HDU 2899 Strange fuction

还没学过导数，不会做……

#include <iostream>

#include <cmath>

using namespace std;



//先求导函数,可知f'(x)=g'(x)+y,g'(x)为递增函数,

//1)若导函数最大值小于0,即g'(100)+y<0.则原函数在区间内单调递减.最小值为f(100).

//2)若导函数最小值大于0,即g'(0)=y>0,则原函数在区间内单调递增,最小值为f(0).

//3)若导函数有正有负,因导函数单调递增,所以必然从负值开始穿过x轴,导函数由负变正,原函数先减后增,其0点即原函数的最小值点.

//(或求二阶导数,在区间内,f''(x)>0,则原函数为凹函数,有最小值点.否则,为凸函数,有最大值点)

double f(double x,int y)

{

    return 6 * pow(x,7) + 8 * pow(x,6) + 7 * pow(x,3) + 5 * pow(x,2) - y * x; 

}



double g(double x,int y)

{

    return 42 * pow(x,6) + 48 * pow(x,5) + 21 * pow(x,2) + 10 * x - y;

}



int main(int argc, const char *argv[])

{

    int T;

    cin>>T;

    while(T--)

    {

        int Y;

        cin>>Y;

        if(g(100.0,Y)<0) printf("%.4lf\n",f(100,Y));

        else if(g(0.0,Y)>0) printf("%.4lf\n",f(0,Y));

        else

        {

            double low = 0 , heigh = 100.0;

            double mid ;

            while (heigh-low>1e-8)

            {

                mid = (low+heigh)/2;

                if(g(mid,Y)>0)

                {

                    heigh = mid;

                }else

                {

                    low = mid;

                }

            }



            printf("%.4lf\n",f(mid,Y));

        }

    }

    return 0;

}