


'''simple docstring'''






from collections.abc import Callable

_A      =     Callable[[float], float]  # type alias for a real -> real function


def A_					(				__SCREAMING_SNAKE_CASE :					RealFunc	,   __SCREAMING_SNAKE_CASE :					RealFunc	,   __SCREAMING_SNAKE_CASE :					int	,   )     ->  float:
					__SCREAMING_SNAKE_CASE					:							Any			   = float(__SCREAMING_SNAKE_CASE       )
					while True:
										try:
															__SCREAMING_SNAKE_CASE					:							Dict			   = prev_guess - function(__SCREAMING_SNAKE_CASE       ) / derivative(__SCREAMING_SNAKE_CASE       )
										except ZeroDivisionError:
															raise ZeroDivisionError('''Could not find root'''       ) from None
										if abs(prev_guess - next_guess       ) < 10**-5:
															return next_guess
										__SCREAMING_SNAKE_CASE					:							List[Any]			   = next_guess


def A_					(				__SCREAMING_SNAKE_CASE :					float       )     ->  float:
					return (x**3) - (2 * x) - 5


def A_					(				__SCREAMING_SNAKE_CASE :					float       )     ->  float:
					return 3 * (x**2) - 2


if __name__ == "__main__":
						print(newton(f, fa, 3))






'''simple docstring'''






from .balanced_parentheses import balanced_parentheses
from .stack import Stack


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


def A_					(				__SCREAMING_SNAKE_CASE :					str       )     ->  str:
					if not balanced_parentheses(__SCREAMING_SNAKE_CASE       ):
										raise ValueError('''Mismatched parentheses'''       )
					__SCREAMING_SNAKE_CASE					:							Stack[str]			   = Stack()
					__SCREAMING_SNAKE_CASE					:							Optional[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()
						_A      =     """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))


