hdoj 2899 Strange fuction【二分求解方程】

Strange fuction

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4599    Accepted Submission(s): 3304

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

题解：先对方程求导，对求导后的方程求x，则此时由数学知识可得解除的x为原方程的一个极小值；带入原方程即可

#include<stdio.h>
#include<string.h>
#include<math.h>
double y;
double f(double x)
{
	return 6*pow(x,7)+8*pow(x,6)+7*pow(x,3)+5*pow(x,2)-y*x;
}
double f1(double x)
{
	return 42*pow(x,6)+48*pow(x,5)+21*pow(x,2)+10*x;
}
int main()
{
	int t;
	double l,r,mid,len;
	scanf("%d",&t);
	while(t--)
	{
		scanf("%lf",&y);
		l=0;r=100;mid;
		while(r - l > 1e-8)
		{
			mid = ( r + l ) / 2;
			if(f1(mid)<y)
			l=mid;
			else
			r=mid;
		}
		len=f(r);
		printf("%.4lf
",len);
	}
  return 0;
}