UVA 10173 （几何凸包）

判断矩形能包围点集的最小面积：凸包

 #include <iostream>
 #include <cmath>
 #include <cstdio>
 #include <cstring>
 #include <cstdlib>
 #include <string>
 #include <sstream>
 #include <algorithm>
 #define Max 2147483647
 #define INF 0x7fffffff
 #define ll long long
 #define mem(a,b) memset(a,b,sizeof(a))
 #define repu(i, a, b) for(int i = (a); i < (b); i++)
 const double PI=-acos(-1.0);
 #define eps 1e-8
 #define N 50010
 using namespace std;
 struct Point
 {
     double x,y;
     Point() {}
     Point(double x0,double y0):x(x0),y(y0) {}
 };
 Point p[N];
 int con[N];
 int cn;
 int n;
 struct Line
 {
     Point a,b;
     Line() {}
     Line(Point a0,Point b0):a(a0),b(b0) {}
 };
 double Xmult(Point o,Point a,Point b)
 {
     return (a.x-o.x)*(b.y-o.y)-(b.x-o.x)*(a.y-o.y);
 }
 double Dmult(Point o,Point a,Point b)
 {
     return (a.x-o.x)*(b.x-o.x)+(a.y-o.y)*(b.y-o.y);
 }
 int Sig(double a)
 {
     return a<-eps?-:a>eps;
 }
 double Dis(Point a,Point b)
 {
     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
 }
 int cmp(Point a,Point b)
 {
     double d=Xmult(p[],a,b);
     if(d>)
         return ;
     if(d== && Dis(p[],a)<Dis(p[],b))
         return ;
     return ;
 }
 double min(double a,double b)
 {
     return a<b?a:b;
 }
 void Graham()
 {
     int i,ind=;
     for(i=; i<n; i++)
         if(p[ind].y>p[i].y || (p[ind].y==p[i].y) && p[ind].x>p[i].x)
             ind=i;
     swap(p[ind],p[]);
     sort(p+,p+n,cmp);
     con[]=;
     con[]=;
     cn=;
     for(i=; i<n; i++)
     {
         while(cn> && Sig(Xmult(p[con[cn-]],p[con[cn]],p[i]))<=)
             cn--;
         con[++cn]=i;
     }
     int tmp=cn;
     for(i=n-; i>=; i--)
     {
         while(cn>tmp && Sig(Xmult(p[con[cn-]],p[con[cn]],p[i]))<=)
             cn--;
         con[++cn]=i;
     }
 }
 double Solve()
 {
     int t,r,l;
     double ans=;
     t=r=;
     if(cn<)
         return ;
     for(int i=; i<cn; i++)
     {
         while(Sig( Xmult(p[con[i]],p[con[i+]],p[con[t+]])-
                    Xmult(p[con[i]],p[con[i+]],p[con[t]])   )>)
             t=(t+)%cn;
         while(Sig( Dmult(p[con[i]],p[con[i+]],p[con[r+]])-
                    Dmult(p[con[i]],p[con[i+]],p[con[r]])   )>)
             r=(r+)%cn;
         if(!i) l=r;
         while(Sig( Dmult(p[con[i]],p[con[i+]],p[con[l+]])-
                    Dmult(p[con[i]],p[con[i+]],p[con[l]])   )<=)
             l=(l+)%cn;
         double d=Dis(p[con[i]],p[con[i+]]);
         double tmp=Xmult(p[con[i]],p[con[i+]],p[con[t]])*
                    ( Dmult(p[con[i]],p[con[i+]],p[con[r]])-
                      Dmult(p[con[i]],p[con[i+]],p[con[l]]) )/d/d;
         ans=min(ans,tmp);
     }
     return ans;
 }
 int main()
 {
     int i,T;
     scanf("%d",&T);
     repu(kase,,T+)
     {
         scanf("%d",&n);
         n *= ;
         for(i=; i<n; i++)
             scanf("%lf%lf",&p[i].x,&p[i].y);
         Graham();
         printf("Case #%d:\n%.0lf\n",kase,Solve());
     }
     return ;
 }