'''simple docstring'''

class       UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self     ,       __lowerCAmelCase = ""     ,       __lowerCAmelCase = False			)  ->  None:
        # Mapping from the first character of the prefix of the node
        lowercase__    :   dict[str, RadixNode]						= {}

        # A node will be a leaf if the tree contains its word
        lowercase__    :   Optional[Any]						= is_leaf

        lowercase__    :   Optional[int]						= prefix

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  tuple[str, str, str]:
        lowercase__    :   Union[str, Any]						= 0
        for q, w in zip(self.prefix     ,       __lowerCAmelCase			):
         if q != w:
          break

         x += 1

        return self.prefix[:x], self.prefix[x:], word[x:]

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  None:
        for word in words:
         self.insert(__lowerCAmelCase			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  None:
        # Case 1: If the word is the prefix of the node
        # Solution: We set the current node as leaf
        if self.prefix == word:
         lowercase__    :   Union[str, Any]						= True

        # Case 2: The node has no edges that have a prefix to the word
        # Solution: We create an edge from the current node to a new one
        # containing the word
        elif word[0] not in self.nodes:
         lowercase__    :   Dict						= RadixNode(prefix=__lowerCAmelCase     ,       is_leaf=__lowerCAmelCase			)

        else:
         lowercase__    :   Tuple						= self.nodes[word[0]]
         lowercase__			,							lowercase__			,							lowercase__    :   Dict						= incoming_node.match(
             __lowerCAmelCase			)

         # Case 3: The node prefix is equal to the matching
         # Solution: We insert remaining word on the next node
         if remaining_prefix == "":
          self.nodes[matching_string[0]].insert(__lowerCAmelCase			)

         # Case 4: The word is greater equal to the matching
         # Solution: Create a node in between both nodes, change
         # prefixes and add the new node for the remaining word
         else:
          lowercase__    :   List[Any]						= remaining_prefix

          lowercase__    :   List[Any]						= self.nodes[matching_string[0]]
          lowercase__    :   Dict						= RadixNode(__lowerCAmelCase     ,       __lowerCAmelCase			)
          lowercase__    :   int						= aux_node

          if remaining_word == "":
           lowercase__    :   Optional[Any]						= True
          else:
           self.nodes[matching_string[0]].insert(__lowerCAmelCase			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  bool:
        lowercase__    :   Union[str, Any]						= self.nodes.get(word[0]     ,       __lowerCAmelCase			)
        if not incoming_node:
         return False
        else:
         lowercase__			,							lowercase__			,							lowercase__    :   int						= incoming_node.match(
             __lowerCAmelCase			)
         # If there is remaining prefix, the word can't be on the tree
         if remaining_prefix != "":
          return False
         # This applies when the word and the prefix are equal
         elif remaining_word == "":
          return incoming_node.is_leaf
         # We have word remaining so we check the next node
         else:
          return incoming_node.find(__lowerCAmelCase			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase			)  ->  bool:
        lowercase__    :   Optional[int]						= self.nodes.get(word[0]     ,       __lowerCAmelCase			)
        if not incoming_node:
         return False
        else:
         lowercase__			,							lowercase__			,							lowercase__    :   Dict						= incoming_node.match(
             __lowerCAmelCase			)
         # If there is remaining prefix, the word can't be on the tree
         if remaining_prefix != "":
          return False
         # We have word remaining so we check the next node
         elif remaining_word != "":
          return incoming_node.delete(__lowerCAmelCase			)
         else:
          # If it is not a leaf, we don't have to delete
          if not incoming_node.is_leaf:
           return False
          else:
           # We delete the nodes if no edges go from it
           if len(incoming_node.nodes			) == 0:
            del self.nodes[word[0]]
            # We merge the current node with its only child
            if len(self.nodes			) == 1 and not self.is_leaf:
             lowercase__    :   Tuple						= list(self.nodes.values()			)[0]
             lowercase__    :   List[str]						= merging_node.is_leaf
             self.prefix += merging_node.prefix
             lowercase__    :   str						= merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
           elif len(incoming_node.nodes			) > 1:
            lowercase__    :   int						= False
           # If there is 1 edge, we merge it with its child
           else:
            lowercase__    :   Any						= list(incoming_node.nodes.values()			)[0]
            lowercase__    :   Tuple						= merging_node.is_leaf
            incoming_node.prefix += merging_node.prefix
            lowercase__    :   List[str]						= merging_node.nodes

           return True


       def _lowerCAmelCase(						self     ,       __lowerCAmelCase = 0			)  ->  None:
        if self.prefix != "":
         print('''-''' * height     ,       self.prefix     ,       '''  (leaf)''' if self.is_leaf else ''''''			)

        for value in self.nodes.values():
         value.print_tree(height + 1			)


def       __UpperCamelCase	(       ):
 lowercase__    :   Optional[Any]						= '''banana bananas bandana band apple all beast'''.split()
 lowercase__    :   List[Any]						= RadixNode()
 root.insert_many(UpperCAmelCase					)

 assert all(root.find(UpperCAmelCase					) for word in words					)
 assert not root.find('''bandanas'''					)
 assert not root.find('''apps'''					)
 root.delete('''all'''					)
 assert not root.find('''all'''					)
 root.delete('''banana'''					)
 assert not root.find('''banana'''					)
 assert root.find('''bananas'''					)

 return True
def       __UpperCamelCase	(       ):
 assert test_trie()
def       __UpperCamelCase	(       ):
 lowercase__    :   Union[str, Any]						= RadixNode()
 lowercase__    :   Dict						= '''banana bananas bandanas bandana band apple all beast'''.split()
 root.insert_many(UpperCAmelCase					)

 print('''Words:'''		,					UpperCAmelCase					)
 print('''Tree:'''					)
 root.print_tree()


if __name__ == "__main__":
  main()


'''simple docstring'''

class       UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self			)  ->  List[str]:
        lowercase__    :   Dict						= {}

       def _lowerCAmelCase(						self			)  ->  None:
        print(self.vertex			)
        for i in self.vertex:
         print(__lowerCAmelCase     ,       ''' -> '''     ,       ''' -> '''.join([str(__lowerCAmelCase			) for j in self.vertex[i]]			)			)

       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase			)  ->  None:
        # check if vertex is already present,
        if from_vertex in self.vertex:
         self.vertex[from_vertex].append(__lowerCAmelCase			)
        else:
         # else make a new vertex
         lowercase__    :   Union[str, Any]						= [to_vertex]

       def _lowerCAmelCase(						self			)  ->  None:
        # visited array for storing already visited nodes
        lowercase__    :   str						= [False] * len(self.vertex			)

        # call the recursive helper function
        for i in range(len(self.vertex			)			):
         if not visited[i]:
          self.dfs_recursive(__lowerCAmelCase     ,       __lowerCAmelCase			)


       def _lowerCAmelCase(						self     ,       __lowerCAmelCase     ,       __lowerCAmelCase			)  ->  None:
        # mark start vertex as visited
        lowercase__    :   List[str]						= True

        print(__lowerCAmelCase     ,       end=''' '''			)

        # Recur for all the vertices that are adjacent to this node
        for i in self.vertex:
         if not visited[i]:
          self.dfs_recursive(__lowerCAmelCase     ,       __lowerCAmelCase			)


if __name__ == "__main__":
  __a:			Optional[Any]	       =       Graph()
  g.add_edge(0, 1)
  g.add_edge(0, 2)
  g.add_edge(1, 2)
  g.add_edge(2, 0)
  g.add_edge(2, 3)
  g.add_edge(3, 3)

  g.print_graph()
  print("""DFS:""")
  g.dfs()

  # OUTPUT:
  # 0  ->  1 -> 2
  # 1  ->  2
  # 2  ->  0 -> 3
  # 3  ->  3
  # DFS:
  #  0 1 2 3

