






from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

snake_case    :						Optional[Any]  =						TypeVar('T')
snake_case    :						List[Any]  =						TypeVar('U')




class 							lowerCAmelCase__  (	Generic[T, U]						):







					def __init__(       self      :     Optional[Any]			,		_A      :     T | None			,		_A      :     U | None):
											A__	:							Union[str, Any]						    = key
											A__	:							Dict						    = val
											A__	:							DoubleLinkedListNode[T, U] | None						    = None
											A__	:							DoubleLinkedListNode[T, U] | None						    = None







					def __repr__(       self      :     Union[str, Any]):
											return (
											    F'Node: key: {self.key}, val: {self.val}, '
											    F'has next: {bool(self.next)}, has prev: {bool(self.prev)}'
											)




class 							lowerCAmelCase__  (	Generic[T, U]						):







					def __init__(       self      :     Union[str, Any]):
											A__	:							DoubleLinkedListNode[T, U]						    = DoubleLinkedListNode(_A			,		_A)
											A__	:							DoubleLinkedListNode[T, U]						    = DoubleLinkedListNode(_A			,		_A)
											A__	:							Tuple						    = self.rear, self.head







					def __repr__(       self      :     List[str]):
											A__	:							Union[str, Any]						    = ["DoubleLinkedList"]
											A__	:							int						    = self.head
											while node.next is not None:
																	rep.append(str(_A))
																	A__	:							str						    = node.next
											rep.append(str(self.rear))
											return ",\n    ".join(_A)







					def  _lowercase			(       self      :     List[Any]			,		_A      :     DoubleLinkedListNode[T, U]):
											A__	:							str						    = self.rear.prev

											# All nodes other than self.head are guaranteed to have non-None previous
											assert previous is not None

											A__	:							Dict						    = node
											A__	:							int						    = previous
											A__	:							Dict						    = node
											A__	:							List[Any]						    = self.rear







					def  _lowercase			(       self      :     int			,		_A      :     DoubleLinkedListNode[T, U]):

											if node.prev is None or node.next is None:
																	return None

											A__	:							List[str]						    = node.next
											A__	:							Union[str, Any]						    = node.prev
											A__	:							Optional[Any]						    = None
											A__	:							List[str]						    = None
											return node




class 							lowerCAmelCase__  (	Generic[T, U]						):
					__A     :    dict[Callable[[T], U], LRUCache[T, U]]           =						{}







					def __init__(       self      :     List[Any]			,		_A      :     int):
											A__	:							DoubleLinkedList[T, U]						    = DoubleLinkedList()
											A__	:							Union[str, Any]						    = capacity
											A__	:							List[str]						    = 0
											A__	:							Any						    = 0
											A__	:							int						    = 0
											A__	:							dict[T, DoubleLinkedListNode[T, U]]						    = {}







					def __repr__(       self      :     Optional[int]):
											return (
											    F'CacheInfo(hits={self.hits}, misses={self.miss}, '
											    F'capacity={self.capacity}, current size={self.num_keys})'
											)







					def __contains__(       self      :     str			,		_A      :     T):
											return key in self.cache







					def  _lowercase			(       self      :     Dict			,		_A      :     T):
											# Note: pythonic interface would throw KeyError rather than return None

											if key in self.cache:
																	self.hits += 1
																	A__	:							DoubleLinkedListNode[T, U]						    = self.cache[key]
																	A__	:							str						    = self.list.remove(self.cache[key])
																	assert node == value_node

																	# node is guaranteed not None because it is in self.cache
																	assert node is not None
																	self.list.add(_A)
																	return node.val
											self.miss += 1
											return None







					def  _lowercase			(       self      :     List[str]			,		_A      :     T			,		_A      :     U):

											if key not in self.cache:
																	if self.num_keys >= self.capacity:
																							# delete first node (oldest) when over capacity
																							A__	:							str						    = self.list.head.next

																							# guaranteed to have a non-None first node when num_keys > 0
																							# explain to type checker via assertions
																							assert first_node is not None
																							assert first_node.key is not None
																							assert (
																							    self.list.remove(_A) is not None
																							)  # node guaranteed to be in list assert node.key is not None

																							del self.cache[first_node.key]
																							self.num_keys -= 1
																	A__	:							Optional[int]						    = DoubleLinkedListNode(_A			,		_A)
																	self.list.add(self.cache[key])
																	self.num_keys += 1

											else:
																	# bump node to the end of the list, update value
																	A__	:							str						    = self.list.remove(self.cache[key])
																	assert node is not None  # node guaranteed to be in list
																	A__	:							int						    = value
																	self.list.add(_A)







					@classmethod
					def  _lowercase			(       cls      :     Dict			,		_A      :     int = 128):

											def cache_decorator_inner(_A      :     Callable[[T], U]) -> Callable[..., U]:
																	def cache_decorator_wrapper(*_A      :     T) -> U:
																							if func not in cls.decorator_function_to_instance_map:
																													A__	:							str						    = LRUCache(_A)

																							A__	:							Optional[int]						    = cls.decorator_function_to_instance_map[func].get(args[0])
																							if result is None:
																													A__	:							Tuple						    = func(*_A)
																													cls.decorator_function_to_instance_map[func].put(args[0]			,		_A)
																							return result

																	def cache_info() -> LRUCache[T, U]:
																							return cls.decorator_function_to_instance_map[func]

																	setattr(_A			,		"cache_info"			,		_A)  # noqa: B010

																	return cache_decorator_wrapper

											return cache_decorator_inner


if __name__ == "__main__":
		import doctest

		doctest.testmod()




from __future__ import annotations

snake_case    :						Optional[Any]  =						{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}




class 							lowerCAmelCase__  :







					def __init__(       self      :     Optional[Any]			,		_A      :     dict[str, list[str]]			,		_A      :     str):
											A__	:							Optional[Any]						    = graph
											# mapping node to its parent in resulting breadth first tree
											A__	:							dict[str, str | None]						    = {}
											A__	:							List[str]						    = source_vertex







					def  _lowercase			(       self      :     List[Any]):
											A__	:							str						    = {self.source_vertex}
											A__	:							List[str]						    = None
											A__	:							List[str]						    = [self.source_vertex]  # first in first out queue

											while queue:
																	A__	:							int						    = queue.pop(0)
																	for adjacent_vertex in self.graph[vertex]:
																							if adjacent_vertex not in visited:
																													visited.add(_A)
																													A__	:							Any						    = vertex
																													queue.append(_A)







					def  _lowercase			(       self      :     int			,		_A      :     str):
											if target_vertex == self.source_vertex:
																	return self.source_vertex

											A__	:							List[Any]						    = self.parent.get(_A)
											if target_vertex_parent is None:
																	A__	:							Union[str, Any]						    = (
																	    F'No path from vertex: {self.source_vertex} to vertex: {target_vertex}'
																	)
																	raise ValueError(_A)

											return self.shortest_path(_A) + F'->{target_vertex}'


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