Expanding Rods解题报告

最新推荐文章于 2020-05-02 19:02:25 发布

xieqinghuang

最新推荐文章于 2020-05-02 19:02:25 发布

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分类专栏：二分法与hash 文章标签： input numbers output each c

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本文介绍了一种基于输入的杆初始长度、温度变化及材料热膨胀系数来计算杆中心位移的方法，并提供了完整的C++代码实现。通过该程序，可以针对不同材料和条件准确计算出热膨胀导致的位移，适用于工程应用和技术研究。

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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
#include<iostream>
#include<cmath>
using namespace std;
const double ep=1e-12;
const double pi=acos(0.0);
int main()
{
	double n,c,L;
	while(scanf("%lf%lf%lf",&L,&n,&c)!=EOF)
	{
		if(L==-1&&n==-1&&c==-1)
			break;
		else
		{ 
			double a;
			a=(1+n*c)*L;   //L'的公式。
			double low=0,high=pi,mia;
			while(low+ep<high)  //精确范围。
			{
				mia=(low+high)/2.0;  //(0,PI)中二分查找。
				if(sin(mia)/mia>L/a)  
				{
					low=mia;
				}
				else
					high=mia;
			}
			printf("%.3lf\n",(1-cos(high))*L/(2*sin(high)));
		}
	}
	return 0;
}