#define _USE_MATH_DEFINES
#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include <fstream>
using namespace std;


vector<double> funcY(int n, vector<double> x, vector<double> y)
{
	for (int k = 0; k < n; k++){
		y[k] = sin(x[k]);
	}
	return y;
}
vector<double> funcX(int n, vector<double> x)
{
	for (int k = 0; k < n; k++){
		x[k] = M_PI*k / 4 / n;
	}
	return x;
}
vector<double> Lagr(double point, vector<double> x)
{
	vector<double> Lagra(x.size());
	for (int i = 0; i < x.size(); i++){
		Lagra[i] = 1;
		for (int j = 0; j <x.size(); j++){
			(j != i) ? Lagra[i] *= (point - x[j]) : 1;
		}
	}
	return Lagra;
}

double Interp(double point, vector<double> x, vector<double> y)
{
	double InterY = 0;
	for (int i = 0; i < x.size(); i++){
		InterY += Lagr(point, x)[i] / Lagr(x[i], x)[i] * y[i];
	}
	return InterY;
}
void main()
{
	ofstream fout("Task 6.txt");
	int n = 4;
	vector<double> x(n), y(n), Lagra(n);
	x = funcX(n, x);
	y = funcY(n, x, y);

	int N = 10;
	int add = 1;
	fout << "X" << endl;
	for (int k = 0; k < N+add; k++){
		if (k != (N +add - 1))
		{
			fout << M_PI*k / N / n << ", ";
		}
		else { fout << sin(M_PI*k / N / n); }
	}

	fout << endl<< "FUNC" << endl;
	for (int k = 0; k < N+add; k++){
		if (k != (N+add - 1))
		{
			fout << sin(M_PI*k / N / n) << ", ";
		}
		else { fout << sin(M_PI*k / N / n); }
	}

	fout << endl<<"INTERP" << endl;
	for (int k = 0; k < N+add; k++){
		if (k != (N+add - 1))
		{
			fout << Interp(M_PI*k / N / n, x, y) << ", ";
		}
		else { fout << Interp(M_PI*k / N / n, x, y); }
	}
	fout <<endl<< "DIFFERENCE" << endl;
	for (int k = 0; k < N+add; k++){
		if (k != (N +add- 1))
		{
			fout << Interp(M_PI*k / N / n, x, y) - sin(M_PI*k / N / n) << ", ";
		}
		else { fout << Interp(M_PI*k / N / n, x, y) - sin(M_PI*k / N / n); }
	}
	fout.close();
}