Expanding Rods

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 60000/30000K (Java/Other)

Total Submission(s) : 123   Accepted Submission(s) : 43

Problem 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. <br>

 

Sample Input

1000 100 0.000115000 10 0.0000610 0 0.001-1 -1 -1

 

Sample Output

61.329225.020
0.000
题意：加热后中间的棒子会变形，给出变形前长度l，温度，形变率，变形后长度计算公式已给出  
问你垂直平分线的顶点距离原来的水平线多远
思路：
通过二分枚举高度，进而确定半径，弧长，与新长度比较判别
Source Code
#include<iostream>#include<stdio.h>#include<cmath>#include<iomanip>using namespace std;int main(){    double l,newl,c,t;    while(cin>>l>>t>>c)    {        if(l==-1.0&&t==-1.0&&c==-1.0)            break;        newl=(1+t*c)*l;        //cout<<newl<<endl;        double mid,low=0,high=l/2;        //cout<<high<<endl;        double r,templ;        while(high-low>1e-6)        {            mid=(low+high)/2;            r=(l*l+4*mid*mid)/(8*mid);            templ=2*r*asin(l/(2*r));            if(templ<newl)                low=mid;            else                high=mid;            }        cout<<fixed<<setprecision(3)<<low<<endl;        }    return 0;}