def factorial(n):
  print(f"計算 {n} 的階乘")
  return 1 if n = 1 else n * factorial(n - 1)

a = factorial(5)
print(f'5! = {a}')
b = factorial(3)
print(f'3! = {b}')

import functools
# 注意 lru_cache 后的一對括號，證明這是帶參數(shù)的裝飾器
@functools.lru_cache()
def factorial(n):
  print(f"計算 {n} 的階乘")
  return 1 if n = 1 else n * factorial(n - 1)

def lru_cache(maxsize=128, typed=False):
  """Least-recently-used cache decorator.
  If *maxsize* is set to None, the LRU features are disabled and the cache
  can grow without bound.
  If *typed* is True, arguments of different types will be cached separately.
  For example, f(3.0) and f(3) will be treated as distinct calls with
  distinct results.
  Arguments to the cached function must be hashable.
  View the cache statistics named tuple (hits, misses, maxsize, currsize)
  with f.cache_info(). Clear the cache and statistics with f.cache_clear().
  Access the underlying function with f.__wrapped__.
  See: http://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)
  """

  # Users should only access the lru_cache through its public API:
  #    cache_info, cache_clear, and f.__wrapped__
  # The internals of the lru_cache are encapsulated for thread safety and
  # to allow the implementation to change (including a possible C version).
  
  if isinstance(maxsize, int):
    # Negative maxsize is treated as 0
    if maxsize  0:
      maxsize = 0
  elif callable(maxsize) and isinstance(typed, bool):
    # The user_function was passed in directly via the maxsize argument
    user_function, maxsize = maxsize, 128
    wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
    wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
    return update_wrapper(wrapper, user_function)
  elif maxsize is not None:
    raise TypeError(
      'Expected first argument to be an integer, a callable, or None')
  
  def decorating_function(user_function):
    wrapper = _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo)
    wrapper.cache_parameters = lambda : {'maxsize': maxsize, 'typed': typed}
    return update_wrapper(wrapper, user_function)
  
  return decorating_function

import functools
# 注意 lru_cache 后面沒有括號，
# 證明這是將其當(dāng)做不帶參數(shù)的裝飾器
@functools.lru_cache
def factorial(n):
  print(f"計算 {n} 的階乘")
  return 1 if n = 1 else n * factorial(n - 1)

def _lru_cache_wrapper(user_function, maxsize, typed, _CacheInfo):
  # Constants shared by all lru cache instances:
  sentinel = object()     # unique object used to signal cache misses
  make_key = _make_key     # build a key from the function arguments
  PREV, NEXT, KEY, RESULT = 0, 1, 2, 3  # names for the link fields

  cache = {}
  hits = misses = 0
  full = False
  cache_get = cache.get  # bound method to lookup a key or return None
  cache_len = cache.__len__ # get cache size without calling len()
  lock = RLock()      # because linkedlist updates aren't threadsafe
  root = []        # root of the circular doubly linked list
  root[:] = [root, root, None, None]   # initialize by pointing to self

  if maxsize == 0:

    def wrapper(*args, **kwds):
      # No caching -- just a statistics update
      nonlocal misses
      misses += 1
      result = user_function(*args, **kwds)
      return result

  elif maxsize is None:

    def wrapper(*args, **kwds):
      # Simple caching without ordering or size limit
      nonlocal hits, misses
      key = make_key(args, kwds, typed)
      result = cache_get(key, sentinel)
      if result is not sentinel:
        hits += 1
        return result
      misses += 1
      result = user_function(*args, **kwds)
      cache[key] = result
      return result

  else:

    def wrapper(*args, **kwds):
      # Size limited caching that tracks accesses by recency
      nonlocal root, hits, misses, full
      key = make_key(args, kwds, typed)
      with lock:
        link = cache_get(key)
        if link is not None:
          # Move the link to the front of the circular queue
          link_prev, link_next, _key, result = link
          link_prev[NEXT] = link_next
          link_next[PREV] = link_prev
          last = root[PREV]
          last[NEXT] = root[PREV] = link
          link[PREV] = last
          link[NEXT] = root
          hits += 1
          return result
        misses += 1
      result = user_function(*args, **kwds)
      with lock:
        if key in cache:
          # Getting here means that this same key was added to the
          # cache while the lock was released. Since the link
          # update is already done, we need only return the
          # computed result and update the count of misses.
          pass
        elif full:
          # Use the old root to store the new key and result.
          oldroot = root
          oldroot[KEY] = key
          oldroot[RESULT] = result
          # Empty the oldest link and make it the new root.
          # Keep a reference to the old key and old result to
          # prevent their ref counts from going to zero during the
          # update. That will prevent potentially arbitrary object
          # clean-up code (i.e. __del__) from running while we're
          # still adjusting the links.
          root = oldroot[NEXT]
          oldkey = root[KEY]
          oldresult = root[RESULT]
          root[KEY] = root[RESULT] = None
          # Now update the cache dictionary.
          del cache[oldkey]
          # Save the potentially reentrant cache[key] assignment
          # for last, after the root and links have been put in
          # a consistent state.
          cache[key] = oldroot
        else:
          # Put result in a new link at the front of the queue.
          last = root[PREV]
          link = [last, root, key, result]
          last[NEXT] = root[PREV] = cache[key] = link
          # Use the cache_len bound method instead of the len() function
          # which could potentially be wrapped in an lru_cache itself.
          full = (cache_len() >= maxsize)
      return result

  def cache_info():
    """Report cache statistics"""
    with lock:
      return _CacheInfo(hits, misses, maxsize, cache_len())

  def cache_clear():
    """Clear the cache and cache statistics"""
    nonlocal hits, misses, full
    with lock:
      cache.clear()
      root[:] = [root, root, None, None]
      hits = misses = 0
      full = False

  wrapper.cache_info = cache_info
  wrapper.cache_clear = cache_clear
  return wrapper

CacheInfo(hits=1, misses=5, maxsize=128, currsize=5)