





"""simple docstring"""
import heapq



def      __lowerCamelCase   (							a_     :		dict							)			->      set[int]:
      __SCREAMING_SNAKE_CASE   :list[list]						=  []

      # 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(a_ ,   [-1 * len(a_							), (key, value)]							)

      # chosen_vertices = set of chosen vertices
      __SCREAMING_SNAKE_CASE   :Tuple						=  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
            __SCREAMING_SNAKE_CASE   :int						=  heapq.heappop(a_							)[1][0]
            chosen_vertices.add(a_							)

            # 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]:
                        __SCREAMING_SNAKE_CASE   :int						=  elem[1][1].index(a_							)
                        del elem[1][1][index]
                        elem[0] += 1
        # re-order the queue
            heapq.heapify(a_							)
      return chosen_vertices


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  lowerCamelCase_								=		{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"""
def      __lowerCamelCase   (							a_     :		int							)			->      bool:
      if not isinstance(a_ ,   a_							):
            __SCREAMING_SNAKE_CASE   :int						=  f'''Input value of [number={number}] must be an integer'''
            raise TypeError(a_							)
      if number < 0:
            return False
      __SCREAMING_SNAKE_CASE   :Any						=  number * number
      while number > 0:
            if number % 10 != number_square % 10:
                  return False
            number //= 10
            number_square //= 10
      return True


if __name__ == "__main__":
  import doctest

  doctest.testmod()