





from typing import Any
def  UpperCamelCase						(       _A			:				list			,							_A			:				list			,							_A			:				dict			,							_A			:				dict			,							_A			:				dict			,							)->       Any:





						"""simple docstring"""





						_validation(
						    __lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							)
						# Creates data structures and fill initial step
						A__							=       {}
						A__							=       {}
						for state in states_space:
												A__							=       observations_space[0]
												A__							=       (
												    initial_probabilities[state] * emission_probabilities[state][observation]
												)
												A__							=       None

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

            # Update probabilities and pointers dicts
																		A__							=       (
																		    probabilities[(arg_max, prior_observation)]
																		    * transition_probabilities[arg_max][state]
																		    * emission_probabilities[state][observation]
																		)

																		A__							=       arg_max

    # The final observation
						A__							=       observations_space[len(__lowerCamelCase    ) - 1]

						# argmax for given final observation
						A__							=       ""
						A__							=       -1
						for k_state in states_space:
												A__							=       probabilities[(k_state, final_observation)]
												if probability > max_probability:
																		A__							=       probability
																		A__							=       k_state
						A__							=       arg_max

						# Process pointers backwards
						A__							=       last_state
						A__							=       []
						for o in range(len(__lowerCamelCase    ) - 1			,							-1			,							-1    ):
												result.append(__lowerCamelCase    )
												A__							=       pointers[previous, observations_space[o]]
						result.reverse()

						return result
def  UpperCamelCase						(       _A			:				Any			,							_A			:				Any			,							_A			:				Any			,							_A			:				Any			,							_A			:				Any			,							)->       Optional[Any]:





						"""simple docstring"""





						_validate_not_empty(
						    __lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							)
						_validate_lists(__lowerCamelCase			,							__lowerCamelCase    )
						_validate_dicts(
						    __lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				Any			,							_A			:				Any			,							_A			:				Any			,							_A			:				Any			,							)->       Optional[int]:





						"""simple docstring"""





						if not all(
						    [
						        observations_space,
						        states_space,
						        initial_probabilities,
						        transition_probabilities,
						        emission_probabilities,
						    ]    ):
												raise ValueError("There's an empty parameter"    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				Any    )->       Optional[Any]:





						"""simple docstring"""





						_validate_list(__lowerCamelCase			,							"observations_space"    )
						_validate_list(__lowerCamelCase			,							"states_space"    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				str    )->       List[str]:





						"""simple docstring"""





						if not isinstance(_object			,							__lowerCamelCase    ):
												A__							=       f"""{var_name} must be a list"""
												raise ValueError(__lowerCamelCase    )
						else:
												for x in _object:
																		if not isinstance(__lowerCamelCase			,							__lowerCamelCase    ):
																								A__							=       f"""{var_name} must be a list of strings"""
																								raise ValueError(__lowerCamelCase    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				Any			,							_A			:				Any			,							)->       Union[str, Any]:





						"""simple docstring"""





						_validate_dict(__lowerCamelCase			,							"initial_probabilities"			,							__lowerCamelCase    )
						_validate_nested_dict(__lowerCamelCase			,							"transition_probabilities"    )
						_validate_nested_dict(__lowerCamelCase			,							"emission_probabilities"    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				str    )->       int:





						"""simple docstring"""





						_validate_dict(_object			,							__lowerCamelCase			,							__lowerCamelCase    )
						for x in _object.values():
												_validate_dict(__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase			,							__lowerCamelCase    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				str			,							_A			:				type			,							_A			:				bool = False    )->       int:





						"""simple docstring"""





						if not isinstance(_object			,							__lowerCamelCase    ):
												A__							=       f"""{var_name} must be a dict"""
												raise ValueError(__lowerCamelCase    )
						if not all(isinstance(__lowerCamelCase			,							__lowerCamelCase    ) for x in _object    ):
												A__							=       f"""{var_name} all keys must be strings"""
												raise ValueError(__lowerCamelCase    )
						if not all(isinstance(__lowerCamelCase			,							__lowerCamelCase    ) for x in _object.values()    ):
												A__							=       "nested dictionary " if nested else ""
												A__							=       f"""{var_name} {nested_text}all values must be {value_type.__name__}"""
												raise ValueError(__lowerCamelCase    )


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

						testmod()










import math
def  UpperCamelCase						(       _A			:				float			,							_A			:				float    )->       float:





						"""simple docstring"""





						if (
						    not isinstance(_A			,							(int, float)    )
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError("power_factor must be a valid float value between -1 and 1."    )
						return apparent_power * power_factor
def  UpperCamelCase						(       _A			:				float			,							_A			:				float    )->       float:





						"""simple docstring"""





						if (
						    not isinstance(_A			,							(int, float)    )
						    or power_factor < -1
						    or power_factor > 1
						):
												raise ValueError("power_factor must be a valid float value between -1 and 1."    )
						return apparent_power * math.sqrt(1 - power_factor**2    )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





