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LRU Cache Implementation using Doubly Linked List

Last Updated : 07 Feb, 2025
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Design a data structure that works like a LRU(Least Recently Used) Cache. The LRUCache class has two methods get() and put() which are defined as follows.

  • LRUCache (Capacity c): Initialize LRU cache with positive size capacity c.
  • get(key): returns the value of the key if it already exists in the cache otherwise returns -1.
  • put(key, value): if the key is already present, update its value. If not present, add the key-value pair to the cache. If the cache reaches its capacity it should remove the key-value pair with the lowest priority.

Example:

Input: [LRUCache cache = new LRUCache(2) , put(1 ,1) , put(2 ,2) , get(1) , put(3 ,3) , get(2) , put(4 ,4) , get(1) , get(3) , get(4)]
Output: [1 ,-1, -1, 3, 4]
Explanation: The values mentioned in the output are the values returned by get operations.

  • Initialize LRUCache class with capacity = 2.
  • cache.put(1, 1): (key, pair) = (1,1) inserted and has the highest priority.
  • cache.put(2, 2): (key , pair) = (2,2) inserted and has the highest priority.
  • cache.get(1): For key 1, value is 1, so 1 returned and (1,1) moved to the highest priority.
  • cache.put(3, 3): Since cache is full, remove least recently used that is (2,2), (3,3) inserted with the highest priority.
  • cache.get(2): returns -1 (key 2 not found)
  • cache.put(4, 4): Since the cache is full, remove least recently used that is (1,1). (4,5) inserted with the highest priority.
  • cache.get(1): return -1 (not found)
  • cache.get(3): return 3 , (3,3) will moved to the highest priority.
  • cache.get(4): return 4 , (4,4) moved to the highest priority.

Thoughts about Implementation Using Arrays, Hashing and/or Heap

We use an array of triplets, where the items are key, value and priority

get(key) : We linearly search the key. If we find the item, we change priorities of all impacted and make the new item as the highest priority.
put(key): If there is space available, we insert at the end. If not, we linearly search items of the lowest priority and replace that item with the new one. We change priorities of all and make the new item as the highest priority.

Time Complexities of both the operations is O(n)

Can we make both operations in O(1) time? we can think of hashing. With hashing, we can insert, get and delete in O(1) time, but changing priorities would take linear time. We can think of using heap along with hashing for priorities. We can find and remove the least recently used (lowest priority) in O(Log n) time which is more than O(1) and changing priority in the heap would also be required.

Using Doubly Linked List and Hashing

The idea is to keep inserting the key-value pair at the head of the doubly linked list. When a node is accessed or added, it is moved to the head of the list (right after the dummy head node). This marks it as the most recently used. When the cache exceeds its capacity, the node at the tail (right before the dummy tail node) is removed as it represents the least recently used item.


Below is the implementation of the above approach: 

C++
// C++ program to implement LRU Least Recently Used)
#include <bits/stdc++.h>
using namespace std;

struct Node {
    int key;
    int value;
    Node *next;
    Node *prev;

    Node(int k, int v) {
        key = k;
        value = v;
        next = nullptr;
        prev = nullptr;
    }
};

// LRU Cache class
class LRUCache
{
  public:
  
    // Constructor to initialize the cache with a given capacity
    int capacity;
    unordered_map<int, Node *> cacheMap;
    Node *head;
    Node *tail;
    LRUCache(int capacity) {
        this->capacity = capacity;
        head = new Node(-1, -1);
        tail = new Node(-1, -1);
        head->next = tail;
        tail->prev = head;
    }

    // Function to get the value for a given key
    int get(int key) {
      
        if (cacheMap.find(key) == cacheMap.end())
            return -1;
  

        Node *node = cacheMap[key];
        remove(node);
        add(node);
        return node->value;
    }

    // Function to put a key-value pair into the cache
    void put(int key, int value) {
        if (cacheMap.find(key) != cacheMap.end()) {
            Node *oldNode = cacheMap[key];
            remove(oldNode);
              delete oldNode;
          
        }

        Node *node = new Node(key, value);
        cacheMap[key] = node;
        add(node);
       
       
        if (cacheMap.size() > capacity) {
            Node *nodeToDelete = tail->prev;
            remove(nodeToDelete);
            cacheMap.erase(nodeToDelete->key);
              delete nodeToDelete;
        }
    }

    // Add a node right after the head 
      // (most recently used position)
    void add(Node *node) {
        Node *nextNode = head->next;
        head->next = node;
        node->prev = head;
        node->next = nextNode;
        nextNode->prev = node;
    }

    // Remove a node from the list
    void remove(Node *node) {
        Node *prevNode = node->prev;
        Node *nextNode = node->next;
        prevNode->next = nextNode;
        nextNode->prev = prevNode;
    }
};

int main(){
    LRUCache cache(2);
  
    cache.put(1, 1); 
    cache.put(2, 2);
    cout << cache.get(1) << endl;
    cache.put(3, 3);
    cout  << cache.get(2) << endl;
    cache.put(4, 4);
    cout << cache.get(1) << endl;
    cout << cache.get(3) << endl;
    cout << cache.get(4) << endl;

    return 0;
}
Java
// Java program to implement LRU Least Recently Used)
import java.util.HashMap;
import java.util.Map;

class Node {
    int key;
    int value;
    Node next;
    Node prev;

    Node(int key, int value) {
        this.key = key;
        this.value = value;
        this.next = null;
        this.prev = null;
    }
}

class LRUCache {
    private int capacity;
    private Map<Integer, Node> cacheMap;
    private Node head;
    private Node tail;

    // Constructor to initialize the cache with a given
    // capacity
    LRUCache(int capacity) {
        this.capacity = capacity;
        this.cacheMap = new HashMap<>();
        this.head = new Node(-1, -1);
        this.tail = new Node(-1, -1);
        this.head.next = this.tail;
        this.tail.prev = this.head;
    }

    // Function to get the value for a given key
    int get(int key) {
        if (!cacheMap.containsKey(key)) {
            return -1;
        }

        Node node = cacheMap.get(key);
        remove(node);
        add(node);
        return node.value;
    }

    // Function to put a key-value pair into the cache
    void put(int key, int value) {
        if (cacheMap.containsKey(key)) {
            Node oldNode = cacheMap.get(key);
            remove(oldNode);
        }

        Node node = new Node(key, value);
        cacheMap.put(key, node);
        add(node);

        if (cacheMap.size() > capacity) {
            Node nodeToDelete = tail.prev;
            remove(nodeToDelete);
            cacheMap.remove(nodeToDelete.key);
        }
    }

    // Add a node right after the head (most recently used
    // position)
    private void add(Node node) {
        Node nextNode = head.next;
        head.next = node;
        node.prev = head;
        node.next = nextNode;
        nextNode.prev = node;
    }

    // Remove a node from the list
    private void remove(Node node) {
        Node prevNode = node.prev;
        Node nextNode = node.next;
        prevNode.next = nextNode;
        nextNode.prev = prevNode;
    }
}


public class Main {
    public static void main(String[] args) {
        LRUCache cache = new LRUCache(2);

        cache.put(1, 1);
        cache.put(2, 2);
        System.out.println(cache.get(1));
        cache.put(3, 3);
        System.out.println(cache.get(2));
        cache.put(4, 4);
        System.out.println(cache.get(1));
        System.out.println(cache.get(3));
        System.out.println(cache.get(4));
    }
}
Python
# Python program to implement LRU Least Recently Used)
class Node:
    def __init__(self, key, value):
        self.key = key
        self.value = value
        self.prev = None
        self.next = None


class LRUCache:
    def __init__(self, capacity: int):
        self.capacity = capacity
        self.cache = {}
        self.head = Node(-1, -1)
        self.tail = Node(-1, -1)
        self.head.next = self.tail
        self.tail.prev = self.head

    def _add(self, node: Node):
      
        # Add a node right after the head
        # (most recently used position).
        next_node = self.head.next
        self.head.next = node
        node.prev = self.head
        node.next = next_node
        next_node.prev = node

    def _remove(self, node: Node):
      
       # emove a node from the
        # doubly linked list.
        prev_node = node.prev
        next_node = node.next
        prev_node.next = next_node
        next_node.prev = prev_node

    def get(self, key: int) -> int:
        # Get the value for a given key
        if key not in self.cache:
            return -1

        node = self.cache[key]
        self._remove(node)
        self._add(node)
        return node.value

    def put(self, key: int, value: int):
      
        #Put a key-value pair into the cache.
        if key in self.cache:
            node = self.cache[key]
            self._remove(node)
            del self.cache[key]

        if len(self.cache) >= self.capacity:
          
            # Remove the least recently used item
            # (just before the tail)
            lru_node = self.tail.prev
            self._remove(lru_node)
            del self.cache[lru_node.key]

        # Add the new node
        new_node = Node(key, value)
        self._add(new_node)
        self.cache[key] = new_node


if __name__ == "__main__":
    cache = LRUCache(2)

    cache.put(1, 1)
    cache.put(2, 2)
    print(cache.get(1))
    cache.put(3, 3)
    print(cache.get(2))
    cache.put(4, 4)
    print(cache.get(1))
    print(cache.get(3))
    print(cache.get(4))
C#
// C# program to implement LRU Least Recently Used)
using System;
using System.Collections.Generic;

class Node {
    public int Key;
    public int Value;
    public Node Prev;
    public Node Next;

    public Node(int key, int value) {
        Key = key;
        Value = value;
        Prev = null;
        Next = null;
    }
}

class LRUCache {
    private int capacity;
    private Dictionary<int, Node> cache;
    private Node head;
    private Node tail;

    // Constructor to initialize the
    // cache with a given capacity
    public LRUCache(int capacity){
        this.capacity = capacity;
        cache = new Dictionary<int, Node>();
        head = new Node(-1, -1);
        tail = new Node(-1, -1);
        head.Next = tail;
        tail.Prev = head;
    }

    // Add a node right after the head
    //(most recently used position)
    private void Add(Node node) {
        Node nextNode = head.Next;
        head.Next = node;
        node.Prev = head;
        node.Next = nextNode;
        nextNode.Prev = node;
    }

    // Remove a node from the doubly linked list
    private void Remove(Node node) {
        Node prevNode = node.Prev;
        Node nextNode = node.Next;
        prevNode.Next = nextNode;
        nextNode.Prev = prevNode;
    }

    // Get the value for a given key
    public int Get(int key) {
        if (!cache.ContainsKey(key)) {
            return -1;
        }

        Node node = cache[key];
        Remove(node);
        Add(node);
        return node.Value;
    }

    // Put a key-value pair into the cache
    public void Put(int key, int value) {
        if (cache.ContainsKey(key)) {
            Node oldNode = cache[key];
            Remove(oldNode);
            cache.Remove(key);
        }

        if (cache.Count >= capacity) {
            Node lruNode = tail.Prev;
            Remove(lruNode);
            cache.Remove(lruNode.Key);
        }

        Node newNode = new Node(key, value);
        Add(newNode);
        cache[key] = newNode;
    }
}

class GfG {
    static void Main() {
        LRUCache cache = new LRUCache(2);

        cache.Put(1, 1);
        cache.Put(2, 2);
        Console.WriteLine(cache.Get(1));
        cache.Put(3, 3);
        Console.WriteLine(cache.Get(2));
        cache.Put(4, 4);
        Console.WriteLine(cache.Get(1));
        Console.WriteLine(cache.Get(3));
        Console.WriteLine(cache.Get(4));
    }
}
JavaScript
// Javascript program to implement LRU Least Recently Used)
class Node {
    constructor(key, value) {
        this.key = key;
        this.value = value;
        this.prev = null;
        this.next = null;
    }
}

class LRUCache {
    constructor(capacity) {
        this.capacity = capacity;
        this.cache = new Map();
        this.head = new Node(-1, -1);
        this.tail = new Node(-1, -1);
        this.head.next = this.tail;
        this.tail.prev = this.head;
    }

    // Add a node right after the head
    //(most recently used position)
    add(node) {
        const nextNode = this.head.next;
        this.head.next = node;
        node.prev = this.head;
        node.next = nextNode;
        nextNode.prev = node;
    }

    // Remove a node from the doubly linked list
    remove(node) {
        const prevNode = node.prev;
        const nextNode = node.next;
        prevNode.next = nextNode;
        nextNode.prev = prevNode;
    }

    // Get the value for a given key
    get(key) {
        if (!this.cache.has(key)) {
            return -1;
        }

        const node = this.cache.get(key);
        this.remove(node);
        this.add(node);
        return node.value;
    }

    // Put a key-value pair into the cache
    put(key, value) {
        if (this.cache.has(key)) {
            const node = this.cache.get(key);
            this.remove(node);
            this.cache.delete(key);
        }

        if (this.cache.size >= this.capacity) {
            const lruNode = this.tail.prev;
            this.remove(lruNode);
            this.cache.delete(lruNode.key);
        }

        const newNode = new Node(key, value);
        this.add(newNode);
        this.cache.set(key, newNode);
    }
}

const cache = new LRUCache(2);
cache.put(1, 1);
cache.put(2, 2);
console.log(cache.get(1));
cache.put(3, 3);
console.log(cache.get(2));
cache.put(4, 4);
console.log(cache.get(1));
console.log(cache.get(3));
console.log(cache.get(4));

Output
1
-1
-1
3
4

Time Complexity : get(key) – O(1) and put(key, value) – O(1)
Auxiliary Space : O(capacity)

Using Inbuilt Doubly Linked List

The idea is to use inbuilt doubly linked list, it simplifies the implementation by avoiding the need to manually manage a doubly linked list while achieving efficient operations. Example – C++ uses a custom doubly linked list as std::list.

Note: Python’s standard library does not include a built-in doubly linked list implementation. To handle use cases that typically require a doubly linked list, such as efficiently managing elements at both ends of a sequence, Python provides the collections.deque class. While deque stands for double-ended queue, it essentially functions as a doubly linked list with efficient operations on both ends.

Below is the implementation of the above approach: 

C++
// C++ program to implement LRU Least Recently Used) using
//Built-in Doubly linked list
#include <bits/stdc++.h>
using namespace std;

class LRUCache {
  public:
    int capacity;
    list<pair<int, int>> List;

    // Map from key to list iterator
    unordered_map<int, list<pair<int, int>>::iterator> cacheMap;

    // Constructor to initialize the 
      //cache with a given capacity
    LRUCache(int capacity) {
        this->capacity = capacity;
    }

    // Function to get the value for a given key
    int get(int key) {
        auto it = cacheMap.find(key);
        if (it == cacheMap.end()) {
            return -1;
        }

        // Move the accessed node to the 
          //front (most recently used position)
        int value = it->second->second;
        List.erase(it->second);
        List.push_front({key, value});

        // Update the iterator in the map
        cacheMap[key] = List.begin();
        return value;
    }

    // Function to put a key-value pair into the cache
    void put(int key, int value) {
        auto it = cacheMap.find(key);
        if (it != cacheMap.end()) {
            // Remove the old node from the list and map
            List.erase(it->second);
            cacheMap.erase(it);
        }

        // Insert the new node at the front of the list
        List.push_front({key, value});
        cacheMap[key] = List.begin();

        // If the cache size exceeds the capacity,
          //remove the least recently used item
        if (cacheMap.size() > capacity) {
            auto lastNode = List.back().first;
            List.pop_back();
            cacheMap.erase(lastNode);
        }
    }
};

int main() {
  
    LRUCache cache(2);
    cache.put(1, 1);
    cache.put(2, 2);
    cout << cache.get(1) << endl;
    cache.put(3, 3);
    cout << cache.get(2) << endl;
    cache.put(4, 4);
    cout << cache.get(1) << endl;
    cout << cache.get(3) << endl;
    cout << cache.get(4) << endl;

    return 0;
}
Java
// Java program to implement LRU Least Recently Used) using
// Built-in Doubly linked list

import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;

class LRUCache {
    private int capacity;

    // Stores key-value pairs
    private Map<Integer, Integer> cacheMap;

    // Stores keys in the order of access
    private LinkedList<Integer> lruList;

    // Constructor to initialize the cache with a given
    // capacity
    LRUCache(int capacity) {
        this.capacity = capacity;
        this.cacheMap = new HashMap<>();
        this.lruList = new LinkedList<>();
    }

    // Function to get the value for a given key
    public int get(int key) {
        if (!cacheMap.containsKey(key)) {
            return -1;
        }

        // Move the accessed key to the front (most recently
        // used position)
        lruList.remove(Integer.valueOf(key));

        // Add key to the front
        lruList.addFirst(key);

        return cacheMap.get(key);
    }

    // Function to put a key-value pair into the cache
    public void put(int key, int value) {
        if (cacheMap.containsKey(key)) {
          
            // Update the value
            cacheMap.put(key, value);
          
            // Move the accessed key to the front
            lruList.remove(Integer.valueOf(key));
        }
        else {
          
            // Add new key-value pair
            if (cacheMap.size() >= capacity) {
              
                // Remove the least recently used item
                int leastUsedKey = lruList.removeLast();
                cacheMap.remove(leastUsedKey);
            }
            cacheMap.put(key, value);
        }
        // Add the key to the front (most recently used
        // position)
        lruList.addFirst(key);
    }

    public static void main(String[] args) {
      
        LRUCache cache = new LRUCache(2);
        cache.put(1, 1);
        cache.put(2, 2);
        System.out.println(cache.get(1));
        cache.put(3, 3);
        System.out.println(cache.get(2));
        cache.put(4, 4);
        System.out.println(cache.get(1));
        System.out.println(cache.get(3));
        System.out.println( cache.get(4));
    }
}
Python
# Python program to implement LRU Least Recently Used) using
# Built-in Doubly linked list
from collections import deque

class LRUCache:
    def __init__(self, capacity: int):
        self.capacity = capacity

        # Dictionary to store key-value pairs
        self.cache = {}

        # Deque to maintain the order of keys
        self.order = deque()

    def get(self, key: int) -> int:
        if key in self.cache:

            # Move the accessed key to 
            # the front of the deque
            self.order.remove(key)
            self.order.appendleft(key)
            return self.cache[key]
        else:
            return -1

    def put(self, key: int, value: int):
        if key in self.cache:

            # Update the value and move
            # the key to the front
            self.cache[key] = value
            self.order.remove(key)
            self.order.appendleft(key)
        else:
            if len(self.cache) >= self.capacity:

                # Remove the least recently used item
                lru_key = self.order.pop()
                del self.cache[lru_key]

            # Add the new key-value pair
            self.cache[key] = value
            self.order.appendleft(key)


if __name__ == "__main__":
  
    cache = LRUCache(2)
    cache.put(1, 1)
    cache.put(2, 2)
    print(cache.get(1))
    cache.put(3, 3)
    print(cache.get(2))
    cache.put(4, 4)
    print(cache.get(1))
    print(cache.get(3))
    print(cache.get(4))
C#
using System;
using System.Collections.Generic;

class LRUCache {
    private int capacity;
    private Dictionary<int, LinkedListNode<KeyValuePair<int, int>>> cacheMap;
    private LinkedList<KeyValuePair<int, int>> lruList;

    // Constructor to initialize the cache with a given capacity
    public LRUCache(int capacity) {
        this.capacity = capacity;
        this.cacheMap = new Dictionary<int, LinkedListNode<KeyValuePair<int, int>>>();
        this.lruList = new LinkedList<KeyValuePair<int, int>>();
    }

    // Function to get the value for a given key
    public int Get(int key) {
        if (cacheMap.TryGetValue(key, out LinkedListNode<KeyValuePair<int, int>> node)) {
          
            // Move the accessed node to the front (most recently used position)
            lruList.Remove(node);
            lruList.AddFirst(node);
            return node.Value.Value;
        } else {
            return -1;
        }
    }

    // Function to put a key-value pair into the cache
    public void Put(int key, int value) {
        if (cacheMap.TryGetValue(key, out LinkedListNode<KeyValuePair<int, int>> node)) {
          
            // Remove the old node from the list and map
            lruList.Remove(node);
            cacheMap.Remove(key);
        }

        // Insert the new node at the front of the list
        var newNode = new KeyValuePair<int, int>(key, value);
        var listNode = new LinkedListNode<KeyValuePair<int, int>>(newNode);
        lruList.AddFirst(listNode);
        cacheMap[key] = listNode;

        // If the cache size exceeds the capacity, remove the 
          // least recently used item
        if (cacheMap.Count > capacity) {
            var lastNode = lruList.Last;
            lruList.RemoveLast();
            cacheMap.Remove(lastNode.Value.Key);
        }
    }
}

class GfG {
    static void Main() {
      
        LRUCache cache = new LRUCache(2);
        cache.Put(1, 1);
        cache.Put(2, 2);
        Console.WriteLine(cache.Get(1));
        cache.Put(3, 3);
        Console.WriteLine(cache.Get(2));
        cache.Put(4, 4);
        Console.WriteLine(cache.Get(1));
        Console.WriteLine(cache.Get(3));
        Console.WriteLine(cache.Get(4));
    }
}
JavaScript
// Javascript program to implement LRU Least Recently Used)
// using Built-in Doubly linked list

class LRUCache {
    constructor(capacity) {
        this.capacity = capacity;
        this.cache = new Map();
    }

    // Get the value for a given key
    get(key) {
        if (!this.cache.has(key)) {
            return -1;
        }

        // Move the accessed key-value pair
        // to the end to mark it as recently used
        const value = this.cache.get(key);
        this.cache.delete(key);
        this.cache.set(key, value);
        return value;
    }

    // Put a key-value pair into the cache
    put(key, value) {
        if (this.cache.has(key)) {
        
            // Update the value and move the key to the end
            this.cache.delete(key);
        }
        else if (this.cache.size >= this.capacity) {
        
            // Remove the least recently used item (the
            // first item in the Map)
            this.cache.delete(this.cache.keys().next().value);
        }

        // Add the new key-value pair
        this.cache.set(key, value);
    }
}

const cache = new LRUCache(2);
cache.put(1, 1);
cache.put(2, 2);
console.log(cache.get(1));
cache.put(3, 3);
console.log(cache.get(2));
cache.put(4, 4);
console.log(cache.get(1));
console.log(cache.get(3));
console.log(cache.get(4));

Output
1
-1
-1
3
4

Time Complexity : get(key) – O(1) and put(key, value) – O(1)
Auxiliary Space: O(capacity)



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