#include <cmath>
#include <iostream>
#include <iomanip>

using namespace std;

void inputdata(double* a, double* b, double* h, double* esp);

double function(double x);

double function_2(double x);

double Dfunction_2(double x);

double function_3(double x);

double Dfunction_3(double x);

double Wegstein(double(*f)(double), double x0, double x1, double eps, int& i_counter);

double New(double(*function_2)(double), double (*Dfunction_2)(double), double x0, double eps, int& i_counter);

double Sec(double(*f)(double), double x0, double x1, double eps, int& num);


int main()
{
    double a = 0, b = 0, h = 0, esp = 0, x = 0;
    int counter = 0, i_counter = 0;
    setlocale(LC_ALL, "ru");
    cout << "1 - x^3 + 10*x^2 - 50 методом Вегстейна" << "          По умолчанию: a = -12, b = 5, h = 0.1, esp = 0.01" << endl;
    cout << "2 - log(x) - 5 * cos(x) методом секущих" << "          По умолчанию: a = 1, b = 8, h = 0.1, esp = 0.01" << endl;
    cout << "3 - x^3 + 5x^2 + 12 методом Ньютона"     << "              По умолчанию: a = -2, b = 5, h = 0.1, esp = 0.01" << endl;
    cout << "Выберите функцию: " << endl;
    char action;
    cin >> action;
    if (action == '1')
    {
        cout << "Использовать значения по умолчанию(1), ввести вручную" << endl;
        char symbol; cin >> symbol;
        if (symbol == '1')
            a = -12, b = 5, h = 0.1, esp = 0.01;
        else
            inputdata(&a, &b, &h, &esp);
        cout << "Корни\tЗначение х \tКорень \t Кол-во итераций" << endl;
        double i = a;
        while (i <= b)
        {
            if (function(i) * function(i + h) < 0)
            {
                counter++;
                x = Wegstein(function, i, i + h, esp, i_counter);
                cout << setw(4) << counter << setw(10) << i << setw(17) << x << setw(10) << i_counter << endl;
            }
            i += h;
        }
        if (counter == 0)
            cout << "На данном отрезке корней нет!";
    }
    else if (action == '2')
    {
        cout << "Использовать значения по умолчанию(1), ввести вручную" << endl;
        char symbol; cin >> symbol;
        if (symbol == '1')
            a = 1, b = 8, h = 0.1, esp = 0.001;
        else
            inputdata(&a, &b, &h, &esp);
        double i2 = a;
        cout << "Корни\tЗначение х \tКорень \t Кол-во итераций" << endl;
        while (i2 <= b)
        {
            if (function_2(i2) * function_2(i2 + h) < 0)
            {
                counter++;
                x = Sec(function_2, i2, b, esp, i_counter);
                cout << setw(4) << counter << setw(10) << i2 << setw(17) << x << setw(10) << i_counter << endl;
            }
            i2 += h;
        }
        if (counter == 0)
            cout << "На данном отрезке корней нет!";

    } else if (action == '3') {
        cout << "Использовать значения по умолчанию(1), ввести вручную" << endl;
        char symbol; cin >> symbol;
        if (symbol == '1')
            a = -2, b = 5, h = 0.1, esp = 0.001;
        else
            inputdata(&a, &b, &h, &esp);
        double i2 = a;
        cout << "Корни\tЗначение х \tКорень \t Кол-во итераций" << endl;
        while (i2 <= b)
        {
            if (function_3(i2) * function_3(i2 + h) < 0)
            {
                counter++;
                x = New(function_3, Dfunction_3, i2, esp, i_counter);
                cout << setw(4) << counter << setw(10) << i2 << setw(17) << x << setw(22) << setw(10) << i_counter << endl;
            }
            i2 += h;
        }
        if (counter == 0)
            cout << "На данном отрезке корней нет!";
    }


}

void inputdata(double* a, double* b, double* h, double* esp)
{

    cout << "Введите начало отрезка: ";
    cin >> *a;
    do
    {
        cout << "Введите конец отрезка: ";
        cin >> *b;
    } while (*b <= *a);
    do
    {
        cout << "введите шаг: ";
        cin >> *h;
    } while (fabs(*b - *a) < *h || *h <= 0);
    do
    {
        cout << "Введите точность: ";
        cin >> *esp;
    } while (*esp > *h);
}

double function(double x)
{
    return x * x * x + 10 * x * x - 50;
}

double function_2(double x)
{
    return log(x) - 5 * cos(x);
}

double function_3(double param) {
    return pow(param, 3.) - 5.*pow(param, 2.) + 12.;
}

double Dfunction_3(double param) {
    return 3.*pow(param, 2.) - 10.*param;
}

double Wegstein(double(*function)(double), double x0, double x1, double eps, int& i_counter)
{
    double fx0 = 0, fx1 = 0, x2 = 0, de = 1;
    fx0 = function(x0);	   fx1 = function(x1);
    while (de > eps)
    {
        x2 = x1 - fx1 * (x1 - x0) / (fx1 - fx0);
        de = fabs(x1 - x2);
        fx0 = fx1;
        fx1 = function(x2);
        x0 = x1;
        x1 = x2;
        i_counter++;
    }
    return x2;
}

double Sec(double(*function_2)(double), double x0, double x1, double eps, int& i_counter)
{
    double fx0 = 0, fx1 = 0;
    fx0 = function_2(x0);	   fx1 = function_2(x1);
    while (fabs(x0-x1) > eps)
    {
        i_counter++;
        x1 = x0 - (x0 - x1) * fx0 / (fx0 - fx1);
    }
    return x1;
}

double New(double(*function_2)(double), double (*Dfunction_2)(double), double x0, double eps, int& i_counter)
{
    double x1 = x0 - function_2(x0) / Dfunction_2(x0);
    while (fabs(x0 - x1) > eps)
    {
        i_counter++;
        x0 = x1;
        x1 = x0 - function_2(x0) / Dfunction_2(x0);
    }
    return x1;
}