




class 				lowerCAmelCase_       :






				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_   : Union[str, Any]					  =      is_leaf

							SCREAMING_SNAKE_CASE_   : List[Any]					  =      prefix






				def 		snake_case	(			self      ,snake_case__ ):
							SCREAMING_SNAKE_CASE_   : Dict					  =      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 		snake_case	(			self      ,snake_case__ ):
							for word in words:
										self.insert(snake_case__ )






				def 		snake_case	(			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_   : 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:
										SCREAMING_SNAKE_CASE_   : int					  =      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_   : Dict					  =      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_   : Any					  =      remaining_prefix

													SCREAMING_SNAKE_CASE_   : List[Any]					  =      self.nodes[matching_string[0]]
													SCREAMING_SNAKE_CASE_   : List[Any]					  =      RadixNode(snake_case__      ,snake_case__ )
													SCREAMING_SNAKE_CASE_   : str					  =      aux_node

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






				def 		snake_case	(			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 		snake_case	(			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[str]					  =      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_   : Any					  =      list(self.nodes.values() )[0]
																						SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      merging_node.is_leaf
																						self.prefix += merging_node.prefix
																						SCREAMING_SNAKE_CASE_   : Dict					  =      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_   : int					  =      False
																# If there is 1 edge, we merge it with its child
																else:
																			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      list(incoming_node.nodes.values() )[0]
																			SCREAMING_SNAKE_CASE_   : Dict					  =      merging_node.is_leaf
																			incoming_node.prefix += merging_node.prefix
																			SCREAMING_SNAKE_CASE_   : Dict					  =      merging_node.nodes

																return True






				def 		snake_case	(			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        __UpperCAmelCase						(							)       ->  bool:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      'banana bananas bandana band apple all beast'.split()
			SCREAMING_SNAKE_CASE_   : List[Any]					  =      RadixNode()
			root.insert_many(lowerCamelCase_  )

			assert all(root.find(lowerCamelCase_  ) 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        __UpperCAmelCase						(							)       ->  None:







			"""simple docstring"""





			assert test_trie()





def        __UpperCAmelCase						(							)       ->  None:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      RadixNode()
			SCREAMING_SNAKE_CASE_   : Dict					  =      'banana bananas bandanas bandana band apple all beast'.split()
			root.insert_many(lowerCamelCase_  )

			print('Words:'  ,							lowerCamelCase_  )
			print('Tree:'  )
			root.print_tree()


if __name__ == "__main__":
						main()





from __future__ import annotations




def 							a		(				snake_case__:   Optional[int]		,  snake_case__:   Optional[int]		,  snake_case__:   Any		,  snake_case__:   Optional[int]   ):  # noqa: E741


				'''simple docstring'''
				while r - l > 1:
								lowercase_	    =   (l + r) // 2
								if v[m] >= key:
												lowercase_	    =   m
								else:
												lowercase_	    =   m  # noqa: E741
				return r




def 							a		(				snake_case__:   list[int]   ):


				'''simple docstring'''
				if len(snake_case__   ) == 0:
								return 0

				lowercase_	    =   [0] * len(snake_case__   )
				lowercase_	    =   1

				lowercase_	    =   v[0]

				for i in range(1		,  len(snake_case__   )   ):
								if v[i] < tail[0]:
												lowercase_	    =   v[i]
								elif v[i] > tail[length - 1]:
												lowercase_	    =   v[i]
												length += 1
								else:
												lowercase_	    =   v[i]

				return length


if __name__ == "__main__":
						import doctest

						doctest.testmod()




