圆和多边形交模板

牛客网暑期ACM多校训练营（第三场）J

#include <iostream>
#include <cstdio>
#include <cmath>
#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define PI acos(-1.0)
#define EPS 1e-7
using namespace std;
 
inline int DB(double x) {
    if(x<-EPS) return -1;
    if(x>EPS) return 1;
    return 0;
}
 
 
struct point {
    double x,y;
 
    point() {}
    point(double _x,double _y):x(_x),y(_y) {}
 
    point operator-(point a) {
        return point(x-a.x,y-a.y);
    }
    point operator+(point a) {
        return point(x+a.x,y+a.y);
    }
 
    double operator*(point a) {
        return x*a.y-y*a.x;
    }
 
    point oppose() {
        return point(-x,-y);
    }
 
    double length() {
        return sqrt(x*x+y*y);
    }
 
    point adjust(double L) {
        L/=length();
        return point(x*L,y*L);
    }
 
    point vertical() {
        return point(-y,x);
    }
 
    double operator^(point a) {
        return x*a.x+y*a.y;
    }
};
 
 
struct segment {
    point a,b;
 
    segment() {}
    segment(point _a,point _b):a(_a),b(_b) {}
 
    point intersect(segment s) {
        double s1=(s.a-a)*(s.b-a);
        double s2=(s.b-b)*(s.a-b);
        double t=s1+s2;
        s1/=t;
        s2/=t;
        return point(a.x*s2+b.x*s1,a.y*s2+b.y*s1);
    }
    point vertical(point p) {
        point t=(b-a).vertical();
        return intersect(segment(p,p+t));
    }
    int isonsegment(point p) {
        return DB(min(a.x,b.x)-p.x)<=0&&
               DB(max(a.x,b.x)-p.x)>=0&&
               DB(min(a.y,b.y)-p.y)<=0&&
               DB(max(a.y,b.y)-p.y)>=0;
    }
};
 
struct circle {
    point p;
    double R;
};
 
circle C;
point p[205];
int n;
 
 
double cross_area(point a,point b,circle C) {
    point p=C.p;
    double R=C.R;
    int sgn=DB((b-p)*(a-p));
    double La=(a-p).length(),Lb=(b-p).length();
    int ra=DB(La-R),rb=DB(Lb-R);
    double ang=acos(((b-p)^(a-p))/(La*Lb));
    segment t(a,b);
    point s;
    point h,u,temp;
    double ans,L,d,ang1;
 
    if(!DB(La)||!DB(Lb)||!sgn) ans=0;
    else if(ra<=0&&rb<=0) ans=fabs((b-p)*(a-p))/2;
    else if(ra>=0&&rb>=0) {
        h=t.vertical(p);
        L=(h-p).length();
        if(!t.isonsegment(h)||DB(L-R)>=0) ans=R*R*(ang/2);
        else {
            ans=R*R*(ang/2);
            ang1=acos(L/R);
            ans-=R*R*ang1;
            ans+=R*sin(ang1)*L;
        }
    } else {
        h=t.vertical(p);
        L=(h-p).length();
        s=b-a;
        d=sqrt(R*R-L*L);
        s=s.adjust(d);
        if(t.isonsegment(h+s)) u=h+s;
        else u=h+s.oppose();
        if(ra==1) temp=a,a=b,b=temp;
        ans=fabs((a-p)*(u-p))/2;
        ang1=acos(((u-p)^(b-p))/((u-p).length()*(b-p).length()));
        ans+=R*R*(ang1/2);
    }
    return ans*sgn;
}
 
double cal_cross(circle C,point p[],int n) {
    double ans=0;
    int i;
    p[n]=p[0];
    for(i=0; i<n; i++) ans+=cross_area(p[i],p[i+1],C);
    return fabs(ans);
}
 
 
int main()
{
    while(scanf("%d", &n)!=EOF){
 
        for(int i=0;i<n;i++) scanf("%lf%lf", &p[i].x, &p[i].y);
        double area1 = 0;
        for(int i = 0; i < n; i++) {
            int nx = (i + 1) % n;
            area1 += p[i] * p[nx];
        }
 
        if(area1 < 0) area1 = -area1;
        area1 /= 2;
 
        int q; scanf("%d", &q);
        while(q--) {
            scanf("%lf%lf", &C.p.x, &C.p.y);
            double a, b, tar;
            scanf("%lf%lf", &a, &b);
            double area2 = area1 * (1 - a / b);
//            printf("%.3f\n", area2);
            double l = 0, r = 3e4;
 
//            printf("%.3f %.3f\n", o.x, o.y);
            for(int i = 1; i <= 60; i++) {
                double mid = (l + r) / 2;
                C.R = mid;
                double area = cal_cross(C, p, n);
                if(area >= area2) r = mid;
                else l = mid;
            }
 
            printf("%.12f\n", l);
        }
    }
    return 0;
}
/********************
4
0 0
1 0
2 0
3 0
1
1 1 1 2
********************/