4

#include <iostream>
#include <math.h>
#include <iomanip>
#include <string>

using namespace std;

int precision, spacing;

double x0, eps, k;

double abs(double x)
{
    if (x > 0)
        return x;
    else
        return -x;
}

bool continueWorking()
{
    string response;
    cout << "Continue working?(y,n)";
    cin >> response;
    cout << endl;
    return response == "y" || response == "Y";
}

double f(double x, int k)
{
    return x - k * cos(x);
}

double y1(double x)
{
    return x - 5 * cos(x);
}

double y2(double x)
{
    return x - 10 * cos(x);
}

double derivedF(double x, int k)
{
    return 1 + k * sin(x);
}

void menu()
{
    precision = 0;

    cout << "x0 = ";
    cin >> x0;
    cout << "k = ";
    cin >> k;
    cout << "eps = ";
    cin >> eps;
    cout << endl;

    double counter = eps;
    while(counter < 1)
    {
        precision++;
        counter *= 10;
    }

    spacing = precision + 4;
}

void task()
{
    double current, last, beginOfInterval, endOfInterval, root;

    int n_max = 100000;
    int j = 0;

    menu();

    current = x0;

    do          //Simple
    {
        j++;

        last = current;
        current = last - f(last, k);
    }
    while((abs(last - current) > eps) && (j < n_max));

    cout << "Simple iteration: ";
    cout << fixed << setw(spacing) << setprecision(precision) << current << endl;
    cout << "Number of iterations = " << j << endl << endl;

    j = 0;
    current = x0;

    do      //Neuton
    {
        j++;

        last = current;
        current = last - f(last, k) / derivedF(last, k);
    }
    while((abs(last - current) > eps) && (j < n_max));

    cout << "Neuton method: ";
    cout << fixed << setw(spacing) << setprecision(precision) << current << endl;
    cout << "Number of iterations = " << j << endl << endl;

    j = 0;

    beginOfInterval = -k;   //halving
    endOfInterval = k;
    root = (beginOfInterval + endOfInterval) / 2;

    while(abs(f(root, k) ) > eps)
    {
        j++;

        if (f(beginOfInterval, k) * f(root, k) < 0)
            endOfInterval = root;
        else
            beginOfInterval = root;

        root = (beginOfInterval + endOfInterval) / 2;
    }

    cout << "Halving method: ";
    cout << fixed << setw(spacing) << setprecision(precision) << root << endl;
    cout << "Number of iterations = " << j << endl << endl;
}

int universal(double (*f)(double) )
{
    double beginOfInterval, endOfInterval, root, xl, xr;

    bool hasRoots = false;

    precision = 0;

    cout << "eps (in format 10^) = ";
    cin >> eps;
    cout << "xl = ";
    cin >> xl;
    cout << "xr = ";
    cin >> xr;
    cout << "Roots: " << endl;

    double counter = eps;
    while(counter < 1)
    {
        precision++;
        counter *= 10;
    }

    spacing = precision + 4;

    int j = 0;

    double step = 0.1;

    for(double i = xl; i < xr; i += step)
    {
        beginOfInterval = i;
        endOfInterval = i + step;
        root = (beginOfInterval + endOfInterval) / 2;

        if(f(beginOfInterval) * f(endOfInterval) < 0)
        {
            hasRoots = true;

            while(abs(f(root)) > eps)
            {
                j++;

                if (f(beginOfInterval) * f(root) < 0)
                    endOfInterval = root;
                else
                    beginOfInterval = root;

                root = (beginOfInterval + endOfInterval) / 2;
            }

            cout << fixed << setw(spacing) << setprecision(precision) << root << endl;
        }
    }

    if(hasRoots == false)
        cout << "None." << endl << endl;
    else
        cout << endl;

    return 0;
}

int main()
{
    int answer;

    cout << "We are solving: x - k * cos(x) = 0" << endl;

    do
    {
        cout << "Type 3 to use universal function and any number to do tasks 1 or 2: ";
        cin >> answer;
        cout << endl;

        if(answer == 3)
        {
            universal(y1);
            universal(y2);
        }
        else
            task();
    }
    while(continueWorking());
}