poj 1905 Expanding Rods---二分

Expanding Rods

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 7775		Accepted: 1876

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

 

                   题目大意：一根会随温度变化长度变化的杆，受宽度限制，升温时会发生如图的弯曲。求图中问号所指处的长度。

             思路： 二分 弧长所对圆心角的一般。  精度控制 我是试出来的。我的是  1e-12。

//Memory: 160 KB		Time: 0 MS
//Language: C++		Result: Accepted
#include<stdio.h>
#include<math.h>
const double PI=acos(-1.0);   //求π。这样可以尽量保证精度
int main()
{
	//freopen("1.txt","r",stdin);
	double s,max,min,mid,l,L,a,n,c;   //a是圆心角的一半
	while(scanf("%lf%lf%lf",&l,&n,&c)!=EOF)
	{
         if ((l<0)&&(n<0)&&(c<0)) break;
		L=(1+n*c)*l;
		max=PI/2,min=0;
		double temp;
		if(l==0||n==0||c==0) s=0;   //之前就是没加这个条件。WA了很多次！ 时间也浪费了很久。
		else
		{
		   do            //二分
		   {
		    	mid=(max+min)/2;
		    	temp=sin(mid)/mid;
		    	if(temp>=l/L) min=mid;
		    	else max=mid;
		   }while(fabs(temp-l/L)>1e-12);
	    	double r=L/2/mid;
	    	s=r-r*cos(mid);
		}
		printf("%.3lf\n",s);
	}
	return 0;
}