




"""simple docstring"""
import heapq





def 						UpperCAmelCase				(			A__:    dict     )  ->     set[int]:
   __lowerCamelCase					:	Union[str, Any]	       =				[]

   # for each node and his adjacency list add them and the rank of the node to queue
   # using heapq module the queue will be filled like a Priority Queue
   # heapq works with a min priority queue, so I used -1*len(v) to build it
   for key, value in graph.items():
      # O(log(n))
      heapq.heappush(snake_case__							,				[-1 * len(snake_case__     ), (key, value)]     )

   # chosen_vertices = set of chosen vertices
   __lowerCamelCase					:	int	       =				set()

   # while queue isn't empty and there are still edges
   #   (queue[0][0] is the rank of the node with max rank)
   while queue and queue[0][0] != 0:
      # extract vertex with max rank from queue and add it to chosen_vertices
      __lowerCamelCase					:	int	       =				heapq.heappop(snake_case__     )[1][0]
      chosen_vertices.add(snake_case__     )

      # Remove all arcs adjacent to argmax
      for elem in queue:
         # if v haven't adjacent node, skip
         if elem[0] == 0:
            continue
         # if argmax is reachable from elem
         # remove argmax from elem's adjacent list and update his rank
         if argmax in elem[1][1]:
            __lowerCamelCase					:	str	       =				elem[1][1].index(snake_case__     )
            del elem[1][1][index]
            elem[0] += 1
        # re-order the queue
      heapq.heapify(snake_case__     )
   return chosen_vertices


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     a_				:    int										=     {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
     print(F"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")









"""simple docstring"""
import random





def 						UpperCAmelCase				(			A__:    Union[str, Any]							,				A__:    List[str]							,				A__:    Union[str, Any]     )  ->     int:
			__lowerCamelCase					:	Optional[Any]	       =				a[left_index]
			__lowerCamelCase					:	int	       =				left_index + 1
			for j in range(left_index + 1							,				A__     ):
						if a[j] < pivot:
									__lowerCamelCase       ,      __lowerCamelCase					:	Optional[int]	       =				a[i], a[j]
									i += 1
			__lowerCamelCase       ,      __lowerCamelCase					:	str	       =				a[i - 1], a[left_index]
			return i - 1





def 						UpperCAmelCase				(			A__:    List[Any]							,				A__:    Tuple							,				A__:    Tuple     )  ->     Dict:
			if left < right:
						__lowerCamelCase					:	Optional[int]	       =				random.randint(A__							,				right - 1     )
						__lowerCamelCase       ,      __lowerCamelCase					:	int	       =				(
						    a[left],
						    a[pivot],
						)  # switches the pivot with the left most bound
						__lowerCamelCase					:	Union[str, Any]	       =				partition(A__							,				A__							,				A__     )
						quick_sort_random(
						    A__							,				A__							,				A__     )  # recursive quicksort to the left of the pivot point
						quick_sort_random(
						    A__							,				pivot_index + 1							,				A__     )  # recursive quicksort to the right of the pivot point





def 						UpperCAmelCase				(			)  ->     int:
			__lowerCamelCase					:	Dict	       =				input('Enter numbers separated by a comma:\n'     ).strip()
			__lowerCamelCase					:	int	       =				[int(A__     ) for item in user_input.split(','     )]

			quick_sort_random(A__							,				0							,				len(A__     )     )

			print(A__     )


if __name__ == "__main__":
					main()



