Problem:
Building a Space Station

You are a member of the space station engineering team,
and are assigned a task in the construction process of the station.
You are expected to write a computer program to complete the task.

The space station is made up with a number of units, called cells.
All cells are sphere-shaped, but their sizes are not necessarily uniform.
Each cell is fixed at its predetermined position
shortly after the station is successfully put into its orbit.
It is quite strange that two cells may be touching each other,
or even may be overlapping.
In an extreme case, a cell may be totally enclosing another one.
I do not know how such arrangements are possible.

All the cells must be connected,
since crew members should be able to walk
from any cell to any other cell.
They can walk from a cell A to another cell B, if,
(1) A and B are touching each other or overlapping,
(2) A and B are connected by a `corridor',
or (3) there is a cell C such that walking from A to C, and also from B to C
are both possible.
Note that the condition (3) should be interpreted transitively.

You are expected to design a configuration,
namely, which pairs of cells are to be connected with corridors.
There is some freedom in the corridor configuration.
For example, if there are three cells A, B and C,
not touching nor overlapping each other,
at least three plans are possible in order to connect all three cells.
The first is to build corridors A-B and A-C,
the second B-C and B-A, the third C-A and C-B.
The cost of building a corridor is proportional to its length.
Therefore, you should choose a plan with the shortest
total length of the corridors.

You can ignore the width of a corridor.
A corridor is built between points on two cells' surfaces.
It can be made arbitrarily long, but of course the shortest one is chosen.
Even if two corridors A-B and C-D intersect in space, they are
not considered to form a connection path between (for example) A and C.
In other words, you may consider that two corridors never intersect.

Input

The input consists of multiple data sets.
Each data set is given in the following format.

n

x1 y1 z1 r1

x2 y2 z2 r2

...

xn yn zn rn

The first line of a data set contains an integer n,
which is the number of cells.
n is positive, and does not exceed 100.

The following n lines are descriptions of cells.
Four values in a line are x-, y- and z-coordinates of
the center, and radius (called r in the rest of the problem) of
the sphere, in this order.
Each value is given by a decimal fraction, with
3 digits after the decimal point.
Values are separated by a space character.

Each of x, y, z and r is positive
and is less than 100.0.

The end of the input is indicated by a line containing a zero.

Output

For each data set, the shortest total length of the corridors
should be printed, each in a separate line.
The printed values should have 3 digits after the decimal point.
They may not have an error greater than 0.001.

Note that if no corridors are necessary, that is,
if all the cells are connected without corridors,
the shortest total length of the corridors is 0.000.

Sample Input

3
10.000 10.000 50.000 10.000
40.000 10.000 50.000 10.000
40.000 40.000 50.000 10.000
2
30.000 30.000 30.000 20.000
40.000 40.000 40.000 20.000
5
5.729 15.143 3.996 25.837
6.013 14.372 4.818 10.671
80.115 63.292 84.477 15.120
64.095 80.924 70.029 14.881
39.472 85.116 71.369 5.553
0

Output for the Sample Input

20.000
0.000
73.834

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Solve{
    static public int mod = 1000000007;
    public static void Main(){
        // 方針
        //
        while(true){
        var n = rint();
        if(n == 0) break;
        var xlist = new List<double>();
        var ylist = new List<double>();
        var zlist = new List<double>();
        var rlist = new List<double>();
        for(int i=0;i<n;i++){
            var a = stra();
            xlist.Add(double.Parse(a[0]));
            ylist.Add(double.Parse(a[1]));
            zlist.Add(double.Parse(a[2]));
            rlist.Add(double.Parse(a[3]));
        }
        var pq3d = new PriorityQueue3d();
        for(int i=0;i<n-1;i++){
            for(int j=i+1;j<n;j++){
                double xdis = (xlist[i]-xlist[j]) * (xlist[i]-xlist[j]);
                double ydis = (ylist[i]-ylist[j]) * (ylist[i]-ylist[j]);
                double zdis = (zlist[i]-zlist[j]) * (zlist[i]-zlist[j]);
                double distance = Max(Sqrt(xdis+ydis+zdis) - rlist[i] - rlist[j],0.0);
                pq3d.Enqueue(distance,i,j);
            }
        }
        
        var uf = new UnionFind(n);
        double ans = 0;
        while(pq3d.Count() > 0){
            var de = pq3d.Dequeue();
            //WriteLine(string.Join(" ",de));
            
            double dis = double.Parse(de[0]);
            int num1 = int.Parse(de[1]);
            int num2 = int.Parse(de[2]);
            if(!uf.same(num1,num2)){
                uf.unite(num1,num2);
                ans += dis;
            }
            
        }
        WriteLine(ans.ToString("F3"));
        }
	
	
    }
    public static void swap(ref int a,ref int b){int temp = a;a= b;b = temp;}
    static void charswap(ref char a,ref char b){char temp = a;a= b;b = temp;}
    static int ncr(int n,int r){if(n<r)return 0;r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    static int square2(int a,int b){long output = 1;var list = new List<long>();int sh = 1;long n = a;list.Add(a);while(sh < b){sh *= 2;n = n*n%mod;list.Add(n);}for(int i=list.Count-1;i>=0;i--){if(b > sh){b -= sh;sh /= 2;output = output*list[i]%mod;}}return (int)output;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static char[] chara(){ string[] a=stra();string b="";for(int i=0;i<a.Length;i++){b+=a[i];}return b.ToCharArray();}
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
    static void WriteArray(int[,] a,int b,int c){for(int i=0;i<b;i++){for(int j=0;j<c;j++){if(j!=0) Write(" ");Write(a[i,j]);}WriteLine();}}
}

class UnionFind{
    private int[] _unionfind;
    private int[] _unionfind_size;
    
    public UnionFind(int a){
        _unionfind = new int[a];
        _unionfind_size = new int[a];
        for(int i=0;i<a;i++){
            _unionfind[i] = i;
            _unionfind_size[i] = 1;
        }
    }
    
    public int root(int x){
        if(_unionfind[x] == x) return x;
        return _unionfind[x] = root(_unionfind[x]);
    }
    
    public void unite(int a,int b){
        a = root(a);
        b = root(b);
        if(a == b) return;
        if(_unionfind_size[a] < _unionfind_size[b]){
            int temp = a;
            a = b;
            b = temp;
        }
        _unionfind[b] = a;
        _unionfind_size[a] += _unionfind_size[b];
    }
    
    public bool same(int a,int b){
        return root(a) == root(b);
    }
    
    public int size(int x){
        return _unionfind_size[root(x)];
    }
}

class PriorityQueue3d{
    private List<double> _priorityqueue = new List<double>();
    private List<int> _accompany_info = new List<int>();
    private List<int> _accompany_info2 = new List<int>();
    
    public void Enqueue(double a,int b,int c){
        _priorityqueue.Add(a);
        _accompany_info.Add(b);
        _accompany_info2.Add(c);
        int num = _priorityqueue.Count-1;
        while(true){
            if(num == 0) break;
            if(_priorityqueue[(num-1)/2] > _priorityqueue[num]){ //大小逆の時弄るとこ
                double tempd = _priorityqueue[(num-1)/2];
                  _priorityqueue[(num-1)/2] = _priorityqueue[num];
                  _priorityqueue[num] = tempd;
                int temp = _accompany_info[(num-1)/2];
                  _accompany_info[(num-1)/2] = _accompany_info[num];
                  _accompany_info[num] = temp;
                temp = _accompany_info2[(num-1)/2];
                  _accompany_info2[(num-1)/2] = _accompany_info2[num];
                  _accompany_info2[num] = temp;
                num = (num-1)/2;
            }else{
                break;
            }
        }
    }
    
    public string[] Dequeue(){
        var re = new string[]{_priorityqueue[0].ToString(),_accompany_info[0].ToString(),_accompany_info2[0].ToString()};
        var qcount = _priorityqueue.Count;
        var tempd = _priorityqueue[0]; _priorityqueue[0] = _priorityqueue[qcount-1]; _priorityqueue[qcount-1] = tempd;
        var temp = _accompany_info[0]; _accompany_info[0] = _accompany_info[qcount-1]; _accompany_info[qcount-1] = temp;
        temp = _accompany_info2[0]; _accompany_info2[0] = _accompany_info2[qcount-1]; _accompany_info2[qcount-1] = temp;
        _priorityqueue.RemoveAt(qcount-1);
        _accompany_info.RemoveAt(qcount-1);
        _accompany_info2.RemoveAt(qcount-1);
        int num = 0;
        while(true){
            int swapnum = -1;
            if((num+1)*2 < _priorityqueue.Count){
                if(_priorityqueue[num*2+1] < _priorityqueue[(num+1)*2]){ //大小逆の時弄るとこ
                    swapnum = num*2+1;
                }else{
                    swapnum = (num+1)*2;
                }
            }else if(num*2+1 < _priorityqueue.Count){
                swapnum = num*2+1;
            }
            if(swapnum == -1) break;
            if(_priorityqueue[swapnum] < _priorityqueue[num]){ //大小逆の時弄るとこ
                tempd = _priorityqueue[swapnum];_priorityqueue[swapnum] = _priorityqueue[num];_priorityqueue[num] = tempd;
                temp = _accompany_info[swapnum];_accompany_info[swapnum] = _accompany_info[num];_accompany_info[num] = temp;
                temp = _accompany_info2[swapnum];_accompany_info2[swapnum] = _accompany_info2[num];_accompany_info2[num] = temp;
                num = swapnum;
            }else{
                break;
            }
        }
        return re;
    }
    
    public string[] Peek(){
        var temp = new string[]{_priorityqueue[0].ToString(),_accompany_info[0].ToString(),_accompany_info2[0].ToString()};
        return temp;
    }
    
    public int Count(){
        return _priorityqueue.Count;
    }
}