// Root calculation (Newton + Secant method)
#include <iostream>
#include <cmath>
using namespace std;

double f(double x)
{
    return (x-1.)*(x-2.)*(x-3.)*(x-4.)*(x-5.);
}

double fp(double x)
{
    double h = 1E-5;
    return (f(x+h/2.)-f(x-h/2.))/h;
}

int main()
{
    double a = 2.4, fa = f(a);
    double b = 2.5, fb = f(b);
    double c = 3.4, fc = f(c);

    if (fa*fc>0. && (a-b)*(c-b)<0.) {
        cout << "Bad initial boundary.\n";
        return 0;
    }

    for(int step = 0; step<50; step++) {
        double delta = -fb/fp(b);
        double d  = b + delta;
        double fd = f(d);

        if ((d-a)*(d-c)>0. || fabs(fd)>fabs(fb)) {
            if (fa*fb>0.) d = (b+c)*0.5;
            else          d = (a+b)*0.5;
            fd = f(d);
        }

        cout << "Step: " << step <<", root = " << d << ", diff = " << fabs(d-3.) << endl;
        if (fabs(b-d)<1E-14) break;

        b = d; fb = fd;
    }
}