Hdoj 1724 Ellipse Adaptive Simpson

Adaptive Simpson

EllipseTime limit:1000/1000 MS (java/others) Memory limit:32768/32768 K (java/others)
Total submission (s): 1268 Accepted Submission (s): 493


Problem Descriptionmath is important!! Many students failed in + 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 at Point O. The l,r lines would be vertical through the x-axis. The problem is calculating, the blue intersection area. But calculating the intersection area was dull, so I had 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)

Inputinput 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 would 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).
Outputfor each case, output one line containing a float, the area of the intersection, accurate to three decimals after th e decimal point.
Sample Input

22 1-2 22 1 0 2

Sample Output

6.2833.142

Author whisky
SOURCEHZIEE Programming Contest

/* ***********************************************author:ckbosscreated time:2014 December 27 Saturday 22:46 38 seconds file Name : hdoj1724.cpp************************************************ * * #include <iostream> #include <cstdio># Include <cstring> #include <algorithm> #include <string> #include <cmath> #include <cstdlib > #include <vector> #include <queue> #include <set> #include <map>using namespace std;double a , B,l,r;double F (double x) {return b*sqrt ((1-x/a) * (1+x/a));} 3-points simpsondouble Simpson (double a,double b) {double c= (a+b)/2;return (F (a) +4*f (c) +f (b)) * (B-A)/6.;} Double ASR (double a,double b,double eps,double a) {double c= (a+b)/2;double L=simpson (a,c), R=simpson (c,b); if (Fabs (l+r-a ) <=15*eps) return l+r+ (l+r-a)/15.0;return ASR (a,c,eps/2,l) +ASR (c,b,eps/2,r);} Double ASR (double a,double b,double EPS) {return ASR (A,b,eps,simpson (b));}    int main () {//freopen ("In.txt", "R", stdin); Freopen ("OUT.txt", "w", stdout); int t_t;scanf("%d", &t_t), while (t_t--) {scanf ("%lf%lf%lf%lf", &a,&b,&l,&r);p rintf ("%.3lf\n", 2.*asr (L,r,        1e-6));} return 0;}

Hdoj 1724 Ellipse Adaptive Simpson