






from typing import Any



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			list			,				__lowercase   :			list			,				__lowercase   :			dict			,				__lowercase   :			dict			,				__lowercase   :			dict			,				)						->      list:





    """simple docstring"""

    _validation(
        __lowercase			,				__lowercase			,				__lowercase			,				__lowercase			,				__lowercase			,				)
    # 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(__lowercase    )    ):
        __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(__lowercase    ) - 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(__lowercase    ) - 1			,				-1			,				-1    ):
        result.append(__lowercase    )
        __A         =	pointers[previous, observations_space[o]]
    result.reverse()

    return result



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				)						->      None:





    """simple docstring"""

    _validate_not_empty(
        __lowercase			,				__lowercase			,				__lowercase			,				__lowercase			,				__lowercase			,				)
    _validate_lists(__lowercase			,				__lowercase    )
    _validate_dicts(
        __lowercase			,				__lowercase			,				__lowercase    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				)						->      None:





    """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   :			Any			,				__lowercase   :			Any    )						->      None:





    """simple docstring"""

    _validate_list(__lowercase			,				"""observations_space"""    )
    _validate_list(__lowercase			,				"""states_space"""    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any			,				__lowercase   :			str    )						->      None:





    """simple docstring"""

    if not isinstance(_object			,				__lowercase    ):
        __A         =	f"{var_name} must be a list"
        raise ValueError(__lowercase    )
    else:
        for x in _object:
            if not isinstance(__lowercase			,				__lowercase    ):
                __A         =	f"{var_name} must be a list of strings"
                raise ValueError(__lowercase    )



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any			,				__lowercase   :			Any			,				__lowercase   :			Any			,				)						->      None:





    """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   :			Any			,				__lowercase   :			str    )						->      None:





    """simple docstring"""

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



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			Any			,				__lowercase   :			str			,				__lowercase   :			type			,				__lowercase   :			bool = False    )						->      None:





    """simple docstring"""

    if not isinstance(_object			,				__lowercase    ):
        __A         =	f"{var_name} must be a dict"
        raise ValueError(__lowercase    )
    if not all(isinstance(__lowercase			,				__lowercase    ) for x in _object    ):
        __A         =	f"{var_name} all keys must be strings"
        raise ValueError(__lowercase    )
    if not all(isinstance(__lowercase			,				__lowercase    ) 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(__lowercase    )


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

  testmod()












__a      :       List[Any]				  =   8.3_1_4_4_5_9_8



def 			_SCREAMING_SNAKE_CASE						( __lowercase   :			float			,				__lowercase   :			float    )						->      float:





    """simple docstring"""

    if temperature < 0:
        raise Exception("""Temperature cannot be less than 0 K"""    )
    if molar_mass <= 0:
        raise Exception("""Molar mass cannot be less than or equal to 0 kg/mol"""    )
    else:
        return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
  import doctest

  # run doctest
  doctest.testmod()

  # example
  __a      :       int				  =   300
  __a      :       int				  =   28
  __a      :       int				  =   rms_speed_of_molecule(temperature, molar_mass)
  print(f"""Vrms of Nitrogen gas at 300 K is {vrms} m/s""")




