






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    0
				lowercase__     				=    len(lowerCamelCase_       )

				for i in range(n - 1       ):
								for j in range(i + 1	,     lowerCamelCase_       ):
												if arr[i] > arr[j]:
																num_inversions += 1

				return num_inversions






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				if len(lowerCamelCase_       ) <= 1:
								return arr, 0
				lowercase__     				=    len(lowerCamelCase_       ) // 2
				lowercase__     				=    arr[0:mid]
				lowercase__     				=    arr[mid:]

				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    _count_cross_inversions(lowerCamelCase_	,     lowerCamelCase_       )

				lowercase__     				=    inversion_p + inversions_q + cross_inversions
				return c, num_inversions






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    []
				lowercase__     				=    lowercase__     				=    lowercase__     				=    0
				while i < len(lowerCamelCase_       ) and j < len(lowerCamelCase_       ):
								if p[i] > q[j]:
												# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
												# These are all inversions. The claim emerges from the
												# property that P is sorted.
												num_inversion += len(lowerCamelCase_       ) - i
												r.append(q[j]       )
												j += 1
								else:
												r.append(p[i]       )
												i += 1

				if i < len(lowerCamelCase_       ):
								r.extend(p[i:]       )
				else:
								r.extend(q[j:]       )

				return r, num_inversion






def 						a    (		):






				'''simple docstring'''
				lowercase__     				=    [10, 2, 1, 5, 5, 2, 11]

				# this arr has 8 inversions:
				# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 8

				print('''number of inversions = '''	,     lowerCamelCase_       )

				# testing an array with zero inversion (a sorted arr_1)

				arr_a.sort()
				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = '''	,     lowerCamelCase_       )

				# an empty list should also have zero inversions
				lowercase__     				=    []
				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = '''	,     lowerCamelCase_       )


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    _UpperCAmelCase      :

				"""simple docstring"""




				lowercase__       							= 42
				lowercase__       							= None
				lowercase__       							= None






def 						a    (		):






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






def 						a    (		lowerCamelCase_       ):






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






def 						a    (		lowerCamelCase_       ):






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






def 						a    (		lowerCamelCase_       ):






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






def 						a    (		lowerCamelCase_       ):






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






def 						a    (		lowerCamelCase_       ):






				'''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 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    []

				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_       ):






				'''simple docstring'''
				lowercase__     				=    []

				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_       ):






				'''simple docstring'''
				if root is None:
								return []

				lowercase__     				=    []

				lowercase__     				=    0
				lowercase__     				=    height(lowerCamelCase_       )

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

				return output






def 						a    (		):  # Main function for testing.






				'''simple docstring'''
				lowercase__     				=    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()




