


"""simple docstring"""







class       SCREAMING_SNAKE_CASE__				:
       """simple docstring"""


       def __init__(						self		,     snake_case__ = ""		,     snake_case__ = False						):






         """simple docstring"""





         lowerCAmelCase     :     dict[str, RadixNode]								=							{}

         # A node will be a leaf if the tree contains its word
         lowerCAmelCase     :     str								=							is_leaf

         lowerCAmelCase     :     str								=							prefix

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     Dict								=							0
         for q, w in zip(self.prefix		,     snake_case__						):
           if q != w:
             break

           x += 1

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

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         for word in words:
           self.insert(snake_case__						)

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         if self.prefix == word:
           lowerCAmelCase     :     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:
           lowerCAmelCase     :     Optional[Any]								=							RadixNode(prefix=snake_case__		,     is_leaf=snake_case__						)

         else:
           lowerCAmelCase     :     Tuple								=							self.nodes[word[0]]
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     Optional[Any]								=							incoming_node.match(
               snake_case__						)

           # 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(snake_case__						)

           # 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:
             lowerCAmelCase     :     Optional[Any]								=							remaining_prefix

             lowerCAmelCase     :     int								=							self.nodes[matching_string[0]]
             lowerCAmelCase     :     List[Any]								=							RadixNode(snake_case__		,     snake_case__						)
             lowerCAmelCase     :     Optional[int]								=							aux_node

             if remaining_word == "":
               lowerCAmelCase     :     Optional[int]								=							True
             else:
               self.nodes[matching_string[0]].insert(snake_case__						)

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     str								=							self.nodes.get(word[0]		,     snake_case__						)
         if not incoming_node:
           return False
         else:
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     int								=							incoming_node.match(
               snake_case__						)
           # 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(snake_case__						)

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     int								=							self.nodes.get(word[0]		,     snake_case__						)
         if not incoming_node:
           return False
         else:
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     Union[str, Any]								=							incoming_node.match(
               snake_case__						)
           # 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(snake_case__						)
           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:
                   lowerCAmelCase     :     List[str]								=							list(self.nodes.values()						)[0]
                   lowerCAmelCase     :     List[str]								=							merging_node.is_leaf
                   self.prefix += merging_node.prefix
                   lowerCAmelCase     :     Optional[int]								=							merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
               elif len(incoming_node.nodes						) > 1:
                 lowerCAmelCase     :     Optional[int]								=							False
               # If there is 1 edge, we merge it with its child
               else:
                 lowerCAmelCase     :     Optional[Any]								=							list(incoming_node.nodes.values()						)[0]
                 lowerCAmelCase     :     int								=							merging_node.is_leaf
                 incoming_node.prefix += merging_node.prefix
                 lowerCAmelCase     :     Tuple								=							merging_node.nodes

               return True







       def        lowercase__							(						self		,     snake_case__ = 0						):






         """simple docstring"""





         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 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Union[str, Any]								=							"banana bananas bandana band apple all beast".split()
  lowerCAmelCase     :     List[str]								=							RadixNode()
  root.insert_many(SCREAMING_SNAKE_CASE				)

  assert all(root.find(SCREAMING_SNAKE_CASE				) 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 					a__			(				):


  '''simple docstring'''







  assert test_trie()
def 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Dict								=							RadixNode()
  lowerCAmelCase     :     Optional[Any]								=							"banana bananas bandanas bandana band apple all beast".split()
  root.insert_many(SCREAMING_SNAKE_CASE				)

  print("Words:"				,      SCREAMING_SNAKE_CASE				)
  print("Tree:"				)
  root.print_tree()


if __name__ == "__main__":
     main()









'''simple docstring'''


import math






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		return math.sqrt(__lowerCAmelCase      ) * math.sqrt(__lowerCAmelCase      ) == num






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				int	    =					0
		_UpperCAmelCase						:				Tuple	    =					n
		while left <= right:
				_UpperCAmelCase						:				int	    =					(left + right) // 2
				if mid**2 == n:
						return True
				elif mid**2 > n:
						_UpperCAmelCase						:				str	    =					mid - 1
				else:
						_UpperCAmelCase						:				List[str]	    =					mid + 1
		return False


if __name__ == "__main__":
						import doctest

						doctest.testmod()



