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(-x*x/(a*a));
 }
 double simpson(double l,double r)
 {
   return (r-l)*(F(l)+*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)<=*eps) return LS+RS+(LS+RS-A)/15.0;
   return asr(l,mid,eps/,LS)+asr(mid,r,eps/,RS);
 }
 int main()
 {double eps=1e-;
   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);
     }
 }