
from __future__ import annotations

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




@dataclass
class 				lowerCamelCase__							:




	'''simple docstring'''




	_A			=  42
	_A			=  None
	_A			=  None




def 			_SCREAMING_SNAKE_CASE      (	)      ->					Node | None:






							'''simple docstring'''





							__UpperCamelCase			:     Union[str, Any]         =      Node(1)
							__UpperCamelCase			:     str         =      Node(2)
							__UpperCamelCase			:     List[Any]         =      Node(3)
							__UpperCamelCase			:     List[Any]         =      Node(4)
							__UpperCamelCase			:     Tuple         =      Node(5)
							return tree




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					list[int]:






							'''simple docstring'''





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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					list[int]:






							'''simple docstring'''





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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					list[int]:






							'''simple docstring'''





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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					int:






							'''simple docstring'''





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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					Sequence[Node | None]:






							'''simple docstring'''





							__UpperCamelCase			:     list[Any]         =      []

							if root is None:
														return output

							__UpperCamelCase			:     Any         =      deque([root])

							while process_queue:
														__UpperCamelCase			:     Any         =      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 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None		,						_lowerCamelCase				:    int)      ->					Sequence[Node | None]:






							'''simple docstring'''





							__UpperCamelCase			:     list[Any]         =      []

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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None		,						_lowerCamelCase				:    int)      ->					Sequence[Node | None]:






							'''simple docstring'''





							__UpperCamelCase			:     list[Any]         =      []

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




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Node | None)      ->					Sequence[Node | None] | list[Any]:






							'''simple docstring'''





							if root is None:
														return []

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

							__UpperCamelCase			:     Optional[Any]         =      0
							__UpperCamelCase			:     Any         =      height(_lowerCamelCase)

							for h in range(1		,						height_tree + 1):
														if not flag:
																					output.append(get_nodes_from_left_to_right(_lowerCamelCase		,						_lowerCamelCase))
																					__UpperCamelCase			:     str         =      1
														else:
																					output.append(get_nodes_from_right_to_left(_lowerCamelCase		,						_lowerCamelCase))
																					__UpperCamelCase			:     Any         =      0

							return output




def 			_SCREAMING_SNAKE_CASE      (	)      ->					None:  # Main function for testing.






							'''simple docstring'''





							__UpperCamelCase			:     Tuple         =      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 __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int | None, int | None, float]:






							'''simple docstring'''





							if not arr:
														return None, None, 0
							if low == high:
														return low, high, arr[low]

							__UpperCamelCase			:     Tuple         =      (low + high) // 2
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Dict         =      max_subarray(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Optional[int]         =      max_subarray(_lowerCamelCase		,						mid + 1		,						_lowerCamelCase)
							__UpperCamelCase     ,		__UpperCamelCase     ,		__UpperCamelCase			:     Dict         =      max_cross_sum(_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase		,						_lowerCamelCase)
							if left_sum >= right_sum and left_sum >= cross_sum:
														return left_low, left_high, left_sum
							elif right_sum >= left_sum and right_sum >= cross_sum:
														return right_low, right_high, right_sum
							return cross_left, cross_right, cross_sum




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    Sequence[float]		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int		,						_lowerCamelCase				:    int)      ->					tuple[int, int, float]:






							'''simple docstring'''





							__UpperCamelCase     ,		__UpperCamelCase			:     Union[str, Any]         =      float("-inf"), -1
							__UpperCamelCase     ,		__UpperCamelCase			:     Optional[int]         =      float("-inf"), -1

							__UpperCamelCase			:     int | float         =      0
							for i in range(_lowerCamelCase		,						low - 1		,						-1):
														summ += arr[i]
														if summ > left_sum:
																					__UpperCamelCase			:     Tuple         =      summ
																					__UpperCamelCase			:     Optional[int]         =      i

							__UpperCamelCase			:     Union[str, Any]         =      0
							for i in range(mid + 1		,						high + 1):
														summ += arr[i]
														if summ > right_sum:
																					__UpperCamelCase			:     Union[str, Any]         =      summ
																					__UpperCamelCase			:     Optional[int]         =      i

							return max_left, max_right, (left_sum + right_sum)




def 			_SCREAMING_SNAKE_CASE      (	_lowerCamelCase				:    int)      ->					float:






							'''simple docstring'''





							__UpperCamelCase			:     Tuple         =      [randint(1		,						_lowerCamelCase) for _ in range(_lowerCamelCase)]
							__UpperCamelCase			:     Optional[Any]         =      time.time()
							max_subarray(_lowerCamelCase		,						0		,						input_size - 1)
							__UpperCamelCase			:     Any         =      time.time()
							return end - start




def 			_SCREAMING_SNAKE_CASE      (	)      ->					None:






							'''simple docstring'''





							__UpperCamelCase			:     Dict         =      [10, 100, 1_000, 10_000, 50_000, 100_000, 200_000, 300_000, 400_000, 500_000]
							__UpperCamelCase			:     Union[str, Any]         =      [time_max_subarray(_lowerCamelCase) for input_size in input_sizes]
							print("No of Inputs\t\tTime Taken")
							for input_size, runtime in zip(_lowerCamelCase		,						_lowerCamelCase):
														print(_lowerCamelCase		,						"\t\t"		,						_lowerCamelCase)
							plt.plot(_lowerCamelCase		,						_lowerCamelCase)
							plt.xlabel("Number of Inputs")
							plt.ylabel("Time taken in seconds")
							plt.show()


if __name__ == "__main__":
		from doctest import testmod

		testmod()