






from typing import Any


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  ):

  """simple docstring"""






  _validation(
      lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  )
  # Creates data structures and fill initial step
  SCREAMING_SNAKE_CASE							:   Union[str, Any]						    =     {}
  SCREAMING_SNAKE_CASE							:   List[str]						    =     {}
  for state in states_space:
    SCREAMING_SNAKE_CASE							:   List[Any]						    =     observations_space[0]
    SCREAMING_SNAKE_CASE							:   int						    =     (
        initial_probabilities[state] * emission_probabilities[state][observation]
    )
    SCREAMING_SNAKE_CASE							:   List[Any]						    =     None

  # Fills the data structure with the probabilities of
  # different transitions and pointers to previous states
  for o in range(1    ,  len(lowerCamelCase__					)					):
    SCREAMING_SNAKE_CASE							:   List[str]						    =     observations_space[o]
    SCREAMING_SNAKE_CASE							:   Any						    =     observations_space[o - 1]
    for state in states_space:
      # Calculates the argmax for probability function
      SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     ""
      SCREAMING_SNAKE_CASE							:   List[str]						    =     -1
      for k_state in states_space:
        SCREAMING_SNAKE_CASE							:   Dict						    =     (
            probabilities[(k_state, prior_observation)]
            * transition_probabilities[k_state][state]
            * emission_probabilities[state][observation]
        )
        if probability > max_probability:
          SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     probability
          SCREAMING_SNAKE_CASE							:   Union[str, Any]						    =     k_state

            # Update probabilities and pointers dicts
      SCREAMING_SNAKE_CASE							:   Optional[int]						    =     (
          probabilities[(arg_max, prior_observation)]
          * transition_probabilities[arg_max][state]
          * emission_probabilities[state][observation]
      )

      SCREAMING_SNAKE_CASE							:   Dict						    =     arg_max

    # The final observation
  SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     observations_space[len(lowerCamelCase__					) - 1]

  # argmax for given final observation
  SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     ""
  SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     -1
  for k_state in states_space:
    SCREAMING_SNAKE_CASE							:   str						    =     probabilities[(k_state, final_observation)]
    if probability > max_probability:
      SCREAMING_SNAKE_CASE							:   List[Any]						    =     probability
      SCREAMING_SNAKE_CASE							:   Dict						    =     k_state
  SCREAMING_SNAKE_CASE							:   Dict						    =     arg_max

  # Process pointers backwards
  SCREAMING_SNAKE_CASE							:   List[Any]						    =     last_state
  SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     []
  for o in range(len(lowerCamelCase__					) - 1    ,  -1    ,  -1					):
    result.append(lowerCamelCase__					)
    SCREAMING_SNAKE_CASE							:   Tuple						    =     pointers[previous, observations_space[o]]
  result.reverse()

  return result


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  ):

  """simple docstring"""






  _validate_not_empty(
      lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  )
  _validate_lists(lowerCamelCase__    ,  lowerCamelCase__					)
  _validate_dicts(
      lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  ):

  """simple docstring"""






  if not all(
      [
          observations_space,
          states_space,
          initial_probabilities,
          transition_probabilities,
          emission_probabilities,
      ]					):
    raise ValueError("There's an empty parameter"					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase					):

  """simple docstring"""






  _validate_list(lowerCamelCase__    ,  "observations_space"					)
  _validate_list(lowerCamelCase__    ,  "states_space"					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase					):

  """simple docstring"""






  if not isinstance(_object    ,  lowerCamelCase__					):
    SCREAMING_SNAKE_CASE							:   Any						    =     F'''{var_name} must be a list'''
    raise ValueError(lowerCamelCase__					)
  else:
    for x in _object:
      if not isinstance(lowerCamelCase__    ,  lowerCamelCase__					):
        SCREAMING_SNAKE_CASE							:   Optional[Any]						    =     F'''{var_name} must be a list of strings'''
        raise ValueError(lowerCamelCase__					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  ):

  """simple docstring"""






  _validate_dict(lowerCamelCase__    ,  "initial_probabilities"    ,  lowerCamelCase__					)
  _validate_nested_dict(lowerCamelCase__    ,  "transition_probabilities"					)
  _validate_nested_dict(lowerCamelCase__    ,  "emission_probabilities"					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase					):

  """simple docstring"""






  _validate_dict(_object    ,  lowerCamelCase__    ,  lowerCamelCase__					)
  for x in _object.values():
    _validate_dict(lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__    ,  lowerCamelCase__					)


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  lowercase = False					):

  """simple docstring"""






  if not isinstance(_object    ,  lowerCamelCase__					):
    SCREAMING_SNAKE_CASE							:   int						    =     F'''{var_name} must be a dict'''
    raise ValueError(lowerCamelCase__					)
  if not all(isinstance(lowerCamelCase__    ,  lowerCamelCase__					) for x in _object					):
    SCREAMING_SNAKE_CASE							:   List[Any]						    =     F'''{var_name} all keys must be strings'''
    raise ValueError(lowerCamelCase__					)
  if not all(isinstance(lowerCamelCase__    ,  lowerCamelCase__					) for x in _object.values()					):
    SCREAMING_SNAKE_CASE							:   Tuple						    =     "nested dictionary " if nested else ""
    SCREAMING_SNAKE_CASE							:   List[str]						    =     F'''{var_name} {nested_text}all values must be {value_type.__name__}'''
    raise ValueError(lowerCamelCase__					)


if __name__ == "__main__":
   from doctest import testmod

   testmod()










# Lint as: python3
import itertools
import os
import re


UpperCAmelCase   :    Any     =		re.compile(r"([A-Z]+)([A-Z][a-z])")
UpperCAmelCase   :    Optional[Any]     =		re.compile(r"([a-z\d])([A-Z])")

UpperCAmelCase   :    Optional[Any]     =		re.compile(r"(?<!_)_(?!_)")
UpperCAmelCase   :    Any     =		re.compile(r"(_{2,})")

UpperCAmelCase   :    List[Any]     =		r"^\w+(\.\w+)*$"

UpperCAmelCase   :    Any     =		r"<>:/\|?*"






def 	__lowerCamelCase						(							lowerCamelCase__		:						Tuple      ):





			'''simple docstring'''




			lowerCamelCase    		=  _uppercase_uppercase_re.sub(R"""\1_\2"""  ,							lowerCamelCase__      )
			lowerCamelCase    		=  _lowercase_uppercase_re.sub(R"""\1_\2"""  ,							lowerCamelCase__      )
			return name.lower()






def 	__lowerCamelCase						(							lowerCamelCase__		:						List[str]      ):





			'''simple docstring'''




			lowerCamelCase    		=  _single_underscore_re.split(lowerCamelCase__      )
			lowerCamelCase    		=  [_multiple_underscores_re.split(lowerCamelCase__      ) for n in name]
			return "".join(n.capitalize() for n in itertools.chain.from_iterable(lowerCamelCase__      ) if n != """"""      )






def 	__lowerCamelCase						(							lowerCamelCase__		:						Any      ):





			'''simple docstring'''




			if os.path.basename(lowerCamelCase__      ) != name:
						raise ValueError(f'Should be a dataset name, not a path: {name}'      )
			return camelcase_to_snakecase(lowerCamelCase__      )






def 	__lowerCamelCase						(							lowerCamelCase__		:						List[str]  ,							lowerCamelCase__		:						int      ):





			'''simple docstring'''




			if os.path.basename(lowerCamelCase__      ) != name:
						raise ValueError(f'Should be a dataset name, not a path: {name}'      )
			if not re.match(_split_re  ,							lowerCamelCase__      ):
						raise ValueError(f'Split name should match \'{_split_re}\'\' but got \'{split}\'.'      )
			return f'{filename_prefix_for_name(lowerCamelCase__      )}-{split}'






def 	__lowerCamelCase						(							lowerCamelCase__		:						List[Any]  ,							lowerCamelCase__		:						Optional[Any]  ,							lowerCamelCase__		:						List[Any]  ,							lowerCamelCase__		:						int=None      ):





			'''simple docstring'''




			lowerCamelCase    		=  filename_prefix_for_split(lowerCamelCase__  ,							lowerCamelCase__      )
			if filetype_suffix:
						prefix += f'.{filetype_suffix}'
			lowerCamelCase    		=  os.path.join(lowerCamelCase__  ,							lowerCamelCase__      )
			return f'{filepath}*'






def 	__lowerCamelCase						(							lowerCamelCase__		:						Dict  ,							lowerCamelCase__		:						List[Any]  ,							lowerCamelCase__		:						List[Any]  ,							lowerCamelCase__		:						int=None  ,							lowerCamelCase__		:						str=None      ):





			'''simple docstring'''




			lowerCamelCase    		=  filename_prefix_for_split(lowerCamelCase__  ,							lowerCamelCase__      )
			lowerCamelCase    		=  os.path.join(lowerCamelCase__  ,							lowerCamelCase__      )

			if shard_lengths:
						lowerCamelCase    		=  len(lowerCamelCase__      )
						lowerCamelCase    		=  [f'{prefix}-{shard_id:05d}-of-{num_shards:05d}' for shard_id in range(lowerCamelCase__      )]
						if filetype_suffix:
									lowerCamelCase    		=  [filename + f'.{filetype_suffix}' for filename in filenames]
						return filenames
			else:
						lowerCamelCase    		=  prefix
						if filetype_suffix:
									filename += f'.{filetype_suffix}'
						return [filename]

