#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <conio.h>
#include <locale.h>
#include <time.h>
#include <math.h>
#include <iostream>
#include <Windows.h>

using namespace std;

const double PI = 3.1415926535897932384626433832795;

typedef double(*functiontype)(double x);


typedef struct Node
{
    double x, y;
}Node;

double Myfunk(double x)
{
    return cos(x);
}
long double R01(long double *v_v[2], long double X, int n)
{
    double x = X - v_v[0][0];
    x *= (X - v_v[0][1]);
    long int fact = 1;
    for (int k = 2; k < n; ++k)
    {
        fact *= k;
        x *= (X - v_v[0][k]);
        x = x / fact;
    }
    return fabs(x);
}

long double lag1(long double* v_v[2], long double x, int n)
{
    long double L = 0;
    long double* l = new long double[n];

    for (int i = 0; i < n; i++)
        l[i] = 1;

    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            if (i != j)
                l[i] *= (x - v_v[0][j]) / (v_v[0][i] - v_v[0][j]);

    for (int i = 0; i < n; i++)
        L += v_v[1][i] * l[i];

    return L;
}

long double lag(Node *Array, long double x, int Count)
{
    long double L = 0;
    long double* l = new long double[Count];

    for (int i = 0; i < Count; i++)
        l[i] = 1;

    for (int i = 0; i < Count; i++)
        for (int j = 0; j < Count; j++)
            if (i != j)
                l[i] *= (x - Array[j].x) / (Array[i].x - Array[j].x);

    for (int i = 0; i < Count; i++)
        L += Array[i].y * l[i];

    return L;
}

long double R0(Node *Array, long double X, int Count)
{
    double x = X - Array[0].x;
    x *= (X - Array[1].x);
    long int fact = 1;
    for (int k = 2; k < Count; ++k)
    {
        fact *= k;
        x *= (X - Array[k].x);
        x = x / fact;
    }
    return fabs(x);
}

void ValueUniformTable(functiontype *f, Node *Array, double Initial, double End, int Count)
{ // Создание равномерной таблицы значений
    double step = abs(Initial - End) / (Count - 1);
    Array[0].x = Initial;
    Array[0].y = (*f)(Array[0].x);
    cout << "   " << "x" << "\t" << "y" << endl;
    cout << "   " << Array[0].x << "\t" << Array[0].y << endl;
    for (int i = 1; i < Count; i++)
    {
        Array[i].x = Array[i - 1].x + step;
        Array[i].y = (*f)(Array[i].x);
        cout << "   " << Array[i].x << "\t" << Array[i].y << endl;
    }
    cout << endl << endl;
}

void ValueChebyshevTable( Node *Array, double Initial, double End, int Count)
{ // Создание таблицы Чебышевских значений
    cout << "   " << "x" << "\t\t" << "y" << endl;
    cout << "   " << Array[0].x << "\t" << Array[0].y << endl;
    for (int i = 0; i < Count; i++)
    {
        long double coss = cos(M_PI * (2 * (i + 1) - 1) / (2 * Count));
        Array[i].x = 0.5 * (Initial + End) + 0.5 * (End - Initial) * coss;
        Array[i].y = cos(Array[i].x);
        cout << "   " << Array[i].x << "\t" << Array[i].y << endl;
    }
}



double maxt(double Initial, double End, int Count, char ans)
{
    {
        long double* v_v[2];

        v_v[0] = new long double[Count];
        v_v[1] = new long double[Count];

        if (ans == 'y')
            for (int i = 0; i < Count; i++)
            {
                long double coss = cos(M_PI * (2 * (i + 1) - 1) / (2 * Count));
                v_v[0][i] = 0.5 * (Initial + End) + 0.5 * (End - Initial) * coss;
                v_v[1][i] = cos(v_v[0][i]);
            }

        long double a1 = Initial;
        if (ans == 'n')
            for (int i = 0; i < Count; i++)
            {
                v_v[0][i] = a1;
                v_v[1][i] = cos(v_v[0][i]);

                a1 += (fabs(Initial) + fabs(End)) / long double(Count - 1);
            }

        long double c = R01(v_v, End, Count);

        for (long double x = End; x >= Initial; x -= 0.01f) // O(100,85) - center
        {
            if (c < fabs((lag1(v_v, x, Count) - cos(x)))) c = fabs((lag1(v_v, x, Count) - cos(x)));
        }

        delete[] v_v[0];
        delete[] v_v[1];

        return c;
    }
}

double maxf(double Initial, double End, int Count, char ans)
{
    long double* v_v[2];

    v_v[0] = new long double[Count];
    v_v[1] = new long double[Count];

    if (ans == 'y')
        for (int i = 0; i < Count; i++)
        {
            long double coss = cos(M_PI * (2 * (i + 1) - 1) / (2 * Count));
            v_v[0][i] = 0.5 * (Initial + End) + 0.5 * (End - Initial) * coss;
            v_v[1][i] = cos(v_v[0][i]);
        }

    long double a1 = Initial;
    if (ans == 'n')
        for (int i = 0; i < Count; i++)
        {
            v_v[0][i] = a1;
            v_v[1][i] = cos(v_v[0][i]);

            a1 += (fabs(Initial) + fabs(End)) / long double(Count - 1);
        }

    long double c = R01(v_v, End, Count);

    for (long double x = End; x >= Initial; x -= 0.01f) // O(100,85) - center
    {
        if (c < fabs(R01(v_v, x, Count))) c = fabs(R01(v_v, x, Count));
    }

    delete[] v_v[0];
    delete[] v_v[1];

    return c;
}




int main()
{
    setlocale(LC_ALL, "Russian");
    srand(static_cast<int>(time(0)));

    long double* v_v[2];
    int CountNodes;
    long double a, b;
    char ans;
    functiontype Func = &Myfunk;
    cout << "Введите количество точек: ";
    cin >> CountNodes;

    cout << "Введите промежуток [a, b] через пробел: ";
    cin >> a >> b;
    Node *ArrayNodes = new Node[CountNodes];

    cout << "Использовать узлы Чебышёва?(y/n): ";
    cin >> ans;

    if (ans == 'y')
        ValueChebyshevTable(ArrayNodes, a, b, CountNodes);

    if (ans == 'n')
        ValueUniformTable(&Func, ArrayNodes, a, b, CountNodes);

    long double d;
    HDC hDC = GetDC(GetConsoleWindow());
    HPEN PenW =

        CreatePen(PS_SOLID, 2, RGB(255, 255, 255));
    HPEN PenR = CreatePen(PS_SOLID, 2, RGB(255, 0, 0));
    HPEN PenG = CreatePen(PS_SOLID, 2, RGB(0, 255, 0));
    HPEN PenB = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));

    SelectObject(hDC, PenW);
    MoveToEx(hDC, 100 - a * 20, 500, NULL);
    LineTo(hDC, 500 - a * 20, 500);
    MoveToEx(hDC, 300 - a * 20, 300, NULL);
    LineTo(hDC, 300 - a * 20, 700);

    for (int i = 0; i < 5; i++)
    {
        MoveToEx(hDC, 300 - a * 20 - (i + 1) * 30, 500 - 3, NULL);
        LineTo(hDC, 300 - a * 20 - (i + 1) * 30, 500 + 3);
        MoveToEx(hDC, 300 - a * 20 - 3, 500 + (i + 1) * 30, NULL);
        LineTo(hDC, 300 - a * 20 + 3, 500 + (i + 1) * 30);
        MoveToEx(hDC, 300 - a * 20 + (i + 1) * 30, 500 - 3, NULL);
        LineTo(hDC, 300 - a * 20 + (i + 1) * 30, 500 + 3);
        MoveToEx(hDC, 300 - a * 20 - 3, 500 - (i + 1) * 30, NULL);
        LineTo(hDC, 300 - a * 20 + 3, 500 - (i + 1) * 30);
    }

    for (d = a - 3; d <= b + 3; d += 0.01f) // O(100,85) - center
    {
        MoveToEx(hDC, 30 * d + 300 - a * 20, -30 * cos(d) + 500, NULL);//10 - scale
        LineTo(hDC, 30 * d + 300 - a * 20, -30 * cos(d) + 500);
    }
    SelectObject(hDC, PenR);
    for (d = a - 3; d <= b + 3; d += 0.01f) // O(100,85) - center
    {
        MoveToEx(hDC, 30 * d + 300 - a * 20, -30 * lag(ArrayNodes, d, CountNodes) + 500, NULL);//10 - scale
        LineTo(hDC, 30 * d + 300 - a * 20, -30 * lag(ArrayNodes, d, CountNodes) + 500);
    }

    SelectObject(hDC, PenW);
    MoveToEx(hDC, 700 - a * 30, 500, NULL);
    LineTo(hDC, 1100 - a * 30, 500);
    MoveToEx(hDC, 900 - a * 30, 300, NULL);
    LineTo(hDC, 900 - a * 30, 700);


    for (int i = 0; i < 5; i++)
    {
        MoveToEx(hDC, 900 - a * 30 - (i + 1) * 30, 500 - 3, NULL);
        LineTo(hDC, 900 - a * 30 - (i + 1) * 30, 500 + 3);
        MoveToEx(hDC, 900 - a * 30 - 3, 500 + (i + 1) * 30, NULL);
        LineTo(hDC, 900 - a * 30 + 3, 500 + (i + 1) * 30);
        MoveToEx(hDC, 900 - a * 30 + (i + 1) * 30, 500 - 3, NULL);
        LineTo(hDC, 900 - a * 30 + (i + 1) * 30, 500 + 3);
        MoveToEx(hDC, 900 - a * 30 - 3, 500 - (i + 1) * 30, NULL);
        LineTo(hDC, 900 - a * 30 + 3, 500 - (i + 1) * 30);
    }


    HANDLE handle = GetStdHandle(STD_OUTPUT_HANDLE);

    SetConsoleTextAttribute(handle, FOREGROUND_RED);

    cout << "\t R0 - отн. погр., ";

    SelectObject(hDC, PenR);
    for (d = a; d <= b; d += 0.01f) // O(100,85) - center
    {
        MoveToEx(hDC, 30 * d + 900 - a * 30, -30 * fabs(R0(ArrayNodes, d, CountNodes)) + 500, NULL);//10 - scale
        LineTo(hDC, 30 * d + 900 - a * 30, -30 * fabs(R0(ArrayNodes, d, CountNodes)) + 500);
    }

    SetConsoleTextAttribute(handle, FOREGROUND_GREEN);

    cout << "Rт - точ. погр.";

    SelectObject(hDC, PenG);
    for (d = a; d <= b; d += 0.01f) // O(100,85) - center
    {
        MoveToEx(hDC, 30 * d + 900 - a * 30, -30 * fabs(lag(ArrayNodes, d, CountNodes) - cos(d)) + 500, NULL);//10 - scale
        LineTo(hDC, 30 * d + 900 - a * 30, -30 * fabs(lag(ArrayNodes, d, CountNodes) - cos(d)) + 500);
    }

    cout << "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nВведите количество проверок: ";

    cin >> CountNodes;

    int *n1 = new int[CountNodes];

    cout << "Введите: ";

    for (int i = 0; i < CountNodes; i++)
        cin >> n1[i];

    for (int i = 0; i < CountNodes; i++)
    {
        cout << "При n = " << n1[i] << " max R0 = " << maxf(a, b, n1[i], ans) << "\t" << "; max Rт = " << maxt(a, b, n1[i], ans) << endl;
    }
    delete[] n1;
    system("pause");
    return 0;
}