


'''simple docstring'''






from typing import Any





def lowerCamelCase__      (						__lowerCamelCase	:							list	,   __lowerCamelCase	:							list	,   __lowerCamelCase	:							dict	,   __lowerCamelCase	:							dict	,   __lowerCamelCase	:							dict	,   ):







   '''simple docstring'''




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

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

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

         _UpperCAmelCase       :       List[Any]							   =arg_max

    # The final observation
   _UpperCAmelCase       :       int							   =observations_space[len(__lowerCamelCase							) - 1]

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

   # Process pointers backwards
   _UpperCAmelCase       :       List[str]							   =last_state
   _UpperCAmelCase       :       Optional[int]							   =[]
   for o in range(len(__lowerCamelCase							) - 1	,   -1	,   -1							):
      result.append(__lowerCamelCase							)
      _UpperCAmelCase       :       Optional[Any]							   =pointers[previous, observations_space[o]]
   result.reverse()

   return result





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   ):







   '''simple docstring'''




   _validate_not_empty(
       __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase	,   )
   _validate_lists(__lowerCamelCase	,   __lowerCamelCase							)
   _validate_dicts(
       __lowerCamelCase	,   __lowerCamelCase	,   __lowerCamelCase							)





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							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__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any							):







   '''simple docstring'''




   _validate_list(__lowerCamelCase	,   'observations_space'							)
   _validate_list(__lowerCamelCase	,   'states_space'							)





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							str							):







   '''simple docstring'''




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





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   __lowerCamelCase	:							Any	,   ):







   '''simple docstring'''




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





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							str							):







   '''simple docstring'''




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





def lowerCamelCase__      (						__lowerCamelCase	:							Any	,   __lowerCamelCase	:							str	,   __lowerCamelCase	:							type	,   __lowerCamelCase	:							bool = False							):







   '''simple docstring'''




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


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

 testmod()









'''simple docstring'''






from __future__ import annotations





def lowerCamelCase__      (						__lowerCamelCase	:							list[int]							):







   '''simple docstring'''




   if not nums:
      return 0
   _UpperCAmelCase       :       Tuple							   =nums[0]
   _UpperCAmelCase       :       int							   =0
   for num in nums[1:]:
      _UpperCAmelCase   ,	_UpperCAmelCase       :       Optional[int]							   =(
          max_excluding + num,
          max(__lowerCamelCase	,   __lowerCamelCase							),
      )
   return max(__lowerCamelCase	,   __lowerCamelCase							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()

