最小圆覆盖（Smallest Enclosing Discs）

随机增量算法（a randomized incremental algorithm）

#define sqr(x) ((x)*(x))
#define EPS 1e-4

struct P{
double x, y;
P(double x, double y):x(x),y(y){}
P(P &a, P &b):x(b.x-a.x),y(b.y-a.y){}
P(){}
P mid(P &a){
return P((a.x+x)/2, (a.y+y)/2);
}
double cross(P &a){
return x*a.y-y*a.x;
}
double len2(){
return sqr(x)+sqr(y);
}
double dis(P &a){
return sqrt(sqr(x-a.x)+sqr(y-a.y));
}
void print(){
printf("%f %f\n", x, y);
}
};

struct Disc{
P o;
double r;
bool cover(P &a){
return r-o.dis(a) >= -EPS;
}
Disc(){}
Disc(P &o, double r):o(o),r(r){}
Disc(P &a, P &b):o(a.mid(b)), r(a.dis(b)/2){}
Disc(P &a, P &b, P &c){
double t1=b.len2()-a.len2();
double t2=c.len2()-a.len2();
P p1(a, b), p2(a, c);
double t3=p1.cross(p2)*2;
P p3(t1, p1.y), p4(t2, p2.y);
P p5(p1.x, t1), p6(p2.x, t2);
o=P(p3.cross(p4)/t3, p5.cross(p6)/t3);
r=o.dis(a);
}
};

Disc MinDisc(vector<P> &p){
if(p.size()<=1) return Disc();
random_shuffle(p.begin(), p.end());
Disc d(p[0], p[1]);
for(int i=2; i<p.size(); i++)
if(!d.cover(p[i])){
d=Disc(p[0], p[i]);
for(int j=1; j<i; j++)
if(!d.cover(p[j])){
d=Disc(p[i], p[j]);
for(int k=0; k<j; k++)
if(!d.cover(p[k]))
d=Disc(p[i], p[j], p[k]);
}
}
return d;
}