
"""simple docstring"""



import heapq


def  _UpperCamelCase	(						_A      )    ->  set[int]:





    """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(_A					,      [-1 * len(_A      ), (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(_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]:
                _UpperCAmelCase          =   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()

 a					:	str							=		{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 __future__ import annotations


def  _UpperCamelCase	(						_A      )    ->  None:





    """simple docstring"""

    create_state_space_tree(_A					,      []					,      0					,      [0 for i in range(len(_A      )      )]      )


def  _UpperCamelCase	(						_A					,      _A					,      _A					,      _A					,      )    ->  None:





    """simple docstring"""

    if index == len(_A      ):
        print(_A      )
        return

    for i in range(len(_A      )      ):
        if not index_used[i]:
            current_sequence.append(sequence[i]      )
            _UpperCAmelCase          =   True
            create_state_space_tree(_A					,      _A					,      index + 1					,      _A      )
            current_sequence.pop()
            _UpperCAmelCase          =   False
a					:	list[int | str]							=		[3, 1, 2, 4]
generate_all_permutations(sequence)

a					:	list[int | str]							=		["A", "B", "C"]







generate_all_permutations(sequence_a)