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
 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 #include<cmath>
 6 using namespace std;
 7 double pi=acos(-1.0);
 8 double a,b;
 9 double F(double x)
10 {
11   return b*sqrt(1-x*x/(a*a));
12 }
13 double simpson(double l,double r)
14 {
15   return (r-l)*(F(l)+4*F((l+r)/2.0)+F(r))/6.0;
16 }
17 double asr(double l,double r,double eps,double A)
18 {
19   double mid=(l+r)/2.0;
20   double LS=simpson(l,mid),RS=simpson(mid,r);
21   if (fabs(LS+RS-A)<=15*eps) return LS+RS+(LS+RS-A)/15.0;
22   return asr(l,mid,eps/2,LS)+asr(mid,r,eps/2,RS);
23 }
24 int main()
25 {double eps=1e-6;
26   int T;
27   double l,r;
28   cin>>T;
29   while (T--)
30     {
31       scanf("%lf%lf%lf%lf",&a,&b,&l,&r);
32       printf("%.3lf\n",asr(l,r,eps,simpson(l,r))*2.0);
33     }
34 }

 

posted @ 2018-01-15 10:22  Z-Y-Y-S  阅读(165)  评论(0编辑  收藏  举报