BZOJ3564:[SHOI2014]信号增幅仪 坐标变换+计算几何+最小圆覆盖

思路:

首先我们将所有的点都顺时针旋转\(a\)度,这样就相当于坐标系逆时针旋转了\(a\)度,那么现在椭圆的长轴就与\(x\)轴平行了.

那么还要考虑椭圆现在是横向伸长了\(p\)倍,于是我们就将所有点目前的横坐标缩小\(p\)倍.

然后就是随机增量法的最小圆覆盖了.

#include<cstdio>
#include<cstring>
#include<cctype>
#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
 
typedef double f2;
 
static const f2 eps=1e-7;
inline int dcmp(const f2&x){return fabs(x)<eps?0:(x<0?-1:1);}
 
#define N 50010
 
struct Point{
    f2 x,y;
    Point(){}
    Point(f2 _x,f2 _y):x(_x),y(_y){}
     
    inline void read(){scanf("%lf%lf",&x,&y);}
     
    bool operator<(const Point&B)const{return dcmp(x-B.x)==0?y<B.y:x<B.x;}
     
    Point operator+(const Point&B)const{return Point(x+B.x,y+B.y);}
    Point operator-(const Point&B)const{return Point(B.x-x,B.y-y);}
    Point operator*(const f2&p)const{return Point(p*x,p*y);}
    Point operator/(const f2&p)const{return Point(x/p,y/p);}
}P[N];
 
f2 getdis(const Point&a,const Point&b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}
f2 cross(const Point&a,const Point&b){return a.x*b.y-a.y*b.x;}
 
Point getmid(const Point&a,const Point&b){return Point((a.x+b.x)/2,(a.y+b.y)/2);}
Point getvec(const Point&v){return Point(-v.y,v.x);}
Point rot(const Point&p,f2 alp){return Point(p.x*cos(alp)-p.y*sin(alp),p.x*sin(alp)+p.y*cos(alp));}
 
struct Line{
    Point p,v;
    Line(){}
    Line(const Point&p1,const Point&p2):p(p1),v(p1-p2){}
};
Line getvecline(const Point&p1,const Point&p2){
    Line re;
    re.p=getmid(p1,p2),re.v=getvec(p1-p2);
    return re;
}
Point getlineintersection(const Line&l1,const Line&l2){
    return l1.p+l1.v*(cross(l1.p-l2.p,l2.v)/cross(l1.v,l2.v));
}
Point getpoint(Point p1,Point p2,Point p3){
    static Point P[3];P[0]=p1,P[1]=p2,P[2]=p3;sort(P,P+3);p1=P[0],p2=P[1],p3=P[2];
    if(dcmp(cross(p1-p2,p2-p3))==0)return getmid(p1,p3);
    else return getlineintersection(getvecline(p1,p2),getvecline(p2,p3));
}
 
int main(){
    int n;scanf("%d",&n);register int i,j,k;
    for(i=1;i<=n;++i)P[i].read();
     
    f2 alp,p;scanf("%lf%lf",&alp,&p);
     
    for(i=1;i<=n;++i)P[i]=rot(P[i],-alp/180*acos(-1.0)),P[i].x/=p;
     
    for(i=2;i<=n;++i)swap(P[i],P[rand()%i+1]);
    Point o=P[1];f2 r=0;
    for(i=2;i<=n;++i)if(getdis(o,P[i])>r){
        o=P[i],r=0;
        for(j=1;j<i;++j)if(getdis(o,P[j])>r){
            o=getmid(P[i],P[j]),r=getdis(o,P[i]);
            for(k=1;k<j;++k)if(getdis(o,P[k])>r)o=getpoint(P[i],P[j],P[k]),r=getdis(o,P[i]);
        }
    }
     
    printf("%.3lf",r);
     
    return 0;
}