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<105). 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
题意：给你一个椭圆，求其内接矩形的周长期望
答案就是aπ+2b，注意它不是四舍五入是截断，不知道怎么积分也没关系，可以暴力然后再找规律
#include<stdio.h>
#include<math.h>
using namespace std;
#define PI acos(-1.0)
int main(void)
{
int T;
double a, b;
scanf("%d", &T);
while(T--)
{
scanf("%lf%lf", &a, &b);
printf("%.6f\n", floor((a*PI+2*b)*1000000)/1000000);
}
return 0;
}