


from __future__ import annotations

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






@dataclass
class 					lowercase__ :

   '''simple docstring'''


   a		:							List[Any]     	=	42
   a		:							Tuple     	=	None
   a		:							int     	=	None




def 	lowerCAmelCase_					(						)   ->			Node | None:
    UpperCamelCase__							:       str      =   Node(1   )
    UpperCamelCase__							:       Optional[int]      =   Node(2   )
    UpperCamelCase__							:       Optional[int]      =   Node(3   )
    UpperCamelCase__							:       Optional[int]      =   Node(4   )
    UpperCamelCase__							:       Optional[int]      =   Node(5   )
    return tree




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			list[int]:
    return [root.data, *preorder(root.left   ), *preorder(root.right   )] if root else []




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			list[int]:
    return postorder(root.left   ) + postorder(root.right   ) + [root.data] if root else []




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			list[int]:
    return [*inorder(root.left   ), root.data, *inorder(root.right   )] if root else []




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			int:
    return (max(height(root.left   )	,     height(root.right   )   ) + 1) if root else 0




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			Sequence[Node | None]:
    UpperCamelCase__							:       list[Any]      =   []

    if root is None:
        return output

    UpperCamelCase__							:       Optional[int]      =   deque([root]   )

    while process_queue:
        UpperCamelCase__							:       Tuple      =   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_					(						__UpperCAmelCase:    Node | None	,     __UpperCAmelCase:    int   )   ->			Sequence[Node | None]:
    UpperCamelCase__							:       list[Any]      =   []

    def populate_output(__UpperCAmelCase:    Node | None	,     __UpperCAmelCase:    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(a_	,     a_   )
    return output




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None	,     __UpperCAmelCase:    int   )   ->			Sequence[Node | None]:
    UpperCamelCase__							:       list[Any]      =   []

    def populate_output(__UpperCAmelCase:    Node | None	,     __UpperCAmelCase:    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(a_	,     a_   )
    return output




def 	lowerCAmelCase_					(						__UpperCAmelCase:    Node | None   )   ->			Sequence[Node | None] | list[Any]:
    if root is None:
        return []

    UpperCamelCase__							:       list[Sequence[Node | None]]      =   []

    UpperCamelCase__							:       List[Any]      =   0
    UpperCamelCase__							:       List[str]      =   height(a_   )

    for h in range(1	,     height_tree + 1   ):
        if not flag:
            output.append(get_nodes_from_left_to_right(a_	,     a_   )   )
            UpperCamelCase__							:       Any      =   1
        else:
            output.append(get_nodes_from_right_to_left(a_	,     a_   )   )
            UpperCamelCase__							:       Optional[Any]      =   0

    return output




def 	lowerCAmelCase_					(						)   ->			None:  # Main function for testing.
    UpperCamelCase__							:       List[str]      =   make_tree()
    print(f"In-order Traversal: {inorder(a_   )}"   )
    print(f"Pre-order Traversal: {preorder(a_   )}"   )
    print(f"Post-order Traversal: {postorder(a_   )}"	,     '''\n'''   )

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

    print('''Complete Level Order Traversal: '''   )
    print(level_order(a_   )	,     '''\n'''   )

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

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

    print('''\nZigZag order Traversal: '''   )
    print(zigzag(a_   )   )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()








def 	lowerCAmelCase_					(						__UpperCAmelCase:    dict   )   ->			set:
    UpperCamelCase__							:       int      =   set()
    # edges = list of graph's edges
    UpperCamelCase__							:       str      =   get_edges(__UpperCAmelCase   )

    # While there are still elements in edges list, take an arbitrary edge
    # (from_node, to_node) and add his extremity to chosen_vertices and then
    # remove all arcs adjacent to the from_node and to_node
    while edges:
        UpperCamelCase__     ,UpperCamelCase__							:       List[Any]      =   edges.pop()
        chosen_vertices.add(__UpperCAmelCase   )
        chosen_vertices.add(__UpperCAmelCase   )
        for edge in edges.copy():
            if from_node in edge or to_node in edge:
                edges.discard(__UpperCAmelCase   )
    return chosen_vertices




def 	lowerCAmelCase_					(						__UpperCAmelCase:    dict   )   ->			set:
    UpperCamelCase__							:       Optional[int]      =   set()
    for from_node, to_nodes in graph.items():
        for to_node in to_nodes:
            edges.add((from_node, to_node)   )
    return edges


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
  # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")

