UVALive - 2572 Viva Confetti 极角排序

题目链接点这里

大白上的经典题，，但是比较难想。。。

安装大白的思路，我们可以用圆弧的中点，前后偏移eps，用点代替圆弧里外的区域，就转化过来了。。。。

这题精度有毒，，，还是看了代码仓库里的代码，，才A的。。计算几何精度太麻烦了，，反正原则就是，，，对于，，sqrt()，cos，sin这些函数能不用就不用，，，对于除法也能不用就不用，，这些写法大概都需要积累吧。。。

//注意精度，直接用rad计算圆弧中点，
#include<iostream>
#include<cstdio>
#include<math.h>
#include<algorithm>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<queue>
#include<string.h>
#include<string>
#include<cstring>
#include<vector>
#include<time.h>
#include<stdlib.h>
using namespace std;
#define INF 0x3f3f3f3f
#define INFLL 0x3f3f3f3f3f3f3f3f
#define FIN freopen("input.txt","r",stdin);
#define mem(x,y) memset(x,y,sizeof(x));
typedef unsigned long long ULL;
typedef long long LL;
#define fuck(x) cout<<x<<endl;
const int MX=333;
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
typedef pair<pair<int,int>,int> PIII;
typedef pair<int,int> PII;
const double eps=5e-13;
const double PI=acos(-1);
struct Point
{
double x, y;
Point() {}
Point(double x,double y):x(x),y(y) {}
};
typedef Point Vector;
int dcmp(double x) //返回x的正负
{
if(fabs(x)<eps)return 0;
return x<0?-1:1;
}
Vector operator-(Vector A,Vector B)
{
return Vector(A.x - B.x, A.y - B.y);
}
Vector operator+(Vector A,Vector B)
{
return Vector(A.x + B.x, A.y + B.y);
}
Vector operator*(Vector A,double p)
{
return Vector(A.x*p, A.y*p);
}
Vector operator/(Vector A,double p)
{
return Vector(A.x/p, A.y/p);
}
bool operator<(const Point&a,const Point&b)
{
return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
bool operator==(const Point&a,const Point&b)
{
return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Dot(Vector A,Vector B) //点积
{
return A.x*B.x+A.y*B.y;//如果改成整形记得加LL
}
double Cross(Vector A,Vector B) //叉积
{
return A.x*B.y-A.y*B.x;//如果改成整形记得加LL
}
//向量长度
double Length(Vector A)
{
return sqrt(Dot(A,A));
}
//2个向量之间的夹角
double Angle(Vector A,Vector B)
{
return acos(Dot(A,B)/Length(A)/Length(B));
}
//向量的极角
double angle(Vector v)
{
return atan2(v.y,v.x);
}
//计算ABC的有向面积
double Area(Point A,Point B,Point C)
{
return Cross(B-A,C-A)/2;
}
//将A向量逆时针旋转rad
Vector Rotate( Vector A,double rad)
{
return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
//返回A的逆时针旋转90度的单位法向量
Vector Normal(Vector A)
{
double L=Length(A);
return Vector(-A.y/L,A.x/L);
}
//计算2条直线P+tv和Q+tw的交点，请先确保不是平行(v！=w)
Point GetLineIntersection(Point P,Vector v,Point Q,Vector w)
{
Vector u=P-Q;
double t=Cross(w,u)/Cross(v,w);
return P+v*t;
}
//P到直线AB的距离
double DistanceToLine(Point P,Point A,Point B)
{
Vector v1=B-A,v2=P-A;
return fabs(Cross(v1,v2))/Length(v1);
}
//计算P到线段AB的距离
double DistanceToSegment(Point P,Point A,Point B)
{
if(A==B)return Length(P-A);
Vector v1=B-A,v2=P-A,v3=P-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);
}
//点P在直线AB上的投影
Point GetLineProjection(Point P,Point A,Point B)
{
Vector v=B-A;
return A+v*(Dot(v,P-A)/Dot(v,v));
}
//线段a1a2和b1b2的相交判定
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2)
{
double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
return (dcmp(c1)^dcmp(c2))==-2&&(dcmp(c3)^dcmp(c4))==-2;
}
//点p是否在线段a1a2上(不包含端点<,包含端点<=)
bool OnSegment(Point p,Point a1,Point a2)
{
return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
//多边形面积
double PolygonArea(Point *p,int n)
{
double area=0;
for(int i=1; i<n-1; i++)
area+=Cross(p[i]-p[0],p[i+1]-p[0]);
return fabs(area/2);
}
//园
struct Circle
{
Point c;
double r;
Circle() {}
Circle(Point c,double r):c(c),r(r) {}
Point getpoint(double rad)
{
return Point(c.x+cos(rad)*r,c.y+sin(rad)*r);
}
};
//有向线段
struct Line
{
Point p;
Vector v;//方向向量，左边为半平面
double ang;//极角
Line() {}
Line(Point p,Vector v):p(p),v(v)
{
ang=atan2(v.y,v.x);
}
bool operator<(const Line &L)const //极角排序
{
return ang<L.ang;
}
Point point(double t)
{
return p + v*t;
}
Line move(double d) //向左边平移d单位
{
return Line(p + Normal(v)*d, v);
}
};
//圆与园的交点
int GetCircleCircleIntersection(Circle C1, Circle C2, vector<double>& sol)
{
double d = Length(C1.c - C2.c);
if(dcmp(d) == 0)
{
if(dcmp(C1.r - C2.r) == 0) return -1; // 重合，无穷多交点
return 0;
}
if(dcmp(C1.r + C2.r - d) < 0) return 0;//相离
if(dcmp(fabs(C1.r-C2.r) - d) > 0) return 0;//内含
double a = angle(C2.c - C1.c);
double da = acos((C1.r*C1.r + d*d - C2.r*C2.r) / (2*C1.r*d));
// Point p1 = C1.getpoint(a-da), p2 = C1.getpoint(a+da);
sol.push_back(a-da);
if(dcmp(da)==0) return 1;//相切
sol.push_back(a+da);//相交
return 2;
}
int n;
Circle w[MX];
vector<Point> p;
vector<double>tmp;
bool vis[MX];
int main()
{
while(cin>>n&&n)
{
p.clear();
for(int i=1; i<=n; i++)
{
scanf("%lf%lf%lf",&w[i].c.x,&w[i].c.y,&w[i].r);
// w[i].c.x*=1000,w[i].c.y*=1000,w[i].r*=1000;
}
mem(vis,0);
for(int i=1; i<=n; i++)
{
tmp.clear();
for(int j=1; j<=n; j++)
if(i!=j)
{
GetCircleCircleIntersection(w[i],w[j], tmp);
}
tmp.push_back(0);
tmp.push_back(2*PI);
sort(tmp.begin(),tmp.end());
for(int j=0; j<tmp.size()-1; j++)
{
double mid=(tmp[j]+tmp[j+1])/2;
//cout<<norm.x<<" "<<norm.y<<" "<<t<<endl;
p.push_back(Point(w[i].c.x+cos(mid)*(w[i].r+eps),w[i].c.y+sin(mid)*(w[i].r+eps)));
//cout<<(w[j].c+norm*t*(w[j].r+eps1)).x<<" "<<(w[j].c+norm*t*(w[j].r+eps1)).y<<" "<<t<<endl;
//cout<<(w[j].r)<<endl;
p.push_back(Point(w[i].c.x+cos(mid)*(w[i].r-eps),w[i].c.y+sin(mid)*(w[i].r-eps)));
//cout<<p[p.size()-1].x<<" "<<p[p.size()-1].y<<" "<<t<<endl;
}
}
for(int i=0; i<p.size(); i++)
{
// printf("%.16f %.16f\n",p[i].x,p[i].y);
for(int j=n; j>=1; j--)
if(dcmp(Length(p[i]-w[j].c)-w[j].r)<=0)
{
vis[j]=1;
//cout<<j<<endl;
break;
}
}
//cout<<p.size()<<endl;
int ans=0;
for(int i=1; i<=n; i++)if(vis[i])ans++;
cout<<ans<<endl;
}
return 0;
}