





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> None:




    """simple docstring"""




    _A     =							generate_pascal_triangle(_SCREAMING_SNAKE_CASE				)
    for row_idx in range(_SCREAMING_SNAKE_CASE				):
        # Print left spaces
        for _ in range(num_rows - row_idx - 1				):
            print(end=' '				)
        # Print row values
        for col_idx in range(row_idx + 1				):
            if col_idx != row_idx:
                print(triangle[row_idx][col_idx]							,     end=' '				)
            else:
                print(triangle[row_idx][col_idx]							,     end=''				)
        print()





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> list[list[int]]:




    """simple docstring"""




    if not isinstance(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				):
        raise TypeError('The input value of \'num_rows\' should be \'int\''				)

    if num_rows == 0:
        return []
    elif num_rows < 0:
        raise ValueError(
            'The input value of \'num_rows\' should be greater than or equal to 0'				)

    _A     =							[]
    for current_row_idx in range(_SCREAMING_SNAKE_CASE				):
        _A     =							populate_current_row(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
        triangle.append(_SCREAMING_SNAKE_CASE				)
    return triangle





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> list[int]:




    """simple docstring"""




    _A     =							[-1] * (current_row_idx + 1)
    # first and last elements of current row are equal to 1
    _A,			_A     =							1, 1
    for current_col_idx in range(1							,     _SCREAMING_SNAKE_CASE				):
        calculate_current_element(
            _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
    return current_row





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     )							-> None:




    """simple docstring"""




    _A     =							triangle[current_row_idx - 1][current_col_idx - 1]
    _A     =							triangle[current_row_idx - 1][current_col_idx]
    _A     =							above_to_left_elt + above_to_right_elt





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> list[list[int]]:




    """simple docstring"""




    if not isinstance(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				):
        raise TypeError('The input value of \'num_rows\' should be \'int\''				)

    if num_rows == 0:
        return []
    elif num_rows < 0:
        raise ValueError(
            'The input value of \'num_rows\' should be greater than or equal to 0'				)

    _A     =							[[1]]

    for row_index in range(1							,     _SCREAMING_SNAKE_CASE				):
        _A     =							[0] + result[-1] + [0]
        _A     =							row_index + 1
        # Calculate the number of distinct elements in a row
        _A     =							sum(divmod(_SCREAMING_SNAKE_CASE							,     2				)				)
        _A     =							[
            temp_row[i - 1] + temp_row[i] for i in range(1							,     distinct_elements + 1				)
        ]
        _A     =							row_first_half[: (row_index + 1) // 2]
        row_second_half.reverse()
        _A     =							row_first_half + row_second_half
        result.append(_SCREAMING_SNAKE_CASE				)

    return result





def 				__lowerCAmelCase(       )							-> None:




    """simple docstring"""




    from collections.abc import Callable
    from timeit import timeit

    def benchmark_a_function(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				) -> None:
        _A     =							F"{func.__name__}({value})"
        _A     =							timeit(F"__main__.{call}"							,     setup='import __main__'				)
        # print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
        print(F"{call:38} -- {timing:.4f} seconds"				)

    for value in range(15				):  # (1, 7, 14):
        for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
            benchmark_a_function(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
        print()


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()












from math import pi, sqrt, tan





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if side_length < 0:
        raise ValueError('surface_area_cube() only accepts non-negative values'				)
    return 6 * side_length**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if length < 0 or breadth < 0 or height < 0:
        raise ValueError('surface_area_cuboid() only accepts non-negative values'				)
    return 2 * ((length * breadth) + (breadth * height) + (length * height))





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('surface_area_sphere() only accepts non-negative values'				)
    return 4 * pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('surface_area_hemisphere() only accepts non-negative values'				)
    return 3 * pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0 or height < 0:
        raise ValueError('surface_area_cone() only accepts non-negative values'				)
    return pi * radius * (radius + (height**2 + radius**2) ** 0.5)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius_a < 0 or radius_a < 0 or height < 0:
        raise ValueError(
            'surface_area_conical_frustum() only accepts non-negative values'				)
    _A     =							(height**2 + (radius_a - radius_a) ** 2) ** 0.5
    return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0 or height < 0:
        raise ValueError('surface_area_cylinder() only accepts non-negative values'				)
    return 2 * pi * radius * (height + radius)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if torus_radius < 0 or tube_radius < 0:
        raise ValueError('surface_area_torus() only accepts non-negative values'				)
    if torus_radius < tube_radius:
        raise ValueError(
            'surface_area_torus() does not support spindle or self intersecting tori'				)
    return 4 * pow(_SCREAMING_SNAKE_CASE							,     2				) * torus_radius * tube_radius





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




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





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if side_length < 0:
        raise ValueError('area_square() only accepts non-negative values'				)
    return side_length**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if base < 0 or height < 0:
        raise ValueError('area_triangle() only accepts non-negative values'				)
    return (base * height) / 2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if sidea < 0 or sidea < 0 or sidea < 0:
        raise ValueError('area_triangle_three_sides() only accepts non-negative values'				)
    elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
        raise ValueError('Given three sides do not form a triangle'				)
    _A     =							(sidea + sidea + sidea) / 2
    _A     =							sqrt(
        semi_perimeter
        * (semi_perimeter - sidea)
        * (semi_perimeter - sidea)
        * (semi_perimeter - sidea)				)
    return area





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if base < 0 or height < 0:
        raise ValueError('area_parallelogram() only accepts non-negative values'				)
    return base * height





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if basea < 0 or basea < 0 or height < 0:
        raise ValueError('area_trapezium() only accepts non-negative values'				)
    return 1 / 2 * (basea + basea) * height





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius < 0:
        raise ValueError('area_circle() only accepts non-negative values'				)
    return pi * radius**2





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if radius_x < 0 or radius_y < 0:
        raise ValueError('area_ellipse() only accepts non-negative values'				)
    return pi * radius_x * radius_y





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if diagonal_a < 0 or diagonal_a < 0:
        raise ValueError('area_rhombus() only accepts non-negative values'				)
    return 1 / 2 * diagonal_a * diagonal_a





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> float:




    """simple docstring"""




    if not isinstance(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				) or sides < 3:
        raise ValueError(
            'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'				)
    elif length < 0:
        raise ValueError(
            'area_reg_polygon() only accepts non-negative values as \
length of a side'				)
    return (sides * length**2) / (4 * tan(pi / sides				))
    return (sides * length**2) / (4 * tan(pi / sides				))


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

 print("[DEMO] Areas of various geometric shapes: \n")
 print(f"Rectangle: {area_rectangle(10, 20) = }")
 print(f"Square: {area_square(10) = }")
 print(f"Triangle: {area_triangle(10, 10) = }")
 print(f"Triangle: {area_triangle_three_sides(5, 12, 13) = }")
 print(f"Parallelogram: {area_parallelogram(10, 20) = }")
 print(f"Rhombus: {area_rhombus(10, 20) = }")
 print(f"Trapezium: {area_trapezium(10, 20, 30) = }")
 print(f"Circle: {area_circle(20) = }")
 print(f"Ellipse: {area_ellipse(10, 20) = }")
 print("\nSurface Areas of various geometric shapes: \n")
 print(f"Cube: {surface_area_cube(20) = }")
 print(f"Cuboid: {surface_area_cuboid(10, 20, 30) = }")
 print(f"Sphere: {surface_area_sphere(20) = }")
 print(f"Hemisphere: {surface_area_hemisphere(20) = }")
 print(f"Cone: {surface_area_cone(10, 20) = }")
 print(f"Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }")
 print(f"Cylinder: {surface_area_cylinder(10, 20) = }")
 print(f"Torus: {surface_area_torus(20, 10) = }")
 print(f"Equilateral Triangle: {area_reg_polygon(3, 10) = }")
 print(f"Square: {area_reg_polygon(4, 10) = }")
 print(f"Reqular Pentagon: {area_reg_polygon(5, 10) = }")





