#include <iostream>
#include <iomanip>

using namespace std;

double f(double x){
    return 2*x*x - x + 3;
}

double df(double x){
    return 4*x - 1;
}

double L(double x, int n, double x_arr[], double y_arr[]){

    double sum = 0;
    for (int i = 0; i < n; ++i){

        double l = 1;
        for (int j = 0; j < n; ++j)
            if (j != i)
                l *= (x - x_arr[j]) / (x_arr[i] - x_arr[j]);
        sum += y_arr[i] * l;
    }

    return sum;
}

double dL(double x, int n, double x_arr[], double y_arr[]){

    double sum1 = 0;
    for (int i = 0; i < n; ++i){

        double sum2 = 0;
        for (int j = 0; j < n; ++j){
            if (j != i){
                double p = 1;
                for (int k = 0; k < n; ++k)
                    if (k != i && k != j)
                        p *= (x - x_arr[k]) / (x_arr[i] - x_arr[k]);
                sum2 += p/(x_arr[i] - x_arr[j]);
            }
        }
        sum1 += y_arr[i]*sum2;
    }

    return sum1;
}

int main(){

    const int N = 3;

    double x_arr[N], y_arr[N];
    for (int i = 0; i < N; ++i){
        x_arr[i] = 2*i;
        y_arr[i] = f(x_arr[i]);
    }

    cout << setw(3) << "x";
    cout << setw(10) << "f(x)";
    cout << setw(10) << "L(x)";
    cout << setw(10) << "df(x)";
    cout << setw(10) << "dL(x)" << endl;

    for (int i = 0; i < 20; ++i){
        double x = i;
        cout << setw(3) << x;
        cout << setw(10) << setprecision(6) << f(x);
        cout << setw(10) << setprecision(6) << L(x, N, x_arr, y_arr);
        cout << setw(10) << setprecision(6) << df(x);
        cout << setw(10) << setprecision(6) << dL(x, N, x_arr, y_arr);
        cout << endl;
    }
}