二分贪心 G - 07

Description

When a thin rod of length L is heated n degrees, it expands to a new length L'=(1+n*C)*L, where C is the coefficient of heat expansion. 
When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment. 

Your task is to compute the distance by which the center of the rod is displaced. 

Input

The input contains multiple lines. Each line of input contains three non-negative numbers: the initial lenth of the rod in millimeters, the temperature change in degrees and the coefficient of heat expansion of the material. Input data guarantee that no rod expands by more than one half of its original length. The last line of input contains three negative numbers and it should not be processed.

Output

For each line of input, output one line with the displacement of the center of the rod in millimeters with 3 digits of precision. 

Sample Input

1000 100 0.0001
15000 10 0.00006
10 0 0.001
-1 -1 -1

Sample Output

61.329
225.020
0.000

         这道题的题意相当于一个圆知道一条切割的弦长跟对应的弧长，然后求这条弦到对应弧最高点的距离。

       几何关系如下：sin(a)=l/2/r,a=s/2/r.(a为角度，s为弧长)。然后用二分查找进行求值。

源代码如下：

#include<iostream>
#include<stdio.h>  
#include<math.h>  
using namespace std;
int main()  
{  
    double l,n,c,s,r,low,high,mid;
    while(scanf("%lf%lf%lf",&l,&n,&c)&&l!=-1&&n!=-1&&c!=-1)
    {
    
low=0,high=0.5*l;
        s=(1+n*c)*l;
        while(high-low>1e-5)
        {
            mid=(low+high)/2;
            r=(4*mid*mid+l*l)/(8*mid);
            if(2*r*asin(l/(2*r))<s) low=mid;
            else high=mid;
        }
        printf("%.3f\n",mid);
       
    }
    return 0;
}  

        需要注意的是输入输出要用scanf跟pritnf。循环条件到1e-5即可，再小的话可能就超时了。