'''simple docstring'''
import heapq



def  __lowerCamelCase       (      _UpperCamelCase  :  dict					):


      '''simple docstring'''


      UpperCAmelCase_            =  []

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

      # chosen_vertices = set of chosen vertices
      UpperCAmelCase_            =  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
            UpperCAmelCase_            =  heapq.heappop(_UpperCamelCase					)[1][0]
            chosen_vertices.add(_UpperCamelCase					)

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      lowercase__  :      Any        =					{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'''
lowercase__  :      Union[str, Any]        =					"\n# Transformers 설치 방법\n! pip install transformers datasets\n# 마지막 릴리스 대신 소스에서 설치하려면, 위 명령을 주석으로 바꾸고 아래 명령을 해제하세요.\n# ! pip install git+https://github.com/huggingface/transformers.git\n"

lowercase__  :      str        =					[{"type": "code", "content": INSTALL_CONTENT}]
lowercase__  :      Any        =					{
    "{processor_class}": "FakeProcessorClass",
    "{model_class}": "FakeModelClass",
    "{object_class}": "FakeObjectClass",
}





