

'''simple docstring'''


from __future__ import annotations

from queue import Queue



class        lowercase    :


							def __init__(      self)				->					None:
								UpperCAmelCase_		:   dict[int, list[int]]													=       {}


							def     _snake_case				(      self)				->					None:
								for i in self.vertices:
									print(_snake_case     ,      ' : '     ,      ' -> '.join([str(_snake_case) for j in self.vertices[i]]))


							def     _snake_case				(      self     ,      _snake_case     ,      _snake_case)				->					None:
								if from_vertex in self.vertices:
									self.vertices[from_vertex].append(_snake_case)
								else:
									UpperCAmelCase_		:   Tuple													=       [to_vertex]





							def     _snake_case				(      self     ,      _snake_case)				->					set[int]:
								UpperCAmelCase_		:   Dict													=       set()

								# create a first in first out queue to store all the vertices for BFS
								UpperCAmelCase_		:   Queue													=       Queue()

								# mark the source node as visited and enqueue it
								visited.add(_snake_case)
								queue.put(_snake_case)

								while not queue.empty():
									UpperCAmelCase_		:   Optional[Any]													=       queue.get()

									# loop through all adjacent vertex and enqueue it if not yet visited
									for adjacent_vertex in self.vertices[vertex]:
										if adjacent_vertex not in visited:
											queue.put(_snake_case)
											visited.add(_snake_case)
								return visited


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

						testmod(verbose=True)

						lowerCAmelCase__      				=			Graph()
						g.add_edge(0, 1)
						g.add_edge(0, 2)
						g.add_edge(1, 2)
						g.add_edge(2, 0)
						g.add_edge(2, 3)
						g.add_edge(3, 3)

						g.print_graph()
						# 0  :  1 -> 2
						# 1  :  2
						# 2  :  0 -> 3
						# 3  :  3

						assert sorted(g.bfs(2)) == [0, 1, 2, 3]









'''simple docstring'''


from __future__ import annotations

from collections.abc import Iterable, Iterator
from typing import Any, Generic, TypeVar

lowerCAmelCase__      				=			TypeVar("T", bound=bool)



class        lowercase    (	Generic[T]			):


							def __init__(      self     ,      _snake_case)				->					None:
								UpperCAmelCase_		:   T													=       value
								UpperCAmelCase_		:   SkewNode[T] | None													=       None
								UpperCAmelCase_		:   SkewNode[T] | None													=       None


							@property
							def     _snake_case				(      self)				->					T:
								return self._value





							@staticmethod
							def     _snake_case				(      _snake_case     ,      _snake_case)				->					SkewNode[T] | None:
								if not roota:
									return roota

								if not roota:
									return roota

								if roota.value > roota.value:
									UpperCAmelCase_						,     UpperCAmelCase_		:   Union[str, Any]													=       roota, roota

								UpperCAmelCase_		:   Dict													=       roota
								UpperCAmelCase_		:   Dict													=       roota.right
								UpperCAmelCase_		:   Optional[int]													=       roota.left
								UpperCAmelCase_		:   Dict													=       SkewNode.merge(_snake_case     ,      _snake_case)

								return result



class        lowercase    (	Generic[T]			):


							def __init__(      self     ,      _snake_case = ())				->					None:
								UpperCAmelCase_		:   SkewNode[T] | None													=       None
								if data:
									for item in data:
										self.insert(_snake_case)


							def __bool__(      self)				->					bool:
								return self._root is not None


							def __iter__(      self)				->					Iterator[T]:
								UpperCAmelCase_		:   list[Any]													=       []
								while self:
									result.append(self.pop())

								# Pushing items back to the heap not to clear it.
								for item in result:
									self.insert(_snake_case)

								return iter(_snake_case)


							def     _snake_case				(      self     ,      _snake_case)				->					None:
								UpperCAmelCase_		:   Any													=       SkewNode.merge(self._root     ,      SkewNode(_snake_case))


							def     _snake_case				(      self)				->					T | None:
								UpperCAmelCase_		:   Union[str, Any]													=       self.top()
								UpperCAmelCase_		:   Tuple													=       (
								    SkewNode.merge(self._root.left     ,      self._root.right) if self._root else None
								)

								return result


							def     _snake_case				(      self)				->					T:
								if not self._root:
									raise IndexError('Can\'t get top element for the empty heap.')
								return self._root.value





							def     _snake_case				(      self)				->					None:
								UpperCAmelCase_		:   Union[str, Any]													=       None


if __name__ == "__main__":
						import doctest

						doctest.testmod()






