POJ-1905-Expanding Rods【二分】【计算几何】

Expanding Rods

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 0.000115000 10 0.00006 10 0 0.001 -1 -1 -1

Sample Output

61.329225.020 0.000

若圆内任意弦AB、弦CD交于点P，则PA·PB=PC·PD（相交弦定理）

sinB=L/R   B=asin(L/R)   反三角函数

这道题好恶心

#include<cstdio>
#include<cmath>
int main()
{
  int t;
  scanf("%d",&t);
  int num=0;
  while(t--)
  {
    double l,n,c,L,left,right,r,mid;
    scanf("%lf %lf %lf",&l,&n,&c);
    L=(1+n*c)*l;
    left=0;
    right=l/2;
    while(right-left>1e-6)   // 以 h 为二分区间 
    {
      mid=(left+right)/2;
      r=l*l/8/mid+mid/2;
      if(r*2*(asin(l/2/r))<L)
      {
        left=mid;
      }
      else
      {
        right=mid;
      }
    }
    printf("Case %d: ",++num);
    printf("%.6f\n",mid);  //输出 mid left right 均可 
  }
}