UVALive 7509 Dome and Steles

三分

#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=a;i<=b;++i)
#define ms(arr,a) memset(arr,a,sizeof arr)
const double eps=1e-14;
const int maxn=1e5+5;
int N;
double r[maxn];
double calc(double o)
{
    double odd=min(1.0-o,o),even=max(1.0-o,o);
        double R=even*even+r[N];
        rep(i,1,N-1)
        {
            if(i&1)
            {
                odd++;
                R=max(R,odd*odd+r[N-i]);
            }
            else
            {
                even++;
                R=max(R,even*even+r[N-i]);
            }
        }
    return sqrt(R);
}
double solve(double l,double r)
{
    double mid,mmid;
    while(l<r)
    {
        mid=(l+r)/2.0;
        mmid=(mid+r)/2.0;
        if(calc(mmid)<calc(mid))
            l=mid+eps;
        else r=mmid-eps;
    }
    return calc(l);
}
int main()
{
    int T;
    scanf("%d",&T);
    for(int Case=1;Case<=T;Case++)
    {
        scanf("%d",&N);
        rep(i,1,N)
        {
            double a,b;
            scanf("%lf%lf",&a,&b);
            double Max,Min;
            Max=max(a,b);
            Min=min(a,b);
            r[i]=(Max/2.0)*(Max/2.0)+Min*Min;
        }
        sort(r+1,r+N+1);
        printf("Case #%d: %.10f
",Case,solve(0,1));
    }
}