# 146. LRU Cache

Design a data structure that follows the constraints of a [**Least Recently Used (LRU) cache**](https://en.wikipedia.org/wiki/Cache_replacement_policies#LRU).

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.

**Example 1:**

```python
Input
["LRUCache", "put", "put", "get", "put", "get", "put", "get", "get", "get"]
[[2], [1, 1], [2, 2], [1], [3, 3], [2], [4, 4], [1], [3], [4]]
Output
[null, null, null, 1, null, -1, null, -1, 3, 4]

Explanation
LRUCache lRUCache = new LRUCache(2);
lRUCache.put(1, 1); // cache is {1=1}
lRUCache.put(2, 2); // cache is {1=1, 2=2}
lRUCache.get(1);    // return 1
lRUCache.put(3, 3); // LRU key was 2, evicts key 2, cache is {1=1, 3=3}
lRUCache.get(2);    // returns -1 (not found)
lRUCache.put(4, 4); // LRU key was 1, evicts key 1, cache is {4=4, 3=3}
lRUCache.get(1);    // return -1 (not found)
lRUCache.get(3);    // return 3
lRUCache.get(4);    // return 4
```

**Constraints:**

* `1 <= capacity <= 3000`
    
* `0 <= key <= 10<sup>4</sup>`
    
* `0 <= value <= 10<sup>5</sup>`
    
* At most `2 * 10<sup>5</sup>` calls will be made to `get` and `put`.
    

Solution:

```python
class Node:
    def __init__(self, key, val):
        self.key, self.val = key, val
        self.prev = self.next = None


class LRUCache:
    def __init__(self, capacity: int):
        self.cap = capacity
        self.cache = {}  # map key to node

        self.left, self.right = Node(0, 0), Node(0, 0)
        self.left.next, self.right.prev = self.right, self.left

    def remove(self, node):
        prev, nxt = node.prev, node.next
        prev.next, nxt.prev = nxt, prev

    def insert(self, node):
        prev, nxt = self.right.prev, self.right
        prev.next = nxt.prev = node
        node.next, node.prev = nxt, prev

    def get(self, key: int) -> int:
        if key in self.cache:
            self.remove(self.cache[key])
            self.insert(self.cache[key])
            return self.cache[key].val
        return -1

    def put(self, key: int, value: int) -> None:
        if key in self.cache:
            self.remove(self.cache[key])
        self.cache[key] = Node(key, value)
        self.insert(self.cache[key])

        if len(self.cache) > self.cap:
            lru = self.left.next
            self.remove(lru)
            del self.cache[lru.key]
```