bzoj 3564 信号增幅仪

bzoj 3564 信号增幅仪

• 一道有意义的好题.启发我们善用坐标变换,如在遇到椭圆时使用坐标变换转化为圆来处理.
• 直接在一个方向上进行伸缩不方便,先将坐标系旋转,使椭圆长轴与 (x) 轴平行,点的坐标变换用旋转公式处理.
• 坐标系逆时针转过了 ( heta) ,相当于点逆时针转过了 (- heta) .
• 再沿长轴方向伸缩,将点的横坐标除以 (p) ,椭圆就转化为了圆,求一个最小圆覆盖即可.

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pii pair<int,int>
inline int read()
{
	int x=0;
	bool pos=1;
	char ch=getchar();
	for(;!isdigit(ch);ch=getchar())
		if(ch=='-')
			pos=0;
	for(;isdigit(ch);ch=getchar())
		x=x*10+ch-'0';
	return pos?x:-x;
}
struct v2{
	double x,y;
	v2(double x=0,double y=0):x(x),y(y) {}
	v2 operator + (const v2 &rhs) const
		{
			return v2(x+rhs.x,y+rhs.y);
		}
	v2 operator / (const double &rhs) const
		{
			return v2(x/rhs,y/rhs);
		}
	v2 operator - (const v2 &rhs) const
		{
			return v2(x-rhs.x,y-rhs.y);
		}
	double operator * (const v2 &rhs) const
		{
			return x*rhs.y-y*rhs.x;
		}
	double modulus()
		{
			return sqrt(x*x+y*y);
		}
};
const double PI=acos(-1.0);
v2 rotate(v2 v,double degree)
{
	double rad=degree/180*PI;
	//v2 res=v2(cos(rad)*v.x-sin(rad)*v.y,sin(rad)*v.x+cos(rad)*v.y);
	v2 res=v2(v.x*cos(rad)-v.y*sin(rad),v.x*sin(rad)+v.y*cos(rad));
	return res;
}
const int MAXN=5e4+10;
int n;
v2 a[MAXN];
double theta,p;
void transform()
{
	for(int i=1;i<=n;++i)
		{
			a[i]=rotate(a[i],theta);
			a[i].x/=p;
		}
}
const double eps=1e-9;
int dcmp(double x)
{
	return fabs(x)<eps?0:(x>0?1:-1);
}
v2 getcentre(v2 a,v2 b,v2 c)
{
	v2 centre;
	double a1=b.x-a.x;
	double b1=b.y-a.y;
	double c1=(a1*a1+b1*b1)/2.0;
	double a2=c.x-a.x;
	double b2=c.y-a.y;
	double c2=(a2*a2+b2*b2)/2.0;
	double d=a1*b2-a2*b1;
	centre.x=a.x+(c1*b2-c2*b1)/d;
	centre.y=a.y+(a1*c2-a2*c1)/d;
	return centre;
}
bool incir(v2 centre,double r,v2 p)
{
	return dcmp((p-centre).modulus()-r)<=0;
}
double MinCircleCover()
{
	srand(19260817);
	random_shuffle(a+1,a+1+n);
	v2 centre=a[1];
	double r=0;
	for(int i=2;i<=n;++i)
		{
			if(!incir(centre,r,a[i]))
				{
					centre=a[i];
					r=0;
					for(int j=1;j<i;++j)
						{
							if(!incir(centre,r,a[j]))
								{
									centre=(a[i]+a[j])/2.0;
									r=(a[i]-centre).modulus();
									for(int k=1;k<j;++k)
										{
											if(!incir(centre,r,a[k]))
												{
													centre=getcentre(a[i],a[j],a[k]);
													r=(a[i]-centre).modulus();
												}
										}
								}
						}
				}
		}
	return r;
}
int main()
{
	n=read();
	for(int i=1;i<=n;++i)
		scanf("%lf%lf",&a[i].x,&a[i].y);
	scanf("%lf%lf",&theta,&p);
	theta*=-1;
	transform();
	double ans=MinCircleCover();
	printf("%.3lf
",ans);
	return 0;
}