[BZOJ2823][BZOJ1336][BZOJ1337]最小圆覆盖(随机增量法)

算法介绍网上有很多，不解释了。

给出三点坐标求圆心方法：https://blog.csdn.net/liyuanbhu/article/details/52891868

记得先random_shuffle()一下。

#include<cmath>
#include<cstdio>
#include<algorithm>
#define rep(i,l,r) for (int i=(l); i<=(r); i++)
using namespace std;

const int N=100010;
const double eps=1e-8;
int n;
double r;
struct P{ double x,y; }a[N],c;

double sqr(double x){ return x*x; }
double dis(P a,P b){ return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y)); }

P get(P &A,P &B,P &C){
    double a=A.x-B.x,b=A.y-B.y,c=A.x-C.x,d=A.y-C.y;
    double e=((sqr(A.x)-sqr(B.x))-(sqr(B.y)-sqr(A.y)))/2;
    double f=((sqr(A.x)-sqr(C.x))-(sqr(C.y)-sqr(A.y)))/2;
    return (P){(d*e-b*f)/(a*d-b*c),(a*f-c*e)/(a*d-b*c)};
}

void work(){
    random_shuffle(a+1,a+n+1);
    r=0; c=a[1];
    rep(i,2,n) if (dis(c,a[i])>r+eps){
        c=a[i]; r=0;
        rep(j,1,i-1) if (dis(a[j],c)>r+eps){
            c=(P){(a[i].x+a[j].x)/2,(a[i].y+a[j].y)/2}; r=dis(c,a[i]);
            rep(k,1,j-1) if (dis(a[k],c)>r+eps){
                c=get(a[i],a[j],a[k]); r=dis(c,a[i]);
            }
        }
    }
}

int main(){
    scanf("%d",&n);
    rep(i,1,n) scanf("%lf%lf",&a[i].x,&a[i].y);
    work(); printf("%lf
%lf %lf
",r,c.x,c.y);
    return 0;
}