code: 
  
  
  
  
  
  
  """simple docstring"""
  
  from __future__ import annotations
  
  from collections.abc import Iterable
  from dataclasses import dataclass
  from typing import Any
  
  
  class 	__lowerCamelCase       :
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  		a_			:       List[Any]      =							("""_front""", """_back""", """_len""")
  
  
  		@dataclass
  		class 	__lowerCamelCase       :
  
  
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				a_			:       Any      =							None
  				a_			:       Deque._Node | None      =							None
  				a_			:       Deque._Node | None      =							None
  
  
  
  
  
  
  
  		class 	__lowerCamelCase       :
  
  
  
  
  
  				'''simple docstring'''
  
  
  
  
  
  
  				a_			:       Dict      =							("""_cur""",)
  
  
  
  
  
  				def __init__(     self							:			int		,    a_							:			Deque._Node | None			):
  						lowerCAmelCase_     :							Dict             =    cur
  
  
  
  
  
  				def __iter__(     self							:			str			):
  						return self
  
  
  
  
  
  				def      lowerCamelCase (     self							:			Dict			):
  						if self._cur is None:
  								# finished iterating
  								raise StopIteration
  						lowerCAmelCase_     :							Union[str, Any]             =    self._cur.val
  						lowerCAmelCase_     :							Any             =    self._cur.next_node
  
  						return val
  
  
  
  
  
  
  
  		def __init__(     self							:			Union[str, Any]		,    a_							:			Iterable[Any] | None = None			):
  				lowerCAmelCase_     :							Any             =    None
  				lowerCAmelCase_     :							Any             =    None
  				lowerCAmelCase_     :							int             =    0
  
  				if iterable is not None:
  						# append every value to the deque
  						for val in iterable:
  								self.append(a_			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Any		,    a_							:			Any			):
  				lowerCAmelCase_     :							Optional[Any]             =    self._Node(a_		,    a_		,    a_			)
  				if self.is_empty():
  						# front = back
  						lowerCAmelCase_     :							Tuple             =    node
  						lowerCAmelCase_     :							str             =    1
  				else:
  						# connect nodes
  						lowerCAmelCase_     :							Optional[Any]             =    node
  						lowerCAmelCase_     :							Optional[int]             =    self._back
  						lowerCAmelCase_     :							List[str]             =    node  # assign new back to the new node
  
  						self._len += 1
  
  						# make sure there were no errors
  						assert not self.is_empty(), "Error on appending value."
  
  
  
  
  
  		def      lowerCamelCase (     self							:			int		,    a_							:			Any			):
  				lowerCAmelCase_     :							List[str]             =    self._Node(a_		,    a_		,    a_			)
  				if self.is_empty():
  						# front = back
  						lowerCAmelCase_     :							Optional[int]             =    node
  						lowerCAmelCase_     :							str             =    1
  				else:
  						# connect nodes
  						lowerCAmelCase_     :							Optional[Any]             =    self._front
  						lowerCAmelCase_     :							Any             =    node
  						lowerCAmelCase_     :							Any             =    node  # assign new front to the new node
  
  						self._len += 1
  
  						# make sure there were no errors
  						assert not self.is_empty(), "Error on appending value."
  
  
  
  
  
  		def      lowerCamelCase (     self							:			str		,    a_							:			Iterable[Any]			):
  				for val in iterable:
  						self.append(a_			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]		,    a_							:			Iterable[Any]			):
  				for val in iterable:
  						self.appendleft(a_			)
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]			):
  				assert not self.is_empty(), "Deque is empty."
  
  				lowerCAmelCase_     :							Any             =    self._back
  				lowerCAmelCase_     :							Dict             =    self._back.prev_node  # set new back
  				# drop the last node - python will deallocate memory automatically
  				lowerCAmelCase_     :							Optional[Any]             =    None
  
  				self._len -= 1
  
  				return topop.val
  
  
  
  
  
  		def      lowerCamelCase (     self							:			Optional[int]			):
  				assert not self.is_empty(), "Deque is empty."
  
  				lowerCAmelCase_     :							List[Any]             =    self._front
  				lowerCAmelCase_     :							List[Any]             =    self._front.next_node  # set new front and drop the first node
  				lowerCAmelCase_     :							Tuple             =    None
  
  				self._len -= 1
  
  				return topop.val
  
  
  
  
  
  		def      lowerCamelCase (     self							:			List[str]			):
  				return self._front is None
  
  
  
  
  
  		def __len__(     self							:			List[Any]			):
  				return self._len
  
  
  
  
  
  		def __eq__(     self							:			Optional[Any]		,    a_							:			object			):
  
  				if not isinstance(a_		,    a_			):
  						return NotImplemented
  
  				lowerCAmelCase_     :							List[str]             =    self._front
  				lowerCAmelCase_     :							str             =    other._front
  
  				# if the length of the dequeues are not the same, they are not equal
  				if len(self			) != len(a_			):
  						return False
  
  				while me is not None and oth is not None:
  						# compare every value
  						if me.val != oth.val:
  								return False
  						lowerCAmelCase_     :							List[str]             =    me.next_node
  						lowerCAmelCase_     :							Tuple             =    oth.next_node
  
  				return True
  
  
  
  
  
  		def __iter__(     self							:			List[str]			):
  				return Deque._Iterator(self._front			)
  
  
  
  
  
  		def __repr__(     self							:			str			):
  				lowerCAmelCase_     :							Tuple             =    []
  				lowerCAmelCase_     :							List[str]             =    self._front
  				while aux is not None:
  						# append the values in a list to display
  						values_list.append(aux.val			)
  						lowerCAmelCase_     :							Union[str, Any]             =    aux.next_node
  
  				return f'''[{", ".join(repr(a_			) for val in values_list			)}]'''
  
  
  if __name__ == "__main__":
  					import doctest
  
  					doctest.testmod()
  
style_context: 
  
  
  
  
  
  
  """simple docstring"""
  
  from __future__ import annotations
  
  import random
  
  # Adjacency list representation of this graph:
  # https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
  lowercase__      =				{
      """1""": ["""2""", """3""", """4""", """5"""],
      """2""": ["""1""", """3""", """4""", """5"""],
      """3""": ["""1""", """2""", """4""", """5""", """10"""],
      """4""": ["""1""", """2""", """3""", """5""", """6"""],
      """5""": ["""1""", """2""", """3""", """4""", """7"""],
      """6""": ["""7""", """8""", """9""", """10""", """4"""],
      """7""": ["""6""", """8""", """9""", """10""", """5"""],
      """8""": ["""6""", """7""", """9""", """10"""],
      """9""": ["""6""", """7""", """8""", """10"""],
      """10""": ["""6""", """7""", """8""", """9""", """3"""],
  }
  
  def 	__lowerCamelCase			(						__UpperCamelCase )		->					set[tuple[str, str]]:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Union[str, Any]             =    {node: {node} for node in graph}
  
  		lowerCAmelCase_     :							List[str]             =    {node: graph[node][:] for node in graph}
  
  		while len(__UpperCamelCase ) > 2:
  				# Choose a random edge.
  				lowerCAmelCase_     :							int             =    random.choice(list(graph_copy.keys() ) )
  				lowerCAmelCase_     :							Any             =    random.choice(graph_copy[u] )
  
  				# Contract edge (u, v) to new node uv
  				lowerCAmelCase_     :							Union[str, Any]             =    u + v
  				lowerCAmelCase_     :							List[Any]             =    list(set(graph_copy[u] + graph_copy[v] ) )
  				uv_neighbors.remove(__UpperCamelCase )
  				uv_neighbors.remove(__UpperCamelCase )
  				lowerCAmelCase_     :							str             =    uv_neighbors
  				for neighbor in uv_neighbors:
  						graph_copy[neighbor].append(__UpperCamelCase )
  
  				lowerCAmelCase_     :							Optional[int]             =    set(contracted_nodes[u].union(contracted_nodes[v] ) )
  
  				# Remove nodes u and v.
  				del graph_copy[u]
  				del graph_copy[v]
  				for neighbor in uv_neighbors:
  						if u in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  						if v in graph_copy[neighbor]:
  								graph_copy[neighbor].remove(__UpperCamelCase )
  
      # Find cutset.
  		lowerCAmelCase_     :							Union[str, Any]             =    [contracted_nodes[node] for node in graph_copy]
  		return {
  		    (node, neighbor)
  		    for node in groups[0]
  		    for neighbor in graph[node]
  		    if neighbor in groups[1]
  		}
  
  
  if __name__ == "__main__":
  					print(partition_graph(TEST_GRAPH))
  