


from typing import Any



def     __lowerCAmelCase						(							snake_case	:    list						,      snake_case	:    list						,      snake_case	:    dict						,      snake_case	:    dict						,      snake_case	:    dict						,      )       ->							Any:
			_validation(
			    lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      )
			# Creates data structures and fill initial step
			__lowerCamelCase:				List[str]     =	{}
			__lowerCamelCase:				Tuple     =	{}
			for state in states_space:
						__lowerCamelCase:				Optional[Any]     =	observations_space[0]
						__lowerCamelCase:				Optional[int]     =	(
						    initial_probabilities[state] * emission_probabilities[state][observation]
						)
						__lowerCamelCase:				List[Any]     =	None

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

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

									__lowerCamelCase:				Dict     =	arg_max

    # The final observation
			__lowerCamelCase:				List[Any]     =	observations_space[len(lowerCamelCase_ ) - 1]

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

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

			return result



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    Any						,      snake_case	:    Any						,      snake_case	:    Any						,      snake_case	:    Any						,      )       ->							int:
			_validate_not_empty(
			    lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      )
			_validate_lists(lowerCamelCase_						,      lowerCamelCase_ )
			_validate_dicts(
			    lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_ )



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



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    Any )       ->							List[str]:
			_validate_list(lowerCamelCase_						,      """observations_space""" )
			_validate_list(lowerCamelCase_						,      """states_space""" )



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    str )       ->							Any:
			if not isinstance(_object						,      lowerCamelCase_ ):
						__lowerCamelCase:				str     =	f'{var_name} must be a list'
						raise ValueError(lowerCamelCase_ )
			else:
						for x in _object:
									if not isinstance(lowerCamelCase_						,      lowerCamelCase_ ):
												__lowerCamelCase:				List[str]     =	f'{var_name} must be a list of strings'
												raise ValueError(lowerCamelCase_ )



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    Any						,      snake_case	:    Any						,      )       ->							Optional[int]:
			_validate_dict(lowerCamelCase_						,      """initial_probabilities"""						,      lowerCamelCase_ )
			_validate_nested_dict(lowerCamelCase_						,      """transition_probabilities""" )
			_validate_nested_dict(lowerCamelCase_						,      """emission_probabilities""" )



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    str )       ->							Optional[int]:
			_validate_dict(_object						,      lowerCamelCase_						,      lowerCamelCase_ )
			for x in _object.values():
						_validate_dict(lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_ )



def     __lowerCAmelCase						(							snake_case	:    Any						,      snake_case	:    str						,      snake_case	:    type						,      snake_case	:    bool = False )       ->							List[str]:
			if not isinstance(_object						,      lowerCamelCase_ ):
						__lowerCamelCase:				List[str]     =	f'{var_name} must be a dict'
						raise ValueError(lowerCamelCase_ )
			if not all(isinstance(lowerCamelCase_						,      lowerCamelCase_ ) for x in _object ):
						__lowerCamelCase:				Optional[Any]     =	f'{var_name} all keys must be strings'
						raise ValueError(lowerCamelCase_ )
			if not all(isinstance(lowerCamelCase_						,      lowerCamelCase_ ) for x in _object.values() ):
						__lowerCamelCase:				Tuple     =	"""nested dictionary """ if nested else """"""
						__lowerCamelCase:				str     =	f'{var_name} {nested_text}all values must be {value_type.__name__}'
						raise ValueError(lowerCamelCase_ )


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

			testmod()






class        a					:





     def __init__(    self					:				Any    ,	SCREAMING_SNAKE_CASE_					:				str = ""    ,	SCREAMING_SNAKE_CASE_					:				bool = False							):
        # Mapping from the first character of the prefix of the node
        __lowerCamelCase:				dict[str, RadixNode]     =	{}

        # A node will be a leaf if the tree contains its word
        __lowerCamelCase:				str     =	is_leaf

        __lowerCamelCase:				Optional[int]     =	prefix





     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				str							):
        __lowerCamelCase:				Optional[Any]     =	0
        for q, w in zip(self.prefix    ,	SCREAMING_SNAKE_CASE_							):
           if q != w:
              break

           x += 1

        return self.prefix[:x], self.prefix[x:], word[x:]





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any    ,	SCREAMING_SNAKE_CASE_					:				list[str]							):
        for word in words:
           self.insert(SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				List[Any]    ,	SCREAMING_SNAKE_CASE_					:				str							):
        # Case 1: If the word is the prefix of the node
        # Solution: We set the current node as leaf
        if self.prefix == word:
           __lowerCamelCase:				Union[str, Any]     =	True

        # Case 2: The node has no edges that have a prefix to the word
        # Solution: We create an edge from the current node to a new one
        # containing the word
        elif word[0] not in self.nodes:
           __lowerCamelCase:				Any     =	RadixNode(prefix=SCREAMING_SNAKE_CASE_    ,	is_leaf=SCREAMING_SNAKE_CASE_							)

        else:
           __lowerCamelCase:				Union[str, Any]     =	self.nodes[word[0]]
           __lowerCamelCase   ,     __lowerCamelCase   ,     __lowerCamelCase:				List[str]     =	incoming_node.match(
               SCREAMING_SNAKE_CASE_							)

           # Case 3: The node prefix is equal to the matching
           # Solution: We insert remaining word on the next node
           if remaining_prefix == "":
              self.nodes[matching_string[0]].insert(SCREAMING_SNAKE_CASE_							)

           # Case 4: The word is greater equal to the matching
           # Solution: Create a node in between both nodes, change
           # prefixes and add the new node for the remaining word
           else:
              __lowerCamelCase:				List[Any]     =	remaining_prefix

              __lowerCamelCase:				Optional[Any]     =	self.nodes[matching_string[0]]
              __lowerCamelCase:				Optional[int]     =	RadixNode(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							)
              __lowerCamelCase:				Union[str, Any]     =	aux_node

              if remaining_word == "":
                 __lowerCamelCase:				Optional[int]     =	True
              else:
                 self.nodes[matching_string[0]].insert(SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				int    ,	SCREAMING_SNAKE_CASE_					:				str							):
        __lowerCamelCase:				int     =	self.nodes.get(word[0]    ,	SCREAMING_SNAKE_CASE_							)
        if not incoming_node:
           return False
        else:
           __lowerCamelCase   ,     __lowerCamelCase   ,     __lowerCamelCase:				Any     =	incoming_node.match(
               SCREAMING_SNAKE_CASE_							)
           # If there is remaining prefix, the word can't be on the tree
           if remaining_prefix != "":
              return False
           # This applies when the word and the prefix are equal
           elif remaining_word == "":
              return incoming_node.is_leaf
           # We have word remaining so we check the next node
           else:
              return incoming_node.find(SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				str    ,	SCREAMING_SNAKE_CASE_					:				str							):
        __lowerCamelCase:				str     =	self.nodes.get(word[0]    ,	SCREAMING_SNAKE_CASE_							)
        if not incoming_node:
           return False
        else:
           __lowerCamelCase   ,     __lowerCamelCase   ,     __lowerCamelCase:				Dict     =	incoming_node.match(
               SCREAMING_SNAKE_CASE_							)
           # If there is remaining prefix, the word can't be on the tree
           if remaining_prefix != "":
              return False
           # We have word remaining so we check the next node
           elif remaining_word != "":
              return incoming_node.delete(SCREAMING_SNAKE_CASE_							)
           else:
              # If it is not a leaf, we don't have to delete
              if not incoming_node.is_leaf:
                 return False
              else:
                 # We delete the nodes if no edges go from it
                 if len(incoming_node.nodes							) == 0:
                    del self.nodes[word[0]]
                    # We merge the current node with its only child
                    if len(self.nodes							) == 1 and not self.is_leaf:
                       __lowerCamelCase:				List[Any]     =	list(self.nodes.values()							)[0]
                       __lowerCamelCase:				Any     =	merging_node.is_leaf
                       self.prefix += merging_node.prefix
                       __lowerCamelCase:				Tuple     =	merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                 elif len(incoming_node.nodes							) > 1:
                    __lowerCamelCase:				int     =	False
                 # If there is 1 edge, we merge it with its child
                 else:
                    __lowerCamelCase:				Union[str, Any]     =	list(incoming_node.nodes.values()							)[0]
                    __lowerCamelCase:				List[str]     =	merging_node.is_leaf
                    incoming_node.prefix += merging_node.prefix
                    __lowerCamelCase:				Union[str, Any]     =	merging_node.nodes

                 return True







     def  SCREAMING_SNAKE_CASE__       (    self					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				int = 0							):
        if self.prefix != "":
           print("""-""" * height    ,	self.prefix    ,	"""  (leaf)""" if self.is_leaf else """"""							)

        for value in self.nodes.values():
           value.print_tree(height + 1							)



def     __lowerCAmelCase						(							)       ->							bool:
   __lowerCamelCase:				Optional[int]     =	"""banana bananas bandana band apple all beast""".split()
   __lowerCamelCase:				Optional[Any]     =	RadixNode()
   root.insert_many(snake_case )

   assert all(root.find(snake_case ) for word in words )
   assert not root.find("""bandanas""" )
   assert not root.find("""apps""" )
   root.delete("""all""" )
   assert not root.find("""all""" )
   root.delete("""banana""" )
   assert not root.find("""banana""" )
   assert root.find("""bananas""" )

   return True



def     __lowerCAmelCase						(							)       ->							None:
   assert test_trie()



def     __lowerCAmelCase						(							)       ->							None:
   __lowerCamelCase:				int     =	RadixNode()
   __lowerCamelCase:				str     =	"""banana bananas bandanas bandana band apple all beast""".split()
   root.insert_many(snake_case )

   print("""Words:"""						,      snake_case )
   print("""Tree:""" )
   root.print_tree()


if __name__ == "__main__":
   main()


