






from math import pi, sqrt, tan


def __A    (      __lowerCAmelCase	)->  float:





						"""simple docstring"""



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


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





						"""simple docstring"""



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


def __A    (      __lowerCAmelCase	)->  float:





						"""simple docstring"""



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


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  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 __A    (      __lowerCAmelCase ,		__lowerCAmelCase ,		__lowerCAmelCase	)->  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'	)
						_UpperCAmelCase									=			(height**2 + (radius_a - radius_a) ** 2) ** 0.5
						return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  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 __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  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(__lowerCAmelCase ,		2	) * torus_radius * tube_radius


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  float:





						"""simple docstring"""



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


def __A    (      __lowerCAmelCase	)->  float:





						"""simple docstring"""



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


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  float:





						"""simple docstring"""



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


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase ,		__lowerCAmelCase	)->  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'	)
						_UpperCAmelCase									=			(sidea + sidea + sidea) / 2
						_UpperCAmelCase									=			sqrt(
						    semi_perimeter
						    * (semi_perimeter - sidea)
						    * (semi_perimeter - sidea)
						    * (semi_perimeter - sidea)	)
						return area


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  float:





						"""simple docstring"""



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


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





						"""simple docstring"""



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


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





						"""simple docstring"""



						if not isinstance(__lowerCAmelCase ,		__lowerCAmelCase	) 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) = }''')








from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat


def __A    (      )->  tuple[list[int], int]:





						"""simple docstring"""



						_UpperCAmelCase									=			[randint(-1_000 ,		1_000	) for i in range(10	)]
						_UpperCAmelCase									=			randint(-5_000 ,		5_000	)
						return (arr, r)


_a      	=  make_dataset()


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  tuple[int, ...]:





						"""simple docstring"""



						for triplet in permutations(__lowerCAmelCase ,		3	):
												if sum(__lowerCAmelCase	) == target:
																		return tuple(sorted(__lowerCAmelCase	)	)
						return (0, 0, 0)


def __A    (      __lowerCAmelCase ,		__lowerCAmelCase	)->  tuple[int, int, int]:





						"""simple docstring"""



						arr.sort()
						_UpperCAmelCase									=			len(__lowerCAmelCase	)
						for i in range(n - 1	):
												_UpperCAmelCase					, _UpperCAmelCase									=			i + 1, n - 1
												while left < right:
																		if arr[i] + arr[left] + arr[right] == target:
																								return (arr[i], arr[left], arr[right])
																		elif arr[i] + arr[left] + arr[right] < target:
																								left += 1
																		elif arr[i] + arr[left] + arr[right] > target:
																								right -= 1
						return (0, 0, 0)


def __A    (      )->  tuple[float, float]:





						"""simple docstring"""



						_UpperCAmelCase									=			'\nfrom __main__ import dataset, triplet_sum1, triplet_sum2\n'
						_UpperCAmelCase									=			'\ntriplet_sum1(*dataset)\n'
						_UpperCAmelCase									=			'\ntriplet_sum2(*dataset)\n'
						_UpperCAmelCase									=			repeat(setup=__lowerCAmelCase ,		stmt=__lowerCAmelCase ,		repeat=5 ,		number=10_000	)
						_UpperCAmelCase									=			repeat(setup=__lowerCAmelCase ,		stmt=__lowerCAmelCase ,		repeat=5 ,		number=10_000	)
						return (min(__lowerCAmelCase	), min(__lowerCAmelCase	))


if __name__ == "__main__":
		from doctest import testmod

		testmod()
		_a      	=  solution_times()
		print(F'''The time for naive implementation is {times[0]}.''')
		print(F'''The time for optimized implementation is {times[1]}.''')
