


'''simple docstring'''


from typing import Any







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      ):







				"""simple docstring"""





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

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

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

												_SCREAMING_SNAKE_CASE :       List[str]     		=      arg_max

    # The final observation
				_SCREAMING_SNAKE_CASE :       str     		=      observations_space[len(SCREAMING_SNAKE_CASE__     ) - 1]

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

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

				return result







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      ):







				"""simple docstring"""





				_validate_not_empty(
				    SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      )
				_validate_lists(SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     )
				_validate_dicts(
				    SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     )







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      ):







				"""simple docstring"""





				if not all(
				    [
				        observations_space,
				        states_space,
				        initial_probabilities,
				        transition_probabilities,
				        emission_probabilities,
				    ]     ):
								raise ValueError("""There's an empty parameter"""     )







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     ):







				"""simple docstring"""





				_validate_list(SCREAMING_SNAKE_CASE__							,      """observations_space"""     )
				_validate_list(SCREAMING_SNAKE_CASE__							,      """states_space"""     )







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     ):







				"""simple docstring"""





				if not isinstance(_object							,      SCREAMING_SNAKE_CASE__     ):
								_SCREAMING_SNAKE_CASE :       List[str]     		=      f"""{var_name} must be a list"""
								raise ValueError(SCREAMING_SNAKE_CASE__     )
				else:
								for x in _object:
												if not isinstance(SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     ):
																_SCREAMING_SNAKE_CASE :       List[str]     		=      f"""{var_name} must be a list of strings"""
																raise ValueError(SCREAMING_SNAKE_CASE__     )







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      ):







				"""simple docstring"""





				_validate_dict(SCREAMING_SNAKE_CASE__							,      """initial_probabilities"""							,      SCREAMING_SNAKE_CASE__     )
				_validate_nested_dict(SCREAMING_SNAKE_CASE__							,      """transition_probabilities"""     )
				_validate_nested_dict(SCREAMING_SNAKE_CASE__							,      """emission_probabilities"""     )







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     ):







				"""simple docstring"""





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







def 			snake_case_   (  SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__ = False     ):







				"""simple docstring"""





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


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

				testmod()








'''simple docstring'''


class     lowercase__  :





							'''simple docstring'''


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

											# A node will be a leaf if the tree contains its word
											_SCREAMING_SNAKE_CASE :       List[Any]     		=      is_leaf

											_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      prefix






							def UpperCAmelCase_	(    self    ,					__snake_case  ):
											_SCREAMING_SNAKE_CASE :       Optional[int]     		=      0
											for q, w in zip(self.prefix    ,					__snake_case  ):
															if q != w:
																			break

															x += 1

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






							def UpperCAmelCase_	(    self    ,					__snake_case  ):
											for word in words:
															self.insert(__snake_case  )






							def UpperCAmelCase_	(    self    ,					__snake_case  ):
											# Case 1: If the word is the prefix of the node
											# Solution: We set the current node as leaf
											if self.prefix == word:
															_SCREAMING_SNAKE_CASE :       List[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:
															_SCREAMING_SNAKE_CASE :       List[str]     		=      RadixNode(prefix=__snake_case    ,					is_leaf=__snake_case  )

											else:
															_SCREAMING_SNAKE_CASE :       int     		=      self.nodes[word[0]]
															_SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE :       Optional[Any]     		=      incoming_node.match(
															    __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(__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:
																			_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      remaining_prefix

																			_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      self.nodes[matching_string[0]]
																			_SCREAMING_SNAKE_CASE :       List[Any]     		=      RadixNode(__snake_case    ,					__snake_case  )
																			_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      aux_node

																			if remaining_word == "":
																							_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      True
																			else:
																							self.nodes[matching_string[0]].insert(__snake_case  )






							def UpperCAmelCase_	(    self    ,					__snake_case  ):
											_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      self.nodes.get(word[0]    ,					__snake_case  )
											if not incoming_node:
															return False
											else:
															_SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE :       Tuple     		=      incoming_node.match(
															    __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(__snake_case  )






							def UpperCAmelCase_	(    self    ,					__snake_case  ):
											_SCREAMING_SNAKE_CASE :       Tuple     		=      self.nodes.get(word[0]    ,					__snake_case  )
											if not incoming_node:
															return False
											else:
															_SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE		,       _SCREAMING_SNAKE_CASE :       List[Any]     		=      incoming_node.match(
															    __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(__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:
																															_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      list(self.nodes.values()  )[0]
																															_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      merging_node.is_leaf
																															self.prefix += merging_node.prefix
																															_SCREAMING_SNAKE_CASE :       Tuple     		=      merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
																							elif len(incoming_node.nodes  ) > 1:
																											_SCREAMING_SNAKE_CASE :       List[str]     		=      False
																							# If there is 1 edge, we merge it with its child
																							else:
																											_SCREAMING_SNAKE_CASE :       int     		=      list(incoming_node.nodes.values()  )[0]
																											_SCREAMING_SNAKE_CASE :       Tuple     		=      merging_node.is_leaf
																											incoming_node.prefix += merging_node.prefix
																											_SCREAMING_SNAKE_CASE :       str     		=      merging_node.nodes

																							return True






							def UpperCAmelCase_	(    self    ,					__snake_case = 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 			snake_case_   (  ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       Union[str, Any]     		=      """banana bananas bandana band apple all beast""".split()
				_SCREAMING_SNAKE_CASE :       Optional[Any]     		=      RadixNode()
				root.insert_many(SCREAMING_SNAKE_CASE__     )

				assert all(root.find(SCREAMING_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 			snake_case_   (  ):







				"""simple docstring"""





				assert test_trie()







def 			snake_case_   (  ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       Tuple     		=      RadixNode()
				_SCREAMING_SNAKE_CASE :       Optional[int]     		=      """banana bananas bandanas bandana band apple all beast""".split()
				root.insert_many(SCREAMING_SNAKE_CASE__     )

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


if __name__ == "__main__":
				main()




