The 36th ACM/ICPC Asia Regional Chengdu Site 1003 Regular Polygon

#include <iostream>
#include <math.h>
#include <stdio.h>
using namespace std;
const int N=102;
double pi=acos(-1);
const double eps=1e-8;
double dis
;
int n;
double solve (double l,double r)
{
if(fabs(l-r)<eps)return -1;
double mid=(l+r)/2;
int i;
double ang=0;
for(i=0;i<n;i++)
{
if(mid-(dis[i]+dis[i+1])>eps)return solve(l,mid);//边太大，构不成三角形
if(mid-fabs(dis[i]-dis[i+1])<eps)return solve(mid,r);//边太小，构不成三角形
double cs=(dis[i]*dis[i]+dis[i+1]*dis[i+1]-mid*mid)/(2*dis[i]*dis[i+1]);
ang+=acos(cs);
}
if(fabs(ang-2*pi)<eps)return mid;//等于360度
else if(ang-2*pi>eps)return solve(l,mid);//大于360度，说明mid太大
else return solve(mid,r);//小于360度说明mid太小
return -1;
}
int main()
{
int t;
cin>>t;
int ca=1;
while(t--)
{
cin>>n;
int i;
for(i=0;i<n;i++)
{
scanf("%lf",&dis[i]);
}
dis
=dis[0];
double ans=solve (0,20000);
if(ans==-1)printf("Case %d: impossible\n",ca);
else printf("Case %d: %.3lf\n",ca,ans);
ca++;
}
return 0;
}
/*
2
3
3.0 4.0 5.0
3
1.0 2.0 3.0
*/