【二分】hdu 4033
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#define LL long long#define PI acos(-1.0)#define N 105#define MAX INT_MAX#define MIN INT_MIN#define eps 1e-8double a[N];int n;double maxm;double cal(double aa,double bb,double cc ){ return (aa*aa+bb*bb-cc*cc)/(2*aa*bb);}int gao(double x){ int i,j; double res=0.0; for(i=0;i<n;i++){ if(a[i]+a[(i+1)%n]<=x)return 0;//big if(fabs( a[i]-a[(i+1)%n] )>=x)return -1;//small double tmp=cal(a[i],a[(i+1)%n],x); res+=acos(tmp); } if(fabs(res-2*PI)<eps)return 1;//equal else if(res<2*PI)return -1;//small else if(res>2*PI) return 0;//big}int main(){ int t; scanf("%d",&t); int ca=1; while(t--){ scanf("%d",&n); int i,j; maxm=0.0; for(i=0;i<n;i++){ scanf("%lf",&a[i]); if(a[i]>maxm)maxm=a[i]; } double l=0,r=2*maxm,mid; bool flag=0; while((r-l)>eps){ mid=(l+r)/2.0;//cout<<mid<<endl; int tag=gao(mid); if(tag==1){ flag=1; break; } if(tag==0){//big r=mid; } else{//small l=mid; } } printf("Case %d: ",ca++); if(!flag)printf("impossible\n"); else{ printf("%.3f\n",mid); } } return 0;}