#include <iostream>
#include <vector>
#include <cmath>
#include <string>
#include <fstream>

using namespace std;

const double np = 150;



struct wezly
{
public:
	wezly()
	{};
	vector <double> wezel;
	vector <double> wartosc;
};

vector<double>punkty;


void wprowadz(double &a, double &b, double &n)
{
	cout << "Poczatek przedzialu: ";
	cin >> a;
	cout << "Koniec przedzialu: ";
	cin >> b;
	cout << "ilosc wezlow: ";
	cin >> n;
}

wezly tablicuj(double a, double b, double n)
{
	wezly x;
	double luka = abs((b - a) / n);
	for (double i = a; i <= b; i += luka)
	{
		x.wezel.push_back(i);
	}
	for (double i = 0; i <= n; i++)
	{
		x.wartosc.push_back(abs(cos(x.wezel[i])*x.wezel[i]));
	}
	return x;
}

void wypunktuj(double a, double b)
{
	double luka = abs((b - a) / np);
	for (double i = a; i <= b; i += luka)
	{
		punkty.push_back(i);
	}
}

vector<double> wielomian(wezly x, double punkt, double n)
{
	vector<double> wielomiany;
	double wielomian = 1.0;
	for (int i = 0; i <= n; i++)
	{
		wielomiany.push_back(wielomian);
		wielomian *= punkt - x.wezel[i];
	}
	return wielomiany;
}

vector<vector<double>> IR_Newtona(wezly x, int n)
{
	vector<vector<double>> choinka;
	for (int i = 0; i <= n; i++)
	{
		vector<double>wnetrze;
		for (int j = 0; j <= n; j++)
			wnetrze.push_back(0);
		choinka.push_back(wnetrze);
	}
	for (int i = 0; i <= n; i++)
	{
		choinka[0][i] = x.wartosc[i];
	}
	int counter = 1;
	for (int i = 1; i <= n; i++)
	{
		for (int j = 0; j <= n-i; j++)
		{
			choinka[i][j] = (choinka[i - 1][j + 1] - choinka[i - 1][j]) / (x.wezel[j + counter] - x.wezel[j]);
		}
		counter++;
	}
	return choinka;
}

double Wzor_newtona(wezly x, double punkt, int n)
{
	vector<vector<double>> choinka;
	vector<double>wielomiany;
	wielomiany = wielomian(x, punkt, n);
	choinka = IR_Newtona(x, n);
	double wartosc = 0.0;
	for (int i = 0; i <= n; i++)
	{
		wartosc += wielomiany[i] * choinka[i][0];
	}
	return wartosc;
}

void wypisz(wezly x, double n)
{
	for (int i = 0; i < np; i++)
	{
		cout << punkty[i] << endl;
		cout << abs(cos(punkty[i])*punkty[i]) << endl;
		cout << Wzor_newtona(x, punkty[i], n) << endl;
	}
}

int main()
{
	double a, b, n;
	wezly x;
	wprowadz(a, b, n);
	x = tablicuj(a, b, n);
	wypunktuj(a, b);
	wypisz(x, n);
	return 0;
}