


'''simple docstring'''
class 						_lowerCamelCase					:




 '''simple docstring'''


 def __init__(      self						):

       """simple docstring"""







       __A  :		Optional[int]       =			0
       __A  :		Optional[Any]       =			0
       __A  :		Dict       =			{}


 def  snake_case__   (      self      ,      __lowercase						):

       """simple docstring"""







       if vertex not in self.adjacency:
             __A  :		Union[str, Any]       =			{}
             self.num_vertices += 1


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase      ,      __lowercase						):

       """simple docstring"""







       self.add_vertex(__lowerCamelCase						)
       self.add_vertex(__lowerCamelCase						)

       if head == tail:
             return

       __A  :		Tuple       =			weight
       __A  :		Optional[Any]       =			weight


 def  snake_case__   (      self						):

       """simple docstring"""







       __A  :		Union[str, Any]       =			self.get_edges()
       for edge in edges:
             __A  :		Union[str, Any]       =			edge
             edges.remove((tail, head, weight)						)
       for i in range(len(__lowerCamelCase						)						):
             __A  :		Optional[Any]       =			list(edges[i]						)

       edges.sort(key=lambda __lowercase						: e[2]						)
       for i in range(len(__lowerCamelCase						) - 1						):
             if edges[i][2] >= edges[i + 1][2]:
                   __A  :		str       =			edges[i][2] + 1
       for edge in edges:
             __A  :		Dict       =			edge
             __A  :		List[str]       =			weight
             __A  :		Union[str, Any]       =			weight


 def __str__(      self						):

       """simple docstring"""







       __A  :		Tuple       =			""
       for tail in self.adjacency:
             for head in self.adjacency[tail]:
                   __A  :		Dict       =			self.adjacency[head][tail]
                   string += F"""{head} -> {tail} == {weight}\n"""
       return string.rstrip('\n'						)


 def  snake_case__   (      self						):

       """simple docstring"""







       __A  :		Optional[int]       =			[]
       for tail in self.adjacency:
             for head in self.adjacency[tail]:
                   output.append((tail, head, self.adjacency[head][tail])						)
       return output


 def  snake_case__   (      self						):

       """simple docstring"""







       return self.adjacency.keys()


 @staticmethod
 def  snake_case__   (      __lowercase=None      ,      __lowercase=None						):

       """simple docstring"""







       __A  :		int       =			Graph()
       if vertices is None:
             __A  :		int       =			[]
       if edges is None:
             __A  :		Any       =			[]
       for vertex in vertices:
             g.add_vertex(__lowerCamelCase						)
       for edge in edges:
             g.add_edge(*__lowerCamelCase						)
       return g

 class 						_lowerCamelCase					:




  '''simple docstring'''


  def __init__(      self						):

        """simple docstring"""







        __A  :		Tuple       =			{}
        __A  :		Optional[Any]       =			{}


  def __len__(      self						):

        """simple docstring"""







        return len(self.parent						)


  def  snake_case__   (      self      ,      __lowercase						):

        """simple docstring"""







        if item in self.parent:
              return self.find(__lowerCamelCase						)

        __A  :		Union[str, Any]       =			item
        __A  :		List[str]       =			0
        return item


  def  snake_case__   (      self      ,      __lowercase						):

        """simple docstring"""







        if item not in self.parent:
              return self.make_set(__lowerCamelCase						)
        if item != self.parent[item]:
              __A  :		Any       =			self.find(self.parent[item]						)
        return self.parent[item]







  def  snake_case__   (      self      ,      __lowercase      ,      __lowercase						):

        """simple docstring"""







        __A  :		int       =			self.find(__lowerCamelCase						)
        __A  :		int       =			self.find(__lowerCamelCase						)

        if roota == roota:
              return roota

        if self.rank[roota] > self.rank[roota]:
              __A  :		int       =			roota
              return roota

        if self.rank[roota] < self.rank[roota]:
              __A  :		Union[str, Any]       =			roota
              return roota

        if self.rank[roota] == self.rank[roota]:
              self.rank[roota] += 1
              __A  :		Any       =			roota
              return roota
        return None


 @staticmethod
 def  snake_case__   (      __lowercase						):

       """simple docstring"""







       __A  :		Any       =			graph.num_vertices

       __A  :		Any       =			Graph.UnionFind()
       __A  :		Dict       =			[]
       while num_components > 1:
             __A  :		Dict       =			{}
             for vertex in graph.get_vertices():
                   __A  :		List[str]       =			-1

             __A  :		List[str]       =			graph.get_edges()
             for edge in edges:
                   __A  :		List[str]       =			edge
                   edges.remove((tail, head, weight)						)
             for edge in edges:
                   __A  :		List[str]       =			edge
                   __A  :		Tuple       =			union_find.find(__lowerCamelCase						)
                   __A  :		List[str]       =			union_find.find(__lowerCamelCase						)
                   if seta != seta:
                         if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
                               __A  :		int       =			[head, tail, weight]

                         if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
                               __A  :		List[Any]       =			[head, tail, weight]
             for vertex in cheap_edge:
                   if cheap_edge[vertex] != -1:
                         __A  :		List[str]       =			cheap_edge[vertex]
                         if union_find.find(__lowerCamelCase						) != union_find.find(__lowerCamelCase						):
                               union_find.union(__lowerCamelCase      ,      __lowerCamelCase						)
                               mst_edges.append(cheap_edge[vertex]						)
                               __A  :		int       =			num_components - 1
       __A  :		Union[str, Any]       =			Graph.build(edges=__lowerCamelCase						)
       return mst










'''simple docstring'''
from math import pi, sqrt, tan


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


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


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


def 			_lowercase       (				UpperCamelCase__       :					float,				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 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if radius_a < 0 or radius_a < 0 or height < 0:
  raise ValueError(
      'surface_area_conical_frustum() only accepts non-negative values'			)
 __A  :		Optional[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 			_lowercase       (				UpperCamelCase__       :					float,				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 			_lowercase       (				UpperCamelCase__       :					float,				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 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float			):
 if length < 0 or width < 0:
  raise ValueError('area_rectangle() only accepts non-negative values'			)
 return length * width


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


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


def 			_lowercase       (				UpperCamelCase__       :					float,				UpperCamelCase__       :					float,				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'			)
 __A  :		int       =			(sidea + sidea + sidea) / 2
 __A  :		List[Any]       =			sqrt(
     semi_perimeter
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)			)
 return area


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


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


def 			_lowercase       (				UpperCamelCase__       :					float,				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 			_lowercase       (				UpperCamelCase__       :					float,				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 			_lowercase       (				UpperCamelCase__       :					int,				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(1_0, 2_0) = }''')
 print(f'''Square: {area_square(1_0) = }''')
 print(f'''Triangle: {area_triangle(1_0, 1_0) = }''')
 print(f'''Triangle: {area_triangle_three_sides(5, 1_2, 1_3) = }''')
 print(f'''Parallelogram: {area_parallelogram(1_0, 2_0) = }''')
 print(f'''Rhombus: {area_rhombus(1_0, 2_0) = }''')
 print(f'''Trapezium: {area_trapezium(1_0, 2_0, 3_0) = }''')
 print(f'''Circle: {area_circle(2_0) = }''')
 print(f'''Ellipse: {area_ellipse(1_0, 2_0) = }''')
 print('\nSurface Areas of various geometric shapes: \n')
 print(f'''Cube: {surface_area_cube(2_0) = }''')
 print(f'''Cuboid: {surface_area_cuboid(1_0, 2_0, 3_0) = }''')
 print(f'''Sphere: {surface_area_sphere(2_0) = }''')
 print(f'''Hemisphere: {surface_area_hemisphere(2_0) = }''')
 print(f'''Cone: {surface_area_cone(1_0, 2_0) = }''')
 print(f'''Conical Frustum: {surface_area_conical_frustum(1_0, 2_0, 3_0) = }''')
 print(f'''Cylinder: {surface_area_cylinder(1_0, 2_0) = }''')
 print(f'''Torus: {surface_area_torus(2_0, 1_0) = }''')
 print(f'''Equilateral Triangle: {area_reg_polygon(3, 1_0) = }''')
 print(f'''Square: {area_reg_polygon(4, 1_0) = }''')
 print(f'''Reqular Pentagon: {area_reg_polygon(5, 1_0) = }''')






