


'''simple docstring'''





import heapq


def        a__     (					UpperCamelCase_						:      dict						):
   UpperCAmelCase__	: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
   UpperCAmelCase__	: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
      UpperCAmelCase__	:int      =      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__	:Optional[int]      =      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'''





class 				UpperCAmelCase			:


 def __init__(      self							:	Union[str, Any] ):
    UpperCAmelCase__	:dict[str, TrieNode]      =      {}  # Mapping from char to TrieNode
    UpperCAmelCase__	:Union[str, Any]      =      False


 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[int]			,       __lowerCamelCase							:	list[str] ):
    for word in words:
       self.insert(__lowerCamelCase )


 def        __SCREAMING_SNAKE_CASE					(      self							:	Dict			,       __lowerCamelCase							:	str ):
    UpperCAmelCase__	:Tuple      =      self
    for char in word:
       if char not in curr.nodes:
          UpperCAmelCase__	:Optional[int]      =      TrieNode()
       UpperCAmelCase__	:Dict      =      curr.nodes[char]
    UpperCAmelCase__	:Optional[int]      =      True


 def        __SCREAMING_SNAKE_CASE					(      self							:	Any			,       __lowerCamelCase							:	str ):
    UpperCAmelCase__	:str      =      self
    for char in word:
       if char not in curr.nodes:
          return False
       UpperCAmelCase__	:Dict      =      curr.nodes[char]
    return curr.is_leaf





 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[Any]			,       __lowerCamelCase							:	str ):

    def _delete(__lowerCamelCase							:	TrieNode			,       __lowerCamelCase							:	str			,       __lowerCamelCase							:	int ) -> bool:
       if index == len(__lowerCamelCase ):
          # If word does not exist
          if not curr.is_leaf:
             return False
          UpperCAmelCase__	:int      =      False
          return len(curr.nodes ) == 0
       UpperCAmelCase__	:str      =      word[index]
       UpperCAmelCase__	:Optional[Any]      =      curr.nodes.get(__lowerCamelCase )
       # If char not in current trie node
       if not char_node:
          return False
       # Flag to check if node can be deleted
       UpperCAmelCase__	:Any      =      _delete(__lowerCamelCase			,       __lowerCamelCase			,       index + 1 )
       if delete_curr:
          del curr.nodes[char]
          return len(curr.nodes ) == 0
       return delete_curr

    _delete(self			,       __lowerCamelCase			,       0 )


def        a__     (					UpperCamelCase_						:      TrieNode,   UpperCamelCase_						:      str						):
   if node.is_leaf:
      print(UpperCamelCase_,   end=''' '''						)

   for key, value in node.nodes.items():
      print_words(UpperCamelCase_,   word + key						)


def        a__     (					):
   UpperCAmelCase__	:Union[str, Any]      =      '''banana bananas bandana band apple all beast'''.split()
   UpperCAmelCase__	:Union[str, Any]      =      TrieNode()
   root.insert_many(UpperCamelCase_						)
   # print_words(root, "")
   assert all(root.find(UpperCamelCase_						) for word in words						)
   assert root.find('''banana'''						)
   assert not root.find('''bandanas'''						)
   assert not root.find('''apps'''						)
   assert root.find('''apple'''						)
   assert root.find('''all'''						)
   root.delete('''all'''						)
   assert not root.find('''all'''						)
   root.delete('''banana'''						)
   assert not root.find('''banana'''						)
   assert root.find('''bananas'''						)
   return True


def        a__     (					UpperCamelCase_						:      str,   UpperCamelCase_						:      bool						):
   print(str(UpperCamelCase_						),   '''works!''' if passes else '''doesn\'t work :('''						)


def        a__     (					):
   assert test_trie()


def        a__     (					):
   print_results('''Testing trie functionality''',   test_trie()						)


if __name__ == "__main__":
    main()



