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(-);
     const double eps=1e-;
     struct Point
     {
         double x,y;
         Point(double x=,double y=):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 ;
         return x<?-:;
     }
     bool operator==(const Vec& a,const Vec& b)
     //判向量相等
     {
         return dcmp(a.x-b.x)==&&dcmp(a.y-b.y)==;
     }
     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))<)    return len(v2);
         else if(dcmp(dot(v1,v3))>)    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)/);
     }
     bool ifpar(const Vec& a,const Vec& b)
     //ifParallel
     //是否共线/平行
     {
         return dcmp(cross(a,b))==;
     }
     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[];
 int n;
 Point a;
 double r2;
 double A,B;
 void make(const Point &x,const Point &y)
 {
     Vec t=(y-x)/;
     a=x+t;
     r2=len2(t);
 }
 void make(const Point &x,const Point &y,const Point &z)
 {
     Vec t1=(y-x)/,t2=(z-y)/;
     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)<=;
 }
 int main()
 {
     int i,j,k;
     srand(time());
     scanf("%d",&n);
     for(i=;i<=n;i++)
         scanf("%lf%lf",&p[i].x,&p[i].y);
     scanf("%lf%lf",&A,&B);A=A/*pi;
     for(i=;i<=n;i++)
         p[i]=rotate(p[i],-A);
     for(i=;i<=n;i++)
         p[i].x/=B;
     random_shuffle(p+,p+n+);
     a=p[];r2=;
     for(i=;i<=n;i++)
         if(!ok(p[i]))
         {
             a=p[i];r2=;
             for(j=;j<i;j++)
                 if(!ok(p[j]))
                 {
                     make(p[i],p[j]);
                     for(k=;k<j;k++)
                         if(!ok(p[k]))
                         {
                             make(p[i],p[j],p[k]);
                         }
                 }
         }
     //uprintf("%.2f %.2f ",a.x,a.y);
     printf("%.3f\n",sqrt(r2));
     return ;
 }