Strange fuction HDU - 2899

原创于 2017-11-02 22:55:54 发布 · 178 阅读

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本文介绍了一个使用三分法来寻找特定多项式在指定区间内的最小值的问题。通过不断缩小搜索范围，最终实现对函数最小值的精确逼近。文章提供了一段C++代码示例，展示了如何实现这一算法。

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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 Input
2
100
200
Sample Output
-74.4291
-178.8534

三分模板题，二分常用于解决单调递增或递减的函数，三分则用于解决抛物线型的函数

#include <iostream>
#include <stdio.h>
using namespace std;
double y;
double check(double a){
    double b;
    b=6*a*a*a*a*a*a*a+8*a*a*a*a*a*a+7*a*a*a+5*a*a-y*a;
    return b;
}

int main()
{
    int T;
    double low,high,mid,mmid,s1,s2;
    scanf("%d",&T);
    while(T--){
        scanf("%lf",&y);
        low=0;high=100;
        while(high-low>1e-8){
            mid=(low+high)/2;
            mmid=(mid+high)/2;
            s1=check(mid);
            s2=check(mmid);
            if(s1<s2){
                high=mmid;
            }else{
                low=mid;
            }
        }
        printf("%.4lf\n",s2);
    }
    return 0;
}