


import heapq
def 				__lowerCamelCase						( UpperCAmelCase_						:		dict						):




      """simple docstring"""





      a						: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(UpperCAmelCase_ ,  [-1 * len(UpperCAmelCase_						), (key, value)]						)

      # chosen_vertices = set of chosen vertices
      a						:Optional[Any] 							=       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
            a						:Tuple 							=       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]:
                        a						:Optional[Any] 							=       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()

     snake_case				:    Optional[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)}""")










from PIL import Image






def 				A				(					_lowerCamelCase  ):





							'''simple docstring'''




							_lowerCAmelCase   ,    _lowerCAmelCase     :							int    =    image.size
							_lowerCAmelCase     :							Any    =    0
							_lowerCAmelCase     :							Tuple    =    image.load()
							for i in range(_lowerCamelCase  ):
														for j in range(_lowerCamelCase  ):
																					_lowerCAmelCase     :							Union[str, Any]    =    pixels[j, i]
																					mean += pixel
							mean //= width * height

							for j in range(_lowerCamelCase  ):
														for i in range(_lowerCamelCase  ):
																					_lowerCAmelCase     :							Optional[Any]    =    255 if pixels[i, j] > mean else 0
							return image


if __name__ == "__main__":
						_snake_case		=  mean_threshold(Image.open("path_to_image").convert("L"))
						image.save("output_image_path")
