【bzoj1185】[HNOI2007]最小矩形覆盖 (旋转卡壳)

给你一些点,让你用最小的矩形覆盖这些点

首先有一个结论，矩形的一条边一定在凸包上！！！

枚举凸包上的边

用旋转卡壳在凸包上找矩形另外三点。。。

注意精度问题

 #include<cstdio>
 #include<cmath>
 #include<ctime>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #include<queue>
 #include<set>
 #define eps 1e-8
 #define inf 1000000000
 using namespace std;
 double ans=1e60;
 int n,top;
 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);
     }
     friend P operator+(P a,P b){
         return P(a.x+b.x,a.y+b.y);
     }
     friend P operator-(P a,P b){
         return P(a.x-b.x,a.y-b.y);
     }
     friend double operator*(P a,P b){
         return a.x*b.y-a.y*b.x;
     }
     friend P operator*(P a,double b){
         return P(a.x*b,a.y*b);
     }
     friend double operator/(P a,P b){
         return a.x*b.x+a.y*b.y;
     }
     friend double dis(P a){
         return sqrt(a.x*a.x+a.y*a.y);
     }
 }p[],q[],t[];
 bool cmp(P a,P b)
 {
     double t=(a-p[])*(b-p[]);
     if(fabs(t)<eps)return dis(p[]-a)-dis(p[]-b)<;
     return t>;
 }
 void graham()
 {
     for(int i=;i<=n;i++)
         if(p[i]<p[])
             swap(p[i],p[]);
     sort(p+,p+n+,cmp);
     q[++top]=p[];
     for(int i=;i<=n;i++)
     {
         while(top>&&(q[top]-q[top-])*(p[i]-q[top])<eps)top--;
         q[++top]=p[i];
     }
     q[]=q[top];
 }
 void RC()
 {
     int l=,r=,p=;
     double L,R,D,H;
     for(int i=;i<top;i++)
     {
         D=dis(q[i]-q[i+]);
         while((q[i+]-q[i])*(q[p+]-q[i])-(q[i+]-q[i])*(q[p]-q[i])>-eps)p=(p+)%top;
         while((q[i+]-q[i])/(q[r+]-q[i])-(q[i+]-q[i])/(q[r]-q[i])>-eps)r=(r+)%top;
         if(i==)l=r;
         while((q[i+]-q[i])/(q[l+]-q[i])-(q[i+]-q[i])/(q[l]-q[i])<eps)l=(l+)%top;
         L=(q[i+]-q[i])/(q[l]-q[i])/D,R=(q[i+]-q[i])/(q[r]-q[i])/D;
         H=(q[i+]-q[i])*(q[p]-q[i])/D;
         if(H<)H=-H;
         double tmp=(R-L)*H;
         if(tmp<ans)
         {
             ans=tmp;
             t[]=q[i]+(q[i+]-q[i])*(R/D);
             t[]=t[]+(q[r]-t[])*(H/dis(t[]-q[r]));
             t[]=t[]-(t[]-q[i])*((R-L)/dis(q[i]-t[]));
             t[]=t[]-(t[]-t[]);
         }
     }
 }
 int main()
 {
     scanf("%d",&n);
     for(int i=;i<=n;i++)
         scanf("%lf%lf",&p[i].x,&p[i].y);
     graham();
     RC();
     printf("%.5lf\n",ans);
     int fir=;
     for(int i=;i<=;i++)
         if(t[i]<t[fir])
             fir=i;
     for(int i=;i<=;i++)
         printf("%.5lf %.5lf\n",t[(i+fir)%].x,t[(i+fir)%].y);
     return ;
 }