三分板子

B - Light Bulb
Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%lld
 & %llu
Submit Status Practice ZOJ
 3203

 

Description

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. Dis distance between the light bulb and the wall. All numbers
 are in range from 10-2 to 103, both inclusive, and H - h >= 10-2.

 

 

Output

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

 

 

Sample Input

 

3
2 1 0.5
2 0.5 3
4 3 4

 

 作用: 处理单调或者峰值函数的极值

 

每次分一个  rmid

再相当于4分 算lmid

 

 code:

//
#include<iostream>
#include<cstdio>
using namespace std;
int T;
double H,h;
double D;
double F(double x)
{
    return ((h-x)/(H-x))*D+x;
}
int main()
{
    cin>>T;
    while(T--)
    {
        cin>>H>>h>>D;
        double  r=h;
        double l=0;
        double rmid=(l+r)/2;
        double lmid=(rmid+l)/2;
        while(rmid-lmid>=1e-9)
        {
            if(F(lmid)>=F(rmid))
            {
                r=rmid;
            }
            else
            l=lmid;
         rmid=(l+r)/2;
         lmid=(rmid+l)/2;
        }
        printf("%.3lf
",F((lmid+rmid)/2));
    }
}

 

Sample Output

 

1.000
0.750
4.000