





"""simple docstring"""



from typing import Any







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



    '''simple docstring'''







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

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

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

            __A   :						Tuple									=					arg_max

    # The final observation
    __A   :						Dict									=					observations_space[len(snake_case_						) - 1]

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

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

    return result







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



    '''simple docstring'''







    _validate_not_empty(
        snake_case_    ,snake_case_    ,snake_case_    ,snake_case_    ,snake_case_    ,)
    _validate_lists(snake_case_    ,snake_case_						)
    _validate_dicts(
        snake_case_    ,snake_case_    ,snake_case_						)







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



    '''simple docstring'''







    _validate_list(snake_case_    ,'''observations_space'''						)
    _validate_list(snake_case_    ,'''states_space'''						)







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



    '''simple docstring'''







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







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



    '''simple docstring'''







    _validate_dict(snake_case_    ,'''initial_probabilities'''    ,snake_case_						)
    _validate_nested_dict(snake_case_    ,'''transition_probabilities'''						)
    _validate_nested_dict(snake_case_    ,'''emission_probabilities'''						)







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



    '''simple docstring'''







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







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



    '''simple docstring'''







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


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

       testmod()











"""simple docstring"""



a_			=      {
    """meter""": """m""",
    """kilometer""": """km""",
    """megametre""": """Mm""",
    """gigametre""": """Gm""",
    """terametre""": """Tm""",
    """petametre""": """Pm""",
    """exametre""": """Em""",
    """zettametre""": """Zm""",
    """yottametre""": """Ym""",
}
# Exponent of the factor(meter)
a_			=      {
    """m""": 0,
    """km""": 3,
    """Mm""": 6,
    """Gm""": 9,
    """Tm""": 12,
    """Pm""": 15,
    """Em""": 18,
    """Zm""": 21,
    """Ym""": 24,
}







def 		__lowercase					(       snake_case_  :  float    ,snake_case_  :  str    ,snake_case_  :  str						)       ->float:



    '''simple docstring'''







    __A   :						Tuple									=					from_type.lower().strip('''s'''						)
    __A   :						Optional[int]									=					to_type.lower().strip('''s'''						)

    __A   :						List[str]									=					UNIT_SYMBOL.get(snake_case_    ,snake_case_						)
    __A   :						Any									=					UNIT_SYMBOL.get(snake_case_    ,snake_case_						)

    if from_sanitized not in METRIC_CONVERSION:
        __A   :						int									=					(
            F"""Invalid 'from_type' value: {from_type!r}.\n"""
            F"""Conversion abbreviations are: {', '.join(snake_case_						)}"""
        )
        raise ValueError(snake_case_						)
    if to_sanitized not in METRIC_CONVERSION:
        __A   :						str									=					(
            F"""Invalid 'to_type' value: {to_type!r}.\n"""
            F"""Conversion abbreviations are: {', '.join(snake_case_						)}"""
        )
        raise ValueError(snake_case_						)
    __A   :						Optional[Any]									=					METRIC_CONVERSION[from_sanitized]
    __A   :						Optional[int]									=					METRIC_CONVERSION[to_sanitized]
    __A   :						Union[str, Any]									=					1

    if from_exponent > to_exponent:
        __A   :						Dict									=					from_exponent - to_exponent
    else:
        __A   :						Union[str, Any]									=					-(to_exponent - from_exponent)

    return value * pow(10    ,snake_case_						)


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

       testmod()




