






"""simple docstring"""

from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any

@dataclass
class 						A_							:
				UpperCAmelCase__        =				42
				UpperCAmelCase__        =				None
				UpperCAmelCase__        =				None






def _lowerCAmelCase	(  ):

						'''simple docstring'''






						__magic_name__            =     Node(1   )
						__magic_name__            =     Node(2   )
						__magic_name__            =     Node(3   )
						__magic_name__            =     Node(4   )
						__magic_name__            =     Node(5   )
						return tree






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						return [root.data, *preorder(root.left   ), *preorder(root.right   )] if root else []






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						return postorder(root.left   ) + postorder(root.right   ) + [root.data] if root else []






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						return [*inorder(root.left   ), root.data, *inorder(root.right   )] if root else []






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						return (max(height(root.left   ) ,						height(root.right   )   ) + 1) if root else 0






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						__magic_name__            =     []

						if root is None:
												return output

						__magic_name__            =     deque([root]   )

						while process_queue:
												__magic_name__            =     process_queue.popleft()
												output.append(node.data   )

												if node.left:
																		process_queue.append(node.left   )
												if node.right:
																		process_queue.append(node.right   )
						return output






def _lowerCAmelCase	(  __lowerCamelCase:Node | None ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     []

						def populate_output(__lowerCamelCase:Node | None ,						__lowerCamelCase:int   ) -> None:
												if not root:
																		return
												if level == 1:
																		output.append(root.data   )
												elif level > 1:
																		populate_output(root.left ,						level - 1   )
																		populate_output(root.right ,						level - 1   )

						populate_output(__lowerCamelCase ,						__lowerCamelCase   )
						return output






def _lowerCAmelCase	(  __lowerCamelCase:Node | None ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     []

						def populate_output(__lowerCamelCase:Node | None ,						__lowerCamelCase:int   ) -> None:
												if root is None:
																		return
												if level == 1:
																		output.append(root.data   )
												elif level > 1:
																		populate_output(root.right ,						level - 1   )
																		populate_output(root.left ,						level - 1   )

						populate_output(__lowerCamelCase ,						__lowerCamelCase   )
						return output






def _lowerCAmelCase	(  __lowerCamelCase:Node | None   ):

						'''simple docstring'''






						if root is None:
												return []

						__magic_name__            =     []

						__magic_name__            =     0
						__magic_name__            =     height(__lowerCamelCase   )

						for h in range(1 ,						height_tree + 1   ):
												if not flag:
																		output.append(get_nodes_from_left_to_right(__lowerCamelCase ,						__lowerCamelCase   )   )
																		__magic_name__            =     1
												else:
																		output.append(get_nodes_from_right_to_left(__lowerCamelCase ,						__lowerCamelCase   )   )
																		__magic_name__            =     0

						return output






def _lowerCAmelCase	(  ):  # Main function for testing.

						'''simple docstring'''






						__magic_name__            =     make_tree()
						print(f'''In-order Traversal: {inorder(__lowerCamelCase   )}'''   )
						print(f'''Pre-order Traversal: {preorder(__lowerCamelCase   )}'''   )
						print(f'''Post-order Traversal: {postorder(__lowerCamelCase   )}''' ,						"\n"   )

						print(f'''Height of Tree: {height(__lowerCamelCase   )}''' ,						"\n"   )

						print("Complete Level Order Traversal: "   )
						print(level_order(__lowerCamelCase   ) ,						"\n"   )

						print("Level-wise order Traversal: "   )

						for level in range(1 ,						height(__lowerCamelCase   ) + 1   ):
												print(f'''Level {level}:''' ,						get_nodes_from_left_to_right(__lowerCamelCase ,						level=__lowerCamelCase   )   )

						print("\nZigZag order Traversal: "   )
						print(zigzag(__lowerCamelCase   )   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()











"""simple docstring"""

from __future__ import annotations

from random import choice






def _lowerCAmelCase	(  __lowerCamelCase:Optional[int]   ):

						'''simple docstring'''






						return choice(__lowerCamelCase   )






def _lowerCAmelCase	(  __lowerCamelCase:list[int] ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     random_pivot(__lowerCamelCase   )

						# partition based on pivot
						# linear time
						__magic_name__            =     [e for e in lst if e < pivot]
						__magic_name__            =     [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(__lowerCamelCase   ) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(__lowerCamelCase   ) < k - 1:
												return kth_number(__lowerCamelCase ,						k - len(__lowerCamelCase   ) - 1   )
						# pivot is in elements smaller than k
						else:
												return kth_number(__lowerCamelCase ,						__lowerCamelCase   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()



