


def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    str:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)
		if n == 0:
				return 0
		lowercase__	     =						float("""-inf"""	)
		for i in range(1       ,       n + 1	):
				lowercase__	     =						max(
				    __magic_name__       ,       prices[i - 1] + naive_cut_rod_recursive(n - i       ,       __magic_name__	)	)

		return max_revue






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Optional[int]:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						[float("""-inf"""	) for _ in range(n + 1	)]
		return _top_down_cut_rod_recursive(__magic_name__       ,       __magic_name__       ,       __magic_name__	)






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list       ,       __magic_name__	:				list	)  ->    int:
		"""simple docstring"""




		if max_rev[n] >= 0:
				return max_rev[n]
		elif n == 0:
				return 0
		else:
				lowercase__	     =						float("""-inf"""	)
				for i in range(1       ,       n + 1	):
						lowercase__	     =						max(
						    __magic_name__       ,       prices[i - 1] + _top_down_cut_rod_recursive(n - i       ,       __magic_name__       ,       __magic_name__	)       ,       )

				lowercase__	     =						max_revenue

		return max_rev[n]






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Tuple:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)

		# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
		# length 0.
		lowercase__	     =						[float("""-inf"""	) for _ in range(n + 1	)]
		lowercase__	     =						0

		for i in range(1       ,       n + 1	):
				lowercase__	     =						max_rev[i]
				for j in range(1       ,       i + 1	):
						lowercase__	     =						max(__magic_name__       ,       prices[j - 1] + max_rev[i - j]	)

				lowercase__	     =						max_revenue_i

		return max_rev[n]






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Union[str, Any]:
		"""simple docstring"""




		if n < 0:
				lowercase__	     =						f'''n must be greater than or equal to 0. Got n = {n}'''
				raise ValueError(__magic_name__	)

		if n > len(__magic_name__	):
				lowercase__	     =						(
				    """Each integral piece of rod must have a corresponding price. """
				    f'''Got n = {n} but length of prices = {len(__magic_name__	)}'''
				)
				raise ValueError(__magic_name__	)






def 					UpperCamelCase   (      )  ->    List[Any]:
		"""simple docstring"""




		lowercase__	     =						[6, 10, 12, 15, 20, 23]
		lowercase__	     =						len(__magic_name__	)

		# the best revenue comes from cutting the rod into 6 pieces, each
		# of length 1 resulting in a revenue of 6 * 6 = 36.
		lowercase__	     =						36

		lowercase__	     =						top_down_cut_rod(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						bottom_up_cut_rod(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						naive_cut_rod_recursive(__magic_name__       ,       __magic_name__	)

		assert expected_max_revenue == max_rev_top_down
		assert max_rev_top_down == max_rev_bottom_up
		assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
	main()





from __future__ import annotations

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



@dataclass
class 				A       :
					'''simple docstring'''






					A__     =					42
					A__     =					None
					A__     =					None






def 					UpperCamelCase   (      )  ->    Node | None:
		"""simple docstring"""




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






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    list[int]:
		"""simple docstring"""




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






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    list[int]:
		"""simple docstring"""




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






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    list[int]:
		"""simple docstring"""




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






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    int:
		"""simple docstring"""




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






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    Sequence[Node | None]:
		"""simple docstring"""




		lowercase__	     =						[]

		if root is None:
				return output

		lowercase__	     =						deque([root]	)

		while process_queue:
				lowercase__	     =						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 					UpperCamelCase   (      __magic_name__	:				Node | None       ,       __magic_name__	:				int	)  ->    Sequence[Node | None]:
		"""simple docstring"""




		lowercase__	     =						[]

		def populate_output(__magic_name__	:				Node | None       ,       __magic_name__	:				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(__magic_name__       ,       __magic_name__	)
		return output






def 					UpperCamelCase   (      __magic_name__	:				Node | None       ,       __magic_name__	:				int	)  ->    Sequence[Node | None]:
		"""simple docstring"""




		lowercase__	     =						[]

		def populate_output(__magic_name__	:				Node | None       ,       __magic_name__	:				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(__magic_name__       ,       __magic_name__	)
		return output






def 					UpperCamelCase   (      __magic_name__	:				Node | None	)  ->    Sequence[Node | None] | list[Any]:
		"""simple docstring"""




		if root is None:
				return []

		lowercase__	     =						[]

		lowercase__	     =						0
		lowercase__	     =						height(__magic_name__	)

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

		return output






def 					UpperCamelCase   (      )  ->    None:  # Main function for testing.
		"""simple docstring"""




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

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

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

		print("""Level-wise order Traversal: """	)

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()

