二分搜索

A narrow street is lined with tall buildings. An x foot long ladder is rested at the base of the building on the right side of the street and leans on the building on the left side. Ay foot long ladder is rested at the base of the building on the left side of the street and leans on the building on the right side. The point where the two ladders cross is exactlyc feet from the ground. How wide is the street?

Input

Input starts with an integer T (≤ 10), denoting the number of test cases.

Each test case contains three positive floating point numbers giving the values ofx,y, andc.

Output

For each case, output the case number and the width of the street in feet. Errors less than10^-6 will be ignored.

Sample Input

4

30 40 10

12.619429 8.163332 3

10 10 3

10 10 1

Sample Output

Case 1: 26.0328775442

Case 2: 6.99999923

Case 3: 8

Case 4: 9.797958971

学会构造表达式，输入在其左端，结果在右端需为定值（代码中与mid比较的 1 便是定值）

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstring>
#include<algorithm>
using namespace std;
double c,y,x,a;
double f(double a)
{
 return c/sqrt(y*y-a*a)+c/sqrt(x*x-a*a);
}
int main()
{
 int t,p=0;
 scanf("%d",&t);
 while(t--)
 {
  scanf("%lf %lf %lf",&x,&y,&c);
  double left=0.0,right=min(x,y),mid,k;//学会使用c++，min函数可以直接调用
  while(right-left>=0.0000000001)//精度
  {
   mid=(left+right)/2;
   if(f(mid)==1)
   {
    break;
   }
   else if(f(mid)>1)
   {
    right=mid;//right=mid-0.0000001;
   }
   else
       left=mid;//left=mid+0.0000001;
  }
  printf("Case %d: %lf\n",++p,mid);
 }
 return 0;
}