






from __future__ import annotations

_a      	=  {
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}





class __lowerCamelCase :





	"""simple docstring"""






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







							_UpperCAmelCase									=			graph
							# mapping node to its parent in resulting breadth first tree
							_UpperCAmelCase									=			{}
							_UpperCAmelCase									=			source_vertex

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







							_UpperCAmelCase									=			{self.source_vertex}
							_UpperCAmelCase									=			None
							_UpperCAmelCase									=			[self.source_vertex]  # first in first out queue

							while queue:
													_UpperCAmelCase									=			queue.pop(0    )
													for adjacent_vertex in self.graph[vertex]:
																			if adjacent_vertex not in visited:
																									visited.add(UpperCAmelCase    )
																									_UpperCAmelCase									=			vertex
																									queue.append(UpperCAmelCase    )

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







							if target_vertex == self.source_vertex:
													return self.source_vertex

							_UpperCAmelCase									=			self.parent.get(UpperCAmelCase    )
							if target_vertex_parent is None:
													_UpperCAmelCase									=			(
													    F"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
													)
													raise ValueError(UpperCAmelCase    )

							return self.shortest_path(UpperCAmelCase    ) + F"""->{target_vertex}"""


if __name__ == "__main__":
		_a      	=  Graph(graph, '''G''')
		g.breath_first_search()
		print(g.shortest_path('''D'''))
		print(g.shortest_path('''G'''))
		print(g.shortest_path('''Foo'''))








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()
