





"""simple docstring"""




from typing import Any






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Optional[Any]       ,			_lowercase		:       Tuple       ,			_lowercase		:       List[str]       ,			_lowercase		:       Any       ,			_lowercase		:       Any       ,			)					->int:






	'''simple docstring'''






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

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

            # Update probabilities and pointers dicts
			a :						List[str]      =							(
			    probabilities[(arg_max, prior_observation)]
			    * transition_probabilities[arg_max][state]
			    * emission_probabilities[state][observation]
			)

			a :						Union[str, Any]      =							arg_max

    # The final observation
	a :						Tuple      =							observations_space[len(lowercase__   ) - 1]

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

	# Process pointers backwards
	a :						Optional[Any]      =							last_state
	a :						Union[str, Any]      =							[]
	for o in range(len(lowercase__   ) - 1       ,			-1       ,			-1   ):
		result.append(lowercase__   )
		a :						Dict      =							pointers[previous, observations_space[o]]
	result.reverse()

	return result






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Optional[int]       ,			_lowercase		:       str       ,			_lowercase		:       Optional[Any]       ,			_lowercase		:       Union[str, Any]       ,			_lowercase		:       Optional[Any]       ,			)					->List[Any]:






	'''simple docstring'''






	_validate_not_empty(
	    lowercase__       ,			lowercase__       ,			lowercase__       ,			lowercase__       ,			lowercase__       ,			)
	_validate_lists(lowercase__       ,			lowercase__   )
	_validate_dicts(
	    lowercase__       ,			lowercase__       ,			lowercase__   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Dict       ,			_lowercase		:       Dict       ,			_lowercase		:       Tuple       ,			_lowercase		:       List[str]       ,			_lowercase		:       Optional[int]       ,			)					->List[str]:






	'''simple docstring'''






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






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Union[str, Any]       ,			_lowercase		:       Dict   )					->List[str]:






	'''simple docstring'''






	_validate_list(lowercase__       ,			"observations_space"   )
	_validate_list(lowercase__       ,			"states_space"   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Tuple       ,			_lowercase		:       Tuple   )					->int:






	'''simple docstring'''






	if not isinstance(_object       ,			lowercase__   ):
		a :						Tuple      =							F"""{var_name} must be a list"""
		raise ValueError(lowercase__   )
	else:
		for x in _object:
			if not isinstance(lowercase__       ,			lowercase__   ):
				a :						int      =							F"""{var_name} must be a list of strings"""
				raise ValueError(lowercase__   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Tuple       ,			_lowercase		:       str       ,			_lowercase		:       Dict       ,			)					->Dict:






	'''simple docstring'''






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






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Union[str, Any]       ,			_lowercase		:       Dict   )					->Tuple:






	'''simple docstring'''






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






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Dict       ,			_lowercase		:       str       ,			_lowercase		:       List[Any]       ,			_lowercase		:       Optional[int] = False   )					->Dict:






	'''simple docstring'''






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


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

		testmod()








"""simple docstring"""






def 	_snake_case     (							lowercase__ = 1				,       lowercase__ = 1000						):
				_lowerCamelCase	:     Optional[int]       =       1
				_lowerCamelCase	:     List[Any]       =       0

				for divide_by_number in range(lowercase__				,       digit + 1						):
								_lowerCamelCase	:     list[int]       =       []
								_lowerCamelCase	:     Dict       =       numerator
								for _ in range(1				,       digit + 1						):
												if now_divide in has_been_divided:
																if longest_list_length < len(lowercase__						):
																				_lowerCamelCase	:     Any       =       len(lowercase__						)
																				_lowerCamelCase	:     Any       =       divide_by_number
												else:
																has_been_divided.append(lowercase__						)
																_lowerCamelCase	:     int       =       now_divide * 10 % divide_by_number

				return the_digit


# Tests
if __name__ == "__main__":
			import doctest

			doctest.testmod()