import sys


def get_num(min_val, max_val):
    while True:
        try:
            num = float(input().strip())
            if num <= min_val:
                print("Введенное число должно быть больше " + str(min_val))
            elif num >= max_val:
                print("Введенное число должно быть меньше " + str(max_val))
            else:
                return num
        except ValueError:
            print("Неверные входные данные! Повторите ввод")


def func(x):
    return x * x * x - 3 * x - 3


def find_point(a, b):
    a1 = a
    b1 = b
    eps = 0.0000000001
    while b1 - a1 >= eps:
        delta = (b1 - a1) / 4
        u1 = (a1 + b1 - delta) / 2
        u2 = (a1 + b1 + delta) / 2
        i1 = func(u1)
        i2 = func(u2)
        if i1 <= i2:
            b1 = u2
        if i1 >= i2:
            a1 = u1
    return (b1 + a1) / 2


def find_golden_point(a, b):
    eps = 0.0000000001
    phi = (5 ** 0.5 - 1) / 2
    u1 = (b - a) * phi ** 2 + a
    u2 = (b - a) * phi + a
    i1 = func(u1)
    i2 = func(u2)
    while b - a > eps:
        if i1 > i2:
            a = u1
            u1 = u2
            i1 = i2
            u2 = phi * (b - a) + a
            i2 = func(u2)
        else:
            b = u2
            u2 = u1
            u1 = a + (b - a) * phi ** 2
            i2 = i1
            i1 = func(u1)
    u = (a + b) / 2
    return u


# ПАРАБОЛ
def find_point_parabola(a, b):
    u_0 = (b - a) / 2
    n = 1000
    h = (b - a) / n
    eps = 0.00000001
    w = eps * 100
    w_pred = 0

    while abs(w - w_pred) > eps:
        f0 = func(u_0)
        u_1 = u_0 + h
        f1 = func(u_1)

        if f1 < f0:
            u_2 = u_1 + h
        else:
            u_1 = u_0 - h
            f1 = func(u_1)
            u_2 = u_1 - h
        f2 = func(u_2)
        w_pred = w
        w = -0.5 * ((f1 - f0) * (u_2 ** 2) + (f0 - f2) * (u_1 ** 2) + (f2 - f1) * (u_0 ** 2)) / \
            ((f0 - f1) * u_2 + (f2 - f0) * u_1 + (f1 - f2) * u_0)
        u_0 = w

    return w


# ГРАДИЕНТНЫЙ
def func2(x, y):
    # return 3 * x * x + 4 * y * y + 1
    return (8 * x * x + 5 * y * y + 10) ** 0.5


def func2_deriv_x(x, y):
    return 16 * x
    # return (func2(x + 0.0000001, y) - func2(x - 0.0000001, y)) / (2 * 0.0000001)


def func2_deriv_y(x, y):
    return 10 * y
    # return (func2(x, y + 0.0000001) - func2(x, y - 0.0000001)) / (2 * 0.0000001)


def norma(x, y):
    # return (x * x + y * y) ** 0.5
    return (func2_deriv_x(x, y) ** 2 + func2_deriv_y(x, y) ** 2) ** 0.5


def find_gradient():
    x0 = 10
    y0 = 20
    h = 0.00001
    f0 = func2(x0, y0)
    eps = 0.0000000001

    while True:
        grad_x_prev = func2_deriv_x(x0, y0)
        grad_y_prev = func2_deriv_y(x0, y0)

        x1 = x0 - h * grad_x_prev
        y1 = y0 - h * grad_y_prev

        grad_x = func2_deriv_x(x1, y1)
        grad_y = func2_deriv_y(x1, y1)
        if norma((grad_x - grad_x_prev), (grad_y - grad_y_prev)) < eps:
            break
        f1 = func2(x1, y1)
        if f1 > f0:
            h = h / 10
        else:
            x0 = x1
            y0 = y1
            f0 = f1
    print("Точка: (" + str(format(x0, ".7f")) + ", " + str(format(y0, ".7f")) + ")")
    print("Значение функции: " + str(func2(x0, y0)))
    return x0, y0


# print("Функция: x^3 - 3x + 1")


find_gradient()
print("Введите левую границу")
a = get_num(sys.float_info.max * (-1), sys.float_info.max)

print("Введите правую границу")
b = get_num(a, sys.float_info.max)

print("Точка минимума: " + str(find_point_parabola(a, b)))
print("Значение функции: " + str(func(find_point_parabola(a, b))))