LA2572 Viva Confetti

题意

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分析

两两圆求交点，对每个圆弧按半径抖动。

时间复杂度\(O(T n^2)\)

代码

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<algorithm>
#include<bitset>
#include<cassert>
#include<ctime>
#include<cstring>
#define rg register
#define il inline
#define co const
template<class T>il T read()
{
    rg T data=0;
    rg int w=1;
    rg char ch=getchar();
    while(!isdigit(ch))
    {
        if(ch=='-')
            w=-1;
        ch=getchar();
    }
    while(isdigit(ch))
    {
        data=data*10+ch-'0';
        ch=getchar();
    }
    return data*w;
}
template<class T>T read(T&x)
{
    return x=read<T>();
}
using namespace std;
typedef long long ll;

co double eps=5e-13;

int dcmp(double x)
{
    if(fabs(x)<0)
        return 0;
    else
        return x<0?-1:1;
}

co double PI=acos(-1);

double NormalizeAngle(double rad,double center=PI)
{
    return rad-PI*2*floor((rad+PI-center)/(PI*2));
}

struct Point
{
    double x,y;
    
    Point(double x=0,double y=0)
    :x(x),y(y){}
    
    double angle()
    {
        return atan2(y,x);
    }
};
typedef Point Vector;

Vector operator+(Vector A,Vector B)
{
    return Vector(A.x+B.x,A.y+B.y);
}

Vector operator-(Point A,Point 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);
}

double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}

double Length(Vector A)
{
    return sqrt(Dot(A,A));
}

void CircleCircleIntersection(Point c1,double r1,Point c2,double r2,vector<double>&rad)
{
    double d=Length(c1-c2);
    if(dcmp(d)==0)
        return;
    if(dcmp(r1+r2-d)<0)
        return;
    if(dcmp(fabs(r1-r2)-d)>0)
        return;
    
    double a=(c2-c1).angle();
    double da=acos((r1*r1+d*d-r2*r2)/(2*r1*d));
    rad.push_back(NormalizeAngle(a-da));
    rad.push_back(NormalizeAngle(a+da));
}

co int N=100;
int n;
Point center[N];
double radius[N];
bool vis[N];

int topmost(Point p)
{
    for(int i=n-1;i>=0;--i)
        if(dcmp(Length(center[i]-p)-radius[i])<0)
            return i;
    return -1;
}

int main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    while(read(n))
    {
        for(int i=0;i<n;++i)
            scanf("%lf %lf %lf",&center[i].x,&center[i].y,&radius[i]);
        fill(vis,vis+n,0);
        for(int i=0;i<n;++i)
        {
            vector<double>rad;
            rad.push_back(0);
            rad.push_back(PI*2);
            for(int j=0;j<n;++j)
                CircleCircleIntersection(center[i],radius[i],center[j],radius[j],rad);
            sort(rad.begin(),rad.end());
            
            for(int j=0;j<rad.size();++j)
            {
                double mid=(rad[j]+rad[j+1])/2;
                for(int side=-1;side<=1;side+=2)
                {
                    double r2=radius[i]-side*eps;
                    int t=topmost(Point(center[i].x+cos(mid)*r2,center[i].y+sin(mid)*r2));
                    if(t>=0)
                        vis[t]=1;
                }
            }
        }
        int ans=0;
        for(int i=0;i<n;++i)
            if(vis[i])
                ++ans;
        printf("%d\n",ans);
    }
    return 0;
}