HDU 5105 Math Problem --数学，求导

官方题解：

f(x)=|a∗x3+b∗x2+c∗x+d|, 求最大值。令g(x)=a∗x3+b∗x2+c∗x+d，f(x)的最大值即为g(x)的正最大值，或者是负最小值。a！=0时，

g′(x)=3∗a∗x2+2∗b∗x+c 求出g′(x)的根（若存在，x1,x2，由导数的性质知零点处有极值。ans=max(f(xi)|L≤xi≤R).然后考虑两个端点的特殊性有ans=max(ans,f(L),f(R)).

当时 x = -c/(2*b) 写成 x = -c/2*b 了，然后过pretest了。 然后。。你敢信？

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#define eps 1e-8
using namespace std;
#define N 50017

int sgn(double x)
{
    if(x > eps) return 1;
    if(x < -eps) return -1;
    return 0;
}

double a,b,c,d,L,R;

double calc(double x) { return fabs(a*x*x*x + b*x*x + c*x + d); }

int main()
{
    while(scanf("%lf%lf%lf%lf%lf%lf",&a,&b,&c,&d,&L,&R)!=EOF)
    {
        if(sgn(a) == 0)
        {
            if(sgn(b) == 0)
            {

                if(sgn(fabs(calc(L))-fabs(calc(R))) >= 0)
                    printf("%.2f
",calc(L));
                else
                    printf("%.2f
",calc(R));
            }
            else
            {
                double X = -c/(2.0*b);
                double k1 = calc(L);
                double k2 = calc(R);
                double k3;
                if(sgn(X-L) >= 0 && sgn(X-R) <= 0)
                    k3 = calc(X);
                else
                    k3 = 0.0;
                printf("%.2f
",max(max(k1,k2),k3));
            }
            continue;
        }
        double delta = 4.0*b*b - 12.0*a*c;
        if(sgn(delta) <= 0)
        {
            if(sgn(fabs(calc(L))-fabs(calc(R))) >= 0)
                printf("%.2f
",calc(L));
            else
                printf("%.2f
",calc(R));
        }
        else
        {
            double X1 = (-2.0*b + sqrt(delta))/(6.0*a);
            double X2 = (-2.0*b - sqrt(delta))/(6.0*a);
            double k1 = calc(L);
            double k2 = calc(R);
            double k3,k4;
            if(sgn(X1-L) >= 0 && sgn(X1-R) <= 0)
                k3 = calc(X1);
            else
                k3 = 0.0;
            if(sgn(X2-L) >= 0 && sgn(X2-R) <= 0)
                k4 = calc(X2);
            else
                k4 = 0.0;
            printf("%.2f
",max(max(max(k1,k2),k3),k4));
        }
    }
    return 0;
}