2013 多校第七场 hdu 4667 Building Fence

题意：

给一些互不相交的圆和三角形

求一个最短的围栏长度将他们包围在内

解法1：

将圆细分成2000个点加入点集（10W个），做凸包（nlogn），比赛的时候shuangde想到了，但是细分成500个点就超时了 精度不够

结束后看到 沉溺大神的博客 他也是使用此方法。。。。。然后G++900+ms能过 给跪

后来改了下模板代码 全加了引用和 inline关键字 几何模板的函数嵌套太多了。。。 加了inline之后从TLE变成700+ms AC 呵了个呵

只能说还是too young

解法2：

将圆和圆 圆和每一点的切点也加入点集，并且标记切点所在的圆

求凸包 最后一个for 如果两点在同一圆上 则求弧长 反之求两点间距离

这方法比较科学 不过不能使用求直线和圆交点的函数 否则超时

解法1代码：

//大白p263
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <queue>
#include <functional>
#include <set>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const double eps=1e-8;//精度
const int INF=0x3f3f3f3f;
const double PI=acos(-1.0);
inline int dcmp(const double& x){//判断double等于0或。。。
if(fabs(x)<eps)return 0;else return x<0?-1:1;
}
struct Point{
double x,y;
Point(){}
Point(double x,double y):x(x),y(y){}
};
typedef Point Vector;
typedef vector<Point> Polygon;
inline Vector operator+(const Vector& a,const Vector& b){return Vector(a.x+b.x,a.y+b.y);}//向量+向量=向量
inline Vector operator-(const Point& a,const Point& b){return Vector(a.x-b.x,a.y-b.y);}//点-点=向量
inline Vector operator*(const Vector& a,const double& p){return Vector(a.x*p,a.y*p);}//向量*实数=向量
inline Vector operator/(const Vector& a,const double& p){return Vector(a.x/p,a.y/p);}//向量/实数=向量
inline bool operator<( const Point& A,const Point& B ){return dcmp(A.x-B.x)<0||(dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)<0);}
inline bool operator==(const Point&a,const Point&b){return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}
inline bool operator!=(const Point&a,const Point&b){return a==b?false:true;}
struct Segment{
Point a,b;
Segment(){}
Segment(Point _a,Point _b){a=_a,b=_b;}
inline bool friend operator<(const Segment& p,const Segment& q){return p.a<q.a||(p.a==q.a&&p.b<q.b);}
inline bool friend operator==(const Segment& p,const Segment& q){return (p.a==q.a&&p.b==q.b)||(p.a==q.b&&p.b==q.a);}
};
struct Circle{
Point c;
double r;
Circle(){}
Circle(Point _c, double _r):c(_c),r(_r) {}
Point point(double a)const{return Point(c.x+cos(a)*r,c.y+sin(a)*r);}
bool friend operator<(const Circle& a,const Circle& b){return a.r<b.r;}
};
struct Line{
Point p;
Vector v;
double ang;
Line() {}
Line(const Point &_p, const Vector &_v):p(_p),v(_v){ang = atan2(v.y, v.x);}
inline bool operator<(const Line &L)const{return  ang < L.ang;}
};
inline double Dot(const Vector& a,const Vector& b){return a.x*b.x+a.y*b.y;}//|a|*|b|*cosθ 点积
inline double Length(const Vector& a){return sqrt(Dot(a,a));}//|a| 向量长度
inline double Angle(const Vector& a,const Vector& b){return acos(Dot(a,b)/Length(a)/Length(b));}//向量夹角θ
inline double Cross(const Vector& a,const Vector& b){return a.x*b.y-a.y*b.x;}//叉积 向量围成的平行四边形的面积
inline double Area2(const Point& a,const Point& b,Point c){return Cross(b-a,c-a);}//同上 参数为三个点
inline double DegreeToRadius(const double& deg){return deg/180*PI;}
inline double GetRerotateAngle(const Vector& a,const Vector& b){//向量a顺时针旋转theta度得到向量b的方向
double tempa=Angle(a,Vector(1,0));
if(a.y<0) tempa=2*PI-tempa;
double tempb=Angle(b,Vector(1,0));
if(b.y<0) tempb=2*PI-tempb;
if((tempa-tempb)>0) return tempa-tempb;
else return tempa-tempb+2*PI;
}
inline double torad(const double& deg){return deg/180*PI;}//角度化为弧度
inline Vector Rotate(const Vector& a,const double& rad){//向量逆时针旋转rad弧度
return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));
}
inline Vector Normal(const Vector& a){//计算单位法线
double L=Length(a);
return Vector(-a.y/L,a.x/L);
}
inline Point GetLineProjection(const Point& p,const Point& a,const Point& b){//点在直线上的投影
Vector v=b-a;
return a+v*(Dot(v,p-a)/Dot(v,v));
}
inline Point GetLineIntersection(Point p,Vector v,Point q,Vector w){//求直线交点 有唯一交点时可用
Vector u=p-q;
double t=Cross(w,u)/Cross(v,w);
return p+v*t;
}
int ConvexHull(Point* p,int n,Point* sol){//计算凸包
sort(p,p+n);
int m=0;
for(int i=0;i<n;i++){
while(m>1&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;
sol[m++]=p[i];
}
int k=m;
for(int i=n-2;i>=0;i--){
while(m>k&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;
sol[m++]=p[i];
}
if(n>0) m--;
return m;
}
double Heron(double a,double b,double c){//海伦公式
double p=(a+b+c)/2;
return sqrt(p*(p-a)*(p-b)*(p-c));
}
bool SegmentProperIntersection(const Point& a1,const Point& a2,const Point& b1,const Point& b2){//线段规范相交判定
double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
double CutConvex(const int& n,Point* poly,const Point& a,const Point& b, vector<Point> result[3]){//有向直线a b 切割凸多边形
vector<Point> points;
Point p;
Point p1=a,p2=b;
int cur,pre;
result[0].clear();
result[1].clear();
result[2].clear();
if(n==0) return 0;
double tempcross;
tempcross=Cross(p2-p1,poly[0]-p1);
if(dcmp(tempcross)==0) pre=cur=2;
else if(tempcross>0) pre=cur=0;
else pre=cur=1;
for(int i=0;i<n;i++){
tempcross=Cross(p2-p1,poly[(i+1)%n]-p1);
if(dcmp(tempcross)==0) cur=2;
else if(tempcross>0) cur=0;
else cur=1;
if(cur==pre){
result[cur].push_back(poly[(i+1)%n]);
}
else{
p1=poly[i];
p2=poly[(i+1)%n];
p=GetLineIntersection(p1,p2-p1,a,b-a);
points.push_back(p);
result[pre].push_back(p);
result[cur].push_back(p);
result[cur].push_back(poly[(i+1)%n]);
pre=cur;
}
}
sort(points.begin(),points.end());
if(points.size()<2){
return 0;
}
else{
return Length(points.front()-points.back());
}
}
double DistanceToSegment(Point p,Segment s){//点到线段的距离
if(s.a==s.b) return Length(p-s.a);
Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b;
if(dcmp(Dot(v1,v2))<0) return Length(v2);
else if(dcmp(Dot(v1,v3))>0) return Length(v3);
else return fabs(Cross(v1,v2))/Length(v1);
}
inline bool isPointOnSegment(const Point& p,const Segment& s){
return dcmp(Cross(s.a-p,s.b-p))==0&&dcmp(Dot(s.a-p,s.b-p))<0;
}
int isPointInPolygon(Point p, Point* poly,int n){//点与多边形的位置关系
int wn=0;
for(int i=0;i<n;i++){
Point& p2=poly[(i+1)%n];
if(isPointOnSegment(p,Segment(poly[i],p2))) return -1;//点在边界上
int k=dcmp(Cross(p2-poly[i],p-poly[i]));
int d1=dcmp(poly[i].y-p.y);
int d2=dcmp(p2.y-p.y);
if(k>0&&d1<=0&&d2>0)wn++;
if(k<0&&d2<=0&&d1>0)wn--;
}
if(wn) return 1;//点在内部
else return 0;//点在外部
}
double PolygonArea(Point* p,int n){//多边形有向面积
double area=0;
for(int i=1;i<n-1;i++)
area+=Cross(p[i]-p[0],p[i+1]-p[0]);
return area/2;
}
int GetLineCircleIntersection(Line L,Circle C,Point& p1,Point& p2){//圆与直线交点 返回交点个数
double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y;
double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r;
double delta = f*f - 4*e*g;
if(dcmp(delta) < 0)  return 0;//相离
if(dcmp(delta) == 0) {//相切
p1=p1=L.p+L.v*(-f/(2*e));
return 1;
}//相交
p1=(L.p+L.v*(-f-sqrt(delta))/(2*e));
p2=(L.p+L.v*(-f+sqrt(delta))/(2*e));
return 2;
}
double rotating_calipers(Point *ch,int n)//旋转卡壳
{
int q=1;
double ans=0;
ch
=ch[0];
for(int p=0;p<n;p++)
{
while(Cross(ch[q+1]-ch[p+1],ch[p]-ch[p+1])>Cross(ch[q]-ch[p+1],ch[p]-ch[p+1]))
q=(q+1)%n;
ans=max(ans,max(Length(ch[p]-ch[q]),Length(ch[p+1]-ch[q+1])));
}
return ans;
}
Polygon CutPolygon(Polygon poly,const Point& a,const Point& b){//用a->b切割多边形 返回左侧
Polygon newpoly;
int n=poly.size();
for(int i=0;i<n;i++){
Point c=poly[i];
Point d=poly[(i+1)%n];
if(dcmp(Cross(b-a,c-a))>=0) newpoly.push_back(c);
if(dcmp(Cross(b-a,c-d))!=0){
Point ip=GetLineIntersection(a,b-a,c,d-c);
if(isPointOnSegment(ip,Segment(c,d))) newpoly.push_back(ip);
}
}
return newpoly;
}
int GetCircleCircleIntersection(Circle c1,Circle c2,Point& p1,Point& p2){//求两圆相交
double d=Length(c1.c-c2.c);
if(dcmp(d)==0){
if(dcmp(c1.r-c2.r)==0) return -1;//两圆重合
return 0;
}
if(dcmp(c1.r+c2.r-d)<0) return 0;
if(dcmp(fabs(c1.r-c2.r)-d)>0) return 0;
double a=Angle(c2.c-c1.c,Vector(1,0));
double da=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
p1=c1.point(a-da);p2=c1.point(a+da);
if(p1==p2) return 1;
return 2;
}
inline bool isPointOnleft(Point p,Line L){return dcmp(Cross(L.v,p-L.p))>0;}//点在直线左边 线上不算
int HalfplaneIntersection(Line *L,int n,Point* poly){//半平面交
sort(L,L+n);
int first,last;
Point* p=new Point
;
Line* q=new Line
;
q[first=last=0]=L[0];
for(int i=1;i<n;i++){
while(first<last&&!isPointOnleft(p[last-1],L[i])) last--;
while(first<last&&!isPointOnleft(p[first],L[i])) first++;
q[++last]=L[i];
if(dcmp(Cross(q[last].v,q[last-1].v))==0){
last--;
if(isPointOnleft(L[i].p,q[last])) q[last]=L[i];
}
if(first<last) p[last-1]=GetLineIntersection(q[last-1].p,q[last-1].v,q[last].p,q[last].v);
}
while(first<last&&!isPointOnleft(p[last-1],q[first])) last--;
if(last-first<=1) return 0;
p[last]=GetLineIntersection(q[last].p,q[last].v,q[first].p,q[first].v);
int m=0;
for(int i=first;i<=last;i++) poly[m++]=p[i];
return m;
}
//两点式化为一般式A = b.y-a.y, B = a.x-b.x, C = -a.y*(B)-a.x*(A);
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
Point point[444444],ppoint[444444];
int main()
{
int n,m;
while(~scanf("%d%d",&n,&m))
{
int tot = 0;
double x,y,r;
for(int i = 0;i<n;i++)
{
scanf("%lf%lf%lf",&x,&y,&r);
for(double j = 0;j<2*PI;j += 0.0032)
{
point[tot++] = Point(x+r*cos(j),y+r*sin(j));
}
}
for(int i = 0;i<m;i++)
for(int j = 0;j<3;j++)
{
scanf("%lf%lf",&x,&y);
point[tot++] = Point(x,y);
}
tot=ConvexHull(point,tot,ppoint);
double ans = 0;
Point pre = ppoint[0];
for(int i = 1;i<tot;i++)
{
ans += Length(ppoint[i]-pre);
pre = ppoint[i];
}
ans += Length(ppoint[0]-pre);
printf("%.5f\n",ans);
}
return 0;
}

解法2：

//大白p263
#include <cmath>
#include <cstdio>
#include <cstring>
#include <string>
#include <queue>
#include <functional>
#include <set>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const double eps=1e-8;//精度
const int INF=0x3f3f3f3f;
const double PI=acos(-1.0);
inline int dcmp(const double& x){//判断double等于0或。。。
if(fabs(x)<eps)return 0;else return x<0?-1:1;
}
struct Point{
int i;
double R;
double x,y;
Point(){}
Point(double x,double y):x(x),y(y){}
};
typedef Point Vector;
typedef vector<Point> Polygon;
inline Vector operator+(const Vector& a,const Vector& b){return Vector(a.x+b.x,a.y+b.y);}//向量+向量=向量
inline Vector operator-(const Point& a,const Point& b){return Vector(a.x-b.x,a.y-b.y);}//点-点=向量
inline Vector operator*(const Vector& a,const double& p){return Vector(a.x*p,a.y*p);}//向量*实数=向量
inline Vector operator/(const Vector& a,const double& p){return Vector(a.x/p,a.y/p);}//向量/实数=向量
inline bool operator<( const Point& A,const Point& B ){return dcmp(A.x-B.x)<0||(dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)<0);}
inline bool operator==(const Point&a,const Point&b){return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}
inline bool operator!=(const Point&a,const Point&b){return a==b?false:true;}
struct Segment{
Point a,b;
Segment(){}
Segment(Point _a,Point _b){a=_a,b=_b;}
inline bool friend operator<(const Segment& p,const Segment& q){return p.a<q.a||(p.a==q.a&&p.b<q.b);}
inline bool friend operator==(const Segment& p,const Segment& q){return (p.a==q.a&&p.b==q.b)||(p.a==q.b&&p.b==q.a);}
};
struct Circle{
Point c;
double r;
Circle(){}
Circle(Point _c, double _r):c(_c),r(_r) {}
Point point(double a)const{return Point(c.x+cos(a)*r,c.y+sin(a)*r);}
bool friend operator<(const Circle& a,const Circle& b){return a.r<b.r;}
};
struct Line{
Point p;
Vector v;
double ang;
Line() {}
Line(const Point &_p, const Vector &_v):p(_p),v(_v){ang = atan2(v.y, v.x);}
inline bool operator<(const Line &L)const{return  ang < L.ang;}
};
inline double Dot(const Vector& a,const Vector& b){return a.x*b.x+a.y*b.y;}//|a|*|b|*cosθ 点积
inline double Length(const Vector& a){return sqrt(Dot(a,a));}//|a| 向量长度
inline double Angle(const Vector& a,const Vector& b){return acos(Dot(a,b)/Length(a)/Length(b));}//向量夹角θ
inline double Cross(const Vector& a,const Vector& b){return a.x*b.y-a.y*b.x;}//叉积 向量围成的平行四边形的面积
inline double Area2(const Point& a,const Point& b,Point c){return Cross(b-a,c-a);}//同上 参数为三个点
inline double DegreeToRadius(const double& deg){return deg/180*PI;}
inline double GetRerotateAngle(const Vector& a,const Vector& b){//向量a顺时针旋转theta度得到向量b的方向
double tempa=Angle(a,Vector(1,0));
if(a.y<0) tempa=2*PI-tempa;
double tempb=Angle(b,Vector(1,0));
if(b.y<0) tempb=2*PI-tempb;
if((tempa-tempb)>0) return tempa-tempb;
else return tempa-tempb+2*PI;
}
inline double torad(const double& deg){return deg/180*PI;}//角度化为弧度
inline Vector Rotate(const Vector& a,const double& rad){//向量逆时针旋转rad弧度
return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));
}
inline Vector Normal(const Vector& a){//计算单位法线
double L=Length(a);
return Vector(-a.y/L,a.x/L);
}
inline Point GetLineProjection(const Point& p,const Point& a,const Point& b){//点在直线上的投影
Vector v=b-a;
return a+v*(Dot(v,p-a)/Dot(v,v));
}
inline Point GetLineIntersection(Point p,Vector v,Point q,Vector w){//求直线交点 有唯一交点时可用
Vector u=p-q;
double t=Cross(w,u)/Cross(v,w);
return p+v*t;
}
int ConvexHull(Point* p,int n,Point* sol){//计算凸包
sort(p,p+n);
int m=0;
for(int i=0;i<n;i++){
while(m>1&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;
sol[m++]=p[i];
}
int k=m;
for(int i=n-2;i>=0;i--){
while(m>k&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;
sol[m++]=p[i];
}
if(n>0) m--;
return m;
}
double Heron(double a,double b,double c){//海伦公式
double p=(a+b+c)/2;
return sqrt(p*(p-a)*(p-b)*(p-c));
}
bool SegmentProperIntersection(const Point& a1,const Point& a2,const Point& b1,const Point& b2){//线段规范相交判定
double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);
double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
double CutConvex(const int& n,Point* poly,const Point& a,const Point& b, vector<Point> result[3]){//有向直线a b 切割凸多边形
vector<Point> points;
Point p;
Point p1=a,p2=b;
int cur,pre;
result[0].clear();
result[1].clear();
result[2].clear();
if(n==0) return 0;
double tempcross;
tempcross=Cross(p2-p1,poly[0]-p1);
if(dcmp(tempcross)==0) pre=cur=2;
else if(tempcross>0) pre=cur=0;
else pre=cur=1;
for(int i=0;i<n;i++){
tempcross=Cross(p2-p1,poly[(i+1)%n]-p1);
if(dcmp(tempcross)==0) cur=2;
else if(tempcross>0) cur=0;
else cur=1;
if(cur==pre){
result[cur].push_back(poly[(i+1)%n]);
}
else{
p1=poly[i];
p2=poly[(i+1)%n];
p=GetLineIntersection(p1,p2-p1,a,b-a);
points.push_back(p);
result[pre].push_back(p);
result[cur].push_back(p);
result[cur].push_back(poly[(i+1)%n]);
pre=cur;
}
}
sort(points.begin(),points.end());
if(points.size()<2){
return 0;
}
else{
return Length(points.front()-points.back());
}
}
double DistanceToSegment(Point p,Segment s){//点到线段的距离
if(s.a==s.b) return Length(p-s.a);
Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b;
if(dcmp(Dot(v1,v2))<0) return Length(v2);
else if(dcmp(Dot(v1,v3))>0) return Length(v3);
else return fabs(Cross(v1,v2))/Length(v1);
}
inline bool isPointOnSegment(const Point& p,const Segment& s){
return dcmp(Cross(s.a-p,s.b-p))==0&&dcmp(Dot(s.a-p,s.b-p))<0;
}
int isPointInPolygon(Point p, Point* poly,int n){//点与多边形的位置关系
int wn=0;
for(int i=0;i<n;i++){
Point& p2=poly[(i+1)%n];
if(isPointOnSegment(p,Segment(poly[i],p2))) return -1;//点在边界上
int k=dcmp(Cross(p2-poly[i],p-poly[i]));
int d1=dcmp(poly[i].y-p.y);
int d2=dcmp(p2.y-p.y);
if(k>0&&d1<=0&&d2>0)wn++;
if(k<0&&d2<=0&&d1>0)wn--;
}
if(wn) return 1;//点在内部
else return 0;//点在外部
}
double PolygonArea(Point* p,int n){//多边形有向面积
double area=0;
for(int i=1;i<n-1;i++)
area+=Cross(p[i]-p[0],p[i+1]-p[0]);
return area/2;
}
int GetLineCircleIntersection(Line L,Circle C,Point& p1,Point& p2){//圆与直线交点 返回交点个数
double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y;
double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r;
double delta = f*f - 4*e*g;
if(dcmp(delta) < 0)  return 0;//相离
if(dcmp(delta) == 0) {//相切
p1=p1=L.p+L.v*(-f/(2*e));
return 1;
}//相交
p1=(L.p+L.v*(-f-sqrt(delta))/(2*e));
p2=(L.p+L.v*(-f+sqrt(delta))/(2*e));
return 2;
}
double rotating_calipers(Point *ch,int n)//旋转卡壳
{
int q=1;
double ans=0;
ch
=ch[0];
for(int p=0;p<n;p++)
{
while(Cross(ch[q+1]-ch[p+1],ch[p]-ch[p+1])>Cross(ch[q]-ch[p+1],ch[p]-ch[p+1]))
q=(q+1)%n;
ans=max(ans,max(Length(ch[p]-ch[q]),Length(ch[p+1]-ch[q+1])));
}
return ans;
}
Polygon CutPolygon(Polygon poly,const Point& a,const Point& b){//用a->b切割多边形 返回左侧
Polygon newpoly;
int n=poly.size();
for(int i=0;i<n;i++){
Point c=poly[i];
Point d=poly[(i+1)%n];
if(dcmp(Cross(b-a,c-a))>=0) newpoly.push_back(c);
if(dcmp(Cross(b-a,c-d))!=0){
Point ip=GetLineIntersection(a,b-a,c,d-c);
if(isPointOnSegment(ip,Segment(c,d))) newpoly.push_back(ip);
}
}
return newpoly;
}
int GetCircleCircleIntersection(Circle c1,Circle c2,Point& p1,Point& p2){//求两圆相交
double d=Length(c1.c-c2.c);
if(dcmp(d)==0){
if(dcmp(c1.r-c2.r)==0) return -1;//两圆重合
return 0;
}
if(dcmp(c1.r+c2.r-d)<0) return 0;
if(dcmp(fabs(c1.r-c2.r)-d)>0) return 0;
double a=Angle(c2.c-c1.c,Vector(1,0));
double da=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
p1=c1.point(a-da);p2=c1.point(a+da);
if(p1==p2) return 1;
return 2;
}
inline bool isPointOnleft(Point p,Line L){return dcmp(Cross(L.v,p-L.p))>0;}//点在直线左边 线上不算
int HalfplaneIntersection(Line *L,int n,Point* poly){//半平面交
sort(L,L+n);
int first,last;
Point* p=new Point
;
Line* q=new Line
;
q[first=last=0]=L[0];
for(int i=1;i<n;i++){
while(first<last&&!isPointOnleft(p[last-1],L[i])) last--;
while(first<last&&!isPointOnleft(p[first],L[i])) first++;
q[++last]=L[i];
if(dcmp(Cross(q[last].v,q[last-1].v))==0){
last--;
if(isPointOnleft(L[i].p,q[last])) q[last]=L[i];
}
if(first<last) p[last-1]=GetLineIntersection(q[last-1].p,q[last-1].v,q[last].p,q[last].v);
}
while(first<last&&!isPointOnleft(p[last-1],q[first])) last--;
if(last-first<=1) return 0;
p[last]=GetLineIntersection(q[last].p,q[last].v,q[first].p,q[first].v);
int m=0;
for(int i=first;i<=last;i++) poly[m++]=p[i];
return m;
}
//两点式化为一般式A = b.y-a.y, B = a.x-b.x, C = -a.y*(B)-a.x*(A);
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
//--------------------------------------
void CirclePointTangent(Point poi, Point o, double r, Point &result1,Point &result2) {
double line = sqrt(
(poi.x - o.x) * (poi.x - o.x) + (poi.y - o.y) * (poi.y - o.y));
double angle = acos(r / line);
Point unitvector, lin;
lin.x = poi.x - o.x;
lin.y = poi.y - o.y;
unitvector.x = lin.x / sqrt(lin.x * lin.x + lin.y * lin.y) * r;
unitvector.y = lin.y / sqrt(lin.x * lin.x + lin.y * lin.y) * r;
result1 = Rotate(unitvector, -angle);
result2 = Rotate(unitvector, angle);
result1.i=result2.i=o.i;
result1.x += o.x;
result1.y += o.y;
result2.x += o.x;
result2.y += o.y;
return;
}

Point P[32010];
Point tri[160];
Point cir[60];
Point ch[32000];
int main(){
int n,m;
while(scanf("%d%d",&n,&m)!=EOF){
if(n==1 && m==0){
double s,d,g;
scanf("%lf %lf %lf",&s,&d,&g);
double xx = 2 *PI* g;
printf("%.5lf\n",xx);
continue;
}
int idx=0,tridx=0;
for(int i=0;i<n;i++){
double x,y,r;
scanf("%lf%lf%lf",&x,&y,&r);
cir[i].x=x;
cir[i].y=y;
cir[i].i=i;
cir[i].R=r;
}
for(int i=0;i<m;i++){
for(int k=0;k<3;k++){
double x,y;
scanf("%lf%lf",&x,&y);
P[idx].x=x;
P[idx].y=y;
P[idx].i=-1;
Point temp=P[idx++];
for(int i=0;i<n;i++){
Point p1,p2;
CirclePointTangent(temp,cir[i],cir[i].R,p1,p2);
P[idx++]=p1;
P[idx++]=p2;
}
}
}
for(int i=0;i<n;i++){
for(int j=i+1;j<n;j++){
Point c1=cir[i],c2=cir[j];
if (dcmp(c1.R-c2.R) > 0) {
swap(c1, c2);
}
double c2c = Length(c1-c2);
double height = c2.R - c1.R;
double alpha = asin(height / c2c) + PI / 2;
Point v1, v2, tmp;
v1 = c2 - c1;
double len = Length(v1- Point(0, 0));
v1.x /= len;
v1.y /= len;
v2 = Rotate(v1, alpha);
tmp = v2 * c1.R + c1;
tmp.i = c1.i;
P[idx++]=tmp;
tmp = v2 * c2.R + c2;
tmp.i = c2.i;
P[idx++]=tmp;
v2 = Rotate(v1, -alpha);
tmp = v2 * c1.R+ c1;
tmp.i = c1.i;
P[idx++]=tmp;
tmp = v2 * c2.R + c2;
tmp.i = c2.i;
P[idx++]=tmp;
}
}
int count=ConvexHull(P,idx,ch);
double ans=0;
for(int i=0;i<count;i++){
const Point& a=ch[i];
const Point& b=ch[(i+1)%count];
if(a.i!=-1&&a.i==b.i){
Vector tt=a-cir[a.i];
double ang=Angle(a-cir[a.i],b-cir[a.i]);
ans+=ang*cir[a.i].R;
}
else ans+=Length(a-b);
}
printf("%.5lf\n",ans);
}
return 0;
}