Gym-101915B Ali and Wi-Fi 计算几何 求两圆交点

题面

题意:给你n个圆,每个圆有一个权值,你可以选择一个点,可以获得覆盖这个点的圆中,权值最大的m个的权值,问最多权值是多少

题解:好像是叙利亚的题....我们画画图就知道,我们要找的就是圆与圆交的那部分里面的点,我们再仔细看看,

        2个圆的交点一定在啊！

        别急啊,两个圆包含了,都是交点,取哪呢？当然小圆圆心就够了啊(圆又不多,写的时候直接把所有的圆心都丢进去了)

        然后枚举判断每个点有没有被在m个圆中就行了,这里维护最大的m个,用个堆就好了

#include<bits/stdc++.h>
using namespace std;
typedef long double ld;
const ld eps = 1e-10;
int dcmp(ld x) 
{
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1 : 1;
}
ld sqr(ld x) { return x * x; }
struct Point
{
    ld x, y;
    Point(ld x = 0, ld y = 0):x(x), y(y) {}
};
Point operator - (const Point& A, const Point& B) 
{
    return Point(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.x) == 0;
}
ld Dot(const Point& A, const Point& B) 
{
    return A.x * B.x + A.y * B.y;
}
ld dis(Point a,Point b)
{
    return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y)); 
}
ld Length(const Point& A) { return sqrt(Dot(A, A)); }
ld angle(Point v) { return atan2(v.y, v.x); }
struct Circle
{
    Point c;
    ld r,v;
    Circle() {}
    Circle(Point c, ld r):c(c), r(r) {}
    inline Point point(double a)
    {
        return Point(c.x+cos(a)*r, c.y+sin(a)*r);
    }    
}a[105];
int getCircleCircleIntersection(Circle C1, Circle C2,Point &t1,Point &t2)
{
    ld d = Length(C1.c - C2.c);
    if(dcmp(d) == 0)
    {
        if(dcmp(C1.r - C2.r) == 0) return -1; 
        return 0;
    }
    if(dcmp(C1.r + C2.r - d) < 0) return 0; 
    if(dcmp(fabs(C1.r-C2.r) - d) > 0) return 0; 
    ld a = angle(C2.c - C1.c);
    ld da = acos((C1.r*C1.r + d*d - C2.r*C2.r) / (2*C1.r*d));
    Point p1 = C1.point(a-da), p2 = C1.point(a+da);
    t1=p1;
    if(p1 == p2) return 1;
    t2=p2;
    return 2;
}
Point jd[20000];
ld ans,sum;
int n,m,T,tot;
priority_queue<int,vector<int>,greater<int> >q;
int main()
{
    scanf("%d",&T);
    while (T--)
    {
        tot=0;
        ans=0;
        scanf("%d%d",&n,&m);
        for (int i=1;i<=n;i++) scanf("%Lf%Lf%Lf%Lf",&a[i].c.x,&a[i].c.y,&a[i].r,&a[i].v);
        for (int i=1;i<=n;i++)
            for (int j=i+1;j<=n;j++)
            {
                Point t1,t2;
                int why=getCircleCircleIntersection(a[i],a[j],t1,t2);
                if (why==1)
                {
                    tot++;
                    jd[tot]=t1;
                }else
                if (why==2)
                {
                    tot++;jd[tot]=t1;
                    tot++;jd[tot]=t2;
                }
            }
        for (int i=1;i<=n;i++) 
        {
            tot++;
            jd[tot]=a[i].c;
        }    
        for (int i=1;i<=tot;i++)
        {
            for (int j=1;j<=n;j++)
                if (dcmp(dis(jd[i],a[j].c)-a[j].r)<=0) 
                {
                    q.push(a[j].v);
                    if ((int)q.size()>m) q.pop();
                }
            sum=0;
            while (!q.empty()) sum+=q.top(),q.pop();
            ans=max(ans,sum);    
        }    
        printf("%.Lf
",ans); 
    } 
}