

import math as m




def      UpperCAmelCase__							(     _A :					List[str]      , _A :					str      , _A :					Tuple=0.001				):





  '''simple docstring'''







  return (f(a + h				) - f(a - h				)) / (2 * h)




def      UpperCAmelCase__							(     _A :					str      , _A :					Union[str, Any]=0      , _A :					Optional[int]=1_00      , _A :					str=0.0_001      , _A :					List[str]=1E-6      , _A :					Union[str, Any]=False				):





  '''simple docstring'''







  a__    =xa  # set the initial guess
  a__    =[a]
  a__    =abs(f(__lowercase				)				)
  a__    =lambda _A				: calc_derivative(__lowercase      , __lowercase      , h=__lowercase				)  # noqa: E731  Derivative of f(x)
  for _ in range(__lowercase				):
    if fa(__lowercase				) == 0:
      raise ValueError('''No converging solution found'''				)
    a__    =a - f(__lowercase				) / fa(__lowercase				)  # Calculate the next estimate
    if logsteps:
      steps.append(__lowercase				)
    if error < maxerror:
      break
  else:
    raise ValueError('''Iteration limit reached, no converging solution found'''				)
  if logsteps:
    # If logstep is true, then log intermediate steps
    return a, error, steps
  return a, error


if __name__ == "__main__":
       from matplotlib import pyplot as plt

       lowerCamelCase 	=   lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
       lowerCamelCase	,			lowerCamelCase	,			lowerCamelCase 	=   newton_raphson(
           f, xa=10, maxiter=1000, step=1e-6, logsteps=True
       )
       plt.plot([abs(f(x)) for x in steps])
       plt.xlabel('''step''')
       plt.ylabel('''error''')
       plt.show()
       print(f"""solution = {{{solution:f}}}, error = {{{error:f}}}""")






'''simple docstring'''


from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

UpperCamelCase			     =					TypeVar('''T''')
UpperCamelCase			     =					TypeVar('''U''')






class 						lowerCAmelCase_	(       Generic[T, U]							):







  '''simple docstring'''

  def __init__( self				:							Tuple					,  SCREAMING_SNAKE_CASE_				:							T | None					,  SCREAMING_SNAKE_CASE_				:							U | None	)			->		Any:







       '''simple docstring'''



       A:		Union[str, Any]          =		key
       A:		Union[str, Any]          =		val
       A:		int          =		0
       A:		DoubleLinkedListNode[T, U] | None          =		None
       A:		DoubleLinkedListNode[T, U] | None          =		None




  def __repr__( self				:							Any	)			->		str:







       '''simple docstring'''



       return "Node: key: {}, val: {}, freq: {}, has next: {}, has prev: {}".format(
           self.key					,  self.val					,  self.freq					,  self.next is not None					,  self.prev is not None	)






class 						lowerCAmelCase_	(       Generic[T, U]							):







  '''simple docstring'''

  def __init__( self				:							int	)			->		None:







       '''simple docstring'''



       A:		DoubleLinkedListNode[T, U]          =		DoubleLinkedListNode(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_	)
       A:		DoubleLinkedListNode[T, U]          =		DoubleLinkedListNode(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_	)
       A     ,    A:		Any          =		self.rear, self.head



  def __repr__( self				:							Optional[int]	)			->		str:







       '''simple docstring'''



       A:		int          =		['''DoubleLinkedList''']
       A:		Dict          =		self.head
       while node.next is not None:
            rep.append(str(SCREAMING_SNAKE_CASE_	)	)
            A:		int          =		node.next
       rep.append(str(self.rear	)	)
       return ",\n    ".join(SCREAMING_SNAKE_CASE_	)



  def 					_snake_case     ( self				:							Any					,  SCREAMING_SNAKE_CASE_				:							DoubleLinkedListNode[T, U]	)			->		None:







       '''simple docstring'''



       A:		Union[str, Any]          =		self.rear.prev

       # All nodes other than self.head are guaranteed to have non-None previous
       assert previous is not None

       A:		Optional[int]          =		node
       A:		int          =		previous
       A:		Dict          =		node
       A:		int          =		self.rear
       node.freq += 1
       self._position_node(SCREAMING_SNAKE_CASE_	)



  def 					_snake_case     ( self				:							int					,  SCREAMING_SNAKE_CASE_				:							DoubleLinkedListNode[T, U]	)			->		None:







       '''simple docstring'''



       while node.prev is not None and node.prev.freq > node.freq:
            # swap node with previous node
            A:		Any          =		node.prev

            A:		Optional[Any]          =		previous_node.prev
            A:		int          =		node.prev
            A:		int          =		previous_node
            A:		Optional[int]          =		node




  def 					_snake_case     ( self				:							Dict					,  SCREAMING_SNAKE_CASE_				:							DoubleLinkedListNode[T, U]	)			->		DoubleLinkedListNode[T, U] | None:







       '''simple docstring'''



       if node.prev is None or node.next is None:
            return None

       A:		List[Any]          =		node.next
       A:		Dict          =		node.prev
       A:		str          =		None
       A:		Union[str, Any]          =		None
       return node






class 						lowerCAmelCase_	(       Generic[T, U]							):







  '''simple docstring'''

  UpperCamelCase_			:      dict[Callable[[T], U], LFUCache[T, U]]										=				{}



  def __init__( self				:							List[str]					,  SCREAMING_SNAKE_CASE_				:							int	)			->		int:







       '''simple docstring'''



       A:		DoubleLinkedList[T, U]          =		DoubleLinkedList()
       A:		Any          =		capacity
       A:		List[Any]          =		0
       A:		Dict          =		0
       A:		Dict          =		0
       A:		dict[T, DoubleLinkedListNode[T, U]]          =		{}



  def __repr__( self				:							Optional[int]	)			->		str:







       '''simple docstring'''



       return (
           f"""CacheInfo(hits={self.hits}, misses={self.miss}, """
           f"""capacity={self.capacity}, current_size={self.num_keys})"""
       )



  def __contains__( self				:							str					,  SCREAMING_SNAKE_CASE_				:							T	)			->		bool:







       '''simple docstring'''



       return key in self.cache



  def 					_snake_case     ( self				:							Dict					,  SCREAMING_SNAKE_CASE_				:							T	)			->		U | None:







       '''simple docstring'''



       if key in self.cache:
            self.hits += 1
            A:		DoubleLinkedListNode[T, U]          =		self.cache[key]
            A:		List[str]          =		self.list.remove(self.cache[key]	)
            assert node == value_node

            # node is guaranteed not None because it is in self.cache
            assert node is not None
            self.list.add(SCREAMING_SNAKE_CASE_	)
            return node.val
       self.miss += 1
       return None



  def 					_snake_case     ( self				:							List[str]					,  SCREAMING_SNAKE_CASE_				:							T					,  SCREAMING_SNAKE_CASE_				:							U	)			->		None:







       '''simple docstring'''



       if key not in self.cache:
            if self.num_keys >= self.capacity:
                 # delete first node when over capacity
                 A:		List[Any]          =		self.list.head.next

                 # guaranteed to have a non-None first node when num_keys > 0
                 # explain to type checker via assertions
                 assert first_node is not None
                 assert first_node.key is not None
                 assert self.list.remove(SCREAMING_SNAKE_CASE_	) is not None
                 # first_node guaranteed to be in list

                 del self.cache[first_node.key]
                 self.num_keys -= 1
            A:		Tuple          =		DoubleLinkedListNode(SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_	)
            self.list.add(self.cache[key]	)
            self.num_keys += 1

       else:
            A:		Optional[Any]          =		self.list.remove(self.cache[key]	)
            assert node is not None  # node guaranteed to be in list
            A:		List[str]          =		value
            self.list.add(SCREAMING_SNAKE_CASE_	)




  @classmethod
  def 					_snake_case     ( cls				:							type[LFUCache[T, U]]					,  SCREAMING_SNAKE_CASE_				:							int = 1_28	)			->		Callable[[Callable[[T], U]], Callable[..., U]]:







       '''simple docstring'''



       def cache_decorator_inner(SCREAMING_SNAKE_CASE_				:							Callable[[T], U]	) -> Callable[..., U]:
            def cache_decorator_wrapper(*SCREAMING_SNAKE_CASE_				:							T	) -> U:
                 if func not in cls.decorator_function_to_instance_map:
                      A:		Tuple          =		LFUCache(SCREAMING_SNAKE_CASE_	)

                 A:		List[Any]          =		cls.decorator_function_to_instance_map[func].get(args[0]	)
                 if result is None:
                      A:		List[str]          =		func(*SCREAMING_SNAKE_CASE_	)
                      cls.decorator_function_to_instance_map[func].put(args[0]					,  SCREAMING_SNAKE_CASE_	)
                 return result

            def cache_info() -> LFUCache[T, U]:
                 return cls.decorator_function_to_instance_map[func]

            setattr(SCREAMING_SNAKE_CASE_					,  '''cache_info'''					,  SCREAMING_SNAKE_CASE_	)  # noqa: B010

            return cache_decorator_wrapper

       return cache_decorator_inner


if __name__ == "__main__":
     import doctest

     doctest.testmod()






