


import math



class 				A       :
					'''simple docstring'''






					def __init__(self       :		Tuple ,   _UpperCAmelCase       :		Union[str, Any]=0						)		->  Union[str, Any]:  # a graph with Node 0,1,...,N-1




							"""simple docstring"""


							lowercase__	     =						n
							lowercase__	     =						[
							    [math.inf for j in range(0 ,   _UpperCAmelCase						)] for i in range(0 ,   _UpperCAmelCase						)
							]  # adjacency matrix for weight
							lowercase__	     =						[
							    [math.inf for j in range(0 ,   _UpperCAmelCase						)] for i in range(0 ,   _UpperCAmelCase						)
							]  # dp[i][j] stores minimum distance from i to j

					def     lowerCamelCase__	(self       :		Any ,   _UpperCAmelCase       :		Any ,   _UpperCAmelCase       :		List[Any] ,   _UpperCAmelCase       :		Optional[Any]						)		->  str:




							"""simple docstring"""


							lowercase__	     =						w

					def     lowerCamelCase__	(self       :		str						)		->  Optional[Any]:




							"""simple docstring"""


							for k in range(0 ,   self.n						):
									for i in range(0 ,   self.n						):
											for j in range(0 ,   self.n						):
													lowercase__	     =						min(self.dp[i][j] ,   self.dp[i][k] + self.dp[k][j]						)


					def     lowerCamelCase__	(self       :		Union[str, Any] ,   _UpperCAmelCase       :		List[str] ,   _UpperCAmelCase       :		List[Any]						)		->  str:




							"""simple docstring"""


							return self.dp[u][v]


if __name__ == "__main__":
	A			:						Dict        =  Graph(5)
	graph.add_edge(0, 2, 9)
	graph.add_edge(0, 4, 1_0)
	graph.add_edge(1, 3, 5)
	graph.add_edge(2, 3, 7)
	graph.add_edge(3, 0, 1_0)
	graph.add_edge(3, 1, 2)
	graph.add_edge(3, 2, 1)
	graph.add_edge(3, 4, 6)
	graph.add_edge(4, 1, 3)
	graph.add_edge(4, 2, 4)
	graph.add_edge(4, 3, 9)
	graph.floyd_warshall()
	graph.show_min(1, 4)
	graph.show_min(0, 3)





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()

