





'''simple docstring'''




from __future__ import annotations

import queue
class 			_lowerCAmelCase		:






     """simple docstring"""






     def __init__(   self							:			Any   ,       __snake_case							:			int						)->	Tuple:
        snake_case 						=   data
        snake_case 						=   None
        snake_case 						=   None





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





def 	__lowerCamelCase			(      __lowerCAmelCase       :							TreeNode		)		->  None:
   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		)		->  None:
   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		)		->  None:
   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		)		->  None:
   if not isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		) or not node:
      return
   snake_case 						=   queue.Queue()
   q.put(__lowerCAmelCase		)
   while not q.empty():
      snake_case 						=   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		)		->  None:
   if not isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		) or not node:
      return
   snake_case 						=   queue.Queue()
   q.put(__lowerCAmelCase		)
   while not q.empty():
      snake_case 						=   []
      while not q.empty():
         snake_case 						=   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		)		->  None:
   if not isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		) or not node:
      return
   snake_case 						=   []
   snake_case 						=   node
   while n or stack:
      while n:  # start from root node, find its left child
         print(n.data      ,    end=""","""		)
         stack.append(__lowerCAmelCase		)
         snake_case 						=   n.left
      # end of while means current node doesn't have left child
      snake_case 						=   stack.pop()
      # start to traverse its right child
      snake_case 						=   n.right





def 	__lowerCamelCase			(      __lowerCAmelCase       :							TreeNode		)		->  None:
   if not isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		) or not node:
      return
   snake_case 						=   []
   snake_case 						=   node
   while n or stack:
      while n:
         stack.append(__lowerCAmelCase		)
         snake_case 						=   n.left
      snake_case 						=   stack.pop()
      print(n.data      ,    end=""","""		)
      snake_case 						=   n.right





def 	__lowerCamelCase			(      __lowerCAmelCase       :							TreeNode		)		->  None:
   if not isinstance(__lowerCAmelCase      ,    __lowerCAmelCase		) or not node:
      return
   snake_case						,    snake_case 						=   [], []
   snake_case 						=   node
   stacka.append(__lowerCAmelCase		)
   while stacka:  # to find the reversed order of post order, store it in stack2
      snake_case 						=   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       :							Dict="*"		)		->  str:
   if not s:
      return "\n" + width * char
   snake_case						,    snake_case 						=   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"))

 _SCREAMING_SNAKE_CASE							     =			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())








'''simple docstring'''




from __future__ import annotations

import os
from collections.abc import Mapping

_SCREAMING_SNAKE_CASE							     =			tuple[int, int]
class 			_lowerCAmelCase		:






     """simple docstring"""






     def __init__(   self							:			List[Any]   ,       __snake_case							:			set[int]   ,       __snake_case							:			Mapping[EdgeT, int]						)->	None:
        snake_case 						=   vertices
        snake_case 						=   {
            (min(__snake_case						), max(__snake_case						)): weight for edge, weight in edges.items()
        }



     def      lowerCAmelCase			(   self							:			Optional[Any]   ,       __snake_case							:			EdgeT   ,       __snake_case							:			int						)->	None:
        self.vertices.add(edge[0]						)
        self.vertices.add(edge[1]						)
        snake_case 						=   weight



     def      lowerCAmelCase			(   self							:			str						)->	Graph:
        snake_case 						=   Graph({min(self.vertices						)}   ,       {}						)
        snake_case 						=   42
        snake_case 						=   42
        snake_case 						=   42
        snake_case 						=   42

        while len(subgraph.vertices						) < len(self.vertices						):
           snake_case 						=   max(self.edges.values()						) + 1
           for edge, weight in self.edges.items():
              if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                 if weight < min_weight:
                    snake_case 						=   edge
                    snake_case 						=   weight

           subgraph.add_edge(__snake_case   ,       __snake_case						)

        return subgraph





def 	__lowerCamelCase			(      __lowerCAmelCase       :							str = "p107_network.txt"		)		->  int:
   snake_case 						=   os.path.abspath(os.path.dirname(__lowerCAmelCase		)		)
   snake_case 						=   os.path.join(__lowerCAmelCase      ,    __lowerCAmelCase		)
   snake_case 						=   {}
   snake_case 						=   42
   snake_case 						=   42
   snake_case 						=   42

   with open(__lowerCAmelCase		) as f:
      snake_case 						=   f.read().strip().split("""\n"""		)

   snake_case 						=   [line.split(""","""		) for line in data]

   for edgea in range(1      ,    len(__lowerCAmelCase		)		):
      for edgea in range(__lowerCAmelCase		):
         if adjaceny_matrix[edgea][edgea] != "-":
            snake_case 						=   int(adjaceny_matrix[edgea][edgea]		)

   snake_case 						=   Graph(set(range(len(__lowerCAmelCase		)		)		)      ,    __lowerCAmelCase		)

   snake_case 						=   graph.prims_algorithm()

   snake_case 						=   sum(graph.edges.values()		)
   snake_case 						=   sum(subgraph.edges.values()		)

   return initial_total - optimal_total


if __name__ == "__main__":
 print(F"""{solution() = }""")

