

def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						list[int]				):





    """simple docstring"""


    if len(_SCREAMING_SNAKE_CASE				) == 1:
        return a[0], a[0]
    else:
        # split A into half.
        SCREAMING_SNAKE_CASE_													=  a[: len(_SCREAMING_SNAKE_CASE				) // 2]
        SCREAMING_SNAKE_CASE_													=  a[len(_SCREAMING_SNAKE_CASE				) // 2 :]

        # 2 sub problems, 1/2 of original size.
        SCREAMING_SNAKE_CASE_							,	SCREAMING_SNAKE_CASE_													=  max_difference(_SCREAMING_SNAKE_CASE				)
        SCREAMING_SNAKE_CASE_							,	SCREAMING_SNAKE_CASE_													=  max_difference(_SCREAMING_SNAKE_CASE				)

        # get min of first and max of second
        # linear time
        SCREAMING_SNAKE_CASE_													=  min(_SCREAMING_SNAKE_CASE				)
        SCREAMING_SNAKE_CASE_													=  max(_SCREAMING_SNAKE_CASE				)

        # 3 cases, either (small1, big1),
        # (min_first, max_second), (small2, big2)
        # constant comparisons
        if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
            return smalla, biga
        elif biga - smalla > max_second - min_first:
            return smalla, biga
        else:
            return min_first, max_second


if __name__ == "__main__":
       import doctest

       doctest.testmod()





from __future__ import annotations

from math import pi, pow


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						int | float				):





    """simple docstring"""


    if side_length < 0:
        raise ValueError('vol_cube() only accepts non-negative values'				)
    return pow(_SCREAMING_SNAKE_CASE       ,      3				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or radius < 0:
        raise ValueError('vol_spherical_cap() only accepts non-negative values'				)
    # Volume is 1/3 pi * height squared * (3 * radius - height)
    return 1 / 3 * pi * pow(_SCREAMING_SNAKE_CASE       ,      2				) * (3 * radius - height)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if radius_a < 0 or radius_a < 0 or centers_distance < 0:
        raise ValueError('vol_spheres_intersect() only accepts non-negative values'				)
    if centers_distance == 0:
        return vol_sphere(min(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)				)

    SCREAMING_SNAKE_CASE_													=  (
        (radius_a - radius_a + centers_distance)
        * (radius_a + radius_a - centers_distance)
        / (2 * centers_distance)
    )
    SCREAMING_SNAKE_CASE_													=  (
        (radius_a - radius_a + centers_distance)
        * (radius_a + radius_a - centers_distance)
        / (2 * centers_distance)
    )

    return vol_spherical_cap(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				) + vol_spherical_cap(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
        raise ValueError(
            'vol_spheres_union() only accepts non-negative values, non-zero radius'				)

    if centers_distance == 0:
        return vol_sphere(max(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)				)

    return (
        vol_sphere(_SCREAMING_SNAKE_CASE				)
        + vol_sphere(_SCREAMING_SNAKE_CASE				)
        - vol_spheres_intersect(_SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE       ,      _SCREAMING_SNAKE_CASE				)
    )


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if width < 0 or height < 0 or length < 0:
        raise ValueError('vol_cuboid() only accepts non-negative values'				)
    return float(width * height * length				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or area_of_base < 0:
        raise ValueError('vol_cone() only accepts non-negative values'				)
    return area_of_base * height / 3.0


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or radius < 0:
        raise ValueError('vol_right_circ_cone() only accepts non-negative values'				)
    return pi * pow(_SCREAMING_SNAKE_CASE       ,      2				) * height / 3.0


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or area_of_base < 0:
        raise ValueError('vol_prism() only accepts non-negative values'				)
    return float(area_of_base * height				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or area_of_base < 0:
        raise ValueError('vol_pyramid() only accepts non-negative values'				)
    return area_of_base * height / 3.0


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if radius < 0:
        raise ValueError('vol_sphere() only accepts non-negative values'				)
    # Volume is 4/3 * pi * radius cubed
    return 4 / 3 * pi * pow(_SCREAMING_SNAKE_CASE       ,      3				)


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if radius < 0:
        raise ValueError('vol_hemisphere() only accepts non-negative values'				)
    # Volume is radius cubed * pi * 2/3
    return pow(_SCREAMING_SNAKE_CASE       ,      3				) * pi * 2 / 3


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if height < 0 or radius < 0:
        raise ValueError('vol_circular_cylinder() only accepts non-negative values'				)
    # Volume is radius squared * height * pi
    return pow(_SCREAMING_SNAKE_CASE       ,      2				) * height * pi


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if inner_radius < 0 or outer_radius < 0 or height < 0:
        raise ValueError(
            'vol_hollow_circular_cylinder() only accepts non-negative values'				)
    if outer_radius <= inner_radius:
        raise ValueError('outer_radius must be greater than inner_radius'				)
    return pi * (pow(_SCREAMING_SNAKE_CASE       ,      2				) - pow(_SCREAMING_SNAKE_CASE       ,      2				)) * height


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if radius_a < 0 or radius_a < 0 or height < 0:
        raise ValueError('vol_conical_frustum() only accepts non-negative values'				)
    return (
        1
        / 3
        * pi
        * height
        * (pow(_SCREAMING_SNAKE_CASE       ,      2				) + pow(_SCREAMING_SNAKE_CASE       ,      2				) + radius_a * radius_a)
    )


def     _UpperCAmelCase				(     _SCREAMING_SNAKE_CASE    :						float       ,      _SCREAMING_SNAKE_CASE    :						float				):





    """simple docstring"""


    if torus_radius < 0 or tube_radius < 0:
        raise ValueError('vol_torus() only accepts non-negative values'				)
    return 2 * pow(_SCREAMING_SNAKE_CASE       ,      2				) * torus_radius * pow(_SCREAMING_SNAKE_CASE       ,      2				)


def     _UpperCAmelCase				(     ):





    """simple docstring"""


    print('Volumes:'				)
    print(f"""Cube: {vol_cube(2				) = }"""				)  # = 8
    print(f"""Cuboid: {vol_cuboid(2       ,      2       ,      2				) = }"""				)  # = 8
    print(f"""Cone: {vol_cone(2       ,      2				) = }"""				)  # ~= 1.33
    print(f"""Right Circular Cone: {vol_right_circ_cone(2       ,      2				) = }"""				)  # ~= 8.38
    print(f"""Prism: {vol_prism(2       ,      2				) = }"""				)  # = 4
    print(f"""Pyramid: {vol_pyramid(2       ,      2				) = }"""				)  # ~= 1.33
    print(f"""Sphere: {vol_sphere(2				) = }"""				)  # ~= 33.5
    print(f"""Hemisphere: {vol_hemisphere(2				) = }"""				)  # ~= 16.75
    print(f"""Circular Cylinder: {vol_circular_cylinder(2       ,      2				) = }"""				)  # ~= 25.1
    print(f"""Torus: {vol_torus(2       ,      2				) = }"""				)  # ~= 157.9
    print(f"""Conical Frustum: {vol_conical_frustum(2       ,      2       ,      4				) = }"""				)  # ~= 58.6
    print(f"""Spherical cap: {vol_spherical_cap(1       ,      2				) = }"""				)  # ~= 5.24
    print(f"""Spheres intersetion: {vol_spheres_intersect(2       ,      2       ,      1				) = }"""				)  # ~= 21.21
    print(f"""Spheres union: {vol_spheres_union(2       ,      2       ,      1				) = }"""				)  # ~= 45.81
    print(
        f"""Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1       ,      2       ,      3				) = }"""				)  # ~= 28.3


if __name__ == "__main__":
       main()


