2

2

5 10 5 8 3 10 3 8

8 8 8 6 7 8 7 6

1

0 0 2 2 2 0 0 2

Case #1:

17

Case #2:

4

旋转卡壳。和bzoj上那题基本同样

#include<cstdio>

#include<cstdlib>

#include<cstring>

#include<iostream>

#include<algorithm>

#include<functional>

#include<cmath>

using namespace std;

#define For(i,n) for(int i=1;i<=n;i++)

#define Fork(i,k,n) for(int i=k;i<=n;i++)

#define Rep(i,n) for(int i=0;i<n;i++)

#define ForD(i,n) for(int i=n;i;i--)

#define RepD(i,n) for(int i=n;i>=0;i--)

#define Forp(x) for(int p=pre[x];p;p=next[p])

#define Forpiter(x) for(int &p=iter[x];p;p=next[p])

#define MAXN (10000+10)

#define INF (1000000000)

#define eps 1e-6

struct P

{

    double x,y;

    P(){}

    P(double _x,double _y):x(_x),y(_y){}

    friend bool operator<(P a,P b){return (fabs(a.y-b.y)<eps)?a.x<b.x:a.y<b.y;  }

    friend bool operator==(P a,P b){return fabs(a.x-b.x)<eps&&fabs(a.y-b.y)<eps;}

    friend bool operator!=(P a,P b){return !(a==b);}  

}a[MAXN],s[MAXN],ansp[5];

int size=0;

double ans=INF;

double dis2(P a,P b){return (a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y);}

struct V

{

    double x,y;

    V(){}

    V(double _x,double _y):x(_x),y(_y){}

    V(P a,P b):x(b.x-a.x),y(b.y-a.y){}

    friend double operator*(V a,V b){return a.x*b.y-a.y*b.x;}

    friend V operator*(double a,V b){return V(a*b.x,a*b.y);}

    friend double operator/(V a,V b){return a.x*b.x+a.y*b.y;}

    friend P operator+(P a,V b){return P(a.x+b.x,a.y+b.y);}

    friend P operator-(P a,V b){return P(a.x-b.x,a.y-b.y);}

    friend V operator~(V a){return V(a.y,-a.x);}

    double dis2(){return x*x+y*y;   }

};

int cmp(P A,P B)

{

    double tmp=V(a[1],A)*V(a[1],B);

    if (tmp>0) return 1;

    else if (fabs(tmp)<eps) return (-dis2(A,a[1])-dis2(B,a[1])>0);

    return 0;

}

int n;  

int main()

{

//	freopen("F.in","r",stdin);

	int T;

	cin>>T;

	For(kcase,T)

	{

		ans=INF;

	    scanf("%d",&n);

	    n*=4;

	    for(int i=1;i<=n;i++) scanf("%lf%lf",&a[i].x,&a[i].y);

	    for (int i=2;i<=n;i++) if (a[i]<a[1]) swap(a[1],a[i]);

	    sort(a+2,a+1+n,cmp);

	    s[1]=a[1];size=1;

	    for (int i=2;i<=n;)

	        if (size<2||V(s[size-1],s[size])*V(s[size],a[i])>eps) s[++size]=a[i++];

	        else size--;

	    s[0]=s[size];  

	    int l=1,r=1,t=1;

	    for (int i=0;i<size;i++)

	    {

	        while (V(s[i],s[i+1])*V(s[i],s[t+1])-V(s[i],s[i+1])*V(s[i],s[t])>-eps) t=(t+1)%size;

	        while (V(s[i],s[i+1])/V(s[i],s[r+1])-V(s[i],s[i+1])/V(s[i],s[r])>-eps) r=(r+1)%size;

	        if (i==0) l=r;

	        while (V(s[i],s[i+1])/V(s[i],s[l+1])-V(s[i],s[i+1])/V(s[i],s[l])<eps) l=(l+1)%size;

	        double Dis2=dis2(s[i],s[i+1]),wlxdis=V(s[i],s[i+1])/V(s[i],s[l]),wrxdis=V(s[i],s[i+1])/V(s[i],s[r]),hxdis=V(s[i],s[i+1])*V(s[i],s[t]);

	        double tmp=hxdis*(wrxdis-wlxdis)/Dis2;

	        if (tmp<0) tmp=-tmp;

	        if (ans>tmp)

	        {

	            ans=tmp;

	            ansp[0]=s[i]-(wlxdis/Dis2)*V(s[i+1],s[i]);

	            ansp[1]=s[i]+(wrxdis/Dis2)*V(s[i],s[i+1]);

	            ansp[2]=ansp[1]+(hxdis/Dis2)*(~V(s[i+1],s[i]));

	            ansp[3]=ansp[0]+(hxdis/Dis2)*(~V(s[i+1],s[i]));

	        }

	    }

	    int p=0;

	    for (int i=1;i<4;i++) if (ansp[i]<ansp[p]) p=i;//p=0;

		printf("Case #%d:\n",kcase);

	    printf("%.0lf\n",ans);    

	}

    return 0;

}