alexey_mod1

#include <iostream>
#include <math.h>
#include <utility>
using namespace std;

typedef pair<double, double> cut;
const double dx = 0.0001;

double f(double x) {
    return pow(sin(x), 2.0) / (2.0 + sin(x));
}

double f_(double x) {
    return (f(x + dx) - f(x)) / dx;
}

double f__(double x) {
    return (f_(x + dx) - f_(x)) / dx;
}

cut Sven(double x0, double h) {
    int k = 1;
    double x1, x2;
    if (f(x0 - h) >= f(x0) && f(x0) >= f(x0 + h)) {
        x1 = x0 + h;
    }
    else if (f(x0 - h) <= f(x0) && f(x0) <= f(x0 + h)) {
        x1 = x0 - h;
        h = -h;
    }
    else if (f(x0 - h) <= f(x0) && f(x0) >= f(x0 + h)) {
        x1 = x0 + h;
    }
    else {
        return cut(x0 - h, x0 + h);
    }

    x2 = x1;
    x1 = x0;
    do {
        x0 = x1;
        x1 = x2;
        x2 = x1 + pow(2.0, k * 1.0) * h;
        k++;
    } while (f(x2) <= f(x1));

    if (h > 0) {
        return cut(x0, x2);
    }
    else {
        return cut(x2, x0);
    }
}

double Newton(cut c, double eps) {
    double x0, x1 = (c.first + c.second) / 2.0;
    do {
        x0 = x1;
        x1 = x0 - f_(x0) / f__(x0);
    } while (abs(x1 - x0) > eps);
    return x1;
}


ostream& operator<<(ostream& out, cut c) {
    out << "(" << c.first << "," << c.second << ")";
    return out;
}

int main(void) {
    cut a = Sven(4, 0.1);
    cout << a << endl;
    cout << Newton(a, 0.001) << endl;
    return 0;
}