题解:
大概是黄学长的博客
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#define N 1010
typedef long long ll;
#define pi acos(-1)
using namespace std;
int n,top;
double ans;
double x[N],y[N],r[N];
struct line
{
double l,r;
}q[N];
bool operator < (line a,line b)
{
return a.l<b.l;
}
inline double dis(int a,int b)
{
return sqrt((x[a]-x[b])*(x[a]-x[b])+(y[a]-y[b])*(y[a]-y[b]));
}
bool conta(int a,int b)
{
if (r[a]>=r[b]+dis(a,b)) return 1;
return 0;
}
void inter(int a,int b)
{
double d,t,st,l;
d=dis(a,b);
t=(r[a]*r[a]-r[b]*r[b]+d*d)/(2*d);
st=atan2((x[a]-x[b]),(y[a]-y[b]));
l=acos(t/r[a]);
q[++top]=(line){(st-l),(st+l)};
}
double cal(int x)
{
for (int i=x+1;i<=n;i++)
if (conta(i,x)) return 0;
top=0;
for (int i=x+1;i<=n;i++)
{
if (!conta(x,i) && r[x]+r[i]>=dis(x,i))
inter(x,i);
}
double tmp=0,now=0;
for (int i=1;i<=top;i++)
{
if (q[i].l<0) q[i].l+=2*pi;
if (q[i].r<0) q[i].r+=2*pi;
if (q[i].l>q[i].r)
{
q[++top]=(line){0,q[i].r};
q[i].r=2*pi;
}
}
sort(q+1,q+1+top);
for (int i=1;i<=top;i++)
if (q[i].l>now)
{
tmp+=q[i].l-now;
now=q[i].r;
}
else now=max(now,q[i].r);
tmp+=2*pi-now;
return r[x]*tmp;
}
int main()
{
scanf("%d",&n);
for (int i=1;i<=n;i++)
scanf("%lf%lf%lf",&r[i],&x[i],&y[i]);
for (int i=1;i<=n;i++)
ans+=cal(i);
printf("%.3f
",ans);
return 0;
}