


'''simple docstring'''



class 						_snake_case   :




					def __init__( self							,							_lowerCamelCase = ""							,							_lowerCamelCase = False):
								# Mapping from the first character of the prefix of the node
								UpperCAmelCase__					:   dict[str, RadixNode]       				=       {}

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

								UpperCAmelCase__					:   Optional[int]       				=       prefix




					def 			snake_case__  ( self							,							_lowerCamelCase):
								UpperCAmelCase__					:   Optional[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 			snake_case__  ( self							,							_lowerCamelCase):
								for word in words:
											self.insert(_lowerCamelCase)




					def 			snake_case__  ( self							,							_lowerCamelCase):
								# Case 1: If the word is the prefix of the node
								# Solution: We set the current node as leaf
								if self.prefix == word:
											UpperCAmelCase__					:   Optional[int]       				=       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:
											UpperCAmelCase__					:   Union[str, Any]       				=       RadixNode(prefix=_lowerCamelCase							,							is_leaf=_lowerCamelCase)

								else:
											UpperCAmelCase__					:   Any       				=       self.nodes[word[0]]
											UpperCAmelCase__				,    UpperCAmelCase__				,    UpperCAmelCase__					:   str       				=       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:
														UpperCAmelCase__					:   Any       				=       remaining_prefix

														UpperCAmelCase__					:   Optional[Any]       				=       self.nodes[matching_string[0]]
														UpperCAmelCase__					:   str       				=       RadixNode(_lowerCamelCase							,							_lowerCamelCase)
														UpperCAmelCase__					:   int       				=       aux_node

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




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

																	return True




					def 			snake_case__  ( self							,							_lowerCamelCase = 0):
								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 (						):
			UpperCAmelCase__					:   Dict       				=       """banana bananas bandana band apple all beast""".split()
			UpperCAmelCase__					:   List[str]       				=       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 (						):
			UpperCAmelCase__					:   str       				=       RadixNode()
			UpperCAmelCase__					:   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'''



import colorsys

from PIL import Image  # type: ignore







def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   ):
			UpperCAmelCase__					:   Optional[Any]       				=       x
			UpperCAmelCase__					:   Optional[int]       				=       y
			for step in range(UpperCamelCase__   ):  # noqa: B007
						UpperCAmelCase__					:   List[str]       				=       a * a - b * b + x
						UpperCAmelCase__					:   Optional[int]       				=       2 * a * b + y
						UpperCAmelCase__					:   int       				=       a_new

						# divergence happens for all complex number with an absolute value
						# greater than 4
						if a * a + b * b > 4:
									break
			return step / (max_step - 1)







def       _UpperCamelCase (						UpperCamelCase__   ):
			if distance == 1:
						return (0, 0, 0)
			else:
						return (2_5_5, 2_5_5, 2_5_5)







def       _UpperCamelCase (						UpperCamelCase__   ):
			if distance == 1:
						return (0, 0, 0)
			else:
						return tuple(round(i * 2_5_5   ) for i in colorsys.hsv_to_rgb(UpperCamelCase__	, 1	, 1   )   )







def       _UpperCamelCase (						UpperCamelCase__ = 8_0_0	, UpperCamelCase__ = 6_0_0	, UpperCamelCase__ = -0.6	, UpperCamelCase__ = 0	, UpperCamelCase__ = 3.2	, UpperCamelCase__ = 5_0	, UpperCamelCase__ = True	, ):
			UpperCAmelCase__					:   str       				=       Image.new("""RGB"""	, (image_width, image_height)   )
			UpperCAmelCase__					:   Optional[int]       				=       img.load()

			# loop through the image-coordinates
			for image_x in range(UpperCamelCase__   ):
						for image_y in range(UpperCamelCase__   ):
									# determine the figure-coordinates based on the image-coordinates
									UpperCAmelCase__					:   Union[str, Any]       				=       figure_width / image_width * image_height
									UpperCAmelCase__					:   Union[str, Any]       				=       figure_center_x + (image_x / image_width - 0.5) * figure_width
									UpperCAmelCase__					:   Tuple       				=       figure_center_y + (image_y / image_height - 0.5) * figure_height

									UpperCAmelCase__					:   List[str]       				=       get_distance(UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   )

									# color the corresponding pixel based on the selected coloring-function
									if use_distance_color_coding:
												UpperCAmelCase__					:   Any       				=       get_color_coded_rgb(UpperCamelCase__   )
									else:
												UpperCAmelCase__					:   Tuple       				=       get_black_and_white_rgb(UpperCamelCase__   )

			return img


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# colored version, full figure
		__A		=get_image()

		# uncomment for colored version, different section, zoomed in
		# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
		# figure_width = 0.8)

		# uncomment for black and white version, full figure
		# img = get_image(use_distance_color_coding = False)

		# uncomment to save the image
		# img.save("mandelbrot.png")

		img.show()