SHOI2012 信用卡凸包

传送门

顶点凸包+一个圆周长。

#include<bits/stdc++.h>
#define re register
#define cs const
cs int N=4e4+10;
cs double eps=1e-8,oo=1e9,pi=acos(-1);
struct Grid{
	double x,y;
	Grid(double X=0,double Y=0){x=X,y=Y;}
	inline double Angle(){return atan2(y,x);}
	inline double len(){return sqrt(x*x+y*y);}
	friend inline Grid operator +(const Grid &a,const Grid &b){return Grid(a.x+b.x,a.y+b.y);}
	friend inline Grid operator -(const Grid &a,const Grid &b){return Grid(a.x-b.x,a.y-b.y);}
	friend inline Grid operator *(const Grid &a,const double &b){return Grid(a.x*b,a.y*b);}
	friend inline Grid operator /(const Grid &a,const double &b){return Grid(a.x/b,a.y/b);}
	friend inline double dot(const Grid &a,const Grid &b){return a.x*b.x+a.y*b.y;}
	friend inline double cross(const Grid &a,const Grid &b){return a.x*b.y-a.y*b.x;}
	inline Grid rotate(double ang){return Grid(x*cos(ang)-y*sin(ang),x*sin(ang)+y*cos(ang));}
}A[N],S[N];
typedef Grid Point,Vector;
inline int sgn(double x){
	if(x>eps) return 1;
	if(x<-eps) return -1;
	return 0;
}

int n,tot,pos,top;double a,b,r,x,y,angle;
inline void get_pnts(cs Point &O,double ang){
	A[++tot]=Vector( b, a).rotate(ang)+O;
	if(A[0].y>A[tot].y||(A[0].y==A[tot].y&&A[0].x>A[tot].x)) A[0]=A[tot],pos=tot;
	A[++tot]=Vector(-b, a).rotate(ang)+O;
	if(A[0].y>A[tot].y||(A[0].y==A[tot].y&&A[0].x>A[tot].x)) A[0]=A[tot],pos=tot;
	A[++tot]=Vector( b,-a).rotate(ang)+O;
	if(A[0].y>A[tot].y||(A[0].y==A[tot].y&&A[0].x>A[tot].x)) A[0]=A[tot],pos=tot;
	A[++tot]=Vector(-b,-a).rotate(ang)+O;
	if(A[0].y>A[tot].y||(A[0].y==A[tot].y&&A[0].x>A[tot].x)) A[0]=A[tot],pos=tot;
}
inline bool cmp(cs Point &a,cs Point &b){
	double P=atan2(a.y-A[1].y,a.x-A[1].x);
	double Q=atan2(b.y-A[1].y,b.x-A[1].x);
	return (P!=Q)?P<Q:a.x<b.x;
}
inline void Graham(){
	std::swap(A[pos],A[1]),std::sort(A+2,A+tot+1,cmp);
	S[1]=A[1],S[top=2]=A[2];
	for(int re i=3;i<=tot;++i){
		while(top>=3&&(cross(A[i]-S[top-1],S[top]-S[top-1])>=0)) --top;
		S[++top]=A[i];
	}S[top+1]=A[1];
}
double ans=0;
int main(){
	scanf("%d%lf%lf%lf",&n,&a,&b,&r),a-=r*2,b-=r*2,a/=2.0,b/=2.0,A[0]=Point(oo,oo);
	for(int re i=1;i<=n;++i) scanf("%lf%lf%lf",&x,&y,&angle),get_pnts(Point(x,y),angle);
	Graham();
	for(int re i=1;i<=top;++i) ans+=(S[i+1]-S[i]).len();
	printf("%.2lf\n",ans+2.0*pi*r);
}