




'''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      lowerCAmelCase :
       __lowercase	:   int
       __lowercase	:   Node | None										=      None
       __lowercase	:   Node | None										=      None







def       _UpperCamelCase			()-> Node | None:




     '''simple docstring'''





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







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




     '''simple docstring'''





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







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




     '''simple docstring'''





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







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




     '''simple docstring'''





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







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




     '''simple docstring'''





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







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




     '''simple docstring'''





     __snake_case            =	[]

     if root is None:
          return output

     __snake_case            =	deque([root]						)

     while process_queue:
          __snake_case            =	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       _UpperCamelCase			(_lowerCamelCase				:  Node | None ,						_lowerCamelCase				:  int						)-> Sequence[Node | None]:




     '''simple docstring'''





     __snake_case            =	[]

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




     '''simple docstring'''





     __snake_case            =	[]

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




     '''simple docstring'''





     if root is None:
          return []

     __snake_case            =	[]

     __snake_case            =	0
     __snake_case            =	height(_lowerCamelCase						)

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

     return output







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




     '''simple docstring'''





     __snake_case            =	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()












'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  Optional[Any]						)-> Dict:




     '''simple docstring'''





     __snake_case            =	[]
     __snake_case            =	[]
     __snake_case            =	{
         '''^''': 3,
         '''*''': 2,
         '''/''': 2,
         '''%''': 2,
         '''+''': 1,
         '''-''': 1,
     }  # Priority of each operator
     __snake_case            =	len(_lowerCamelCase						) if (len(_lowerCamelCase						) > 7) else 7

     # Print table header for output
     print(
         '''Symbol'''.center(8						) ,						'''Stack'''.center(_lowerCamelCase						) ,						'''Postfix'''.center(_lowerCamelCase						) ,						sep=''' | ''' ,						)
     print('''-''' * (print_width * 3 + 7)						)

     for x in infix:
          if x.isalpha() or x.isdigit():
               post_fix.append(_lowerCamelCase						)  # if x is Alphabet / Digit, add it to Postfix
          elif x == "(":
               stack.append(_lowerCamelCase						)  # if x is "(" push to Stack
          elif x == ")":  # if x is ")" pop stack until "(" is encountered
               while stack[-1] != "(":
                    post_fix.append(stack.pop()						)  # Pop stack & add the content to Postfix
               stack.pop()
          else:
               if len(_lowerCamelCase						) == 0:
                    stack.append(_lowerCamelCase						)  # If stack is empty, push x to stack
               else:  # while priority of x is not > priority of element in the stack
                    while len(_lowerCamelCase						) > 0 and priority[x] <= priority[stack[-1]]:
                         post_fix.append(stack.pop()						)  # pop stack & add to Postfix
                    stack.append(_lowerCamelCase						)  # push x to stack

          print(
              x.center(8						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						sep=''' | ''' ,						)  # Output in tabular format

     while len(_lowerCamelCase						) > 0:  # while stack is not empty
          post_fix.append(stack.pop()						)  # pop stack & add to Postfix
          print(
              ''' '''.center(8						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						(''''''.join(_lowerCamelCase						)).ljust(_lowerCamelCase						) ,						sep=''' | ''' ,						)  # Output in tabular format

     return "".join(_lowerCamelCase						)  # return Postfix as str







def       _UpperCamelCase			(_lowerCamelCase				:  Optional[Any]						)-> str:




     '''simple docstring'''





     __snake_case            =	list(infix[::-1]						)  # reverse the infix equation

     for i in range(len(_lowerCamelCase						)						):
          if infix[i] == "(":
               __snake_case            =	''')'''  # change "(" to ")"
          elif infix[i] == ")":
               __snake_case            =	'''('''  # change ")" to "("

     return (infix_2_postfix(''''''.join(_lowerCamelCase						)						))[
         ::-1
     ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
     UpperCAmelCase_							:	Dict	     =		input('''\nEnter an Infix Equation = ''')  # Input an Infix equation
     UpperCAmelCase_							:	Optional[Any]	     =		''''''.join(Infix.split())  # Remove spaces from the input
     print('''\n\t''', Infix, '''(Infix) -> ''', infix_2_prefix(Infix), '''(Prefix)''')






