oval-and-rectangle

 

oval-and-rectangle

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 0    Accepted Submission(s): 0

Problem Description

Patrick Star find an oval.
The half of longer axes is on the x-axis with length $a$.
The half of shorter axes is on the y-axis with length $b$.
Patrick Star plan to choose a real number $c$ randomly from $[0, b]$, after that, Patrick Star will get a rectangle :

1. The four vertexes of it are on the outline of the oval.
2. The two sides of it parallel to coordinate axis.
3. One of its side is $y = c$.
Patrick Star want to know the expectations of the rectangle's perimeter.

 

Input

The first line contain a integer $T$ (no morn than 10), the following is $T$ test case, for each test case :
Each line contains contains two integer a, b ($0 < b < a < 10^5$). Separated by an white space.

 

Output

For each test case output one line denotes the expectations of the rectangle's perimeter .
You should keep exactly 6 decimal digits and ignore the remain decimal digits.
It is guaranted that the 7-th decimal digit of answer wont be 0 or 9.

 

Sample Input

1 2 1

 

Sample Output

8.283185

 

分析：椭圆性质有：
将y=c带入，求出内接矩形的周长，通过积分求出答案。
ac代码：

#include <iostream>
#include <cstdio>
using namespace std;

int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        int a, b;
        int x, y;
        cin>>a>>b>>x>>y;
        int w = b * (-1) * x / a;
        printf("%d\n", x/(w-y));
    }
    return 0;
}