UVA10652 Board Wrapping

题意

PDF

分析

就是一个裸的凸包。

如何确定点？就用中心向四边连垂直的向量然后旋转，加上中心点，即可得出旋转后的点。

时间复杂度\(O(T n \log n)\)

代码

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<algorithm>
#include<bitset>
#include<cassert>
#include<ctime>
#include<cstring>
#define rg register
#define il inline
#define co const
template<class T>il T read()
{
    rg T data=0;
    rg int w=1;
    rg char ch=getchar();
    while(!isdigit(ch))
    {
        if(ch=='-')
            w=-1;
        ch=getchar();
    }
    while(isdigit(ch))
    {
        data=data*10+ch-'0';
        ch=getchar();
    }
    return data*w;
}
template<class T>T read(T&x)
{
    return x=read<T>();
}
using namespace std;
typedef long long ll;

co double eps=1e-10;

int dcmp(double x)
{
    return fabs(x)<=eps?0:(x<0?-1:1);
}

struct Point
{
    double x,y;

    Point(double x=0,double y=0)
    :x(x),y(y){}

    bool operator<(co Point&rhs)co
    {
        return dcmp(x-rhs.x)?x<rhs.x:y<rhs.y;
    }
};
typedef Point Vector;

Vector operator+(Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}

Vector operator-(Vector A,Vector B)
{
    return Vector(A.x-B.x,A.y-B.y);
}

Vector operator*(Vector A,double p)
{
    return Vector(A.x*p,A.y*p);
}

Vector operator/(Vector A,double p)
{
    return Vector(A.x/p,A.y/p);
}

double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}

double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}

Vector Rotate(Vector A,double rad)
{
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}

int ConvexHull(Point*p,int n,Point*ch)
{
    sort(p,p+n);
    int m=0;
    for(int i=0;i<n;++i)
    {
        while(m>1&&dcmp(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&&dcmp(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 PolygonArea(Point *p,int n)
{
    double area=0;
    for(int i=1;i<n-1;++i)
        area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    return area/2;
}

int n,pc;
Point P[2500],ch[2500];

double torad(double deg)
{
    return deg*acos(-1)/180;
}

int main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    int T=read<int>();
    while(T--)
    {
        pc=0;
        double area1=0;
        read(n);
        for(int i=0;i<n;++i)
        {
            double x,y,w,h,ang;
            scanf("%lf %lf %lf %lf %lf",&x,&y,&w,&h,&ang);
            Point o(x,y);
            ang=-torad(ang);
            P[pc++]=o+Rotate(Vector(-w/2,-h/2),ang);
            P[pc++]=o+Rotate(Vector(w/2,-h/2),ang);
            P[pc++]=o+Rotate(Vector(-w/2,h/2),ang);
            P[pc++]=o+Rotate(Vector(w/2,h/2),ang);
            area1+=w*h;
        }
        int m=ConvexHull(P,pc,ch);
        double area2=PolygonArea(ch,m);
        printf("%.1lf %%\n",area1*100/area2);
    }
    return 0;
}