





'''simple docstring'''


def 							UpperCAmelCase_  (						__lowerCamelCase : float     ,__lowerCamelCase : float     ,__lowerCamelCase : float     ,__lowerCamelCase : float     ,__lowerCamelCase : float     ,):
   lowercase_      :Union[str, Any]         =			[redshift, radiation_density, matter_density, dark_energy]
   if any(p < 0 for p in parameters			):
      raise ValueError("All input parameters must be positive"			)

   if any(p > 1 for p in parameters[1:4]			):
      raise ValueError("Relative densities cannot be greater than one"			)
   else:
      lowercase_      :Dict         =			1 - (matter_density + radiation_density + dark_energy)

      lowercase_      :Dict         =			(
          radiation_density * (redshift + 1) ** 4
          + matter_density * (redshift + 1) ** 3
          + curvature * (redshift + 1) ** 2
          + dark_energy
      )

      lowercase_      :Optional[Any]         =			hubble_constant * e_a ** (1 / 2)
      return hubble


if __name__ == "__main__":
 import doctest

 # run doctest
 doctest.testmod()

 # demo LCDM approximation
 lowerCAmelCase :					str 							=0.3

 print(
     hubble_parameter(
         hubble_constant=68.3,
         radiation_density=1E-4,
         matter_density=matter_density,
         dark_energy=1 - matter_density,
         redshift=0,
     )
 )









'''simple docstring'''


from __future__ import annotations

lowerCAmelCase :					Any 							={
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}
class 				a_       :





     def __init__(			self		: List[Any]     ,				lowercase		: dict[str, list[str]]     ,				lowercase		: str						):





        """simple docstring"""




        lowercase_      :List[str]         =			graph
        # mapping node to its parent in resulting breadth first tree
        lowercase_      :dict[str, str | None]         =			{}
        lowercase_      :Dict         =			source_vertex





     def 							lowercase__				(			self		: Tuple						):





        """simple docstring"""




        lowercase_      :Union[str, Any]         =			{self.source_vertex}
        lowercase_      :Tuple         =			None
        lowercase_      :Dict         =			[self.source_vertex]  # first in first out queue

        while queue:
           lowercase_      :int         =			queue.pop(0						)
           for adjacent_vertex in self.graph[vertex]:
              if adjacent_vertex not in visited:
                 visited.add(lowercase						)
                 lowercase_      :Optional[Any]         =			vertex
                 queue.append(lowercase						)







     def 							lowercase__				(			self		: Tuple     ,				lowercase		: str						):





        """simple docstring"""




        if target_vertex == self.source_vertex:
           return self.source_vertex

        lowercase_      :List[str]         =			self.parent.get(lowercase						)
        if target_vertex_parent is None:
           lowercase_      :Union[str, Any]         =			(
               F'No path from vertex: {self.source_vertex} to vertex: {target_vertex}'
           )
           raise ValueError(lowercase						)

        return self.shortest_path(lowercase						) + F'->{target_vertex}'


if __name__ == "__main__":
 lowerCAmelCase :					Dict 							=Graph(graph, '''G''')
 g.breath_first_search()
 print(g.shortest_path('''D'''))
 print(g.shortest_path('''G'''))
 print(g.shortest_path('''Foo'''))


