

from __future__ import annotations

def       a__					(		UpperCAmelCase							:      int    ,			UpperCAmelCase							:      Any    ,			UpperCAmelCase							:      Any    ,			UpperCAmelCase							:      int    ,			UpperCAmelCase							:      str    ,			)  ->						int:
		UpperCAmelCase	:							Optional[Any]						=			len(UpperCAmelCase      )

		# If row is equal to the size of the board it means there are a queen in each row in
		# the current board (possible_board)
		if row == n:
				# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
				# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
				boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board]      )
				return

		# We iterate each column in the row to find all possible results in each row
		for col in range(UpperCAmelCase      ):
				# We apply that we learned previously. First we check that in the current board
				# (possible_board) there are not other same value because if there is it means
				# that there are a collision in vertical. Then we apply the two formulas we
				# learned before:
				#
				# 45º: y - x = b or 45: row - col = b
				# 135º: y + x = b or row + col = b.
				#
				# And we verify if the results of this two formulas not exist in their variables
				# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
				#
				# If any or these are True it means there is a collision so we continue to the
				# next value in the for loop.
				if (
				    col in possible_board
				    or row - col in diagonal_right_collisions
				    or row + col in diagonal_left_collisions
				):
						continue

				# If it is False we call dfs function again and we update the inputs
				depth_first_search(
				    [*possible_board, col]    ,			[*diagonal_right_collisions, row - col]    ,			[*diagonal_left_collisions, row + col]    ,			UpperCAmelCase    ,			UpperCAmelCase    ,			)

def       a__					(		UpperCAmelCase							:      Dict      )  ->						Optional[Any]:
		UpperCAmelCase	:							Any						=			[]
		depth_first_search([]    ,			[]    ,			[]    ,			UpperCAmelCase    ,			UpperCAmelCase      )

		# Print all the boards
		for board in boards:
				for column in board:
						print(UpperCAmelCase      )
				print(''''''      )

		print(len(UpperCAmelCase      )    ,			'''solutions were found.'''      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)








from __future__ import annotations

import queue





class  __UpperCAmelCase					:



   def __init__(							self							:					str,		__A							:					Union[str, Any]						):
     UpperCAmelCase	:							Dict						=			data
     UpperCAmelCase	:							Tuple						=			None
     UpperCAmelCase	:							Any						=			None






def       a__					(		)  ->						TreeNode:
  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	:							Tuple						=			TreeNode(int(UpperCAmelCase      )      )
  q.put(UpperCAmelCase      )
  while not q.empty():
    UpperCAmelCase	:							int						=			q.get()
    UpperCAmelCase	:							Union[str, Any]						=			f'''Enter the left node of {node_found.data}: '''
    UpperCAmelCase	:							List[Any]						=			input(UpperCAmelCase      ).strip().lower() or '''n'''
    if check == "n":
      return tree_node
    UpperCAmelCase	:							List[str]						=			TreeNode(int(UpperCAmelCase      )      )
    UpperCAmelCase	:							List[str]						=			left_node
    q.put(UpperCAmelCase      )
    UpperCAmelCase	:							List[Any]						=			f'''Enter the right node of {node_found.data}: '''
    UpperCAmelCase	:							List[Any]						=			input(UpperCAmelCase      ).strip().lower() or '''n'''
    if check == "n":
      return tree_node
    UpperCAmelCase	:							Dict						=			TreeNode(int(UpperCAmelCase      )      )
    UpperCAmelCase	:							Dict						=			right_node
    q.put(UpperCAmelCase      )
  raise

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  print(node.data    ,			end=''','''      )
  pre_order(node.left      )
  pre_order(node.right      )

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  in_order(node.left      )
  print(node.data    ,			end=''','''      )
  in_order(node.right      )

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  post_order(node.left      )
  post_order(node.right      )
  print(node.data    ,			end=''','''      )

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  UpperCAmelCase	:							queue.Queue						=			queue.Queue()
  q.put(UpperCAmelCase      )
  while not q.empty():
    UpperCAmelCase	:							List[Any]						=			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       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  UpperCAmelCase	:							queue.Queue						=			queue.Queue()
  q.put(UpperCAmelCase      )
  while not q.empty():
    UpperCAmelCase	:							int						=			[]
    while not q.empty():
      UpperCAmelCase	:							List[str]						=			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(UpperCAmelCase      )

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) 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(UpperCAmelCase      )
      UpperCAmelCase	:							Dict						=			n.left
    # end of while means current node doesn't have left child
    UpperCAmelCase	:							Union[str, Any]						=			stack.pop()
    # start to traverse its right child
    UpperCAmelCase	:							List[str]						=			n.right

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  UpperCAmelCase	:							list[TreeNode]						=			[]
  UpperCAmelCase	:							Any						=			node
  while n or stack:
    while n:
      stack.append(UpperCAmelCase      )
      UpperCAmelCase	:							Dict						=			n.left
    UpperCAmelCase	:							Optional[int]						=			stack.pop()
    print(n.data    ,			end=''','''      )
    UpperCAmelCase	:							Any						=			n.right

def       a__					(		UpperCAmelCase							:      TreeNode      )  ->						None:
  if not isinstance(UpperCAmelCase    ,			UpperCAmelCase      ) or not node:
    return
  UpperCAmelCase			,						UpperCAmelCase	:							Dict						=			[], []
  UpperCAmelCase	:							Any						=			node
  stacka.append(UpperCAmelCase      )
  while stacka:  # to find the reversed order of post order, store it in stack2
    UpperCAmelCase	:							Union[str, Any]						=			stacka.pop()
    if n.left:
      stacka.append(n.left      )
    if n.right:
      stacka.append(n.right      )
    stacka.append(UpperCAmelCase      )
  while stacka:  # pop up from stack2 will be the post order
    print(stacka.pop().data    ,			end=''','''      )

def       a__					(		UpperCAmelCase							:      str = ""    ,			UpperCAmelCase							:      int=50    ,			UpperCAmelCase							:      Union[str, Any]="*"      )  ->						str:
  if not s:
    return "\n" + width * char
  UpperCAmelCase			,						UpperCAmelCase	:							int						=			divmod(width - len(UpperCAmelCase      ) - 2    ,			2      )
  return f'''{left * char} {s} {(left + extra) * char}'''


if __name__ == "__main__":
     import doctest

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

     _lowerCamelCase    :       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())





