hdu 4033 2011成都赛区网络赛 余弦定理+二分 **

二分边长，判断最后内角和是否为2pi，注意l与r的选取，保证能组成三角形

 #include<cstdio>
 #include<iostream>
 #include<algorithm>
 #include<cstring>
 #include<cmath>
 #include<queue>
 #include<map>
 using namespace std;
 #define MOD 1000000007
 const int INF=0x3f3f3f3f;
 typedef long long ll;
 #define cl(a) memset(a,0,sizeof(a))
 #define ts printf("*****\n");
 const int MAXN=;
 int n,m,tt;
 const double eps = 1e-;
 const double pi = acos(-1.0);
 double a[MAXN];
 int main()
 {
     int i,j,k;
     #ifndef ONLINE_JUDGE
     freopen("1.in","r",stdin);
     #endif
     scanf("%d",&tt);
     int ca=;
     while(tt--)
     {
         scanf("%d",&n);
         for(i=;i<n;i++)
         {
             scanf("%lf",&a[i]);
         }
         a[n]=a[];
         bool flag=;
         double l=,r=;
         double mid;
         for(i=;i<=n;i++)
         {
             r = min(r,a[i]+a[i-]);
             l = max(l,fabs(a[i]-a[i-]));
         }
         while(r-l>eps)
         {
             mid=(l+r)/2.0;
             double s,sum=;
             for(i=;i<=n;i++)
             {
                 s=(a[i]*a[i]+a[i-]*a[i-]-mid*mid)/(2.0*a[i]*a[i-]);
                 sum+=acos(s);
             }
             if(fabs(sum-*pi)<eps)
             {
                 flag=;
                 break;
             }
             else if(sum>*pi)
             {
                 r=mid;
             }
             else l=mid;
         }
         printf("Case %d: ",ca++);
         if(flag)
             printf("%.3f\n",mid);
         else
             printf("impossible\n");
     }
 }