27. LRU Cache

The problem can be found at the following link: Question Link

Problem Description

Design a data structure that works like an LRU (Least Recently Used) Cache. The cache should have the following operations:

1. GET x: Return the value associated with key x if it exists in the cache. Otherwise, return -1.

2. PUT x y: Set the value of key x to y. If the key is already present, update its value. If the cache reaches its capacity, remove the least recently used item before inserting the new item.

Input:

• cap (integer): The capacity of the cache.

• Q (integer): The number of queries.

• Queries: A list of queries where each query is either a PUT or GET operation.

Output:

• A list of results for the GET operations.

Example:

Input:

cap = 2
Q = 8
Queries = [["PUT", 1, 2], ["PUT", 2, 3], ["PUT", 1, 5], ["PUT", 4, 5], ["PUT", 6, 7], ["GET", 4], ["PUT", 1, 2], ["GET", 3]]

Output:

[5, -1]

Explanation:

1. PUT 1, 2 inserts (1, 2) into the cache.

2. PUT 2, 3 inserts (2, 3) into the cache.

3. PUT 1, 5 updates (1, 2) to (1, 5) as the key 1 already exists.

4. PUT 4, 5 removes the least recently used (2, 3) and inserts (4, 5).

5. PUT 6, 7 removes the least recently used (1, 5) and inserts (6, 7).

6. GET 4 returns 5 as key 4 is present in the cache.

7. PUT 1, 2 removes the least recently used (6, 7) and inserts (1, 2).

8. GET 3 returns -1 as key 3 is not in the cache.

Constraints:

• 1 <= cap <= $10^3$

• 1 <= Q <= $10^5$

• 1 <= x, y <= $10^4$

My Approach

1. Key Data Structures:

   • Use a combination of a doubly linked list and a hash map to implement the cache.

     • The doubly linked list stores the cache keys and their values, maintaining the order of usage (most recently used at the head, least recently used at the tail).

     • The hash map stores the mapping of keys to their corresponding nodes in the doubly linked list, allowing for O(1) access.

2. Implementation Details:

   • GET operation: Check if the key exists in the hash map:

     • If yes, move the key to the head of the linked list (marking it as most recently used) and return its value.

     • If no, return -1.

   • PUT operation:

     • If the key already exists, update its value and move it to the head of the linked list.

     • If the key does not exist:

       • If the cache size is at capacity, remove the least recently used item (the tail of the linked list).

       • Insert the new key-value pair at the head of the linked list and update the hash map.

Time and Auxiliary Space Complexity

• Expected Time Complexity:

  • GET: O(1), as both the hash map lookup and linked list operations are O(1).

  • PUT: O(1), as both insertion/removal from the linked list and updating the hash map are O(1).

• Expected Auxiliary Space Complexity: O(capacity), where capacity is the maximum number of key-value pairs in the cache. This space is used for the doubly linked list and hash map.

Code (C++)

class LRUCache {
    int capacity;
    list<pair<int, int>> cache;
    unordered_map<int, list<pair<int, int>>::iterator> map;
public:
    LRUCache(int cap) : capacity(cap) {}
    int get(int key) {
        if (!map.count(key)) return -1;
        cache.splice(cache.begin(), cache, map[key]); // Move the accessed node to the front
        return map[key]->second;
    }
    void put(int key, int value) {
        if (map.count(key)) cache.splice(cache.begin(), cache, map[key]), map[key]->second = value;
        else {
            if (cache.size() == capacity) map.erase(cache.back().first), cache.pop_back();
            cache.emplace_front(key, value), map[key] = cache.begin();
        }
    }
};

Code (Java)

class LRUCache {
    private int capacity;
    private LinkedHashMap<Integer, Integer> cache;

    LRUCache(int cap) {
        this.capacity = cap;
        this.cache = new LinkedHashMap<>(cap, 0.75f, true) {
            protected boolean removeEldestEntry(Map.Entry<Integer, Integer> eldest) {
                return size() > capacity;
            }
        };
    }
    public int get(int key) {
        return cache.getOrDefault(key, -1);
    }
    public void put(int key, int value) {
        cache.put(key, value);
    }
}

Code (Python)

from collections import OrderedDict

class LRUCache:
    def __init__(self, cap):
        self.cap = cap
        self.cache = OrderedDict()

    def get(self, key):
        if key not in self.cache:
            return -1
        self.cache.move_to_end(key)
        return self.cache[key]

    def put(self, key, value):
        if key in self.cache:
            self.cache.move_to_end(key)
        self.cache[key] = value
        if len(self.cache) > self.cap:
            self.cache.popitem(last=False)

Contribution and Support

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