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圆包含最多点问题
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;
}
圆包含最多点问题