HDU1724[辛普森公式求积分]Ellipse
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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
题意:要你求l与r之间椭圆的面积
分析:用辛普森公式求积分
简单模板题直接套
分析:用辛普森公式求积分
简单模板题直接套
#include<stdio.h>#include<math.h>#define eps 1e-9double a,b,l,r;double F(double x){ return 2*b*sqrt(1.0-x*x/(a*a));}double cal(double l,double r){ return (r-l)/6.0*(F(r)+4.0*F((r+l)/2.0)+F(l));}double simpson(double l,double r){ double m=(l+r)/2.0; double fl=cal(l,m),fr=cal(m,r); if(fabs(fl+fr-cal(l,r))<eps) return fr+fl; else return simpson(l,m)+simpson(m,r);}int main(){ int t; scanf("%d",&t); while(t--) { scanf("%lf%lf%lf%lf",&a,&b,&l,&r); printf("%.3lf\n",simpson(l,r)); } return 0;}
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