






from __future__ import annotations

import queue
class        a       :



      """simple docstring"""


      def __init__( self   :     Union[str, Any]						, __lowercase   :     Optional[int]   )				-> Union[str, Any]:
        __UpperCAmelCase				:      Optional[int]	 =    data
        __UpperCAmelCase				:      Optional[Any]	 =    None
        __UpperCAmelCase				:      Union[str, Any]	 =    None






def 							lowerCamelCase__ (       ):
  print("""\n********Press N to stop entering at any point of time********\n"""						)
  __UpperCAmelCase				:      List[str]	 =    input("""Enter the value of the root node: """						).strip().lower()
  __UpperCAmelCase				:      queue.Queue	 =    queue.Queue()
  __UpperCAmelCase				:      Any	 =    TreeNode(int(__lowerCamelCase						)						)
  q.put(__lowerCamelCase						)
  while not q.empty():
    __UpperCAmelCase				:      Optional[int]	 =    q.get()
    __UpperCAmelCase				:      str	 =    f"""Enter the left node of {node_found.data}: """
    __UpperCAmelCase				:      List[str]	 =    input(__lowerCamelCase						).strip().lower() or """n"""
    if check == "n":
      return tree_node
    __UpperCAmelCase				:      Union[str, Any]	 =    TreeNode(int(__lowerCamelCase						)						)
    __UpperCAmelCase				:      int	 =    left_node
    q.put(__lowerCamelCase						)
    __UpperCAmelCase				:      Optional[int]	 =    f"""Enter the right node of {node_found.data}: """
    __UpperCAmelCase				:      str	 =    input(__lowerCamelCase						).strip().lower() or """n"""
    if check == "n":
      return tree_node
    __UpperCAmelCase				:      Any	 =    TreeNode(int(__lowerCamelCase						)						)
    __UpperCAmelCase				:      Union[str, Any]	 =    right_node
    q.put(__lowerCamelCase						)
  raise






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  print(node.data    ,						end=""","""						)
  pre_order(node.left						)
  pre_order(node.right						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  in_order(node.left						)
  print(node.data    ,						end=""","""						)
  in_order(node.right						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  post_order(node.left						)
  post_order(node.right						)
  print(node.data    ,						end=""","""						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  __UpperCAmelCase				:      queue.Queue	 =    queue.Queue()
  q.put(__lowerCamelCase						)
  while not q.empty():
    __UpperCAmelCase				:      int	 =    q.get()
    print(node_dequeued.data    ,						end=""","""						)
    if node_dequeued.left:
      q.put(node_dequeued.left						)
    if node_dequeued.right:
      q.put(node_dequeued.right						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  __UpperCAmelCase				:      queue.Queue	 =    queue.Queue()
  q.put(__lowerCamelCase						)
  while not q.empty():
    __UpperCAmelCase				:      Optional[int]	 =    []
    while not q.empty():
      __UpperCAmelCase				:      int	 =    q.get()
      print(node_dequeued.data    ,						end=""","""						)
      if node_dequeued.left:
        list_.append(node_dequeued.left						)
      if node_dequeued.right:
        list_.append(node_dequeued.right						)
    print()
    for node in list_:
      q.put(__lowerCamelCase						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  __UpperCAmelCase				:      list[TreeNode]	 =    []
  __UpperCAmelCase				:      List[str]	 =    node
  while n or stack:
    while n:  # start from root node, find its left child
      print(n.data    ,						end=""","""						)
      stack.append(__lowerCamelCase						)
      __UpperCAmelCase				:      Optional[int]	 =    n.left
    # end of while means current node doesn't have left child
    __UpperCAmelCase				:      Optional[Any]	 =    stack.pop()
    # start to traverse its right child
    __UpperCAmelCase				:      Any	 =    n.right






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  __UpperCAmelCase				:      list[TreeNode]	 =    []
  __UpperCAmelCase				:      str	 =    node
  while n or stack:
    while n:
      stack.append(__lowerCamelCase						)
      __UpperCAmelCase				:      List[Any]	 =    n.left
    __UpperCAmelCase				:      Any	 =    stack.pop()
    print(n.data    ,						end=""","""						)
    __UpperCAmelCase				:      List[str]	 =    n.right






def 							lowerCamelCase__ (       __lowerCamelCase     :	TreeNode						):
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not node:
    return
  __UpperCAmelCase ,					__UpperCAmelCase				:      Union[str, Any]	 =    [], []
  __UpperCAmelCase				:      str	 =    node
  stacka.append(__lowerCamelCase						)
  while stacka:  # to find the reversed order of post order, store it in stack2
    __UpperCAmelCase				:      str	 =    stacka.pop()
    if n.left:
      stacka.append(n.left						)
    if n.right:
      stacka.append(n.right						)
    stacka.append(__lowerCamelCase						)
  while stacka:  # pop up from stack2 will be the post order
    print(stacka.pop().data    ,						end=""","""						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	str = ""    ,						__lowerCamelCase     :	str=50    ,						__lowerCamelCase     :	Optional[Any]="*"						):
  if not s:
    return "\n" + width * char
  __UpperCAmelCase ,					__UpperCAmelCase				:      Dict	 =    divmod(width - len(__lowerCamelCase						) - 2    ,						2						)
  return f"""{left * char} {s} {(left + extra) * char}"""


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       print(prompt("Binary Tree Traversals"))

       a						:			TreeNode     	=					build_tree()
       print(prompt("Pre Order Traversal"))
       pre_order(node)
       print(prompt() + "\n")

       print(prompt("In Order Traversal"))
       in_order(node)
       print(prompt() + "\n")

       print(prompt("Post Order Traversal"))
       post_order(node)
       print(prompt() + "\n")

       print(prompt("Level Order Traversal"))
       level_order(node)
       print(prompt() + "\n")

       print(prompt("Actual Level Order Traversal"))
       level_order_actual(node)
       print("*" * 50 + "\n")

       print(prompt("Pre Order Traversal - Iteration Version"))
       pre_order_iter(node)
       print(prompt() + "\n")

       print(prompt("In Order Traversal - Iteration Version"))
       in_order_iter(node)
       print(prompt() + "\n")

       print(prompt("Post Order Traversal - Iteration Version"))
       post_order_iter(node)
       print(prompt())









from __future__ import annotations

import math
from collections.abc import Callable


def       UpperCamelCase__(			UpperCamelCase__     :			Callable[[int | float], int | float]					,	UpperCamelCase__     :			int | float					,	UpperCamelCase__     :			int | float					,	UpperCamelCase__     :			int = 1_00					,	)->float:
       A__		   =		x_start
       A__		   =		fnc(UpperCamelCase__    )
       A__		   =		0.0

       for _ in range(UpperCamelCase__    ):
              # Approximates curve as a sequence of linear lines and sums their length
              A__		   =		(x_end - x_start) / steps + xa
              A__		   =		fnc(UpperCamelCase__    )
              length += math.hypot(xa - xa					,	fxa - fxa    )

              # Increment step
              A__		   =		xa
              A__		   =		fxa

       return length


if __name__ == "__main__":


       def       UpperCamelCase__(			UpperCamelCase__     :			Union[str, Any]    )->Dict:
              return math.sin(10 * x    )

       print('f(x) = sin(10 * x)')
       print('The length of the curve from x = -10 to x = 10 is:')
       a__: str							   =						10
       while i <= 100_000:
              print(F"With {i} steps: {line_length(f, -10, 10, i)}")
              i *= 10





