HDU2899 Strange fuction 二分

Posted 2020-09-21 yxysuanfa

Strange fuction

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 2982    Accepted Submission(s): 2202

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

 

#include <stdio.h>
#include <math.h>
double y, ans;

double f(double x){
	return 6 * pow(x, 7) + 8 * pow(x, 6) + 
		7 * pow(x, 3) + 5 * x * x - y * x;
}

double ff(double x){ //求导
	return 42 * pow(x, 6) + 48 * pow(x, 5) 
		+ 21 * x * x + 10 * x - y;
}

int main(){
	int n;
	scanf("%d", &n);
	while(n--){
		scanf("%lf", &y);
		if(ff(0) >= 0) ans = f(0);
		else if(ff(100) <= 0) ans = f(100);
		else{
			double left = 0, right = 100, mid;
			while(left + 1e-8 < right){
				mid = (left + right) / 2;
				if(ff(mid) > 0) right = mid;
				else if(ff(mid) < 0) left = mid;
				else break;
			}
			ans = f(mid);
		}
		printf("%.4lf\n", ans);
	}
	return 0;
}