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?-1: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[0],a,b);
    if(d>0)
        return 1;
    if(d==0 && Dis(p[0],a)<Dis(p[0],b))
        return 1;
    return 0;
}
double min(double a,double b)
{
    return a<b?a:b;
}
void Graham()
{
    int i,ind=0;
    for(i=1; 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[0]);
    sort(p+1,p+n,cmp);
    con[0]=0;
    con[1]=1;
    cn=1;
    for(i=2; i<n; i++)
    {
        while(cn>0 && Sig(Xmult(p[con[cn-1]],p[con[cn]],p[i]))<=0)
            cn--;
        con[++cn]=i;
    }
    int tmp=cn;
    for(i=n-2; i>=0; i--)
    {
        while(cn>tmp && Sig(Xmult(p[con[cn-1]],p[con[cn]],p[i]))<=0)
            cn--;
        con[++cn]=i;
    }
}
double Solve()
{
    int t,r,l;
    double ans=999999999;
    t=r=1;
    if(cn<3)
        return 0;
    for(int i=0; i<cn; i++)
    {
        while(Sig( Xmult(p[con[i]],p[con[i+1]],p[con[t+1]])-
                   Xmult(p[con[i]],p[con[i+1]],p[con[t]])   )>0)
            t=(t+1)%cn;
        while(Sig( Dmult(p[con[i]],p[con[i+1]],p[con[r+1]])-
                   Dmult(p[con[i]],p[con[i+1]],p[con[r]])   )>0)
            r=(r+1)%cn;
        if(!i) l=r;
        while(Sig( Dmult(p[con[i]],p[con[i+1]],p[con[l+1]])-
                   Dmult(p[con[i]],p[con[i+1]],p[con[l]])   )<=0)
            l=(l+1)%cn;
        double d=Dis(p[con[i]],p[con[i+1]]);
        double tmp=Xmult(p[con[i]],p[con[i+1]],p[con[t]])*
                   ( Dmult(p[con[i]],p[con[i+1]],p[con[r]])-
                     Dmult(p[con[i]],p[con[i+1]],p[con[l]]) )/d/d;
        ans=min(ans,tmp);
    }
    return ans;
}
int main()
{
    int i,T;
    scanf("%d",&T);
    repu(kase,1,T+1)
    {
        scanf("%d",&n);
        n *= 4;
        for(i=0; i<n; i++)
            scanf("%lf%lf",&p[i].x,&p[i].y);
        Graham();
        printf("Case #%d:
%.0lf
",kase,Solve());
    }
    return 0;
}