2031 几何+MST

只要算出两者距离减去半径之和，就变成平面图了

/* ***********************************************
Author        :PeterBishop
Created Time  :Sat 02 Mar 2019 17:18:28 CST
File Name     :t.cpp
Origin        :P O J  2031
************************************************ */

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>

using namespace std;
const int MAXN=101;
double cost[MAXN][MAXN];
const double INF=10000;
bool vis[MAXN];
double lowc[MAXN];
struct node{
    double x;
    double y;
    double z;
    double r;
}p[MAXN];
double dis(node a,node b){
    double d=(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)+(a.z-b.z)*(a.z-b.z);
    d=sqrt(d)-a.r-b.r;
    if(d<0)
        d=0;
    return  d;
}
double prim(int n){
    memset(vis,false,sizeof(vis));
    double ans=0;
    for(int i=0;i<n;i++)
        lowc[i]=cost[0][i];
    vis[0]=true;
    for(int i=1;i<n;i++){
        int p;
        double minc=INF;
        for(int j=1;j<n;j++)
            if(!vis[j]&&minc>lowc[j]){
                p=j;
                minc=lowc[j];
            }
        vis[p]=true;
        ans+=minc;
        if(minc==INF)
            return -1;
        for(int j=0;j<n;j++)
            if(!vis[j]&&lowc[j]>cost[p][j])
                lowc[j]=cost[p][j];
    }
    return ans;
}
int main()
{
    //freopen("out.txt","w",stdout);
    freopen("in.txt","r",stdin);
    int n;
    while(cin>>n){
        if(n==0)
            break;
        for(int i=0;i<MAXN;i++)
            for(int j=0;j<MAXN;j++)
                cost[i][j]=i==j?0:INF;
        for(int i=0;i<n;i++){
            cin>>p[i].x>>p[i].y>>p[i].z>>p[i].r;
        }

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                double d=dis(p[i],p[j]);
                cost[i][j]=cost[j][i]=d;
            }
        }
        printf("%.3f\n",prim(n));
    }    
    return 0;
}