




from __future__ import annotations

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

@dataclass
class 						__lowerCAmelCase      :
							UpperCamelCase__   	=    42
							UpperCamelCase__   	=    None
							UpperCamelCase__   	=    None







def 						__A						(      ) ->			Node | None:
	a									=				Node(1       )
	a									=				Node(2       )
	a									=				Node(3       )
	a									=				Node(4       )
	a									=				Node(5       )
	return tree





def 						__A						(      __lowerCamelCase       ) ->			list[int]:
	return [root.data, *preorder(root.left       ), *preorder(root.right       )] if root else []





def 						__A						(      __lowerCamelCase       ) ->			list[int]:
	return postorder(root.left       ) + postorder(root.right       ) + [root.data] if root else []





def 						__A						(      __lowerCamelCase       ) ->			list[int]:
	return [*inorder(root.left       ), root.data, *inorder(root.right       )] if root else []





def 						__A						(      __lowerCamelCase       ) ->			int:
	return (max(height(root.left       )				,     height(root.right       )       ) + 1) if root else 0





def 						__A						(      __lowerCamelCase       ) ->			Sequence[Node | None]:
	a									=				[]

	if root is None:
		return output

	a									=				deque([root]       )

	while process_queue:
		a									=				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 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Sequence[Node | None]:
	a									=				[]

	def populate_output(__lowerCamelCase				,     __lowerCamelCase       ) -> 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 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Sequence[Node | None]:
	a									=				[]

	def populate_output(__lowerCamelCase				,     __lowerCamelCase       ) -> 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 						__A						(      __lowerCamelCase       ) ->			Sequence[Node | None] | list[Any]:
	if root is None:
		return []

	a									=				[]

	a									=				0
	a									=				height(__lowerCamelCase       )

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

	return output





def 						__A						(      ) ->			None:  # Main function for testing.
	a									=				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()







from bisect import bisect
from itertools import accumulate





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase				,     __lowerCamelCase				,     __lowerCamelCase       ) ->			Dict:
	a									=				sorted(zip(__lowerCamelCase				,     __lowerCamelCase       )				,     key=lambda __lowerCamelCase       : x[0] / x[1]				,     reverse=__lowerCamelCase       )
	a							,					a									=				[i[0] for i in r], [i[1] for i in r]
	a									=				list(accumulate(__lowerCamelCase       )       )
	a									=				bisect(__lowerCamelCase				,     __lowerCamelCase       )
	return (
	    0
	    if k == 0
	    else sum(vl[:k]       ) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
	    if k != n
	    else sum(vl[:k]       )
	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()

