



"""simple docstring"""





from typing import Any
def 	__lowerCAmelCase						(		__UpperCamelCase      :			list					, __UpperCamelCase      :			list					, __UpperCamelCase      :			dict					, __UpperCamelCase      :			dict					, __UpperCamelCase      :			dict					, ):


						'''simple docstring'''






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

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

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

																		snake_case_   : str						=			arg_max

    # The final observation
						snake_case_   : List[str]						=			observations_space[len(__UpperCamelCase    ) - 1]

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

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

						return result
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, ):


						'''simple docstring'''






						_validate_not_empty(
						    __UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase					, )
						_validate_lists(__UpperCamelCase					, __UpperCamelCase    )
						_validate_dicts(
						    __UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, ):


						'''simple docstring'''






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


						'''simple docstring'''






						_validate_list(__UpperCamelCase					, """observations_space"""    )
						_validate_list(__UpperCamelCase					, """states_space"""    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			str    ):


						'''simple docstring'''






						if not isinstance(_object					, __UpperCamelCase    ):
												snake_case_   : Any						=			F'{var_name} must be a list'
												raise ValueError(__UpperCamelCase    )
						else:
												for x in _object:
																		if not isinstance(__UpperCamelCase					, __UpperCamelCase    ):
																								snake_case_   : str						=			F'{var_name} must be a list of strings'
																								raise ValueError(__UpperCamelCase    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, __UpperCamelCase      :			Any					, ):


						'''simple docstring'''






						_validate_dict(__UpperCamelCase					, """initial_probabilities"""					, __UpperCamelCase    )
						_validate_nested_dict(__UpperCamelCase					, """transition_probabilities"""    )
						_validate_nested_dict(__UpperCamelCase					, """emission_probabilities"""    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			str    ):


						'''simple docstring'''






						_validate_dict(_object					, __UpperCamelCase					, __UpperCamelCase    )
						for x in _object.values():
												_validate_dict(__UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase					, __UpperCamelCase    )
def 	__lowerCAmelCase						(		__UpperCamelCase      :			Any					, __UpperCamelCase      :			str					, __UpperCamelCase      :			type					, __UpperCamelCase      :			bool = False    ):


						'''simple docstring'''






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


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

					testmod()






"""simple docstring"""





def 	__lowerCAmelCase						(		__UpperCamelCase      :			int					, __UpperCamelCase      :			int    ):


						'''simple docstring'''






						if a < 0 or b < 0:
												raise ValueError("""the value of both inputs must be positive"""    )

						snake_case_   : List[str]						=			str(bin(__UpperCamelCase    )    )[2:]  # remove the leading "0b"
						snake_case_   : Union[str, Any]						=			str(bin(__UpperCamelCase    )    )[2:]  # remove the leading "0b"

						snake_case_   : int						=			max(len(__UpperCamelCase    )					, len(__UpperCamelCase    )    )

						return "0b" + "".join(
						    str(int(char_a != char_b    )    )
						    for char_a, char_b in zip(a_binary.zfill(__UpperCamelCase    )					, b_binary.zfill(__UpperCamelCase    )    )    )


if __name__ == "__main__":
					import doctest

					doctest.testmod()

