双向链表和哈希表实现 LRUCache

背景

LRUCache 是一个很常用的缓存实现,本文会首先介绍一下 LRUCache 的定义,然后尝试用 Python 实现它。

定义

LRUCache 首先是一个 Cache,那么对于一个 Cache 而言,肯定需要提供 getset 两个方法,而且,这两个方法的时间复杂度越低越好,最好达到 O(1) 级别。

LRU 是 Least Recently Used 的缩写,近期最少使用策略。
LRUCache 意味着一个带有容量的缓存,当缓存的容量已满而且需要插入新值的时候,缓存需要淘汰一个旧值。具体淘汰的策略就是 LRU。

LRU 意味着这样的功能:

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# 如果 Cache 里有两个 key => `a` 和 `b`,而且 Cache 的容量是 2
cache.get('a')
# ... 无数次
cache.get('a')
cache.get('b')
cache.put('c', 'c-value')
# cache => {'b': 'b-value', 'c': 'c-value'}

我们可以看到,无论 a 之前 get,过多少次,只要最后一个 get('b') 的操作在最后一个 get('a') 的操作之后,那么 淘汰 b 的优先级肯定在 a 之后,这就是 LRU 策略的实例化解释。

实现

通常使用双向链表和字典来实现 LRUCache。

为了能很快找到双向链表的头和尾,我们需要一个虚拟头节点,这个头节点的 next 指针始终指向真实的头节点(以下称为头节点);类似地,我们也需要一个虚拟尾节点,它的 pre 指针始终指向真实的尾节点(以下称为尾节点)。

双向链表的头节点就是淘汰优先级最低的点,尾节点就是淘汰优先级最高的点。
当 LRUCache 容量达到上限后,应该首先淘汰尾节点。

链表节点的 val 字段指向一个数组 [key, value]。这个 key 和 value 就是整个 LRUCache 中 getset 方法的 key 和 value。

map 的 key 也是 LRUCache 的 key,但是 map 的 value 是双向链表的节点。

那么对应 LRUCache 的两个方法 get put,我们可以想出以下思路:

get(key)

get 方法需要考虑两件事情:

  1. 找到 key 对应的 value 值
  2. 更新 key 的淘汰优先级

具体思路如下:

  • 如果这个 key 在 map 中不存在,那么我们只需返回 null 即可
  • 如果这个 key 在 map 中存在,那么我们此时能马上获取到这个 key 对应的链表节点,通过链表节点我们能读取到真正的缓存的值。此时我们需要先将这个链表节点挪动到链表的头部,然后再返回链表的 value 字段
put(key, value)

put 方法需要考虑三个事情:

  1. 更新 key 对应的 value
  2. 更新 key 对应的淘汰优先级
  3. 如果当前缓存容量达到上限,淘汰一个链表节点。

具体思路如下:

  • 如果这个 key 原本就存在需要通过 map 找到链表节点,然后更新链表节点中的 value,然后将这个链表节点挪动到链表的头部
  • 如果这个 key 存在,那么我们需要构造一个 node,并插入到链表头部
    • 如果容量未满,不用管
    • 如果容量满了,那么我们需要移除链表尾部的 node,并将其从 map 中也移除
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# -*- coding: utf-8 -*-

import sys


class ListNode(object):
"""
LinkedListNode
"""

__slots__ = ['val', 'next', 'pre']

def __init__(self, x):
self.val = x
self.next = None
self.pre = None


class LinkedList(object):
"""
LinkedList
"""

__slots__ = ['head', 'tail', 'length']

def __init__(self):
"""
init
"""

self.head, self.tail = ListNode(-1), ListNode(-1)
self.head.next = self.tail
self.tail.pre = self.head
self.length = 0

def insert_head(self, node):
"""
insert a value to head
:param node: the value
:return: ListNode the node has been inserted
"""

node.next = self.head.next
self.head.next.pre = node
node.pre = self.head
self.head.next = node
self.length += 1
return node

def insert_tail(self, node):
"""
insert a node to tail
:param node: the value
:return: ListNode the node has been inserted
"""

node.pre = self.tail.pre
node.next = self.tail
self.tail.pre = node
self.length += 1
return node

def pop_head(self):
"""
pop a node from head
:return: ListNode the node has been popped
"""

if self.length == 0:
return None
tempNode = self.head.next.next
tempNode.pre = self.head
self.head.next = tempNode
self.length -= 1
return tempNode

def remove_node(self, node):
"""
remove a node from linkedlist
:param node: ListNode
:return: ListNode the node has been removed
"""

node.next.pre = node.pre
node.pre.next = node.next
self.length -= 1

def pop_tail(self):
"""
pop a node from tail
:return: ListNode the node has been popped
"""

if self.length == 0:
return None
shouldRemoveNode = self.tail.pre
tempNode = shouldRemoveNode.pre
tempNode.next = self.tail
self.tail.pre = tempNode
self.length -= 1
return shouldRemoveNode

def print_self(self):
if self.length == 0:
print('none')
return
current_node = self.head.next
while current_node.next is not None:
sys.stdout.write(str(current_node.val[0]) + ":" + str(current_node.val[1]) + " => ")
current_node = current_node.next
if current_node.next is None:
break
sys.stdout.write(" None ")
sys.stdout.write(" :: Length: " + str(self.length))
sys.stdout.flush()
print('')


class LRUCache(object):
"""
LRUCache
"""

__slots__ = ['map', 'linkedlist', 'cap']

def __init__(self, cap):
self.cap = cap
self.map = {}
self.linkedlist = LinkedList()

def put(self, key, value):
# if this key is exist, just update the value of the node and move this node to head
if key in self.map:
node = self.map[key]
node.val[1] = value
self.get(key)
self.linkedlist.print_self()
return

# not exist yet, insert this value to head and put this node to map
newNode = self.linkedlist.insert_head(ListNode([key, value]))
self.map[key] = newNode

# check the capacity, remove the tail node if LRUCache is full
if self.linkedlist.length > self.cap:
oldNode = self.linkedlist.pop_tail()
oldKey = oldNode.val[0]
self.map.pop(oldKey)

self.linkedlist.print_self()

def get(self, key):
if key not in self.map:
self.linkedlist.print_self()
return -1

# get the node, move this node to head
node = self.map[key]
self.linkedlist.remove_node(node)
self.linkedlist.insert_head(node)
# return the value
self.linkedlist.print_self()
return node.val[1]


cmds = ["put", "put", "put", "put", "put", "get", "put", "get", "get", "put", "get", "put", "put", "put", "get",
"put", "get", "get", "get", "get", "put", "put", "get", "get", "get", "put", "put", "get", "put", "get", "put",
"get",
"get", "get", "put", "put", "put", "get", "put", "get", "get", "put", "put", "get", "put", "put", "put", "put",
"get",
"put", "put", "get", "put", "put", "get", "put", "put", "put", "put", "put", "get", "put", "put", "get", "put",
"get",
"get", "get", "put", "get", "get", "put", "put", "put", "put", "get", "put", "put", "put", "put", "get", "get",
"get",
"put", "put", "put", "get", "put", "put", "put", "get", "put", "put", "put", "get", "get", "get", "put", "put",
"put",
"put", "get", "put", "put", "put", "put", "put", "put", "put"]

params = [[10, 13], [3, 17], [6, 11], [10, 5], [9, 10], [13], [2, 19], [2], [3], [5, 25], [8], [9, 22], [5, 5], [1, 30],
[11], [9, 12], [7], [5], [8], [9], [4, 30], [9, 3], [9], [10], [10], [6, 14], [3, 1], [3], [10, 11], [8],
[2, 14], [1],
[5], [4], [11, 4], [12, 24], [5, 18], [13], [7, 23], [8], [12], [3, 27], [2, 12], [5], [2, 9], [13, 4],
[8, 18],
[1, 7], [6], [9, 29], [8, 21], [5], [6, 30], [1, 12], [10], [4, 15], [7, 22], [11, 26], [8, 17], [9, 29], [5],
[3, 4],
[11, 30], [12], [4, 29], [3], [9], [6], [3, 4], [1], [10], [3, 29], [10, 28], [1, 20], [11, 13], [3], [3, 12],
[3, 8],
[10, 9], [3, 26], [8], [7], [5], [13, 17], [2, 27], [11, 15], [12], [9, 19], [2, 15], [3, 16], [1], [12, 17],
[9, 1],
[6, 19], [4], [5], [5], [8, 1], [11, 7], [5, 2], [9, 28], [1], [2, 2], [7, 4], [4, 22], [7, 24], [9, 26],
[13, 28],
[11, 26]]




def print_list(l):
sys.stdout.write('[')
sys.stdout.write(', '.join(str(p) for p in l))
sys.stdout.write(']')

cache = LRUCache(10)

for i in xrange(len(cmds)):
cmd = cmds[i]
param = params[i]

sys.stdout.write(str(i) + " " + cmd + " ")
print_list(param)
sys.stdout.write("\n")
val = getattr(cache, cmd)(*param)
print("result " + str(val))
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