[hdu5251]矩形面积 旋转卡壳求最小矩形覆盖

　　旋转卡壳求最小矩形覆盖的模板题。

　　因为最小矩形必定与凸包的一条边平行，则枚举凸包的边，通过旋转卡壳的思想去找到其他3个点，构成矩形，求出最小面积即可。

 #include<cstdio>
 #include<iostream>
 #include<cstring>
 #include<algorithm>
 #include<queue>
 #include<set>
 #include<map>
 #include<stack>
 #include<time.h>
 #include<cstdlib>
 #include<cmath>
 #include<list>
 using namespace std;
 #define MAXN 100100
 #define eps 1e-9
 #define For(i,a,b) for(int i=a;i<=b;i++)
 #define Fore(i,a,b) for(int i=a;i>=b;i--)
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define mkp make_pair
 #define pb push_back
 #define cr clear()
 #define sz size()
 #define met(a,b) memset(a,b,sizeof(a))
 #define iossy ios::sync_with_stdio(false)
 #define fre freopen
 #define pi acos(-1.0)
 #define inf 1e6+7
 #define Vector Point
 const int Mod=1e9+;
 typedef unsigned long long ull;
 typedef long long ll;
 int dcmp(double x){
     if(fabs(x)<=eps) return ;
     return x<?-:;
 }
 struct Point{
     double x,y;
     Point(double x=,double y=):x(x),y(y) {}
     bool operator < (const Point &a)const{
         if(x==a.x) return y<a.y;
         return x<a.x;
     }
     Point operator - (const Point &a)const{
         return Point(x-a.x,y-a.y);
     }
     Point operator + (const Point &a)const{
         return Point(x+a.x,y+a.y);
     }
     Point operator * (const double &a)const{
         return Point(x*a,y*a);
     }
     Point operator / (const double &a)const{
         return Point(x/a,y/a);
     }
     void read(){
         scanf("%lf%lf",&x,&y);
     }
     void out(){
         cout<<"debug: "<<x<<" "<<y<<endl;
     }
     bool operator == (const Point &a)const{
         return dcmp(x-a.x)== && dcmp(y-a.y)==;
     }
 };
 double Dot(Vector a,Vector b) {
     return a.x*b.x+a.y*b.y;
 }
 double dis(Vector a) {
     return sqrt(Dot(a,a));
 }
 double Cross(Point a,Point b){
     return a.x*b.y-a.y*b.x;
 }
 int ConvexHull(Point *p,int n,Point *ch){
     int m=;
     For(i,,n-) {
         while(m> && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     int k=m;
     Fore(i,n-,){
         while(m>k && Cross(ch[m-]-ch[m-],p[i]-ch[m-])<=) m--;
         ch[m++]=p[i];
     }
     if(n>) m--;
     return m;
 }
 double ANS(Point *p,int n){
     int L,R=,U=;
     double ans=1e9+;
     p[n]=p[];
     For(i,,n-) {
         while(Cross(p[i+]-p[i],p[U+]-p[i])>=Cross(p[i+]-p[i],p[U]-p[i])) U=(U+)%n;
         while(Dot(p[i+]-p[i],p[R+]-p[i])>Dot(p[i+]-p[i],p[R]-p[i])) R=(R+)%n;
         if(!i) L=R;
         while(Dot(p[i+]-p[i],p[L+]-p[i])<=Dot(p[i+]-p[i],p[L]-p[i])) L=(L+)%n;
         double tmp=fabs(Cross(p[U]-p[i],p[i+]-p[i]))/dis(p[i+]-p[i]);
         double cnt1=fabs(Dot(p[L]-p[i],p[i+]-p[i]))/dis(p[i+]-p[i]),cnt2=fabs(Dot(p[R]-p[i],p[i+]-p[i]))/dis(p[i+]-p[i]);
         ans=min(ans,(cnt2+cnt1)*tmp);
     }
     return ans;
 }
 int n,m;
 Point p[];
 Point ch[];
 void solve(){
     scanf("%d",&n);
     int rt=;
     For(i,,n-) {
         p[rt++].read();
         p[rt++].read();
         p[rt++].read();
         p[rt++].read();
     }
     sort(p,p+rt);
     m=ConvexHull(p,rt,ch);
     printf("%.0lf\n",ANS(ch,m));
 }
 int main(){
 //    fre("in.txt","r",stdin);
     int t=;
     cin>>t;
     For(i,,t) printf("Case #%d:\n",i),solve();
     return ;
 }