hdu 1724 Ellipse (辛普森积分模板题)
题意:
求图示区域的面积。
思路:
容易推出被积函数为 f(x)=b_sqrt(1-(x_x/a/a));
1/* ***********************************************
2Author :111qqz
3Created Time :2017年10月09日 星期一 21时09分36秒
4File Name :1724.cpp
5************************************************ */
6
7#include <cstdio>
8#include <cstring>
9#include <iostream>
10#include <algorithm>
11#include <vector>
12#include <queue>
13#include <set>
14#include <map>
15#include <string>
16#include <cmath>
17#include <cstdlib>
18#include <ctime>
19#define PB push_back
20#define fst first
21#define sec second
22#define lson l,m,rt<<1
23#define rson m+1,r,rt<<1|1
24#define ms(a,x) memset(a,x,sizeof(a))
25typedef long long LL;
26#define pi pair < int ,int >
27#define MP make_pair
28
29using namespace std;
30const double eps = 1E-10;
31const int dx4[4]={1,0,0,-1};
32const int dy4[4]={0,-1,1,0};
33const int inf = 0x3f3f3f3f;
34double a,b,l,r;
35double dblcmp(double d){ return d<-eps?-1:d>eps;}
36double f(double x)
37{
38 double ret;
39 ret = sqrt((1-(x*x/a/a))*b*b);
40 return ret;
41}
42double simpson(double l,double r)
43{
44 return (r-l)*(f(l) + f(r) + 4*f((l+r)*0.5))/6;
45}
46double di( double l,double r)
47{
48 //cout<<"l:"<<l<<" r:"<<r<<endl;
49 double m = (l+r)*0.5;
50 double ans = simpson(l,r);
51 if (dblcmp(ans-simpson(l,m)-simpson(m,r))==0) return ans;
52 return di(l,m) + di(m,r);
53}
54int main()
55{
56 #ifndef ONLINE_JUDGE
57 freopen("./in.txt","r",stdin);
58 #endif
59 int T;
60 cin>>T;
61 while (T--)
62 {
63 scanf("%lf %lf %lf %lf",&a,&b,&l,&r);
64 double ans = di (l,r)*2.0;
65 printf("%.3f\n",ans);
66 }
67
68
69
70 #ifndef ONLINE_JUDGE
71 fclose(stdin);
72 #endif
73 return 0;
74}