Implementing LRU Cache

Implementing LRU Cache [LC#146]

Design a data structure that follows the constraints of a Least Recently Used (LRU) cache.
Implement the LRUCache class:
LRUCache(int capacity) Initialize the LRU cache with positive size capacity.
int get(int key) Return the value of the key if the key exists, otherwise return -1.
void put(int key, int value) Update the value of the key if the key exists. Otherwise, add the key-value pair to the cache. If the number of keys exceeds the capacity from this operation, evict the least recently used key. The functions get and put must each run in $O(1)$ average time complexity.

Intuition

Values can be stored in a dictionary
For keeping track of freshness, we use a doubly linked list.
- New values are inserted at the right end
- existing values are removed and nserted at the right end to implement recently used property
- Capacity can be enforced by removing nodes from left. Nodes in the left are least recently used.

Code

class Node:
    def __init__(self, key, val, nxt=None, prev=None):
        self.key = key
        self.val = val
        self.next = nxt
        self.prev = prev
    
class LRUCache:
    def __init__(self, capacity: int):
        self.capacity = capacity
        self.storage = {}
        self.head = Node(-1, -1, None, None)
        self.tail = Node(-2, -2, None, None)
        self.head.next = self.tail
        self.tail.prev = self.head

    def add_at_end(self, node):
        node.prev = self.tail.prev
        node.next = self.tail 
        self.tail.prev.next = node
        self.tail.prev = node

    def remove_node(self, node):
        node.next.prev = node.prev
        node.prev.next = node.next
        return node.key

    def get(self, key: int) -> int:
        if key in self.storage:
            # update freshness
            node = self.storage[key]
            self.remove_node(node)
            self.add_at_end(node)
            return node.val
        return -1

    def put(self, key: int, value: int) -> None:
        if key in self.storage:
            self.storage[key].val = value
            self.get(key)
        else:
            node = Node(key, value, None, None)
            self.storage[key] = node
            self.add_at_end(node)
            if len(self.storage)>self.capacity:
                rm_key = self.remove_node(self.head.next)
                del self.storage[rm_key]

Time Complexity

$O(1)$ for get and put
$O(n)$ storage for dictionary and linkeidnlist