German Collegiate Programming Contest 2013:E

数值计算：

这种积分的计算方法很好，学习一下！

代码：

#include <iostream>
#include <cmath>
using namespace std;
const double eps = 10e-5;

double func(double a, double b, double x)
{
    double r = a * exp(- x*x) + b * sqrt(x);
    return r*r;
}

double integrate(double a, double b, double h)
{
    unsigned long steps = 1, it = 1;
    double V = h*(func(a,b,0)+func(a,b,h))/2.0;
    double Vold;
    do
    {
        double tmp = 0;
        steps *= 2;
        for (unsigned long i = 1; i < steps; i += 2)
        {
            tmp += func(a, b, (h * i) / steps);
        }
        Vold = V;
        V = (V / 2.0) + ((tmp * h) / steps);
    }
    while (fabs(V - Vold) > eps);
    return V;
}

int main()
{
    double V, a, b, h;
    double e_min = 2e100;
    int i_min = 0;
    int N;
    cin >> V >> N;
    V /= 3.14159265358979;
    for (int i = 0; i < N; i++)
    {
        cin >> a >> b >> h;
        double e = fabs(V -integrate(a, b, h));
        if (e < e_min)
        {
            e_min = e;
            i_min = i;
        }
    }
    cout << i_min << endl;
    return 0;
}