hdu 1724 Ellipse (辛普森积分模板题)

hdu1724题目链接

题意:

求图示区域的面积。

思路:

辛普森积分学习笔记

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}