



'''simple docstring'''





import heapq
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase      ) ->    set[int]:



    """simple docstring"""





    lowerCAmelCase__			:  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
    lowerCAmelCase__			:  List[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
        lowerCAmelCase__			:  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]:
                lowerCAmelCase__			:  Union[str, 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()

 _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'''





from PIL import Image
def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase      ):



    """simple docstring"""





    lowerCAmelCase__				,       lowerCAmelCase__			:  Dict											= image.size
    lowerCAmelCase__			:  int											= 0
    lowerCAmelCase__			:  int											= image.load()
    for i in range(UpperCamelCase      ):
        for j in range(UpperCamelCase      ):
            lowerCAmelCase__			:  int											= pixels[j, i]
            mean += pixel
    mean //= width * height

    for j in range(UpperCamelCase      ):
        for i in range(UpperCamelCase      ):
            lowerCAmelCase__			:  Dict											= 255 if pixels[i, j] > mean else 0
    return image


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


