#include <stdio.h>
#include <conio.h>
#include <locale.h>
#include <math.h>
#include <malloc.h>
#include <process.h>
#include <stdlib.h>
#include <windows.h>
#include <iostream>
double lagrange(double*, double*, int, double);
double line(double*, double*, int, double);
void knot(int, int, int, double*, double*);
void approx(int, int, int, int, double*, double*);
using namespace std;
void main()
{
	setlocale(LC_CTYPE, "Russian");

	int a, b, m, n = 8;
//	double *arr_x = new double[10];
//double *arr_y = new double[10];

	cout << "Введите начало интервала:" << endl;
	cin >> a;

	cout << "Введите конец интервала:" << endl;
	cin >> b;

	cout << "Введите количество точек интерполяции (не более 10!):" << endl;
	cin >> m;
	double *arr_x = new double[b - a];
	double *arr_y = new double[b - a];

	knot(m, a, b, arr_x, arr_y);
	approx(m, n, a, b, arr_x, arr_y);
	system("pause");

}

void knot(int m, int a, int b, double *arr_x, double *arr_y)
{
	double x, y;

	cout << "Значение функции в узловых точках";
	printf("\n N \t X \t Y");

	for (int i = 1; i <= m; i++){
		x = a + (double)(i - 1)*(b - a) / (m - 1);
		y = pow(x, 3) - 5 * (pow(x, 2));

		arr_x[(i - 1)] = x;
		arr_y[(i - 1)] = y;
		printf("\n %d \t %.2lf \t %.6lf", i, x, y) ;
	}
	cout << endl;

	cout << "-------------------------------------" << endl;

}

void approx(int m, int n, int a, int b, double *arr_x, double *arr_y)
{
	double x, y, yi, yl;

	cout <<"Значение функции в узловых точках и аппроксимация";
	printf("\n N\t| X    | F(x)     | Fi(x)    |delta(Fi)  | Fl(x)    | delta(Fl)");
	for (int i = 1; i <= n; i++){
		x = a + (double)(i - 1)*(b - a) /(n - 1);
		y = pow(x, 3)-5*(pow(x,2));
	yi = lagrange(arr_x, arr_y, m, x);
		yl = line(arr_x, arr_y, m, x);
		printf("\n %d\t| %.2lf | %.6lf | %.6lf | %.6lf | %.6lf | %.6lf", i, x, y, yi, abs(y - yi), yl, abs(y - yl) );
	}
	puts("\n");
}

double lagrange(double *arr_x, double *arr_y, int m, double x)
{
	double L = 0, z;

	for (int i = 0; i < m; i++){
		z = 1;
		for (int j = 0; j < m; j++){
			if (j != i)
				z *= (x - arr_x[j]) / (arr_x[i] - arr_x[j]);
		}
		L += z * arr_y[i];

	}

	return L;
}

double line(double *arr_x, double *arr_y, int m, double x)
{
	double L;
	int el = 0;

	for (int i = 0; i<m; i++)
		if (x >= arr_x[i] && x <= arr_x[i])
			el = i;

	L = arr_y[el] + (arr_y[el + 1] - arr_y[el])*(x - arr_x[el]) / (arr_x[el + 1] - arr_x[el]);

	return L;
}