


"""simple docstring"""


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'''







							__UpperCAmelCase						:    int
							__UpperCAmelCase						:    Node | None				      =None
							__UpperCAmelCase						:    Node | None				      =None


def _lowerCamelCase	(		):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			if root is None:
						return output

			__lowerCAmelCase				    =			deque([root]      )

			while process_queue:
						__lowerCAmelCase				    =			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    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			def populate_output(_UpperCamelCase    , _UpperCamelCase      ) -> 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(_UpperCamelCase    , _UpperCamelCase      )
			return output


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			def populate_output(_UpperCamelCase    , _UpperCamelCase      ) -> 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(_UpperCamelCase    , _UpperCamelCase      )
			return output


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			if root is None:
						return []

			__lowerCAmelCase				    =			[]

			__lowerCAmelCase				    =			0
			__lowerCAmelCase				    =			height(_UpperCamelCase      )

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

			return output


def _lowerCamelCase	(		):  # Main function for testing.

			'''simple docstring'''




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

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

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

			print("Level-wise order Traversal: "      )

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

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()





"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

__lowerCAmelCase    :       str					     =list[list[float | int]]


def 			UpperCAmelCase__       (				lowerCAmelCase__     :Matrix					,		lowerCAmelCase__     :Matrix		) ->    Matrix:
      '''simple docstring'''


      lowercase														=	len(lowerCAmelCase__		)
      lowercase														=	[[0 for _ in range(size + 1		)] for _ in range(lowerCAmelCase__		)]
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42

      for row in range(lowerCAmelCase__		):
            for col in range(lowerCAmelCase__		):
                  lowercase														=	matrix[row][col]

            lowercase														=	vector[row][0]

      lowercase														=	0
      lowercase														=	0
      while row < size and col < size:
            # pivoting
            lowercase														=	max((abs(augmented[rowa][col]		), rowa) for rowa in range(lowerCAmelCase__					,		lowerCAmelCase__		)		)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  lowercase							,							lowercase														=	augmented[pivot_row], augmented[row]

            for rowa in range(row + 1					,		lowerCAmelCase__		):
                  lowercase														=	augmented[rowa][col] / augmented[row][col]
                  lowercase														=	0
                  for cola in range(col + 1					,		size + 1		):
                        augmented[rowa][cola] -= augmented[row][cola] * ratio

            row += 1
            col += 1

      # back substitution
      for col in range(1					,		lowerCAmelCase__		):
            for row in range(lowerCAmelCase__		):
                  lowercase														=	augmented[row][col] / augmented[col][col]
                  for cola in range(lowerCAmelCase__					,		size + 1		):
                        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
      return [
          [round(augmented[row][size] / augmented[row][row]					,		1_0		)] for row in range(lowerCAmelCase__		)
      ]


def 			UpperCAmelCase__       (				lowerCAmelCase__     :list[int]		) ->    Callable[[int], int]:
      '''simple docstring'''


      lowercase														=	len(lowerCAmelCase__		)
      lowercase														=	[[0 for _ in range(lowerCAmelCase__		)] for _ in range(lowerCAmelCase__		)]
      lowercase														=	[[0] for _ in range(lowerCAmelCase__		)]
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42
      lowercase														=	42

      for x_val, y_val in enumerate(lowerCAmelCase__		):
            for col in range(lowerCAmelCase__		):
                  lowercase														=	(x_val + 1) ** (size - col - 1)
            lowercase														=	y_val

      lowercase														=	solve(lowerCAmelCase__					,		lowerCAmelCase__		)

      def interpolated_func(lowerCAmelCase__     :int		) -> int:
            return sum(
                round(coeffs[x_val][0]		) * (var ** (size - x_val - 1))
                for x_val in range(lowerCAmelCase__		)		)

      return interpolated_func


def 			UpperCAmelCase__       (				lowerCAmelCase__     :int		) ->    int:
      '''simple docstring'''


      return (
          1
          - variable
          + variable**2
          - variable**3
          + variable**4
          - variable**5
          + variable**6
          - variable**7
          + variable**8
          - variable**9
          + variable**1_0
      )


def 			UpperCAmelCase__       (				lowerCAmelCase__     :Callable[[int], int] = question_function					,		lowerCAmelCase__     :int = 1_0		) ->    int:
      '''simple docstring'''


      lowercase														=	[func(lowerCAmelCase__		) for x_val in range(1					,		order + 1		)]

      lowercase														=	[
          interpolate(data_points[:max_coeff]		) for max_coeff in range(1					,		order + 1		)
      ]

      lowercase														=	0
      lowercase														=	42
      lowercase														=	42

      for poly in polynomials:
            lowercase														=	1
            while func(lowerCAmelCase__		) == poly(lowerCAmelCase__		):
                  x_val += 1

            ret += poly(lowerCAmelCase__		)

      return ret


if __name__ == "__main__":
       print(F"""{solution() = }""")



