Do not pour out HDU

题目：题目链接

思路：纯高等数学问题，不过不是很好积分，具体积分思路及过程参考大佬博客——https://blog.csdn.net/danliwoo/article/details/53002695

AC代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <iomanip>

using namespace std;

#define pi acos(-1.0)

double h;

double cal(double a) {
    return pi * cos(a) - a * cos(a) + sin(a) - pow(sin(a), 3) / 3;
}

double calV(double b) {
    double a = acos(2 * tan(b) - 1.0);
    return (cal(a) - cal(pi)) / tan(b);
}

int main()
{
    int T;
    scanf("%d", &T);
    while(T--) {
        scanf("%lf", &h);
        double v = pi * h;
        if(h < 1e-10)
            printf("0.00000
");
        else if(h >= 1.0) {
            double a = atan(2.0 - h);
            printf("%.5f
", pi / cos(a));
        }
        else {
            double l = 0, r = pi / 4;
            while(r - l > 1e-9) {
                double m = (l + r) / 2;
                if(calV(m) < v) 
                    l = m;
                else
                    r = m;
            }
            double x = 2 * tan(r);
            double a = acos(x - 1);
            double s = (pi - a + sin(a) * cos(a)) / sin(r);
            printf("%.5f
", s);
        }
    }
    return 0;
}