





import colorsys

from PIL import Image  # type: ignore


def 					A__	(       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		)   ->     float:
		_SCREAMING_SNAKE_CASE   : Optional[int]								=x
		_SCREAMING_SNAKE_CASE   : List[str]								=y
		for step in range(SCREAMING_SNAKE_CASE_		):  # noqa: B007
				_SCREAMING_SNAKE_CASE   : Optional[Any]								=a * a - b * b + x
				_SCREAMING_SNAKE_CASE   : int								=2 * a * b + y
				_SCREAMING_SNAKE_CASE   : Optional[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 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     tuple:
		if distance == 1:
				return (0, 0, 0)
		else:
				return (2_5_5, 2_5_5, 2_5_5)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     tuple:
		if distance == 1:
				return (0, 0, 0)
		else:
				return tuple(round(i * 2_5_5		) for i in colorsys.hsv_to_rgb(SCREAMING_SNAKE_CASE_							,       1							,       1		)		)


def 					A__	(       SCREAMING_SNAKE_CASE_ = 8_0_0							,       SCREAMING_SNAKE_CASE_ = 6_0_0							,       SCREAMING_SNAKE_CASE_ = -0.6							,       SCREAMING_SNAKE_CASE_ = 0							,       SCREAMING_SNAKE_CASE_ = 3.2							,       SCREAMING_SNAKE_CASE_ = 5_0							,       SCREAMING_SNAKE_CASE_ = True							,       )   ->     Image.Image:
		_SCREAMING_SNAKE_CASE   : Any								=Image.new('''RGB'''							,       (image_width, image_height)		)
		_SCREAMING_SNAKE_CASE   : str								=img.load()

		# loop through the image-coordinates
		for image_x in range(SCREAMING_SNAKE_CASE_		):
				for image_y in range(SCREAMING_SNAKE_CASE_		):
						# determine the figure-coordinates based on the image-coordinates
						_SCREAMING_SNAKE_CASE   : Tuple								=figure_width / image_width * image_height
						_SCREAMING_SNAKE_CASE   : Any								=figure_center_x + (image_x / image_width - 0.5) * figure_width
						_SCREAMING_SNAKE_CASE   : Optional[int]								=figure_center_y + (image_y / image_height - 0.5) * figure_height

						_SCREAMING_SNAKE_CASE   : int								=get_distance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		)

						# color the corresponding pixel based on the selected coloring-function
						if use_distance_color_coding:
								_SCREAMING_SNAKE_CASE   : Dict								=get_color_coded_rgb(SCREAMING_SNAKE_CASE_		)
						else:
								_SCREAMING_SNAKE_CASE   : Optional[int]								=get_black_and_white_rgb(SCREAMING_SNAKE_CASE_		)

		return img


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				# colored version, full figure
				snake_case_							=			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()








from __future__ import annotations

import queue
class        snake_case_		:







		def __init__(		self			,     __lowercase   )				->   int:
				lowerCamelCase   : int								=data
				lowerCamelCase   : str								=None
				lowerCamelCase   : Dict								=None


def 					A__	(       )   ->     TreeNode:
		print('''\n********Press N to stop entering at any point of time********\n'''		)
		lowerCamelCase   : Tuple								=input('''Enter the value of the root node: '''		).strip().lower()
		lowerCamelCase   : queue.Queue								=queue.Queue()
		lowerCamelCase   : Dict								=TreeNode(int(SCREAMING_SNAKE_CASE_		)		)
		q.put(SCREAMING_SNAKE_CASE_		)
		while not q.empty():
				lowerCamelCase   : Dict								=q.get()
				lowerCamelCase   : Optional[int]								=F"Enter the left node of {node_found.data}: "
				lowerCamelCase   : Tuple								=input(SCREAMING_SNAKE_CASE_		).strip().lower() or '''n'''
				if check == "n":
						return tree_node
				lowerCamelCase   : Union[str, Any]								=TreeNode(int(SCREAMING_SNAKE_CASE_		)		)
				lowerCamelCase   : Optional[Any]								=left_node
				q.put(SCREAMING_SNAKE_CASE_		)
				lowerCamelCase   : List[Any]								=F"Enter the right node of {node_found.data}: "
				lowerCamelCase   : int								=input(SCREAMING_SNAKE_CASE_		).strip().lower() or '''n'''
				if check == "n":
						return tree_node
				lowerCamelCase   : str								=TreeNode(int(SCREAMING_SNAKE_CASE_		)		)
				lowerCamelCase   : Optional[Any]								=right_node
				q.put(SCREAMING_SNAKE_CASE_		)
		raise


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		print(node.data							,       end=''','''		)
		pre_order(node.left		)
		pre_order(node.right		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		in_order(node.left		)
		print(node.data							,       end=''','''		)
		in_order(node.right		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		post_order(node.left		)
		post_order(node.right		)
		print(node.data							,       end=''','''		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		lowerCamelCase   : queue.Queue								=queue.Queue()
		q.put(SCREAMING_SNAKE_CASE_		)
		while not q.empty():
				lowerCamelCase   : Optional[int]								=q.get()
				print(node_dequeued.data							,       end=''','''		)
				if node_dequeued.left:
						q.put(node_dequeued.left		)
				if node_dequeued.right:
						q.put(node_dequeued.right		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		lowerCamelCase   : queue.Queue								=queue.Queue()
		q.put(SCREAMING_SNAKE_CASE_		)
		while not q.empty():
				lowerCamelCase   : Tuple								=[]
				while not q.empty():
						lowerCamelCase   : List[str]								=q.get()
						print(node_dequeued.data							,       end=''','''		)
						if node_dequeued.left:
								list_.append(node_dequeued.left		)
						if node_dequeued.right:
								list_.append(node_dequeued.right		)
				print()
				for node in list_:
						q.put(SCREAMING_SNAKE_CASE_		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		lowerCamelCase   : list[TreeNode]								=[]
		lowerCamelCase   : Tuple								=node
		while n or stack:
				while n:  # start from root node, find its left child
						print(n.data							,       end=''','''		)
						stack.append(SCREAMING_SNAKE_CASE_		)
						lowerCamelCase   : Any								=n.left
				# end of while means current node doesn't have left child
				lowerCamelCase   : Tuple								=stack.pop()
				# start to traverse its right child
				lowerCamelCase   : Union[str, Any]								=n.right


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		lowerCamelCase   : list[TreeNode]								=[]
		lowerCamelCase   : List[Any]								=node
		while n or stack:
				while n:
						stack.append(SCREAMING_SNAKE_CASE_		)
						lowerCamelCase   : List[Any]								=n.left
				lowerCamelCase   : Dict								=stack.pop()
				print(n.data							,       end=''','''		)
				lowerCamelCase   : Union[str, Any]								=n.right


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     None:
		if not isinstance(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		) or not node:
				return
		lowerCamelCase		,   lowerCamelCase   : Optional[int]								=[], []
		lowerCamelCase   : Dict								=node
		stacka.append(SCREAMING_SNAKE_CASE_		)
		while stacka:  # to find the reversed order of post order, store it in stack2
				lowerCamelCase   : int								=stacka.pop()
				if n.left:
						stacka.append(n.left		)
				if n.right:
						stacka.append(n.right		)
				stacka.append(SCREAMING_SNAKE_CASE_		)
		while stacka:  # pop up from stack2 will be the post order
				print(stacka.pop().data							,       end=''','''		)


def 					A__	(       SCREAMING_SNAKE_CASE_ = ""							,       SCREAMING_SNAKE_CASE_=5_0							,       SCREAMING_SNAKE_CASE_="*"		)   ->     str:
		if not s:
				return "\n" + width * char
		lowerCamelCase		,   lowerCamelCase   : Dict								=divmod(width - len(SCREAMING_SNAKE_CASE_		) - 2							,       2		)
		return F"{left * char} {s} {(left + extra) * char}"


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				print(prompt('''Binary Tree Traversals'''))

				snake_case_							=			build_tree()
				print(prompt('''Pre Order Traversal'''))
				pre_order(node)
				print(prompt() + '''\n''')

				print(prompt('''In Order Traversal'''))
				in_order(node)
				print(prompt() + '''\n''')

				print(prompt('''Post Order Traversal'''))
				post_order(node)
				print(prompt() + '''\n''')

				print(prompt('''Level Order Traversal'''))
				level_order(node)
				print(prompt() + '''\n''')

				print(prompt('''Actual Level Order Traversal'''))
				level_order_actual(node)
				print('''*''' * 5_0 + '''\n''')

				print(prompt('''Pre Order Traversal - Iteration Version'''))
				pre_order_iter(node)
				print(prompt() + '''\n''')

				print(prompt('''In Order Traversal - Iteration Version'''))
				in_order_iter(node)
				print(prompt() + '''\n''')

				print(prompt('''Post Order Traversal - Iteration Version'''))
				post_order_iter(node)
				print(prompt())

