'''simple docstring'''





from __future__ import annotations

import queue




class        __A      :



    def __init__(self    :    Optional[Any]   ,			__a    :    str ):
         UpperCAmelCase_           =   data
         UpperCAmelCase_           =   None
         UpperCAmelCase_           =   None





def 	lowerCAmelCase_				(					)    ->      TreeNode:


     '''simple docstring'''




     print("\n********Press N to stop entering at any point of time********\n"			)
     UpperCAmelCase_           =   input("Enter the value of the root node: "			).strip().lower()
     UpperCAmelCase_           =   queue.Queue()
     UpperCAmelCase_           =   TreeNode(int(snake_case_			)			)
     q.put(snake_case_			)
     while not q.empty():
          UpperCAmelCase_           =   q.get()
          UpperCAmelCase_           =   f"""Enter the left node of {node_found.data}: """
          UpperCAmelCase_           =   input(snake_case_			).strip().lower() or "n"
          if check == "n":
               return tree_node
          UpperCAmelCase_           =   TreeNode(int(snake_case_			)			)
          UpperCAmelCase_           =   left_node
          q.put(snake_case_			)
          UpperCAmelCase_           =   f"""Enter the right node of {node_found.data}: """
          UpperCAmelCase_           =   input(snake_case_			).strip().lower() or "n"
          if check == "n":
               return tree_node
          UpperCAmelCase_           =   TreeNode(int(snake_case_			)			)
          UpperCAmelCase_           =   right_node
          q.put(snake_case_			)
     raise





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




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





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




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





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




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





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




     if not isinstance(snake_case_					,    snake_case_			) or not node:
          return
     UpperCAmelCase_           =   queue.Queue()
     q.put(snake_case_			)
     while not q.empty():
          UpperCAmelCase_           =   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_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




     if not isinstance(snake_case_					,    snake_case_			) or not node:
          return
     UpperCAmelCase_           =   queue.Queue()
     q.put(snake_case_			)
     while not q.empty():
          UpperCAmelCase_           =   []
          while not q.empty():
               UpperCAmelCase_           =   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(snake_case_			)





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




     if not isinstance(snake_case_					,    snake_case_			) or not node:
          return
     UpperCAmelCase_           =   []
     UpperCAmelCase_           =   node
     while n or stack:
          while n:  # start from root node, find its left child
               print(n.data					,    end=","			)
               stack.append(snake_case_			)
               UpperCAmelCase_           =   n.left
          # end of while means current node doesn't have left child
          UpperCAmelCase_           =   stack.pop()
          # start to traverse its right child
          UpperCAmelCase_           =   n.right





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




     if not isinstance(snake_case_					,    snake_case_			) or not node:
          return
     UpperCAmelCase_           =   []
     UpperCAmelCase_           =   node
     while n or stack:
          while n:
               stack.append(snake_case_			)
               UpperCAmelCase_           =   n.left
          UpperCAmelCase_           =   stack.pop()
          print(n.data					,    end=","			)
          UpperCAmelCase_           =   n.right





def 	lowerCAmelCase_				(					snake_case_       : TreeNode			)    ->      None:


     '''simple docstring'''




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





def 	lowerCAmelCase_				(					snake_case_       : str = ""					,    snake_case_       : Any=50					,    snake_case_       : Union[str, Any]="*"			)    ->      str:


     '''simple docstring'''




     if not s:
          return "\n" + width * char
     UpperCAmelCase_    , UpperCAmelCase_           =   divmod(width - len(snake_case_			) - 2					,    2			)
     return f"""{left * char} {s} {(left + extra) * char}"""


if __name__ == "__main__":
    import doctest

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

    SCREAMING_SNAKE_CASE_:     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())







class   __lowercase				:




			"""simple docstring"""







			def __init__( self  :     List[Any]   ,						lowerCAmelCase__  :     Optional[int]   ,						lowerCAmelCase__  :     List[Any]):
									SCREAMING_SNAKE_CASE_: List[str]  		=       name
									SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       val



			def __str__( self  :     Dict):
									return F"{self.__class__.__name__}({self.name}, {self.val})"




			def __lt__( self  :     List[str]   ,						lowerCAmelCase__  :     Any):
									return self.val < other.val







class   __lowercase				:




			"""simple docstring"""







			def __init__( self  :     Tuple   ,						lowerCAmelCase__  :     Dict):
									SCREAMING_SNAKE_CASE_: str  		=       {}
									SCREAMING_SNAKE_CASE_: int  		=       {}
									SCREAMING_SNAKE_CASE_: Any  		=       self.build_heap(lowerCAmelCase__)



			def __getitem__( self  :     List[Any]   ,						lowerCAmelCase__  :     Dict):
									return self.get_value(lowerCAmelCase__)



			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[Any]   ,						lowerCAmelCase__  :     Dict):
									return (idx - 1) // 2



			def        _SCREAMING_SNAKE_CASE			( self  :     Union[str, Any]   ,						lowerCAmelCase__  :     Optional[Any]):
									return idx * 2 + 1



			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[int]   ,						lowerCAmelCase__  :     Tuple):
									return idx * 2 + 2



			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[int]   ,						lowerCAmelCase__  :     Optional[int]):
									return self.heap_dict[key]



			def        _SCREAMING_SNAKE_CASE			( self  :     List[Any]   ,						lowerCAmelCase__  :     Union[str, Any]):
									SCREAMING_SNAKE_CASE_: Tuple  		=       len(lowerCAmelCase__) - 1
									SCREAMING_SNAKE_CASE_: List[str]  		=       self.get_parent_idx(lowerCAmelCase__)

									for idx, i in enumerate(lowerCAmelCase__):
															SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       idx
															SCREAMING_SNAKE_CASE_: str  		=       i.val

									for i in range(lowerCAmelCase__   ,						-1   ,						-1):
															self.sift_down(lowerCAmelCase__   ,						lowerCAmelCase__)
									return array



			def        _SCREAMING_SNAKE_CASE			( self  :     str   ,						lowerCAmelCase__  :     Optional[int]   ,						lowerCAmelCase__  :     List[str]):
									while True:
															SCREAMING_SNAKE_CASE_: Optional[Any]  		=       self.get_left_child_idx(lowerCAmelCase__)  # noqa: E741
															SCREAMING_SNAKE_CASE_: Dict  		=       self.get_right_child_idx(lowerCAmelCase__)

															SCREAMING_SNAKE_CASE_: int  		=       idx
															if l < len(lowerCAmelCase__) and array[l] < array[idx]:
																					SCREAMING_SNAKE_CASE_: List[str]  		=       l
															if r < len(lowerCAmelCase__) and array[r] < array[smallest]:
																					SCREAMING_SNAKE_CASE_: str  		=       r

															if smallest != idx:
																					SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: Any  		=       array[smallest], array[idx]
																					(
																					    (
																					    SCREAMING_SNAKE_CASE_
																					)		,    (
																					    SCREAMING_SNAKE_CASE_
																					)		,    
																					): Optional[Any]  		=       (
																					    self.idx_of_element[array[smallest]],
																					    self.idx_of_element[array[idx]],
																					)
																					SCREAMING_SNAKE_CASE_: Optional[int]  		=       smallest
															else:
																					break



			def        _SCREAMING_SNAKE_CASE			( self  :     Dict   ,						lowerCAmelCase__  :     str):
									SCREAMING_SNAKE_CASE_: Any  		=       self.get_parent_idx(lowerCAmelCase__)
									while p >= 0 and self.heap[p] > self.heap[idx]:
															SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: List[Any]  		=       self.heap[idx], self.heap[p]
															SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: Tuple  		=       (
															    self.idx_of_element[self.heap[idx]],
															    self.idx_of_element[self.heap[p]],
															)
															SCREAMING_SNAKE_CASE_: Union[str, Any]  		=       p
															SCREAMING_SNAKE_CASE_: Optional[int]  		=       self.get_parent_idx(lowerCAmelCase__)



			def        _SCREAMING_SNAKE_CASE			( self  :     List[Any]):
									return self.heap[0]



			def        _SCREAMING_SNAKE_CASE			( self  :     Dict):
									SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: Tuple  		=       self.heap[-1], self.heap[0]
									SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_: List[str]  		=       (
									    self.idx_of_element[self.heap[-1]],
									    self.idx_of_element[self.heap[0]],
									)

									SCREAMING_SNAKE_CASE_: int  		=       self.heap.pop()
									del self.idx_of_element[x]
									self.sift_down(0   ,						self.heap)
									return x



			def        _SCREAMING_SNAKE_CASE			( self  :     Union[str, Any]   ,						lowerCAmelCase__  :     Tuple):
									self.heap.append(lowerCAmelCase__)
									SCREAMING_SNAKE_CASE_: List[str]  		=       len(self.heap) - 1
									SCREAMING_SNAKE_CASE_: List[str]  		=       node.val
									self.sift_up(len(self.heap) - 1)



			def        _SCREAMING_SNAKE_CASE			( self  :     List[Any]):
									return len(self.heap) == 0




			def        _SCREAMING_SNAKE_CASE			( self  :     Optional[Any]   ,						lowerCAmelCase__  :     Any   ,						lowerCAmelCase__  :     Optional[int]):
									assert (
									    self.heap[self.idx_of_element[node]].val > new_value
									), "newValue must be less that current value"
									SCREAMING_SNAKE_CASE_: Any  		=       new_value
									SCREAMING_SNAKE_CASE_: Tuple  		=       new_value
									self.sift_up(self.idx_of_element[node])







lowerCAmelCase							:  int   	=						Node("""R""", -1)
lowerCAmelCase							:  str   	=						Node("""B""", 6)
lowerCAmelCase							:  str   	=						Node("""A""", 3)
lowerCAmelCase							:  List[str]   	=						Node("""X""", 1)
lowerCAmelCase							:  Union[str, Any]   	=						Node("""E""", 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array
lowerCAmelCase							:  Optional[Any]   	=						MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method
# myMinHeap.insert(a)
# myMinHeap.insert(b)
# myMinHeap.insert(x)
# myMinHeap.insert(r)
# myMinHeap.insert(e)

# Before
print("""Min Heap - before decrease key""")
for i in my_min_heap.heap:
						print(i)

print("""Min Heap - After decrease key of node [B -> -17]""")
my_min_heap.decrease_key(b, -17)

# After
for i in my_min_heap.heap:
						print(i)

if __name__ == "__main__":
						import doctest

						doctest.testmod()






