





class    _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''

 def __init__(self				:   Any       , UpperCAmelCase_				:   str = ""       , UpperCAmelCase_				:   bool = False)       ->None:



   '''simple docstring'''



   lowerCamelCase__:      dict[str, RadixNode]			  ={}

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

   lowerCamelCase__:      List[str]			  =prefix

 def 							SCREAMING_SNAKE_CASE_					(self				:   List[str]       , UpperCAmelCase_				:   str)       ->tuple[str, str, str]:



   '''simple docstring'''



   lowerCamelCase__:      Any			  =0
   for q, w in zip(self.prefix       , UpperCAmelCase_):
     if q != w:
       break

     x += 1

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

 def 							SCREAMING_SNAKE_CASE_					(self				:   Optional[Any]       , UpperCAmelCase_				:   list[str])       ->None:



   '''simple docstring'''



   for word in words:
     self.insert(UpperCAmelCase_)

 def 							SCREAMING_SNAKE_CASE_					(self				:   List[str]       , UpperCAmelCase_				:   str)       ->None:



   '''simple docstring'''



   if self.prefix == word:
     lowerCamelCase__:      Optional[int]			  =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=UpperCAmelCase_       , is_leaf=UpperCAmelCase_)

   else:
     lowerCamelCase__:      Union[str, Any]			  =self.nodes[word[0]]
     lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__:      Tuple			  =incoming_node.match(
         UpperCAmelCase_)

     # 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(UpperCAmelCase_)

     # 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__:      Union[str, Any]			  =remaining_prefix

       lowerCamelCase__:      Optional[int]			  =self.nodes[matching_string[0]]
       lowerCamelCase__:      Dict			  =RadixNode(UpperCAmelCase_       , UpperCAmelCase_)
       lowerCamelCase__:      Tuple			  =aux_node

       if remaining_word == "":
         lowerCamelCase__:      Dict			  =True
       else:
         self.nodes[matching_string[0]].insert(UpperCAmelCase_)

 def 							SCREAMING_SNAKE_CASE_					(self				:   int       , UpperCAmelCase_				:   str)       ->bool:



   '''simple docstring'''



   lowerCamelCase__:      Dict			  =self.nodes.get(word[0]       , UpperCAmelCase_)
   if not incoming_node:
     return False
   else:
     lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__:      str			  =incoming_node.match(
         UpperCAmelCase_)
     # 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(UpperCAmelCase_)

 def 							SCREAMING_SNAKE_CASE_					(self				:   Any       , UpperCAmelCase_				:   str)       ->bool:



   '''simple docstring'''



   lowerCamelCase__:      Union[str, Any]			  =self.nodes.get(word[0]       , UpperCAmelCase_)
   if not incoming_node:
     return False
   else:
     lowerCamelCase__  ,					lowerCamelCase__  ,					lowerCamelCase__:      List[Any]			  =incoming_node.match(
         UpperCAmelCase_)
     # 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(UpperCAmelCase_)
     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__:      int			  =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__:      Dict			  =False
         # If there is 1 edge, we merge it with its child
         else:
           lowerCamelCase__:      str			  =list(incoming_node.nodes.values())[0]
           lowerCamelCase__:      Any			  =merging_node.is_leaf
           incoming_node.prefix += merging_node.prefix
           lowerCamelCase__:      Optional[Any]			  =merging_node.nodes

         return True







 def 							SCREAMING_SNAKE_CASE_					(self				:   List[Any]       , UpperCAmelCase_				:   int = 0)       ->None:



   '''simple docstring'''



   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:







  """simple docstring"""





  lowerCamelCase__:      str			  ="banana bananas bandana band apple all beast".split()
  lowerCamelCase__:      List[Any]			  =RadixNode()
  root.insert_many(__a		)

  assert all(root.find(__a		) 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:







  """simple docstring"""





  assert test_trie()





def      lowerCAmelCase_ (       )     ->		None:







  """simple docstring"""





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

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


if __name__ == "__main__":
     main()


'''simple docstring'''




from typing import Any

def 	UpperCamelCase_							(					_UpperCAmelCase  :      list			,	_UpperCAmelCase  :      list			,	_UpperCAmelCase  :      dict			,	_UpperCAmelCase  :      dict			,	_UpperCAmelCase  :      dict			,	)    ->    list:


       """simple docstring"""







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

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

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

                     _UpperCAmelCase     :  Tuple							      =    arg_max

    # The final observation
       _UpperCAmelCase     :  Optional[Any]							      =    observations_space[len(_UpperCAmelCase    ) - 1]

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

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

       return result

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	)    ->    None:


       """simple docstring"""







       _validate_not_empty(
           _UpperCAmelCase			,	_UpperCAmelCase			,	_UpperCAmelCase			,	_UpperCAmelCase			,	_UpperCAmelCase			,	)
       _validate_lists(_UpperCAmelCase			,	_UpperCAmelCase    )
       _validate_dicts(
           _UpperCAmelCase			,	_UpperCAmelCase			,	_UpperCAmelCase    )

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      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 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any    )    ->    None:


       """simple docstring"""







       _validate_list(_UpperCAmelCase			,	"observations_space"    )
       _validate_list(_UpperCAmelCase			,	"states_space"    )

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      str    )    ->    None:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      Any			,	)    ->    None:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      str    )    ->    None:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      Any			,	_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      type			,	_UpperCAmelCase  :      bool = False    )    ->    None:


       """simple docstring"""







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


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

  testmod()

