
from __future__ import annotations

import queue





class 	_lowerCAmelCase					:




				def __init__(					self				,				_UpperCamelCase     )				->      str:
							lowerCAmelCase_						=	data
							lowerCAmelCase_						=	None
							lowerCAmelCase_						=	None






def    lowerCamelCase__				(				):




			"""simple docstring"""


			print("\n********Press N to stop entering at any point of time********\n"				)
			lowerCAmelCase_						=	input("Enter the value of the root node: "				).strip().lower()
			lowerCAmelCase_						=	queue.Queue()
			lowerCAmelCase_						=	TreeNode(int(__lowerCAmelCase				)				)
			q.put(__lowerCAmelCase				)
			while not q.empty():
						lowerCAmelCase_						=	q.get()
						lowerCAmelCase_						=	F"""Enter the left node of {node_found.data}: """
						lowerCAmelCase_						=	input(__lowerCAmelCase				).strip().lower() or "n"
						if check == "n":
									return tree_node
						lowerCAmelCase_						=	TreeNode(int(__lowerCAmelCase				)				)
						lowerCAmelCase_						=	left_node
						q.put(__lowerCAmelCase				)
						lowerCAmelCase_						=	F"""Enter the right node of {node_found.data}: """
						lowerCAmelCase_						=	input(__lowerCAmelCase				).strip().lower() or "n"
						if check == "n":
									return tree_node
						lowerCAmelCase_						=	TreeNode(int(__lowerCAmelCase				)				)
						lowerCAmelCase_						=	right_node
						q.put(__lowerCAmelCase				)
			raise






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			print(node.data    ,							end=","				)
			pre_order(node.left				)
			pre_order(node.right				)






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			in_order(node.left				)
			print(node.data    ,							end=","				)
			in_order(node.right				)






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			post_order(node.left				)
			post_order(node.right				)
			print(node.data    ,							end=","				)






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			lowerCAmelCase_						=	queue.Queue()
			q.put(__lowerCAmelCase				)
			while not q.empty():
						lowerCAmelCase_						=	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    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			lowerCAmelCase_						=	queue.Queue()
			q.put(__lowerCAmelCase				)
			while not q.empty():
						lowerCAmelCase_						=	[]
						while not q.empty():
									lowerCAmelCase_						=	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(__lowerCAmelCase				)






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			lowerCAmelCase_						=	[]
			lowerCAmelCase_						=	node
			while n or stack:
						while n:  # start from root node, find its left child
									print(n.data    ,							end=","				)
									stack.append(__lowerCAmelCase				)
									lowerCAmelCase_						=	n.left
						# end of while means current node doesn't have left child
						lowerCAmelCase_						=	stack.pop()
						# start to traverse its right child
						lowerCAmelCase_						=	n.right






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			lowerCAmelCase_						=	[]
			lowerCAmelCase_						=	node
			while n or stack:
						while n:
									stack.append(__lowerCAmelCase				)
									lowerCAmelCase_						=	n.left
						lowerCAmelCase_						=	stack.pop()
						print(n.data    ,							end=","				)
						lowerCAmelCase_						=	n.right






def    lowerCamelCase__				(				__lowerCAmelCase  :  TreeNode				):




			"""simple docstring"""


			if not isinstance(__lowerCAmelCase    ,							__lowerCAmelCase				) or not node:
						return
			lowerCAmelCase_	,  lowerCAmelCase_						=	[], []
			lowerCAmelCase_						=	node
			stacka.append(__lowerCAmelCase				)
			while stacka:  # to find the reversed order of post order, store it in stack2
						lowerCAmelCase_						=	stacka.pop()
						if n.left:
									stacka.append(n.left				)
						if n.right:
									stacka.append(n.right				)
						stacka.append(__lowerCAmelCase				)
			while stacka:  # pop up from stack2 will be the post order
						print(stacka.pop().data    ,							end=","				)






def    lowerCamelCase__				(				__lowerCAmelCase  :  str = ""    ,							__lowerCAmelCase  :  Union[str, Any]=50    ,							__lowerCAmelCase  :  int="*"				):




			"""simple docstring"""


			if not s:
						return "\n" + width * char
			lowerCAmelCase_	,  lowerCAmelCase_						=	divmod(width - len(__lowerCAmelCase				) - 2    ,							2				)
			return F"""{left * char} {s} {(left + extra) * char}"""


if __name__ == "__main__":
			import doctest

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

			_A   =     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("*" * 50 + "\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())





import functools






def    lowerCamelCase__				(				__lowerCAmelCase  :  str    ,							__lowerCAmelCase  :  str				):




			"""simple docstring"""


			lowerCAmelCase_						=	len(__lowerCAmelCase				)
			lowerCAmelCase_						=	len(__lowerCAmelCase				)

			@functools.cache
			def min_distance(__lowerCAmelCase  :  int    ,							__lowerCAmelCase  :  int				) -> int:
						# if first word index is overflow - delete all from the second word
						if indexa >= len_worda:
									return len_worda - indexa
						# if second word index is overflow - delete all from the first word
						if indexa >= len_worda:
									return len_worda - indexa
						lowerCAmelCase_						=	int(worda[indexa] != worda[indexa]				)  # current letters not identical
						return min(
						    1 + min_distance(indexa + 1    ,							__lowerCAmelCase				)    ,							1 + min_distance(__lowerCAmelCase    ,							indexa + 1				)    ,							diff + min_distance(indexa + 1    ,							indexa + 1				)    ,							)

			return min_distance(0    ,							0				)


if __name__ == "__main__":
			import doctest

			doctest.testmod()



