圆包含最多点问题

Posted 2020-09-08 Pacify

一片区域内有许多个点，给出一半径，问这个圆最多能包含几个点

 

模板题，套模板即可(Gym 100004C Party Location http://codeforces.com/gym/100004/attachments)

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;

double eps=1e-8;
double r = 2.5;

struct Point
{
    double x,y;
    Point() {}
    Point(double tx,double ty)
    {
        x=tx;
        y=ty;
    }
}p[300];
double dist(Point p1,Point p2)
{
    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

Point get_circle(Point p1,Point p2)
{
    Point mid = Point((p1.x+p2.x)/2,(p1.y+p2.y)/2);
    double angle = atan2(p1.x-p2.x,p2.y-p1.y);
    double d = sqrt(r*r-pow(dist(p1,mid),2));
    return Point(mid.x+d*cos(angle),mid.y+d*sin(angle));
}

int main()
{
    //freopen("in.txt","r",stdin);
    int num = 0;
    double a,b;
    while(scanf("%lf%lf",&a,&b) != EOF)
    {
        p[num].x = a;
        p[num].y = b;
        num++;
    }
    int i,j;
    int ans = 1;
    for(i=0; i<num; i++)
    {
        for(j=i+1; j<num; j++)
        {
            if(dist(p[i],p[j]) > 2.0*r) continue;
            Point center = get_circle(p[i],p[j]);
            int cnt = 0;
            for(int k=0; k<num; k++)
                if(dist(center,p[k]) < 1.0*r+eps) cnt++;
            ans = max(ans,cnt);
        }
    }
    cout<<ans<<endl;
    return 0;
}

 

一片区域内有许多个点，给出一半径，问这个圆最多能包含几个点

模板题，套模板即可

代码：

#include <iostream>

#include <cstdio>

#include <cmath>

#include <algorithm>

using namespace std;

 

double eps=1e-8;

double r = 2.5;

 

struct Point

{

    double x,y;

    Point() {}

    Point(double tx,double ty)

    {

        x=tx;

        y=ty;

    }

}p[300];

double dist(Point p1,Point p2)

{

    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));

}

 

Point get_circle(Point p1,Point p2)

{

         Point mid = Point((p1.x+p2.x)/2,(p1.y+p2.y)/2);

         double angle = atan2(p1.x-p2.x,p2.y-p1.y);

         double d = sqrt(r*r-pow(dist(p1,mid),2));

         return Point(mid.x+d*cos(angle),mid.y+d*sin(angle));

}

 

int main()

{

    //freopen("in.txt","r",stdin);

    int num = 0;

    double a,b;

    while(scanf("%lf%lf",&a,&b) != EOF)

    {

        p[num].x = a;

        p[num].y = b;

        num++;

    }

    int i,j;

    int ans = 1;

    for(i=0; i<num; i++)

    {

        for(j=i+1; j<num; j++)

        {

            if(dist(p[i],p[j]) > 2.0*r) continue;

            Point center = get_circle(p[i],p[j]);

            int cnt = 0;

            for(int k=0; k<num; k++)

                if(dist(center,p[k]) < 1.0*r+eps) cnt++;

            ans = max(ans,cnt);

        }

    }

    cout<<ans<<endl;

    return 0;

}