HDU 5251 矩形面积(二维凸包旋转卡壳最小矩形覆盖问题) --2015百度之星题目

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#define MAX 50010
using namespace std;
struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
Point P[MAX],ch[MAX];
typedef Point Vector;
typedef Point point;
Vector operator - (Point A,Point B)
{
    return Vector(A.x-B.x,A.y-B.y);
}
bool operator <(const Point &a,const Point &b)
{
    return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
const double eps=1e-10;
int dcmp(double x)
{
    if(fabs(x)<eps) return 0; else return x<0?-1:1;
}
bool operator ==(const Point &a,const Point &b)
{
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}
double dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}
int ConvexHull(Point *p,int n)
{
    sort(p,p+n);
    n=unique(p,p+n)-p;
    int m=0;
    for(int i=0;i<n;i++)
    {
        while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<0) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--)
    {
        while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;
        ch[m++]=p[i];
    }
    if(n>1) m--;
    return m;
}
double Length(Vector A)
{
    return dot(A,A);
}
double  rotating_calipers(Point *p,int n)
{
    int l=1,r=1,w;
    double ans=1e30;
    p[n]=p[0];
    for(int i=0;i<n;i++)
    {
        //注意这里等于0一定要算上
        //这里debug了整整一个小时 - -|||||
        //找到至高点
        while(dcmp(Cross(p[i+1]-p[i],p[w+1]-p[i])-Cross(p[i+1]-p[i],p[w]-p[i]))>=0) //因为边平行的时候面积相等 虽然如此但还是要继续找下一个 横着爬不动的意思
        w=(w+1)%n;
        //找到最右的点 不可能向左的
        while(dcmp(dot(p[i+1]-p[i],p[r+1]-p[i])-dot(p[i+1]-p[i],p[r]-p[i]))>0) //凸包不可能凹进去 所以不需要等号 加深对凸包求解过程的理解
        r=(r+1)%n;
        if(i==0) l=r;
        while(dcmp(dot(p[i+1]-p[i],p[l+1]-p[i])-dot(p[i+1]-p[i],p[l]-p[i]))<=0) //必须加等号 否则凸包遇到直边的时候拐不过来 上不去 第二组样例可以完美说明问题
        l=(l+1)%n;
        double d=Length(p[i+1]-p[i]);
        double area=fabs(Cross(p[i+1]-p[i],p[w]-p[i]))
        *fabs(dot(p[i+1]-p[i],p[r]-p[i])-dot(p[i+1]-p[i],p[l]-p[i]))/d;
        //cout<<fabs(Cross(p[i+1]-p[i],p[w]-p[i]))<<"     ";
        //cout<<"rrrrr    "<<r<<"   lll    "<<l<<endl;
        //cout<<dot(p[i+1]-p[i],p[r]-p[i])<<" "<<dot(p[i+1]-p[i],p[l]-p[i])<<endl;
        ans=min(ans,area);
    }
    return ans;
}
int main()
{
    int t,n,cas=1;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        n*=4;
        for(int i=0;i<n;i++)
        scanf("%lf%lf",&P[i].x,&P[i].y);
        int m=ConvexHull(P,n);
        //for(int i=0;i<n;i++)
            //cout<<ch[i].x<<"  "<<ch[i].y<<endl;
        double ans;
        if(m<3) ans=0;
        else ans=rotating_calipers(ch,m);
        long long tmp = ans+0.5;
        printf("Case #%d:\n%lld\n",cas++,tmp);
    }
    return 0;
}