HDU 1724 Ellipse

Problem Description

Math is important!! Many students failed in 2+2’s mathematical test, so let's AC this problem to mourn for our lost youth..
Look this sample picture:



A ellipses in the plane and center in point O. the L,R lines will be vertical through the X-axis. The problem is calculating the blue intersection area. But calculating the intersection area is dull, so I have turn to you, a talent of programmer. Your task is tell me the result of calculations.(defined PI=3.14159265 , The area of an ellipse A=PI*a*b )

Input

Input may contain multiple test cases. The first line is a positive integer N, denoting the number of test cases below. One case One line. The line will consist of a pair of integers a and b, denoting the ellipse equation , A pair of integers l and r, mean the L is (l, 0) and R is (r, 0). (-a <= l <= r <= a).

Output

For each case, output one line containing a float, the area of the intersection, accurate to three decimals after the decimal point.

Sample Input

2

2 1 -2 2

2 1 0 2

Sample Output

6.283

3.142

自适应辛普森的模板

http://blog.csdn.net/u014800748/article/details/44343955

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
double pi=acos(-1.0);
double a,b;
double F(double x)
{
  return b*sqrt(1-x*x/(a*a));
}
double simpson(double l,double r)
{
  return (r-l)*(F(l)+4*F((l+r)/2.0)+F(r))/6.0;
}
double asr(double l,double r,double eps,double A)
{
  double mid=(l+r)/2.0;
  double LS=simpson(l,mid),RS=simpson(mid,r);
  if (fabs(LS+RS-A)<=15*eps) return LS+RS+(LS+RS-A)/15.0;
  return asr(l,mid,eps/2,LS)+asr(mid,r,eps/2,RS);
}
int main()
{double eps=1e-6;
  int T;
  double l,r;
  cin>>T;
  while (T--)
    {
      scanf("%lf%lf%lf%lf",&a,&b,&l,&r);
      printf("%.3lf\n",asr(l,r,eps,simpson(l,r))*2.0);
    }
}