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| #include <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <algorithm>
#include <sstream>
#include <map>
#include <set>
#include <cmath>
#define REP(i,k,n) for(int i=k;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define INF 1<<30
#define pb push_back
#define mp make_pair
#define EPS 1e-8
#define equals(a,b) fabs((a) - (b)) < EPS
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
struct Point3D {
double x, y, z;
Point3D() : x(0), y(0), z(0) {}
Point3D(double x, double y, double z) : x(x), y(y), z(z) {}
Point3D operator+(const Point3D &o) const { return Point3D(x+o.x, y+o.y, z+o.z); }
Point3D operator-(const Point3D &o) const { return Point3D(x-o.x, y-o.y, z-o.z); }
Point3D operator*(const double m) const { return Point3D(x*m, y*m, z*m); }
Point3D operator/(const double d) const { return Point3D(x/d, y/d, z/d); }
bool operator==(const Point3D &o) const { return fabs(x-o.x) < EPS && fabs(y-o.y) < EPS; }
};
ostream& operator << (ostream& os, const Point3D& p) {
os << "(" << p.x << ", " << p.y << ", " << p.z << ")";
return os;
}
double dot(Point3D a, Point3D b) { return a.x * b.x + a.y * b.y + a.z * b.z; }
Point3D cross(Point3D a, Point3D b) { return Point3D(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x); }
double norm(Point3D p) { return dot(p, p); }
double abs(Point3D p) { return sqrt(norm(p)); }
struct Line {
Point3D a, b;
Line() : a(Point3D(0, 0, 0)), b(Point3D(0, 0, 0)) {}
Line(Point3D a, Point3D b) : a(a), b(b) {}
};
ostream& operator << (ostream& os, const Line& l) {
os << "(" << l.a.x << ", " << l.a.y << ", " << l.a.z << ")-(" << l.b.x << "," << l.b.y << ", " << l.b.z << ")";
return os;
}
Point3D project(Line l, Point3D p) {
Point3D base = l.b - l.a;
double t = dot(base, p-l.a) / dot(base, base);
return l.a + base * t;
}
struct Sphere {
Point3D p;
double r;
Sphere() : p(Point3D(0, 0, 0)), r(0.0) {}
Sphere(Point3D p, double r) : p(p), r(r) {}
};
ostream& operator << (ostream& os, const Sphere& s) {
os << "(" << s.p.z << ", " << s.p.y << ", " << s.p.z << " :" << s.r << ")";
return os;
}
double distanceSphSph(Sphere s1, Sphere s2) {
Point3D p = s2.p - s1.p;
double dist = abs(p) - s1.r - s2.r;
return max(0.0, dist);
}
struct UnionFind {
vector<int> par,rank;
int N;
UnionFind(int n) {
N = n;
par.resize(n);
rank.resize(n);
rep(i,n) {
par[i] = i;
rank[i] = 0;
}
}
int find(int x) {
if(par[x] == x) return x;
else return par[x] = find(par[x]);
}
void unite(int x,int y) {
x = find(x);
y = find(y);
if(x == y) return;
if(rank[x] < rank[y]) {
par[x] = y;
}
else {
par[y] = x;
if(rank[x] == rank[y]) rank[x]++;
}
}
bool same(int x,int y) {
return find(x) == find(y);
}
int size() {
int cnt = 0;
rep(i,N) if(find(i) == i) cnt++;
return cnt;
}
};
struct edge {
int from,to;
double cost;
edge(int t, int c) : to(t),cost(c) {}
edge(int f, int t, double c) : from(f),to(t),cost(c) {}
bool operator<(const edge &e) const {
return cost < e.cost;
}
};
double kruskal(int n, vector<edge> v) {
sort(v.begin(),v.end());
UnionFind uf(n);
double ret = 0;
rep(i, v.size()) {
edge e = v[i];
if(!uf.same(e.from,e.to)) {
uf.unite(e.from,e.to);
ret += e.cost;
}
}
return ret;
}
int main() {
int n;
while(cin >> n && n) {
vector<Sphere> s(n);
rep(i, n) cin >> s[i].p.x >> s[i].p.y >> s[i].p.z >> s[i].r;
vector<edge> v;
rep(i, n) {
REP(j, i+1, n) {
double dist = distanceSphSph(s[i], s[j]);
v.push_back(edge(i, j, dist));
}
}
cout << fixed;
cout.precision(3);
cout << kruskal(n, v) << endl;
}
return 0;
}
|