin>>n&&n)
    {
        for(i=1;i<=n;i++)
        {
            cin>>x[i]>>y[i]>>z[i];
            for(j=1;j<i;j++)
            {
                t=fun(i,j);
                dist[i][j]=dist[j][i]=t;
                cost[i][j]=cost[j][i]=abs(z[i]-z[j]);
            }
        }
        double l=0.0,r=1000.0,mid;
        while(r-l>1e-5)
        {
            mid=(l+r)/2;
            if(prim(mid)>=0) l=mid;
            else r=mid;
        }
        cout<<l<<endl;
    }
}