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));
/* ***********************************************
Author :111qqz
Created Time :2017年10月09日 星期一 21时09分36秒
File Name :1724.cpp
************************************************ */
1#include <cstdio>
2#include <cstring>
3#include <iostream>
4#include <algorithm>
5#include <vector>
6#include <queue>
7#include <set>
8#include <map>
9#include <string>
10#include <cmath>
11#include <cstdlib>
12#include <ctime>
13#define PB push_back
14#define fst first
15#define sec second
16#define lson l,m,rt<<1
17#define rson m+1,r,rt<<1|1
18#define ms(a,x) memset(a,x,sizeof(a))
19typedef long long LL;
20#define pi pair < int ,int >
21#define MP make_pair
1using namespace std;
2const double eps = 1E-10;
3const int dx4[4]={1,0,0,-1};
4const int dy4[4]={0,-1,1,0};
5const int inf = 0x3f3f3f3f;
6double a,b,l,r;
7double dblcmp(double d){ return d<-eps?-1:d>eps;}
8double f(double x)
9{
10 double ret;
11 ret = sqrt((1-(x*x/a/a))*b*b);
12 return ret;
13}
14double simpson(double l,double r)
15{
16 return (r-l)*(f(l) + f(r) + 4*f((l+r)*0.5))/6;
17}
18double di( double l,double r)
19{
20 //cout<<"l:"<<l<<" r:"<<r<<endl;
21 double m = (l+r)*0.5;
22 double ans = simpson(l,r);
23 if (dblcmp(ans-simpson(l,m)-simpson(m,r))==0) return ans;
24 return di(l,m) + di(m,r);
25}
26int main()
27{
28 #ifndef ONLINE_JUDGE
29 freopen("./in.txt","r",stdin);
30 #endif
31 int T;
32 cin>>T;
33 while (T--)
34 {
35 scanf("%lf %lf %lf %lf",&a,&b,&l,&r);
36 double ans = di (l,r)*2.0;
37 printf("%.3f\n",ans);
38 }
1 #ifndef ONLINE_JUDGE
2 fclose(stdin);
3 #endif
4 return 0;
5}