hdu 2899 Strange fuction

http://acm.hdu.edu.cn/showproblem.php?pid=2899

Strange fuction

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4865    Accepted Submission(s): 3468

Problem Description

Now, here is a fuction:
  F(x) = 6 * x^7+8*x^6+7*x^3+5*x^2-y*x (0 <= x <=100)
Can you find the minimum value when x is between 0 and 100.

 

Input

The first line of the input contains an integer T(1<=T<=100) which means the number of test cases. Then T lines follow, each line has only one real numbers Y.(0 < Y <1e10)

 

Output

Just the minimum value (accurate up to 4 decimal places),when x is between 0 and 100.

 

Sample Input

2

100

200

 

Sample Output

-74.4291

-178.8534

 

二分搜索+求导

对函数进行求导，导数为0时，x的值是函数值最小

导数小于0函数递减，导数大于0函数递增

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#include<algorithm>
#define N 1010
#define INF 0x3f3f3f3f

using namespace std;

int main()
{
    int t;
    double y, f, f1;
    scanf("%d", &t);
    while(t--)
    {
        scanf("%lf", &y);
        double mid, low = 0, high = 100;
        while(high - low > 1e-8)/***此处注意*/
        {
            mid = (low + high) / 2;
            f1 = 42 * pow(mid, 6) + 48 * pow(mid, 5) + 21 * pow(mid, 2) + 10 * mid;//导数
            if(f1 < y)
                low = mid;
            else if(f1 == y)
                break;
            else
                high = mid;
        }
        f = 6 * pow(mid, 7) + 8 * pow(mid, 6) + 7 * pow(mid, 3) + 5 * pow(mid, 2) - mid * y;
        printf("%.4f
", f);
    }
    return  0;
}