





def lowerCamelCase__    (							snake_case_	:  float       ,      snake_case_	:  float       ,      snake_case_	:  float       ,      snake_case_	:  float       ,      snake_case_	:  float       ,      )      ->				float:
   __snake_case							       =   [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:
      __snake_case							       =   1 - (matter_density + radiation_density + dark_energy)

      __snake_case							       =   (
          radiation_density * (redshift + 1) ** 4
          + matter_density * (redshift + 1) ** 3
          + curvature * (redshift + 1) ** 2
          + dark_energy
      )

      __snake_case							       =   hubble_constant * e_a ** (1 / 2)
      return hubble


if __name__ == "__main__":
    import doctest

    # run doctest
    doctest.testmod()

    # demo LCDM approximation
    snake_case_				=			0.3

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








from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       )      ->				list[int]:  # This function is recursive
   __snake_case							       =   len(snake_case_       )
   # If the array contains only one element, we return it (it's the stop condition of
   # recursion)
   if array_length <= 1:
      return array
      # Else
   __snake_case							       =   array[0]
   __snake_case							       =   False
   __snake_case							       =   1
   __snake_case							       =   []
   while not is_found and i < array_length:
      if array[i] < pivot:
         __snake_case							       =   True
         __snake_case							       =   [element for element in array[i:] if element >= array[i]]
         __snake_case							       =   longest_subsequence(snake_case_       )
         if len(snake_case_       ) > len(snake_case_       ):
            __snake_case							       =   temp_array
      else:
         i += 1

   __snake_case							       =   [element for element in array[1:] if element >= pivot]
   __snake_case							       =   [pivot, *longest_subsequence(snake_case_       )]
   if len(snake_case_       ) > len(snake_case_       ):
      return temp_array
   else:
      return longest_subseq


if __name__ == "__main__":
    import doctest

    doctest.testmod()

