






'''simple docstring'''







from math import pi, sqrt, tan





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> float:
							if side_length < 0:
														raise ValueError("""surface_area_cube() only accepts non-negative values"""   )
							return 6 * side_length**2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> float:
							if radius < 0:
														raise ValueError("""surface_area_sphere() only accepts non-negative values"""   )
							return 4 * pi * radius**2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> float:
							if radius < 0:
														raise ValueError("""surface_area_hemisphere() only accepts non-negative values"""   )
							return 3 * pi * radius**2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if radius_a < 0 or radius_a < 0 or height < 0:
														raise ValueError(
														    """surface_area_conical_frustum() only accepts non-negative values"""   )
							lowerCamelCase__      :			List[Any] 						= (height**2 + (radius_a - radius_a) ** 2) ** 0.5
							return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if radius < 0 or height < 0:
														raise ValueError("""surface_area_cylinder() only accepts non-negative values"""   )
							return 2 * pi * radius * (height + radius)





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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(UpperCamelCase       ,    2   ) * torus_radius * tube_radius





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if length < 0 or width < 0:
														raise ValueError("""area_rectangle() only accepts non-negative values"""   )
							return length * width





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> float:
							if side_length < 0:
														raise ValueError("""area_square() only accepts non-negative values"""   )
							return side_length**2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if base < 0 or height < 0:
														raise ValueError("""area_triangle() only accepts non-negative values"""   )
							return (base * height) / 2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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"""   )
							lowerCamelCase__      :			Optional[int] 						= (sidea + sidea + sidea) / 2
							lowerCamelCase__      :			Optional[Any] 						= sqrt(
							    semi_perimeter
							    * (semi_perimeter - sidea)
							    * (semi_perimeter - sidea)
							    * (semi_perimeter - sidea)   )
							return area





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if base < 0 or height < 0:
														raise ValueError("""area_parallelogram() only accepts non-negative values"""   )
							return base * height





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> float:
							if radius < 0:
														raise ValueError("""area_circle() only accepts non-negative values"""   )
							return pi * radius**2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if radius_x < 0 or radius_y < 0:
														raise ValueError("""area_ellipse() only accepts non-negative values"""   )
							return pi * radius_x * radius_y





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							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 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> float:
							if not isinstance(UpperCamelCase       ,    UpperCamelCase   ) 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) = }')









'''simple docstring'''







# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase   )   -> Optional[Any]:
							lowerCamelCase__      :			str 						= [False] * len(UpperCamelCase   )
							lowerCamelCase__      :			str 						= [-1] * len(UpperCamelCase   )

							def dfs(UpperCamelCase       ,    UpperCamelCase   ):
														lowerCamelCase__      :			Optional[int] 						= True
														lowerCamelCase__      :			Union[str, Any] 						= c
														for u in graph[v]:
																					if not visited[u]:
																												dfs(UpperCamelCase       ,    1 - c   )

							for i in range(len(UpperCamelCase   )   ):
														if not visited[i]:
																					dfs(UpperCamelCase       ,    0   )

							for i in range(len(UpperCamelCase   )   ):
														for j in graph[i]:
																					if color[i] == color[j]:
																												return False

							return True


# Adjacency list of graph
_A			:    int					  ={0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}



print(check_bipartite_dfs(graph))

