# POJ 1905 Expanding Rods （二分）

Expanding Rods

 Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 15745 Accepted: 4185

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

### 思路

L=(4*h^2+l^2)*arcsin(4*h*l/(4*h^2+l^2))/(4*h)

### AC 代码

#include <iostream>
#include<stdio.h>
#include<math.h>
#define maxx (1<<25)
using namespace std;

int main()
{
double l,c,n;
while(~scanf("%lf%lf%lf",&l,&n,&c))
{
if(l<0||n<0||c<0)break;
double L=(1.0+n*c)*l;
double low=0,high=0.5*l,mid;
while(high-low>1e-7)
{
mid=(low+high)*.5;
double r=((4.0*mid*mid)+l*l)/(8.0*mid);
double as=2.0*r*asin(l/(2.0*r));
if(as>L)high=mid;
else if(as<L)low=mid;
else break;
}
printf("%.3f\n",mid);
}
}

### 只捉到一只哎 伤心~

• 千千 Chrome | 57.0.2950.5 Windows 10

验证函数单调性还可以给它求导，那么复杂的式子，我可不想试