2014
11-05

# How many times

There are N circles on the plane. Dumbear wants to find a region which is covered by as many circles as possible. But Dumbear is very dumb, so he turns to momodi for help. But momodi is very busy. Can you help him find out the maximum times that a region can be covered? Notice that a point on a circle’s boundary is considered to be covered by this circle.

There are several test cases in the input.

For each case, the first line contains an integer N (1≤ N ≤ 100) denotes the number of circles.
For the next N lines, each line contains three integers X, Y, R denotes a circle whose center is (X, Y) (-10000 ≤ X, Y ≤ 10000) and radius is R (0 < R ≤ 5000).

The input terminates by end of file marker.

There are several test cases in the input.

For each case, the first line contains an integer N (1≤ N ≤ 100) denotes the number of circles.
For the next N lines, each line contains three integers X, Y, R denotes a circle whose center is (X, Y) (-10000 ≤ X, Y ≤ 10000) and radius is R (0 < R ≤ 5000).

The input terminates by end of file marker.

3
0 0 1
1 0 1
2 0 1

3

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;
const double eps=1e-6;

struct point {
double x,y;
point(double a=0,double b=0) {x=a,y=b;};

friend bool operator <(const point&a,const point&b) {
if (fabs(a.x-b.x)>eps) return a.x<b.x;
if (fabs(a.y-b.y)>eps) return a.y<b.y;
return 0;
}
}ia,ib;

struct cir {
double x,y,r;
// vector<int> dot;
}c[1000];

double sqr(double x){ return x*x;}

double dist(double x1,double y1,double x2,double y2){
return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}

int circle_intersect(cir A,cir B,point &ia,point &ib) {
ia.x=A.x+A.r;
ia.y=A.y;
ib.x=A.x;
ib.y=A.y+A.r;
if ( fabs(A.x-B.x)<eps && fabs(A.y-B.y)<eps ){
return 1; //���
}
double dd=dist(A.x,A.y,B.x,B.y);
if (A.r+B.r+eps<dd) return 1; //����

double k,a,b,d,aa,bb,cc,c,drt;
k=A.r;
a=B.x-A.x;
b=B.y-A.y;
c=B.r;
d=sqr(c)-sqr(k)-sqr(a)-sqr(b);

aa=4*sqr(a)+4*sqr(b);
bb=4*b*d;
cc=sqr(d)-4*sqr(a)*sqr(k);

drt=sqr(bb)-4*aa*cc;
if (drt<0) return 5; //���
drt=sqrt(drt);
ia.y=(-bb+drt)/2/aa;
ib.y=(-bb-drt)/2/aa;
if (abs(a)<eps) {
ia.x=sqrt (sqr(k)-sqr(ia.y));
ib.x=-ia.x;
} else {
ia.x=(2*b*ia.y+d)/-2/a;
ib.x=(2*b*ib.y+d)/-2/a;
}
ia.x+=A.x,ia.y+=A.y;
ib.x+=A.x,ib.y+=A.y;
if (fabs(ia.y-ib.y)<eps) {
if (fabs(A.r+B.r-dd)<eps) return 2; //����
if (fabs(dd-(max(A.r,B.r)-min(A.r,B.r)))<eps) return 3; //����
}
return 4; //�ཻ
}
int n;

int inside(cir a,point b){
if ( dist(a.x,a.y,b.x,b.y)<a.r+eps ) return true;
else return false;
}

int main(){
while ( scanf("%d",&n)!=EOF ){
for (int i=1;i<=n;i++) scanf("%lf%lf%lf",&c[i].x,&c[i].y,&c[i].r);
int ans=0;
for (int i=1;i<=n;i++)
for (int j=1;j<=n;j++){
circle_intersect(c[i],c[j],ia,ib);
int x=0;
for (int k=1;k<=n;k++)
if ( inside(c[k],ia) )x++;
ans=max(ans,x);
x=0;
for (int k=1;k<=n;k++)
if ( inside(c[k],ib) ) x++;
ans=max(ans,x);
}
printf("%d\n",ans);
}
}