B - Light Bulb

最新推荐文章于 2019-09-18 23:13:59 发布

原创最新推荐文章于 2019-09-18 23:13:59 发布 · 371 阅读

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Compared to wildleopard's wealthiness, his brother mildleopard is rather poor. His house is narrow and he has only one light bulb in his house. Every night, he is wandering in his incommodious house, thinking of how to earn more money. One day, he found that the length of his shadow was changing from time to time while walking between the light bulb and the wall of his house. A sudden thought ran through his mind and he wanted to know the maximum length of his shadow.

Input

The first line of the input contains an integer T (T <= 100), indicating the number of cases.

Each test case contains three real numbers H, h and D in one line.H is the height of the light bulb while h is the height of mildleopard.D is distance between the light bulb and the wall. All numbers are in range from 10^-2 to 10³, both inclusive, andH - h >= 10^-2.

<b< dd="">

Output

For each test case, output the maximum length of mildleopard's shadow in one line, accurate up to three decimal places..

<b< dd="">

Sample Input

<b< dd="">

Sample Output

1.000
0.750
4.000

火柴人从灯泡下向D前进，影子开始会慢慢变长，而当影子的落点到达D时，如果继续向D前进，影子也许会继续变长，也许会变短，所以火柴人前进的距离与影子的长度的函数是个开口向下的凸函数（当有凹凸时可以试试三分），因此比较适合三分法#include <stdio.h>
#include <iostream>
#include <math.h>
using namespace std;
int main()
{

    int T;
    //freopen("1.txt","r",stdin);
    scanf("%d",&T);
    while (T--)
    {
        double H,h,D,t1,t2,l,r,mid,midd;
        scanf("%lf%lf%lf",&H,&h,&D);
        l=(H - h) * D / H,r=D;
        while(r-l>=1e-8)
        {
            mid=(r+l)/2,midd=(mid+r)/2;
            t1=D - mid + H - (H - h) * D / mid;
            t2=D - midd + H - (H - h) * D / midd;

            if(t1<t2)l=mid;
            else r=midd;
        }
        printf("%.3lf\n",t2);
    }
    return 0;
}