






"""simple docstring"""






def 					_A			(__a							) ->       str:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_      :  set[int]    						=		set()
    # To detect a back edge, keep track of vertices currently in the recursion stack
    SCREAMING_SNAKE_CASE_      :  set[int]    						=		set()
    return any(
        node not in visited and depth_first_search(lowerCAmelCase_    ,				lowerCAmelCase_    ,				lowerCAmelCase_    ,				lowerCAmelCase_							)
        for node in graph							)



def 					_A			(__a    ,				__a    ,				__a    ,				__a							) ->       List[Any]:
    """simple docstring"""






    visited.add(lowerCAmelCase_							)
    rec_stk.add(lowerCAmelCase_							)

    for node in graph[vertex]:
        if node not in visited:
            if depth_first_search(lowerCAmelCase_    ,				lowerCAmelCase_    ,				lowerCAmelCase_    ,				lowerCAmelCase_							):
                return True
        elif node in rec_stk:
            return True

    # The node needs to be removed from recursion stack before function ends
    rec_stk.remove(lowerCAmelCase_							)
    return False


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

  testmod()










from __future__ import annotations
def 					snake_case_						(   lowerCAmelCase_				:  int				,				lowerCAmelCase_				:  int					):
							if partitions <= 0:
														raise ValueError("""partitions must be a positive number!"""					)
							if partitions > number_of_bytes:
														raise ValueError("""partitions can not > number_of_bytes!"""					)
							__lowercase					:							Dict			=   number_of_bytes // partitions
							__lowercase					:							Union[str, Any]			=   []
							for i in range(lowerCAmelCase_					):
														__lowercase					:							str			=   i * bytes_per_partition + 1
														__lowercase					:							List[Any]			=   (
														    number_of_bytes if i == partitions - 1 else (i + 1) * bytes_per_partition
														)
														allocation_list.append(F"{start_bytes}-{end_bytes}"					)
							return allocation_list


if __name__ == "__main__":
	import doctest

	doctest.testmod()