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("*****
");
const int MAXN=1005;
int n,m,tt;
const double eps = 1e-8;
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=1;
    while(tt--)
    {
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%lf",&a[i]);
        }
        a[n]=a[0];
        bool flag=0;
        double l=0,r=20000;
        double mid;
        for(i=1;i<=n;i++)
        {
            r = min(r,a[i]+a[i-1]);
            l = max(l,fabs(a[i]-a[i-1]));
        }
        while(r-l>eps)
        {
            mid=(l+r)/2.0;
            double s,sum=0;
            for(i=1;i<=n;i++)
            {
                s=(a[i]*a[i]+a[i-1]*a[i-1]-mid*mid)/(2.0*a[i]*a[i-1]);
                sum+=acos(s);
            }
            if(fabs(sum-2*pi)<eps)
            {
                flag=1;
                break;
            }
            else if(sum>2*pi)
            {
                r=mid;
            }
            else l=mid;
        }
        printf("Case %d: ",ca++);
        if(flag)
            printf("%.3f
",mid);
        else
            printf("impossible
");
    }
}