洛谷P4288||bzoj3564 [SHOI2014]信号增幅仪

bzoj3564

洛谷P4288

可以旋转一下坐标轴使得x轴与长轴方向对齐，然后将所有的横坐标变为自身除以放大倍数，然后就做一个最小圆覆盖

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<cmath>
#include<ctime>
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define pb push_back
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
namespace X
{
    const double pi=acos(-1);
    const double eps=1e-6;
    struct Point
    {
        double x,y;
        Point(double x=0,double y=0):x(x),y(y){}
    };
    typedef Point Vec;
    Vec operator+(const Vec& a,const Vec& b)
    {
        return Vec(a.x+b.x,a.y+b.y);
    }
    Vec operator-(const Vec& a,const Vec& b)
    {
        return Vec(a.x-b.x,a.y-b.y);
    }
    Vec operator*(double a,const Vec& b)
    {
        return Vec(a*b.x,a*b.y);
    }
    Vec operator*(const Vec& a,double b)
    {
        return Vec(b*a.x,b*a.y);
    }
    Vec operator/(const Vec& a,double b)
    {
        return Vec(a.x/b,a.y/b);
    }
    int dcmp(double x)
    //正为1，负为-1，0为0
    {
        if(fabs(x)<eps)    return 0;
        return x<0?-1:1;
    }
    bool operator==(const Vec& a,const Vec& b)
    //判向量相等
    {
        return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
    }
    double dot(const Vec& a,const Vec& b)
    //点积
    {
        return a.x*b.x+a.y*b.y;
    }
    double cross(const Vec& a,const Vec& b)
    //叉积
    {
        return a.x*b.y-a.y*b.x;
    }
    double len(const Vec& x)
    //向量长度
    {
        return sqrt(dot(x,x));
    }
    double angle(const Vec& a,const Vec& b)
    //夹角，0~180°
    {
        return acos(dot(a,b)/len(a)/len(b));
    }
    double angle1(const Vec& a,const Vec& b)
    //夹角，带方向，a到b逆时针为正，顺时针为负，共线为0
    {
        return acos(dot(a,b)/len(a)/len(b))*(dcmp(cross(a,b)));
    }
    Vec rotate(const Vec& a,double rad)
    //旋转，正为逆时针，负为顺时针
    {
        return Vec(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));
    }
    Vec normal(const Vec& x)
    //单位法线，左转90°后除以自身长度
    {
        double l=len(x);
        return Vec(-x.y/l,x.x/l);
    }
    Vec normal1(const Vec& x)
    //法线，不归一化
    {
        return Vec(-x.y,x.x);
    }
    Point lineline(const Point& p,const Vec& v,const Point& q,const Vec& w)
    //直线交点,GetLineIntersection
    {
        return p+v*cross(w,p-q)/cross(v,w);
    }
    double ptline(const Point& p,const Point& a,const Point& b)
    //point_to_line,点到直线距离,DistanceToLine
    {
        Vec v1=b-a,v2=p-a;
        return fabs(cross(v1,v2)/len(v1));
    }
    double ptseg(const Point& p,const Point& a,const Point& b)
    //point_to_segment,点到线段距离,DistanceToSegment
    {
        if(a==b)    return len(p-a);
        //Vec v1=b-a,v2=a-p,v3=p-b;
        Vec v1=b-a,v2=p-a,v3=p-b;
        if(dcmp(dot(v1,v2))<0)    return len(v2);
        else if(dcmp(dot(v1,v3))>0)    return len(v3);
        else return fabs(cross(v1,v2)/len(v1));
    }
    double area2(const Point& a,const Point& b,const Point& c)
    //叉积对应平行四边形的面积
    {
        return cross(b-a,c-a);
    }
    double thrarea(const Point& a,const Point& b,const Point& c)
    //三角形面积，绝对值
    {
        return fabs(cross(b-a,c-a)/2);
    }
    bool ifpar(const Vec& a,const Vec& b)
    //ifParallel
    //是否共线/平行
    {
        return dcmp(cross(a,b))==0;
    }
    Point pointline(const Point& p,const Point& a,const Vec& v)
    //点在直线上投影,GetLineProjection
    {
        return a+v*(dot(p-a,v)/dot(v,v));
    }
    double sqr(double x){return x*x;} 
    double dis2(const Point &x,const Point &y)
    {
        return sqr(x.x-y.x)+sqr(x.y-y.y);
    }
    double len2(const Vec &x){return dot(x,x);}
};
using namespace X;
Point p[1000100];
int n;
Point a;
double r2;
double A,B;
void make(const Point &x,const Point &y)
{
    Vec t=(y-x)/2;
    a=x+t;
    r2=len2(t);
}
void make(const Point &x,const Point &y,const Point &z)
{
    Vec t1=(y-x)/2,t2=(z-y)/2;
    Point x1=x+t1,y1=y+t2;
    t1=normal1(t1);t2=normal1(t2);
    a=lineline(x1,t1,y1,t2);
    r2=dis2(a,x);
}
bool ok(const Point &x)
{
    return dcmp(dis2(x,a)-r2)<=0;
}
int main()
{
    int i,j,k;
    srand(time(0));
    scanf("%d",&n);
    for(i=1;i<=n;i++)
        scanf("%lf%lf",&p[i].x,&p[i].y);    
    scanf("%lf%lf",&A,&B);A=A/180*pi;
    for(i=1;i<=n;i++)
        p[i]=rotate(p[i],-A);
    for(i=1;i<=n;i++)
        p[i].x/=B;
    random_shuffle(p+1,p+n+1);
    a=p[1];r2=0;
    for(i=2;i<=n;i++)
        if(!ok(p[i]))
        {
            a=p[i];r2=0;
            for(j=1;j<i;j++)
                if(!ok(p[j]))
                {
                    make(p[i],p[j]);
                    for(k=1;k<j;k++)
                        if(!ok(p[k]))
                        {
                            make(p[i],p[j],p[k]);
                        }
                }
        }
    //uprintf("%.2f %.2f ",a.x,a.y);
    printf("%.3f
",sqrt(r2));
    return 0;
}