uva 11168

凸包+一点直线的知识；

#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#define eps 1e-9
using namespace std;
const double pi = acos(-1);

int dcmp(double x)
{
    return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);
}

struct Point
{
    double x;
    double y;

    Point(double x = 0, double y = 0):x(x), y(y) {}

    bool operator < (const Point& e) const
    {
        return dcmp(x - e.x) < 0 || (dcmp(x - e.x) == 0 && dcmp(y - e.y) < 0);
    }

    bool operator == (const Point& e) const
    {
        return dcmp(x - e.x) == 0 && dcmp(y - e.y) == 0;
    }
};

typedef Point Vector;

Vector operator + (Point A, Point B)
{
    return Vector(A.x + B.x, A.y + B.y);
}

Vector operator - (Point A, Point B)
{
    return Vector(A.x - B.x, A.y - B.y);
}

Vector operator * (Point A, double p)
{
    return Vector(A.x * p, A.y * p);
}

Vector operator / (Point A, double p)
{
    return Vector(A.x / p, A.y / p);
}

double cross(Point a,Point b){return a.x*b.y-a.y*b.x;}
Point rotate(Point a,double ang){return Point(a.x*cos(ang)-a.y*sin(ang),a.x*sin(ang)+a.y*cos(ang));}
int convexhull(Point *p,int n,Point *ch)
{
    sort(p,p+n);
    int m=0;
    for(int i=0;i<n;i++)
    {
        while(m>1&&cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--)
    {
        while(m>k&&cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    if(n>1)m--;
    return m;
}
Point p[100009],ch[100009];

int main()
{
    int t,n,ca=1;
    scanf("%d",&t);
    while(t--)
    {
        double sumx=0;
        double sumy=0;
        scanf("%d",&n);
        for(int i=0;i<n;i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
            sumx+=p[i].x;
            sumy+=p[i].y;
        }
        printf("Case #%d: ",ca++);
        double mi=99999999999.0;
        int m=convexhull(p,n,ch);
        for(int i=0;i<m;i++)
        {
            double a=-ch[(i+1)%m].y+ch[i].y;
            double b=ch[(i+1)%m].x-ch[i].x;
            double c=ch[i].x*ch[(i+1)%m].y-ch[i].y*ch[(i+1)%m].x;
            double d=fabs(a*sumx+b*sumy+c*n)/sqrt(a*a+b*b);
            mi=min(mi,d);
        }
        printf("%.3lf
",n>2?mi/n:0);
    }
    return 0;
}