




from typing import Any

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	list     ,							lowercase     :	list     ,							lowercase     :	dict     ,							lowercase     :	dict     ,							lowercase     :	dict     ,							):


      '''simple docstring'''



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

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

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

                  lowerCamelCase_							=   arg_max

    # The final observation
      lowerCamelCase_							=   observations_space[len(lowercase					) - 1]

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

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

      return result

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	Any     ,							lowercase     :	Any     ,							lowercase     :	Any     ,							lowercase     :	Any     ,							lowercase     :	Any     ,							):


      '''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     ,							):


      '''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					):


      '''simple docstring'''



      _validate_list(lowercase     ,							'observations_space'					)
      _validate_list(lowercase     ,							'states_space'					)

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	Any     ,							lowercase     :	str					):


      '''simple docstring'''



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

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	Any     ,							lowercase     :	Any     ,							lowercase     :	Any     ,							):


      '''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					):


      '''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					):


      '''simple docstring'''



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


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

 testmod()









import math

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	float     ,							lowercase     :	float					):


      '''simple docstring'''



      return math.pow(lowercase     ,							2					) - a

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	float					):


      '''simple docstring'''



      return 2 * x

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	float					):


      '''simple docstring'''



      lowerCamelCase_							=   2.0

      while start <= a:
            lowerCamelCase_							=   math.pow(lowercase     ,							2					)

      return start

def       _SCREAMING_SNAKE_CASE      (							lowercase     :	float     ,							lowercase     :	int = 99_99     ,							lowercase     :	float = 0.00_0000_0000_0001					):


      '''simple docstring'''



      if a < 0:
            raise ValueError('math domain error'					)

      lowerCamelCase_							=   get_initial_point(lowercase					)

      for _ in range(lowercase					):
            lowerCamelCase_							=   value
            lowerCamelCase_							=   value - fx(lowercase     ,							lowercase					) / fx_derivative(lowercase					)
            if abs(prev_value - value					) < tolerance:
                  return value

      return value


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

 testmod()



