
from __future__ import annotations

from collections.abc import Iterator
from typing import Any





class 							UpperCAmelCase      :




	'''simple docstring'''





	def __init__(       self					: List[Any]							,A					: Union[str, Any] ):
					__A   			= data
					__A   			= None





class 							UpperCAmelCase      :




	'''simple docstring'''





	def __init__(       self					: List[Any] ):
					__A   			= None
					__A   			= None






	def __iter__(       self					: Dict ):
					__A   			= self.head
					while self.head:
									yield node.data
									__A   			= node.next
									if node == self.head:
													break






	def __len__(       self					: Union[str, Any] ):
					return sum(1 for _ in self )






	def __repr__(       self					: Optional[int] ):
					return "->".join(str(A ) for item in iter(self ) )






	def 				UpperCamelCase_  (       self					: Dict							,A					: Union[str, Any] ):
					self.insert_nth(len(self )							,A )






	def 				UpperCamelCase_  (       self					: Tuple							,A					: Optional[int] ):
					self.insert_nth(0							,A )






	def 				UpperCamelCase_  (       self					: str							,A					: Dict							,A					: List[Any] ):







					if index < 0 or index > len(self ):
									raise IndexError("list index out of range." )
					__A   			= Node(A )
					if self.head is None:
									__A   			= new_node  # first node points itself
									__A   			= __A   			= new_node
					elif index == 0:  # insert at head
									__A   			= self.head
									__A   			= __A   			= new_node
					else:
									__A   			= self.head
									for _ in range(index - 1 ):
													__A   			= temp.next
									__A   			= temp.next
									__A   			= new_node
									if index == len(self ) - 1:  # insert at tail
													__A   			= new_node






	def 				UpperCamelCase_  (       self					: Optional[Any] ):
					return self.delete_nth(0 )






	def 				UpperCamelCase_  (       self					: Any ):
					return self.delete_nth(len(self ) - 1 )






	def 				UpperCamelCase_  (       self					: Optional[int]							,A					: List[str] = 0 ):







					if not 0 <= index < len(self ):
									raise IndexError("list index out of range." )
					__A   			= self.head
					if self.head == self.tail:  # just one node
									__A   			= __A   			= None
					elif index == 0:  # delete head node
									__A   			= self.tail.next.next
									__A   			= self.head.next
					else:
									__A   			= self.head
									for _ in range(index - 1 ):
													__A   			= temp.next
									__A   			= temp.next
									__A   			= temp.next.next
									if index == len(self ) - 1:  # delete at tail
													__A   			= temp
					return delete_node.data







	def 				UpperCamelCase_  (       self					: List[Any] ):
					return len(self ) == 0





def 						UpperCAmelCase			(	)		->	None:







				"""simple docstring"""



				__A   			= CircularLinkedList()
				assert len(__lowerCAmelCase						) == 0
				assert circular_linked_list.is_empty() is True
				assert str(__lowerCAmelCase						) == ""

				try:
								circular_linked_list.delete_front()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_tail()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_nth(-1						)
								raise AssertionError
				except IndexError:
								assert True

				try:
								circular_linked_list.delete_nth(0						)
								raise AssertionError
				except IndexError:
								assert True

				assert circular_linked_list.is_empty() is True
				for i in range(5						):
								assert len(__lowerCAmelCase						) == i
								circular_linked_list.insert_nth(__lowerCAmelCase		,   i + 1						)
				assert str(__lowerCAmelCase						) == "->".join(str(__lowerCAmelCase						) for i in range(1		,   6						)						)

				circular_linked_list.insert_tail(6						)
				assert str(__lowerCAmelCase						) == "->".join(str(__lowerCAmelCase						) for i in range(1		,   7						)						)
				circular_linked_list.insert_head(0						)
				assert str(__lowerCAmelCase						) == "->".join(str(__lowerCAmelCase						) for i in range(0		,   7						)						)

				assert circular_linked_list.delete_front() == 0
				assert circular_linked_list.delete_tail() == 6
				assert str(__lowerCAmelCase						) == "->".join(str(__lowerCAmelCase						) for i in range(1		,   6						)						)
				assert circular_linked_list.delete_nth(2						) == 3

				circular_linked_list.insert_nth(2		,   3						)
				assert str(__lowerCAmelCase						) == "->".join(str(__lowerCAmelCase						) for i in range(1		,   6						)						)

				assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
					import doctest

					doctest.testmod()








class __lowerCamelCase :





	"""simple docstring"""






	def __init__(							self       ,    UpperCAmelCase = ""       ,    UpperCAmelCase = False    ):
							"""simple docstring"""







							_UpperCAmelCase									=			{}

							# A node will be a leaf if the tree contains its word
							_UpperCAmelCase									=			is_leaf

							_UpperCAmelCase									=			prefix

	def        UpperCamelCase    (							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							_UpperCAmelCase									=			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        UpperCamelCase    (							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							for word in words:
													self.insert(UpperCAmelCase    )

	def        UpperCamelCase    (							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							if self.prefix == word:
													_UpperCAmelCase									=			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:
													_UpperCAmelCase									=			RadixNode(prefix=UpperCAmelCase       ,    is_leaf=UpperCAmelCase    )

							else:
													_UpperCAmelCase									=			self.nodes[word[0]]
													_UpperCAmelCase					, _UpperCAmelCase					, _UpperCAmelCase									=			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:
																			_UpperCAmelCase									=			remaining_prefix

																			_UpperCAmelCase									=			self.nodes[matching_string[0]]
																			_UpperCAmelCase									=			RadixNode(UpperCAmelCase       ,    UpperCAmelCase    )
																			_UpperCAmelCase									=			aux_node

																			if remaining_word == "":
																									_UpperCAmelCase									=			True
																			else:
																									self.nodes[matching_string[0]].insert(UpperCAmelCase    )

	def        UpperCamelCase    (							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							_UpperCAmelCase									=			self.nodes.get(word[0]       ,    UpperCAmelCase    )
							if not incoming_node:
													return False
							else:
													_UpperCAmelCase					, _UpperCAmelCase					, _UpperCAmelCase									=			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        UpperCamelCase    (							self       ,    UpperCAmelCase    ):
							"""simple docstring"""







							_UpperCAmelCase									=			self.nodes.get(word[0]       ,    UpperCAmelCase    )
							if not incoming_node:
													return False
							else:
													_UpperCAmelCase					, _UpperCAmelCase					, _UpperCAmelCase									=			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:
																																					_UpperCAmelCase									=			list(self.nodes.values()    )[0]
																																					_UpperCAmelCase									=			merging_node.is_leaf
																																					self.prefix += merging_node.prefix
																																					_UpperCAmelCase									=			merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
																									elif len(incoming_node.nodes    ) > 1:
																															_UpperCAmelCase									=			False
																									# If there is 1 edge, we merge it with its child
																									else:
																															_UpperCAmelCase									=			list(incoming_node.nodes.values()    )[0]
																															_UpperCAmelCase									=			merging_node.is_leaf
																															incoming_node.prefix += merging_node.prefix
																															_UpperCAmelCase									=			merging_node.nodes

																									return True

	def        UpperCamelCase    (							self       ,    UpperCAmelCase = 0    ):
							"""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 __A    (      )->  bool:





						"""simple docstring"""



						_UpperCAmelCase									=			'banana bananas bandana band apple all beast'.split()
						_UpperCAmelCase									=			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 __A    (      )->  None:





						"""simple docstring"""



						assert test_trie()


def __A    (      )->  None:





						"""simple docstring"""



						_UpperCAmelCase									=			RadixNode()
						_UpperCAmelCase									=			'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()
