HDU 1724 Ellipse 自适应simpson函数模板题(二)
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Ellipse
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2012 Accepted Submission(s): 857
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 )
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
22 1 -2 22 1 0 2
Sample Output
6.2833.142
Author
威士忌
Source
HZIEE 2007 Programming Contest
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模板如图:
模板如图:
模板理解:a和b分别代表所求积分的上下限。eps的值一般为 : 1e-6
同时还要加上一个函数double F(double x);这个函数就是你要求的函数(这题要求出x关于y的函数,所以要化简一下)
上代码:
#include<cstdio>#include<cstring>#include<iostream>#include<cmath>#include<algorithm>using namespace std;const double eps=1e-6;///eps的值double a,b,l,r;double F(double x ){ return b*sqrt(1-x*x/(a*a));///对应题目所需求解的方程 ///求出x关于y的方程}double simpson(double l,double r){ double c=l+(r-l)/2; return (F(l) +4*F(c)+F(r))*(r-l)/6;}double asr(double l,double r,double eps, double A){ double c=l+(b-l)/2; double L=simpson(l,c),R=simpson(c,r); if(fabs(L+R-A) <= 15*eps ) return L+R+(L+R-A)/15; return asr(l,c,eps/2,L) + asr(c,r,eps/2,R);}double asr(double l,double r,double eps){ return asr(l,r,eps,simpson(l,r));}int main(){ int t; cin>>t; while(t--) { scanf("%lf%lf%lf%lf",&a,&b,&l,&r); printf("%.3lf\n",2*asr(l,r,eps));///传入上下限和eps ///此题不要忘记把最终结果乘2 } return 0;}
要努力啊QAQ
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