hdu oval-and-rectangle

                            oval-and-rectangle

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 32768/32768K (Java/Other)

Total Submission(s) : 5   Accepted Submission(s) : 4

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

 

 

Source

2018 Multi-University Training Contest 6

其实就是让求均值，把所有可能周长加起来除去变化范围即可

首先要求出周长公式

我们都知道椭圆的公式

我们知道y的变化范围是[0,b][0,b]，并且我们可以求出x用y表示

 

因为题目要求保留6位小数，并且后面的全部舍去，因此为了防止%.6f造成四舍五入，因此给答案-0.0000005

 

#include<bits/stdc++.h>
using namespace std;
#define PI acos(-1)
int main()
{
    int t,a,b;
    double s;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&a,&b);
        s=a*PI+2*b-0.0000005;
        printf("%.6lf\n",s);
    }
}