Xi'an-2014-Online-J.cpp

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <map>
#include <queue>
#include <cassert>
using namespace std;

typedef long long LL;

const int N = 50005;
double a , b , c , d , e , f;
double Range;
double pa(double X , double Y) {
    double A = c;
    double B = d * Y + e * X;
    double C = a * X * X + b * Y * Y + f * X * Y - 1;
    double D = B * B - 4 * A * C;
    if (D < 0) return sqrt(X * X + Y * Y) + 1e10;
    D = sqrt(D);
    double Z1 = (-B + D) / (2 * A) , Z2 = (-B - D) / (2 * A);
    return sqrt(X * X + Y * Y + min(Z1 * Z1 , Z2 * Z2));
}

pair<double , double> cal(double X) {
    double L = -Range , R = Range , m1 , m2;
    while (R - L > 1e-10) {
        m1 = (L + L + R) / 3;
        m2 = (L + R + R) / 3;
        if (pa(X , m1) < pa(X , m2))
            R = m2;
        else
            L = m1;
    }
    return make_pair(pa(X , (L + R) / 2) , (L + R) / 2);
}

void work() {
    Range = min(a , min(b , c));
    Range = sqrt(1 / Range) + 0.5;
    Range = 1e9;
    double L = -Range , R = Range , m1 , m2;
    /*for (double i = 0.9999999 ; i <= Range ; i += 0.1) {
        printf("%f %f\n" , i , cal(i).first);
    }*/
    while (R - L > 1e-10) {
        m1 = (L + L + R) / 3;
        m2 = (L + R + R) / 3;
        if (cal(m1).first < cal(m2).first)
            R = m2;
        else
            L = m1;
    }
    pair<double , double> res = cal((L + R) / 2);
    printf("%.10f\n" , res.first);
}

int main() {
    while (~scanf("%lf%lf%lf%lf%lf%lf",&a,&b,&c,&d,&e,&f))
       work();
    return 0;
}