#include<Windows.h>
#include<iostream>
#include<stdio.h>
#include<math.h>
int n;
double *x, *y,*ch,*cy, a, b,lo;
HDC hDC = GetDC(GetConsoleWindow());
HPEN Pen = CreatePen(PS_SOLID, 2, RGB(255, 255, 255));
HPEN Pens = CreatePen(PS_SOLID, 2, RGB(0, 255, 255));
HPEN Pene = CreatePen(PS_SOLID, 2, RGB(255, 255, 0));
HPEN Peny = CreatePen(PS_SOLID, 2, RGB(255, 0, 125));

double Lagrang(double x0)
	{
		int k, j;
		double sum, znam, chis;
		sum = 0;
		znam = 1;
		chis = 1;
		for (j = 0; j < n + 1; j++)
		{

			for (k = 0; k < n + 1; k++)
			{
				if (k != j)
				{
					znam = znam * (x[j] - x[k]);
					chis = chis * (x0 - x[k]);
				}
				else
				{
					znam = znam * 1;
					chis = chis * 1;
				}
			}
			sum = sum + y[j] * (chis / znam);
			chis = 1;
			znam = 1;
		}
		return sum;
	}
double Lch(double x0)
{
	int k, j;
	double sum, znam, chis;
	sum = 0;
	znam = 1;
	chis = 1;
	for (j = 0; j < n + 1; j++)
	{

		for (k = 0; k < n + 1; k++)
		{
			if (k != j)
			{
				znam = znam * (ch[j] - ch[k]);
				chis = chis * (x0 - ch[k]);
			}
			else
			{
				znam = znam * 1;
				chis = chis * 1;
			}
		}
		sum = sum + cy[j] * (chis / znam);
		chis = 1;
		znam = 1;
	}
	return sum;
}
void graf()
{SelectObject(hDC, Pen);
	int i;
	double q, w = 0.001,c;
	q = x[0];
	MoveToEx(hDC, 50* q,150 -50*Lagrang(q), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC,  50*q,  150 -50 * Lagrang(q));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC,  50*q,  150- 50 * Lagrang(q), NULL);
	}
}
void grafch()
{
	SelectObject(hDC, Pen);
	int i;
	double q, w = 0.001, c;
	q = ch[0];
	MoveToEx(hDC, 50 * q, 350 - 50 * Lch(q), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC, 50 * q, 350 - 50 * Lch(q));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 350 - 50 * Lch(q), NULL);
	}
}
void grafs()
{
	SelectObject(hDC, Pens);
	double q, w = 0.001, c;
	q = x[0];
	MoveToEx(hDC, 50 * q, 150 -50 * sin(q), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC, 50 * q, 150 - 50 * sin(q));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 150 - 50 * sin(q), NULL);
	}


}
void grafsch()
{
	SelectObject(hDC, Pens);
	double q, w = 0.001, c;
	q = ch[0];
	MoveToEx(hDC, 50 * q, 350 - 50 * sin(q), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC, 50 * q, 350 - 50 * sin(q));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 350 - 50 * sin(q), NULL);
	}


}
void epsL()
{

	SelectObject(hDC, Pene);
	int i;
	double q, w = 0.001, c,eps;
	eps = 0;
	q = x[0];
	MoveToEx(hDC, 50 * q, 150 - 50 * (Lagrang(q)-sin(q)), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC, 50 * q, 150 - 50 * (Lagrang(q) - sin(q)));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 150 - 50 * (Lagrang(q) - sin(q) ), NULL);
	}

}
void epsLch()
{

	SelectObject(hDC, Pene);
	int i;
	double q, w = 0.001, c, eps;
	eps = 0;
	q = ch[0];
	MoveToEx(hDC, 50 * q, 350 - 50 * (Lch(q) - sin(q)), NULL);
	while (q < b)
	{
		q = q + w;

		LineTo(hDC, 50 * q, 350 - 50 * (Lch(q) - sin(q)));
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 350 - 50 * (Lch(q) - sin(q)), NULL);
	}

}
void eps()
{
	SelectObject(hDC, Peny);
	int i;
	double q, w = 0.001, c, eps;
	eps = 1;
	q = x[0];
	for (i = 0; i <= n ; i++)
	{

		eps = eps * (q - x[i]);

	}
	for (i = 1; i <= n + 1; i++)
	{

		eps = eps / i;

	}
	if (eps < 0) eps = eps * (-1);
	MoveToEx(hDC, 50 * q, 150 - 50 *eps, NULL);
	while (q < b)
	{  q+= w;
	    eps=1;
		for (i = 0; i <= n; i++)	eps = eps* (q - x[i]);
		for (i = 1; i <= n + 1; i++)eps = eps/i;
		if (eps < 0) eps= eps * (-1);

		LineTo(hDC, 50 * q, 150 - 50 * eps);
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 150 - 50 *eps, NULL);

	}


}
void epsch()
{
	SelectObject(hDC, Peny);
	int i;
	double q, w = 0.001, c, eps;
	eps = 1;
	q = ch[0]+w;
	for (i = 0; i <= n; i++)
	{

		eps = eps * (q - ch[i]);

	}
	for (i = 1; i <= n + 1; i++)
	{

		eps = eps / i;

	}
	if (eps < 0) eps = eps * (-1);
	MoveToEx(hDC, 50 * q, 350 - 50 * eps, NULL);
	while (q < b)
	{
		q += w;
		eps = 1;
		for (i = 0; i <= n; i++)	eps = eps * (q - ch[i]);
		for (i = 1; i <= n + 1; i++)eps = eps / i;
		if (eps < 0) eps = eps * (-1);

		LineTo(hDC, 50 * q, 350 - 50 * eps);
		//std::cout << Lagrang(q)<<"\n";
		MoveToEx(hDC, 50 * q, 350 - 50 * eps, NULL);

	}


}

int main()
{
	int i;
	double p,pi, h;
	std::cout << "Write your kol-vo of points" << "\n";
	std::cin >> n;
	std::cout << "Write yourinterval  " << "\n";
	std::cin >> a >> b;
	std::cout << "\n";
	x = new double[n + 1];
	y = new double[n + 1];
	ch = new double[n + 1];
	cy = new double[n + 1];
	p = ( b-a) / n;
	pi = 3.1415;
	for (i = 0; i < n + 1; i++)
	{
		x[i] = a + i * p;
		y[i] = sin(x[i]);
	}
	ch[0] = a;
	cy[0] = sin(a);
	for (i = 1; i < n ; i++)
	{
		ch[i] = ((b - a)*cos((2 * i + 1)*pi / (2 * n + 2))+a+b) / 2;

		cy[i] = sin(ch[i]);
	}
	/*for (i = 0; i < n + 1; i++)
	{
		std::cout <<sin(x[i])<<"  " <<Lagrang(x[i])<<"\n";
	}*/

	graf();//построение интерполянта


	grafs();//построение sin

	epsL();//построение  точной погрешности
	eps();//построение приближенной погрешности

	grafch();
	grafsch();
	epsLch();
	epsch();

	std::cin >> h;

}