I - Expanding Rods解题报告（黄杰）

I - Expanding Rods

Time Limit:1000MS     Memory Limit:30000KB     64bit IO Format:%I64d & %I64u

Submit  Status

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：一个长度为L的杆，在温度n下，会扩展到一个新长度L'=（1+n*C)*L，c为形变系数，题目要求计算如图扩展后，拉长杆的中心与圆杆中心的距离，输入为-1,-1,-1则退出程序。
题目链接：http://poj.org/problem?id=1905
方法：二分法
思路：这个就很简单啦，二分的对象显然是中心的距离，然后通过中心距离和圆杆长来计算扩展后的长度（不要告诉我你不会算--），在比较实际扩展的长度，这样就行了，注意精确度。
算法实现：

#include<stdio.h>
#include<math.h>
int main()
{
	double l,n,c,L,r,len;
	double low,high,mid;
	while(scanf("%lf%lf%lf",&l,&n,&c)!=EOF)
	{
		if(l<0&&n<0&&c<0)
			break;
		else
		{
			low=0;
			L=(1+n*c)*l;
			high=l/2;
			while(high-low>=1e-5)
			{
				mid=(low+high)/2.0;//由mid和l求出此时的理论长度len，然后进行比较。
				r=l*l/(8*mid)+mid/2;
				len=2*r*asin(l/(2*r));
				if(len>=L)
					high=mid;
				else
					low=mid;

			}
			printf("%.3lf\n",mid);
		}
	}
	return 0;
}