python circular doubly linked list

最近写装饰器看了 functools.lru_cache 的源码¹，里面发现了这样的代码：

    root = []                # root of the circular doubly linked listroot[:] = [root, root, None, None]     # initialize by pointing to self

类似的代码之前在 collections.OrderedDict 的源码里见过，之前也写过相关文章² ，但再看依然理解不深，于是今天再来聊聊这个。

需求

• lru_cache

  首先是记录和调整顺序（插入移动删除），由双向链表来实现；其次是通过键查询到值，由哈希表来实现。

• OrderedDict

  先讲个题外话，虽然自 Python 3.7 之后，字典的顺序会确保为插入顺序，但是 OrderedDict 并没有被干掉，搜了下只发现了这个答案³，它谈到了 OrderedDict.move_to_end() 和比较相等时的顺序敏感性。
  那么 OrderedDict 需要啥呢，本质上和上面一样，哈希表查找快，但是数据无固定顺序；链表有顺序之分，插入删除快，但是查找慢，结合一下就是哈希双向链表。

码

因为经常需要对队头和队尾进行操作，为了简化算法，设置一个哨兵节点 root

    PREV, NEXT, KEY, RESULT = 0, 1, 2, 3   # names for the link fieldsroot = []                # root of the circular doubly linked listroot[:] = [root, root, None, None]     # initialize by pointing to self

root[PERV] 表示队尾的节点， root[NEXT] 表示队头的节点。

下面是一些操作

# 添加节点到队尾
# 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# 移动节点到队尾
# 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# 删除头节点并添加节点到队尾 这里把要删除的节点的key/result清空 变成新的哨兵节点 
# 旧哨兵节点直接存入添加节点的key/result
# 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

关于 collections.OrderedDict 为什么舍弃掉这种写法，而使用了节点类和弱引用，我想就是因为 OrderedDict 里面有一些删除操作，在循环引用下可能会有内存的问题。

可以看到 lru_cache 装饰器里没有删除单个节点的操作，当缓存数量达到 maxsize 时，优化的算法没有先删除再添加，而是修改节点然后移动哨兵节点的位置。

番外

对函数传入的参数做哈希可以参考源码这部分，当然参数必须是可哈希的

class _HashedSeq(list):""" This class guarantees that hash() will be called no more than onceper element.  This is important because the lru_cache() will hashthe key multiple times on a cache miss."""__slots__ = 'hashvalue'def __init__(self, tup, hash=hash):self[:] = tupself.hashvalue = hash(tup)def __hash__(self):return self.hashvaluedef _make_key(args, kwds, typed,kwd_mark = (object(),),fasttypes = {int, str},tuple=tuple, type=type, len=len):"""Make a cache key from optionally typed positional and keyword argumentsThe key is constructed in a way that is flat as possible rather thanas a nested structure that would take more memory.If there is only a single argument and its data type is known to cacheits hash value, then that argument is returned without a wrapper.  Thissaves space and improves lookup speed."""# All of code below relies on kwds preserving the order input by the user.# Formerly, we sorted() the kwds before looping.  The new way is *much*# faster; however, it means that f(x=1, y=2) will now be treated as a# distinct call from f(y=2, x=1) which will be cached separately.key = argsif kwds:key += kwd_markfor item in kwds.items():key += itemif typed:key += tuple(type(v) for v in args)if kwds:key += tuple(type(v) for v in kwds.values())elif len(key) == 1 and type(key[0]) in fasttypes:return key[0]return _HashedSeq(key)

最后贴两篇也是分析 lru_cache 源码的文章^{4 5}，别人都会实现双向链表，我好菜呜呜呜~

其他存替换策略（cache replacement policies）⁶