Crossed Ladders - UVa 10566 几何+二分

Crossed Ladders
Input: Standard Input

Output: Standard Output

Time Limit: 1 Second

 

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. A y 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 exactly c feet from the ground. How wide is the street?

Each line of input contains three positive floating point numbers giving the values of x, y, and c.

For each line of input, output one line with a floating point number giving the width of the street in feet, with three decimal digits in the fraction.

Sample Input                             Output for Sample Input

30 40 10 12.619429 8.163332 3 10 10 3 10 10 1

26.033 7.000 8.000 9.798

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Problemsetter: Alberta Local Contest

原文好像不好复制……就这样吧。

题意：给你两个梯子的长度，和交点的高度，问你放置的宽度。

思路：二分，比较简单的几何。

AC代码如下：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
typedef long long ll;
using namespace std;
double x1,x2,l1,l2,h,h1,h2,ans,l,r,mi;
double solve()
{ h1=sqrt(l1*l1-mi*mi);
  h2=sqrt(l2*l2-mi*mi);
  x1=l1*h1/(h1+h2);
  x2=l1*h2/(h1+h2);
  return x2*h1/l1;
}
int main()
{ while(~scanf("%lf%lf%lf",&l1,&l2,&h))
  { l=0;r=min(l1,l2);
    while(r-l>0.0001)
    { mi=(l+r)/2;
      if(solve()>h)
       l=mi;
      else
       r=mi;
    }
    printf("%.3f\n",l);
  }
}