POJ 1905 Expanding Rods（二分）

Expanding Rods

Time Limit: 1000MS Memory Limit: 30000K

Total Submissions: 20224 Accepted: 5412

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

Source

Waterloo local 2004.06.12

二分，看到网上都是asin acos 做的，其实只要有一个关系式，就能进行二分，二分是一种思想，别要人云亦云。

#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
#define esp 1e-8
int main()
{
	double len,c,lv,h,up,lo,r;
	while(scanf("%lf%lf%lf",&len,&c,&lv)==3&&!(len==-1))
	{
        double len2=(1+c*lv)*len;
            up=len/2.0;
            lo=0.0;
	    while(up-lo>esp){
            h=(up+lo)/2.0;
             r=(len*len+4*h*h)/8/h;
     //       cout<<len2/2.0/r<<"  "<<asin(len/2.0/r)<<"   "<<up<<"  "<<lo<<"  "<<h<<endl;
            if((len2/2.0/r)>asin(len/2.0/r)) lo=h;
            else up=h;
        }
        printf("%.3f\n",h);
	}
	return 0;
}