MethodMath

#include <iostream>
#include <cmath>
#include <math.h>

using namespace std;

double MethodHalf();
double SimpleIteration();
double function(double x);

int main()
{
    int menu = 0;
    cout << "Methods:\n1.Half-division Method\n2.Simple Iteration Method\nChoice: "; cin >> menu;
    if (menu == 1) { MethodHalf(); }
    if (menu == 2) { SimpleIteration(); }


    return 0;
}

double function(double x)
{
    return pow(x, 3) + 3 * x + 1;
}

double MethodHalf()
{
    int n = 0;
    double a = 0, b = 0, eps = 0, c = 0;
    cout << "~~~~Half Division Method~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    if (function(a) * function(b) > 0)
    {
        cout << "#Error# Wrong interval\n";
        return 0;
    }
    cout << "Enter eps: "; cin >> eps; cout << endl;
    cout << "Left border: " << a << " || Right border: " << b << " || Eps: " << eps << endl;
    cout << "Equation: x^3 + 3*x + 1 = 0\n";

    do
    {
        c = (a + b) / 2;
        if (function(c) * function(a) <= 0) b = c;
        else a = c;
        n += 1;
    } while (fabs(a - b) >= eps);

    cout << "\n~~~~Result~~~~\n";
    cout << "Root of the equation: " << c << endl;
    cout << "Number of iteration: " << n << endl;
    cout << "Checking the resulting root: " << function(c) << endl;
}

double SimpleIteration()
{
    int n = 0;
    double a = 0, b = 0, eps = 0, c = 0, x1 = 0, x0 = 0;
    cout << "~~~~Simple Iteration Method~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    cout << "Enter eps: "; cin >> eps; cout << endl;
    cout << "Enter X1: "; cin >> x1; cout << endl;
    cout << "Left border: " << a << " || Right border: " << b << " || Eps: " << eps << endl;
    cout << "Equation: x^3 + 3*x + 1 = 0\n";

    //c = (a + b) / 2;
    do
    {
        n++;
        x0 = x1;
        x1 = function(x0);

    } while (fabs(x1 - x0) <= eps);

    cout << "\n~~~~Result~~~~\n";
    cout << "Root of the equation: " << c << endl;
    cout << "Number of iteration: " << n << endl;
    cout << "Checking the resulting root: " << function(c) << endl;
    return 0;
}