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-;

 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 = , it = ;
     double V = h*(func(a,b,)+func(a,b,h))/2.0;
     double Vold;
     do
     {
         double tmp = ;
         steps *= ;
         for (unsigned long i = ; i < steps; i += )
         {
             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 = ;
     int N;
     cin >> V >> N;
     V /= 3.14159265358979;
     for (int i = ; 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 ;
 }