
'''simple docstring'''
from __future__ import annotations

from queue import Queue







def 							A_  (    __SCREAMING_SNAKE_CASE    :	Dict      ,  __SCREAMING_SNAKE_CASE    :	Optional[int]			)					->							tuple[int, int]:





  """simple docstring"""

  a ^= b
  b ^= a
  a ^= b
  return a, b







def 							A_  (    __SCREAMING_SNAKE_CASE    :	int      ,  __SCREAMING_SNAKE_CASE    :	List[str]			)					->							list[list[int]]:





  """simple docstring"""

  __A		:  Any       				=		1
  while (1 << j) < max_node:
    for i in range(1      ,  max_node + 1			):
      __A		:  List[Any]       				=		parent[j - 1][parent[j - 1][i]]
    j += 1
  return parent







def 							A_  (    __SCREAMING_SNAKE_CASE    :	Union[str, Any]      ,  __SCREAMING_SNAKE_CASE    :	List[str]      ,  __SCREAMING_SNAKE_CASE    :	int      ,  __SCREAMING_SNAKE_CASE    :	Optional[Any]			)					->							int:





  """simple docstring"""

  if level[u] < level[v]:
    __A		:  Any       				=		swap(SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)
  # making depth of u same as depth of v
  for i in range(18      ,  -1      ,  -1			):
    if level[u] - (1 << i) >= level[v]:
      __A		:  Dict       				=		parent[i][u]
    # at the same depth if u==v that mean lca is found
  if u == v:
    return u
  # moving both nodes upwards till lca in found
  for i in range(18      ,  -1      ,  -1			):
    if parent[i][u] not in [0, parent[i][v]]:
      __A		:  List[str]       				=		parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
  return parent[0][u]







def 							A_  (    __SCREAMING_SNAKE_CASE    :	List[str]      ,  __SCREAMING_SNAKE_CASE    :	Optional[Any]      ,  __SCREAMING_SNAKE_CASE    :	Dict      ,  __SCREAMING_SNAKE_CASE    :	Tuple      ,  __SCREAMING_SNAKE_CASE    :	Tuple = 1      ,  )					->							tuple[list[int], list[list[int]]]:





  """simple docstring"""

  __A		:  Tuple       				=		0
  __A		:  Queue[int]       				=		Queue(maxsize=SCREAMING_SNAKE_CASE__			)
  q.put(SCREAMING_SNAKE_CASE__			)
  while q.qsize() != 0:
    __A		:  Tuple       				=		q.get()
    for v in graph[u]:
      if level[v] == -1:
        __A		:  List[Any]       				=		level[u] + 1
        q.put(SCREAMING_SNAKE_CASE__			)
        __A		:  Optional[Any]       				=		u
  return level, parent







def 							A_  (    )					->							None:





  """simple docstring"""

  __A		:  Optional[Any]       				=		13
  # initializing with 0
  __A		:  Union[str, Any]       				=		[[0 for _ in range(max_node + 10			)] for _ in range(20			)]
  # initializing with -1 which means every node is unvisited
  __A		:  Optional[int]       				=		[-1 for _ in range(max_node + 10			)]
  __A		:  dict[int, list[int]]       				=		{
      1: [2, 3, 4],
      2: [5],
      3: [6, 7],
      4: [8],
      5: [9, 10],
      6: [11],
      7: [],
      8: [12, 13],
      9: [],
      10: [],
      11: [],
      12: [],
      13: [],
  }
  __A		:  Dict       				=		breadth_first_search(SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__      ,  1			)
  __A		:  List[str]       				=		create_sparse(SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)
  print("""LCA of node 1 and 3 is: """      ,  lowest_common_ancestor(1      ,  3      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)
  print("""LCA of node 5 and 6 is: """      ,  lowest_common_ancestor(5      ,  6      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)
  print("""LCA of node 7 and 11 is: """      ,  lowest_common_ancestor(7      ,  11      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)
  print("""LCA of node 6 and 7 is: """      ,  lowest_common_ancestor(6      ,  7      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)
  print("""LCA of node 4 and 12 is: """      ,  lowest_common_ancestor(4      ,  12      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)
  print("""LCA of node 8 and 8 is: """      ,  lowest_common_ancestor(8      ,  8      ,  SCREAMING_SNAKE_CASE__      ,  SCREAMING_SNAKE_CASE__			)			)


if __name__ == "__main__":
     main()










from .balanced_parentheses import balanced_parentheses
from .stack import Stack







def      A__				(       SCREAMING_SNAKE_CASE__)  ->       int:
  return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(SCREAMING_SNAKE_CASE__   ,   -1)







def      A__				(       SCREAMING_SNAKE_CASE__)  ->       str:
  if not balanced_parentheses(SCREAMING_SNAKE_CASE__):
    raise ValueError("""Mismatched parentheses""")
  __snake_case:		Stack[str]					    =		Stack()
  __snake_case:		Any					    =		[]
  for char in expression_str:
    if char.isalpha() or char.isdigit():
      postfix.append(SCREAMING_SNAKE_CASE__)
    elif char == "(":
      stack.push(SCREAMING_SNAKE_CASE__)
    elif char == ")":
      while not stack.is_empty() and stack.peek() != "(":
        postfix.append(stack.pop())
      stack.pop()
    else:
      while not stack.is_empty() and precedence(SCREAMING_SNAKE_CASE__) <= precedence(stack.peek()):
        postfix.append(stack.pop())
      stack.push(SCREAMING_SNAKE_CASE__)
  while not stack.is_empty():
    postfix.append(stack.pop())
  return " ".join(SCREAMING_SNAKE_CASE__)


if __name__ == "__main__":
      from doctest import testmod

      testmod()
      __UpperCAmelCase			:  Optional[int]										=				"a+b*(c^d-e)^(f+g*h)-i"

      print("Infix to Postfix Notation demonstration:\n")
      print("Infix notation: " + expression)
      print("Postfix notation: " + infix_to_postfix(expression))






