



'''simple docstring'''






from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_ = False		)->		list[float]:





       '''simple docstring'''


       if radian_mode:
              return [magnitude * cos(lowerCAmelCase_		), magnitude * sin(lowerCAmelCase_		)]
       return [magnitude * cos(radians(lowerCAmelCase_		)		), magnitude * sin(radians(lowerCAmelCase_		)		)]




def     snake_case_					(     lowerCAmelCase_       ,   lowerCAmelCase_       ,   lowerCAmelCase_ = 10**-1		)->		bool:





       '''simple docstring'''


       _UpperCAmelCase  :						NDArray[floataa]			     = cross(lowerCAmelCase_       ,   lowerCAmelCase_		)
       _UpperCAmelCase  :						float			     = sum(lowerCAmelCase_		)
       return abs(lowerCAmelCase_		) < eps


if __name__ == "__main__":
   # Test to check if it works
   A_							: str						 =	array(
       [
           polar_force(718.4, 1_8_0 - 3_0),
           polar_force(879.54, 4_5),
           polar_force(1_0_0, -9_0),
       ]
   )

   A_							: NDArray[floataa]						 =	array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem 1 in image_data/2D_problems.jpg
   A_							: List[str]						 =	array(
       [
           polar_force(3_0 * 9.81, 1_5),
           polar_force(2_1_5, 1_8_0 - 4_5),
           polar_force(2_6_4, 9_0 - 3_0),
       ]
   )

   A_							: Tuple						 =	array([[0, 0], [0, 0], [0, 0]])

   assert in_static_equilibrium(forces, location)

   # Problem in image_data/2D_problems_1.jpg
   A_							: Dict						 =	array([[0, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

   A_							: Union[str, Any]						 =	array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

   assert in_static_equilibrium(forces, location)

   import doctest

   doctest.testmod()








'''simple docstring'''






from __future__ import annotations

import queue



class 							lowercase       :


 """simple docstring"""


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







def     snake_case_					(     )->		TreeNode:





       '''simple docstring'''


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




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       print(node.data       ,   end=""","""		)
       pre_order(node.left		)
       pre_order(node.right		)




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       in_order(node.left		)
       print(node.data       ,   end=""","""		)
       in_order(node.right		)




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       post_order(node.left		)
       post_order(node.right		)
       print(node.data       ,   end=""","""		)




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       _UpperCAmelCase  :						queue.Queue			     = queue.Queue()
       q.put(lowerCAmelCase_		)
       while not q.empty():
              _UpperCAmelCase  :						Dict			     = 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     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       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  :						Optional[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     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


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




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       _UpperCAmelCase  :						list[TreeNode]			     = []
       _UpperCAmelCase  :						Optional[Any]			     = node
       while n or stack:
              while n:
                     stack.append(lowerCAmelCase_		)
                     _UpperCAmelCase  :						Tuple			     = n.left
              _UpperCAmelCase  :						Union[str, Any]			     = stack.pop()
              print(n.data       ,   end=""","""		)
              _UpperCAmelCase  :						Any			     = n.right




def     snake_case_					(     lowerCAmelCase_		)->		None:





       '''simple docstring'''


       if not isinstance(lowerCAmelCase_       ,   lowerCAmelCase_		) or not node:
              return
       _UpperCAmelCase     ,_UpperCAmelCase  :						str			     = [], []
       _UpperCAmelCase  :						Dict			     = node
       stacka.append(lowerCAmelCase_		)
       while stacka:  # to find the reversed order of post order, store it in stack2
              _UpperCAmelCase  :						Optional[int]			     = 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     snake_case_					(     lowerCAmelCase_ = ""       ,   lowerCAmelCase_=50       ,   lowerCAmelCase_="*"		)->		str:





       '''simple docstring'''


       if not s:
              return "\n" + width * char
       _UpperCAmelCase     ,_UpperCAmelCase  :						Optional[Any]			     = 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("""*""" * 5_0 + """\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())



