#include <iostream>
#include <cmath>
#include <ctime>
#include <iomanip>

typedef double (*method)(double f(double), double, double, int);


#define N_1 100
#define N_2 1000




using namespace std;

double f(double x){
    return sin(4 / (x + 1)) + cos(4 * x) * cos(4 * x);
}

double rectangle(double f(double), double LEFT, double RIGHT, int N){

    double sq = 0, x, dx;
    dx = (RIGHT - LEFT) / N;

    for (int i = 0; i < N; i++){
        x = (RIGHT - LEFT) * (i + 1) / N;
        sq += f(x) * dx;
    }

    return sq;

}

double trapeze(double f(double), double LEFT, double RIGHT, int N){
    double sq = 0, x, dx;
    dx = (RIGHT - LEFT) / N;

    for (int i = 0; i < N; i++){
        x = (RIGHT - LEFT) * (i + 1) / N;
        sq += dx * (f(x) + f(x + dx)) / 2;
    }

    return sq;
}

double simp(double f(double), double LEFT, double RIGHT, int N){
    double sq = 0, a, b, dx;
    dx = (RIGHT - LEFT) / N;

    for (int i = 0; i < N; i++){
        a = (RIGHT - LEFT) * (i + 1) / N;
        b = a + dx;
        sq += (dx / 6) * (f(a) + f(b) + 4 * f((a + b) / 2));
    }

    return sq;
}

double method_time(method Method, int N){

    unsigned int start;
    double time;

    start = clock();
    for (int i = 0; i < 1000; i++){
        Method(f, 0, 2, N);
    }
    time = (clock() - start) / 1000.0;

    return time;
}


int main(int argc, char *argv[])
{

    cout << "For 100:\n";

    cout << "rectangle: " << setw(6) << rectangle(f, 0, 2, N_1);
    cout << " time: " << setw(7) << method_time(rectangle, N_1) << "ms" << endl;

    cout << "trapeze: " << setw(7) << trapeze(f, 0, 2, N_1);
    cout << " time: " << setw(7) << method_time(trapeze, N_1) << "ms" <<  endl;

    cout << "simp: " << setw(7) << simp(f, 0, 2, N_1);
    cout << " time: " << setw(7) << method_time(simp, N_1) << "ms" <<  endl;
    cout << endl << endl;


    cout << "For 1000:\n";

    cout << "rectangle: " << setw(7) << rectangle(f, 0, 2, N_2);
    cout << " time: " << setw(7) << method_time(rectangle, N_2) << "ms" << endl;

    cout << "trapeze: " << setw(7) << trapeze(f, 0, 2, N_2);
    cout << " time: " << setw(7) << method_time(trapeze, N_2) << "ms" << endl;

    cout << "simp: " << setw(7) << simp(f, 0, 2, N_2);
    cout << " time: " << setw(7) << method_time(simp, N_2) << "ms" << endl;

    return 0;
}