
'''simple docstring'''



def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     list:




   """simple docstring"""

   # bit count represents no. of bits in the gray code
   if bit_count < 0:
      raise ValueError("""The given input must be positive"""						)

   # get the generated string sequence
   _SCREAMING_SNAKE_CASE      =				gray_code_sequence_string(SCREAMING_SNAKE_CASE_						)
   #
   # convert them to integers
   for i in range(len(SCREAMING_SNAKE_CASE_						)						):
      _SCREAMING_SNAKE_CASE      =				int(sequence[i]    ,      2						)

   return sequence
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     list:




   """simple docstring"""

   # The approach is a recursive one
   # Base case achieved when either n = 0 or n=1
   if bit_count == 0:
      return ["0"]

   if bit_count == 1:
      return ["0", "1"]

   _SCREAMING_SNAKE_CASE      =				1 << bit_count  # defines the length of the sequence
   # 1<< n is equivalent to 2^n

   # recursive answer will generate answer for n-1 bits
   _SCREAMING_SNAKE_CASE      =				gray_code_sequence_string(bit_count - 1						)

   _SCREAMING_SNAKE_CASE      =				[]

   # append 0 to first half of the smaller sequence generated
   for i in range(seq_len // 2						):
      _SCREAMING_SNAKE_CASE      =				"""0""" + smaller_sequence[i]
      sequence.append(SCREAMING_SNAKE_CASE_						)

   # append 1 to second half ... start from the end of the list
   for i in reversed(range(seq_len // 2						)						):
      _SCREAMING_SNAKE_CASE      =				"""1""" + smaller_sequence[i]
      sequence.append(SCREAMING_SNAKE_CASE_						)

   return sequence


if __name__ == "__main__":
     import doctest

     doctest.testmod()

'''simple docstring'''



def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""multiplicative_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""multiplicative_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				1
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total *= numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     int:




   """simple docstring"""

   if not isinstance(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_						):
      raise ValueError("""additive_persistence() only accepts integral values"""						)
   if num < 0:
      raise ValueError("""additive_persistence() does not accept negative values"""						)

   _SCREAMING_SNAKE_CASE      =				0
   _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

   while len(SCREAMING_SNAKE_CASE_						) != 1:
      _SCREAMING_SNAKE_CASE      =				[int(SCREAMING_SNAKE_CASE_						) for i in num_string]

      _SCREAMING_SNAKE_CASE      =				0
      for i in range(0    ,      len(SCREAMING_SNAKE_CASE_						)						):
         total += numbers[i]

      _SCREAMING_SNAKE_CASE      =				str(SCREAMING_SNAKE_CASE_						)

      steps += 1
   return steps


if __name__ == "__main__":
     import doctest

     doctest.testmod()






