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 )

 

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

 

Sample Output

 

Author

威士忌

#include<cstdio>

#include<iostream>

#include<cmath>

#define db double

using namespace std;

db a,b,l,r;

int t;

db f(db x)

{

    return sqrt(b*b*(1.0-x*x/a/a));

}

db xin(db l,db r)

{

    db mid=(l+r)/;

    return (r-l)*(f(l)+*f(mid)+f(r))/6.0;

}

db getans(db x,db y,db eps,db val)

{

    db mid=(x+y)/;

    db aa=xin(x,mid),bb=xin(mid,y);

    if(fabs(val-aa-bb)<=eps*15.0) return aa+bb+(aa+bb-val)/15.0;

    return getans(x,mid,eps/2.0,aa)+getans(mid,y,eps/2.0,bb);

}

int main()

{

    scanf("%d",&t);

    while(t--)

    {

        scanf("%lf%lf%lf%lf",&a,&b,&l,&r);

        printf("%.3lf\n",2.0*getans(l,r,0.00005,xin(l,r)));

    }

    return ;

}