






from __future__ import annotations






def 				lowerCamelCase__      (    __lowerCamelCase			:     dict  ,		__lowerCamelCase			:     str		):
  __UpperCAmelCase      , __UpperCAmelCase							:	str           =  set(__lowerCamelCase		), [start]

  while stack:
    __UpperCAmelCase							:	Tuple           =  stack.pop()
    explored.add(__lowerCamelCase		)
    # Differences from BFS:
    # 1) pop last element instead of first one
    # 2) add adjacent elements to stack without exploring them
    for adj in reversed(graph[v]		):
      if adj not in explored:
        stack.append(__lowerCamelCase		)
  return explored


a		:       Union[str, Any]			     = {
    "A": ["B", "C", "D"],
    "B": ["A", "D", "E"],
    "C": ["A", "F"],
    "D": ["B", "D"],
    "E": ["B", "F"],
    "F": ["C", "E", "G"],
    "G": ["F"],
}

if __name__ == "__main__":
       import doctest

       doctest.testmod()
       print(depth_first_search(G, "A"))










def 				lowerCamelCase__      (    __lowerCamelCase			:     Tuple  ,		__lowerCamelCase			:     Union[str, Any]		):
  __UpperCAmelCase							:	Tuple           =  [1]
  for i in range(2  ,		__lowerCamelCase		):
    factorials.append(factorials[-1] * i		)
  assert 0 <= k < factorials[-1] * n, "k out of bounds"

  __UpperCAmelCase							:	Optional[Any]           =  []
  __UpperCAmelCase							:	str           =  list(range(__lowerCamelCase		)		)

  # Find permutation
  while factorials:
    __UpperCAmelCase							:	Any           =  factorials.pop()
    __UpperCAmelCase      , __UpperCAmelCase							:	Optional[Any]           =  divmod(__lowerCamelCase  ,		__lowerCamelCase		)
    permutation.append(elements[number]		)
    elements.remove(elements[number]		)
  permutation.append(elements[0]		)

  return permutation


if __name__ == "__main__":
       import doctest

       doctest.testmod()


