Strange Fuction

最新推荐文章于 2024-04-19 20:40:32 发布

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本文介绍了一道使用二分法寻找多项式函数在特定区间内最小值的问题。通过求导确定函数变化趋势，利用二分查找算法逼近极小值点，最终精确计算出函数在闭区间[0,100]内的最小值。

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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 Intput

2
100
200

Sample Output

-74.4291
-178.8534

入门级二分法的题目。先对方程求导式写出来。然后根据数学里面学的怎么通过求导找方程最小值。注意精度嘿。

AC代码：

#include<iostream>
#include<cmath>
#include <cstdio>
using namespace std;
int main(){
int t;
double y,lo,hi,mi,d,f,x;
cin>>t;
while(t--)
{
cin>>y;
lo=0.0; hi=100.0;
while(hi-lo>1e-6)
{
mi=(hi+lo)/2;
d=42*pow(mi,6)+48*pow(mi,5)+21*pow(mi,2)+10*mi-y;
if(d<0) lo=mi;
else hi=mi;
}
x=mi;
f=6*pow(x,7)+8*pow(x,6)+7*pow(x,3)+5*pow(x,2)-y*x;
printf("%.4f\n",f);
}
return 0;
}