





from __future__ import annotations







def      A__				(       SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__)  ->       int | float:
  if len(SCREAMING_SNAKE_CASE__) == 0:
    raise ValueError("""find_min() arg is an empty sequence""")
  if (
      left >= len(SCREAMING_SNAKE_CASE__)
      or left < -len(SCREAMING_SNAKE_CASE__)
      or right >= len(SCREAMING_SNAKE_CASE__)
      or right < -len(SCREAMING_SNAKE_CASE__)
  ):
    raise IndexError("""list index out of range""")
  if left == right:
    return nums[left]
  __snake_case:		Optional[Any]					    =		(left + right) >> 1  # the middle
  __snake_case:		int					    =		find_min(SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__   ,   SCREAMING_SNAKE_CASE__)  # find min in range[left, mid]
  __snake_case:		Optional[int]					    =		find_min(SCREAMING_SNAKE_CASE__   ,   mid + 1   ,   SCREAMING_SNAKE_CASE__)  # find min in range[mid + 1, right]

  return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)













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))






