# Question

Formatted question description: https://leetcode.ca/all/146.html

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.

Example 1:

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 <= 104
• 0 <= value <= 105
• At most 2 * 105 calls will be made to get and put.

# Algorithm

## Solution

Create a class MyNode, which contains data fields int key, int value, Node prev and Node next. That is, each node of type MyNode has a key and a value, and have references to its previous node and the next node.

In class LRUCache, data fields include int capacity that stores the capacity of the cache, Map<Integer, MyNode> map that maps each key to its node, MyNode head and Node tail that represents the head node and the tail node respectively. For Least Recently Used cache, the most recently used node is the head node and the least recently used node is the tail node.

In the constructor, initialize capacity with the given capacity.

In get(key), if key is not in map, then key is not in the cache, so return -1. If key is in map, obtain the node and its value, remove the node and set the node to be the head, and return value.

In put(key, value), if map contains key, then obtain the node and update its value, remove the node, and set the node to be the head. If map does not contain key, then create a new node using key and value, and set the new node to be the head. If the size of map is greater than or equal to capacity, then remove the node tail and remove the corresponding entry in map. Add a new entry of the new node into the map.

Two supplementary methods are needed.

1. Method remove(MyNode node). Obtain MyNode’s previous node and next node, and update their references to other nodes accordingly. If MyNode is head or tail, then update head or tail accordingly.
2. Method setHead(MyNode node). Set MyNode to be the new head and set the previous head’s reference accordingly. If tail is null, then update tail as well.

# Code

Java

• class LRUCache {
int capacity;
Map<Integer, MyNode> map = new HashMap<Integer, MyNode>(); // key => Node[key,val]
MyNode head = null;
MyNode tail = null;

public LRUCache(int capacity) {
this.capacity = capacity;
}

public int get(int key) {
MyNode node = map.get(key);
if (node == null) {
return -1;
} else {
remove(node);
setHead(node);
return node.value;
}
}

public void put(int key, int value) {
if (map.containsKey(key)) {
MyNode node = map.get(key);
node.value = value;
remove(node);
setHead(node);
} else {
MyNode node = new MyNode(key, value);
setHead(node);
map.put(key, node);
if (map.size() >= capacity) { // @note: also = , after if will add one more
map.remove(tail.key);
remove(tail);
}
}
}

public void remove(MyNode node) {
MyNode prev = node.prev;
MyNode next = node.next;

// process previous node
if (prev != null)
prev.next = next;
else
head = next;

// process next node
if (next != null)
next.prev = prev;
else
tail = prev;
}

public void setHead(MyNode node) {
node.next = head;
node.prev = null;
if (head != null)
head.prev = node;
head = node;
if (tail == null)
tail = head;
}
}

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

public MyNode(int key, int value) {
this.key = key;
this.value = value;
}
}
/**
* Your LRUCache object will be instantiated and called as such:
* LRUCache obj = new LRUCache(capacity);
* int param_1 = obj.get(key);
* obj.put(key,value);
*/

############

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

Node() {
}

Node(int key, int val) {
this.key = key;
this.val = val;
}
}

class LRUCache {
private Map<Integer, Node> cache = new HashMap<>();
private Node head = new Node();
private Node tail = new Node();
private int capacity;
private int size;

public LRUCache(int capacity) {
this.capacity = capacity;
head.next = tail;
tail.prev = head;
}

public int get(int key) {
if (!cache.containsKey(key)) {
return -1;
}
Node node = cache.get(key);
moveToHead(node);
return node.val;
}

public void put(int key, int value) {
if (cache.containsKey(key)) {
Node node = cache.get(key);
node.val = value;
moveToHead(node);
} else {
Node node = new Node(key, value);
cache.put(key, node);
addToHead(node);
++size;
if (size > capacity) {
node = removeTail();
cache.remove(node.key);
--size;
}
}
}

private void moveToHead(Node node) {
removeNode(node);
addToHead(node);
}

private void removeNode(Node node) {
node.prev.next = node.next;
node.next.prev = node.prev;
}

private void addToHead(Node node) {
node.next = head.next;
node.prev = head;
head.next = node;
node.next.prev = node;
}

private Node removeTail() {
Node node = tail.prev;
removeNode(node);
return node;
}
}

/**
* Your LRUCache object will be instantiated and called as such:
* LRUCache obj = new LRUCache(capacity);
* int param_1 = obj.get(key);
* obj.put(key,value);
*/

• // OJ: https://leetcode.com/problems/lru-cache
// Time:
//    LRUCache: O(1)
//    get: O(1)
//    put: O(1)
// Space: O(N)
class LRUCache {
int capacity;
list<pair<int, int>> data;
unordered_map<int, list<pair<int, int>>::iterator> m;
void moveToFront(int key) {
auto node = m[key];
data.splice(data.begin(), data, node);
m[key] = data.begin();
}
public:
LRUCache(int capacity) : capacity(capacity) {}
int get(int key) {
// get node given key, put the node at the beginning of the list, return the value in the node
if (m.count(key)) {
moveToFront(key);
return m[key]->second;
}
return -1;
}
void put(int key, int value) {
// if key exists in the map, get node given key, put the node at the beginning of the list and update the value in the node
// otherwise, put a new node at the beginning of the list with the <key, value> and update the map. If capacity exceeded, remove the last node from the list and map.
if (m.count(key)) {
moveToFront(key);
m[key]->second = value;
} else {
data.emplace_front(key, value);
m[key] = data.begin();
if (data.size() > capacity) {
m.erase(data.rbegin()->first);
data.pop_back();
}
}
}
};

• class Node:
def __init__(self, key=0, val=0):
self.key = key
self.val = val
self.prev = None
self.next = None

class LRUCache:
def __init__(self, capacity: int):
self.cache = {} # key ==> Node(val)
self.head = Node() # dummy node
self.tail = Node() # dummy node
self.capacity = capacity
self.size = 0
self.head.next = self.tail
self.tail.prev = self.head

def get(self, key: int) -> int:
if key not in self.cache:
return -1
node = self.cache[key]
self.move_to_head(node)
return node.val

def put(self, key: int, value: int) -> None:
if key in self.cache:
node = self.cache[key]
node.val = value
self.move_to_head(node)
else:
node = Node(key, value)
self.cache[key] = node
self.add_to_head(node)
self.size += 1
if self.size > self.capacity:
tail = self.remove_tail()
self.cache.pop(tail.key)
self.size -= 1

def move_to_head(self, node):
self.remove_node(node)
self.add_to_head(node)

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

def add_to_head(self, node):
node.next = self.head.next
node.prev = self.head
self.head.next = node
node.next.prev = node

def remove_tail(self):
node = self.tail.prev
self.remove_node(node)
return node

# Your LRUCache object will be instantiated and called as such:
# obj = LRUCache(capacity)
# param_1 = obj.get(key)
# obj.put(key,value)

############

'''
example:

>>> od = collections.OrderedDict()
>>>
>>> od[1]=1
>>> od[2]=2
>>> od[3]=3
>>>
>>> od
OrderedDict([(1, 1), (2, 2), (3, 3)])
>>> od.move_to_end(1)
>>> od
OrderedDict([(2, 2), (3, 3), (1, 1)])
>>>
>>> od.get(1)
1
>>> od.popitem()
(1, 1)
>>> od
OrderedDict([(2, 2), (3, 3)])
>>>
>>> od[1]=1
>>> od
OrderedDict([(2, 2), (3, 3), (1, 1)])
>>>
>>> od.popitem(last=False)
(2, 2)
>>> od
OrderedDict([(3, 3), (1, 1)])

'''

import collections

class LRUCache:
def __init__(self, capacity: 'int'):
self.cache = collections.OrderedDict()
self.remain = capacity

def get(self, key: 'int') -> 'int':
if key not in self.cache:
return -1
self.cache.move_to_end(key) # meaning end is the most recently used
return self.cache.get(key)

def put(self, key: 'int', value: 'int') -> 'None':
if key not in self.cache:
if self.remain > 0:
self.remain -= 1
else:
self.cache.popitem(last=False) # pop start position
else:
self.cache.pop(key)
self.cache[key] = value # add to end of dict, meaning most recently used

############

### below solution with no ordered-dict
class DLinkedNode:

def __init__(self, key=0, value=0):
self.key = key
self.val = value
self.next = None
self.prev = None

class DLinkedList:

def __init__(self):
self.head = DLinkedNode() # dummy head, its next is real head
self.tail = DLinkedNode() # dummy tail, its prev is real tail
self.head.next, self.tail.prev = self.tail, self.head

def add_node(self, node): # add to head
node.prev, node.next = self.head, self.head.next
node.next.prev, node.prev.next = node, node

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

def remove_tail(self):
return self.remove_node(self.tail.prev) # dummy tail's prev is real tail

def move_to_head(self, node):
self.remove_node(node)
self.add_node(node)

# def __repr__(self):
#     ans = []
#     h = self.head
#     while h:
#         ans.append(str(h.val))
#         h = h.next
#     return '<DLinkedList: {}>'.format('->'.join(ans))

class LRUCache:

def __init__(self, capacity: int):
self.capacity = capacity
self.nodes_map = {}
self.cache_list = DLinkedList()

def get(self, key: int) -> int:
node = self.nodes_map.get(key, None)
if node:
self.cache_list.move_to_head(node)
return node.val
else:
return -1

def put(self, key: int, value: int) -> None:
node = self.nodes_map.get(key, None)
if not node:
if self.capacity > 0:
self.capacity -= 1
else:
rm_key = self.cache_list.remove_tail()
self.nodes_map.pop(rm_key) # note api
new_node = DLinkedNode(key, value)
self.nodes_map[key] = new_node
self.cache_list.add_node(new_node)
else:
self.cache_list.move_to_head(node)
node.val = value


• type node struct {
key, val   int
prev, next *node
}

type LRUCache struct {
capacity   int
cache      map[int]*node
head, tail *node
}

func Constructor(capacity int) LRUCache {
head := new(node)
tail := new(node)
head.next = tail
tail.prev = head
return LRUCache{
capacity: capacity,
cache:    make(map[int]*node, capacity),
head:     head,
tail:     tail,
}
}

func (this *LRUCache) Get(key int) int {
n, ok := this.cache[key]
if !ok {
return -1
}
this.moveToFront(n)
return n.val
}

func (this *LRUCache) Put(key int, value int) {
n, ok := this.cache[key]
if ok {
n.val = value
this.moveToFront(n)
return
}
if len(this.cache) == this.capacity {
back := this.tail.prev
this.remove(back)
delete(this.cache, back.key)
}
n = &node{key: key, val: value}
this.pushFront(n)
this.cache[key] = n
}

func (this *LRUCache) moveToFront(n *node) {
this.remove(n)
this.pushFront(n)
}

func (this *LRUCache) remove(n *node) {
n.prev.next = n.next
n.next.prev = n.prev
n.prev = nil
n.next = nil
}

func (this *LRUCache) pushFront(n *node) {
n.prev = this.head
n.next = this.head.next
this.head.next.prev = n
this.head.next = n
}


• ﻿// https://leetcode.com/problems/lru-cache/

using System.Collections.Generic;

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

private Node _head;
private Node _tail;
private Dictionary<int, Node> keyMap;
private readonly int _capacity;

public LRUCache(int capacity)
{
_capacity = capacity;
keyMap = new Dictionary<int, Node>();
}

public int Get(int key)
{
Node node;
if (keyMap.TryGetValue(key, out node))
{
MoveToHead(node);
return node.Value;
}
return -1;
}

public void Put(int key, int value)
{
Node node;
if (keyMap.TryGetValue(key, out node))
{
MoveToHead(node);
node.Value = value;
}
else
{
if (keyMap.Count == _capacity)
{
if (_capacity > 0)
{
keyMap.Remove(_tail.Key);
RemoveTail();
}
else
{
return;
}
}
node = new Node() { Key = key, Value = value };
keyMap.Add(key, node);
MoveToHead(node);
}
}

private void MoveToHead(Node node)
{
if (_head != node)
{
if (_head == null)
{
_head = node;
_tail = node;
}
else
{
if (_tail == node)
{
_tail = node.Prev;
}
if (node.Next != null)
{
node.Next.Prev = node.Prev;
}
if (node.Prev != null)
{
node.Prev.Next = node.Next;
}
node.Next = _head;
_head.Prev = node;
_head = node;
}
}
}

private void RemoveTail()
{
if (_tail != null)
{
if (_tail.Prev == null)
{
_head = null;
_tail = null;
}
else
{
_tail = _tail.Prev;
_tail.Next = null;
}
}
}
}

• use std::cell::RefCell;
use std::collections::HashMap;
use std::rc::Rc;

struct Node {
key: i32,
value: i32,
prev: Option<Rc<RefCell<Node>>>,
next: Option<Rc<RefCell<Node>>>,
}

impl Node {
#[inline]
fn new(key: i32, value: i32) -> Self {
Self {
key,
value,
prev: None,
next: None,
}
}
}

struct LRUCache {
capacity: usize,
cache: HashMap<i32, Rc<RefCell<Node>>>,
head: Option<Rc<RefCell<Node>>>,
tail: Option<Rc<RefCell<Node>>>,
}

/**
* &self means the method takes an immutable reference.
* If you need a mutable reference, change it to &mut self instead.
*/
impl LRUCache {
fn new(capacity: i32) -> Self {
Self {
capacity: capacity as usize,
cache: HashMap::new(),
head: None,
tail: None,
}
}

fn get(&mut self, key: i32) -> i32 {
match self.cache.get(&key) {
Some(node) => {
let node = Rc::clone(node);
self.remove(&node);
self.push_front(&node);
let value = node.borrow().value;
value
}
None => -1,
}
}

fn put(&mut self, key: i32, value: i32) {
match self.cache.get(&key) {
Some(node) => {
let node = Rc::clone(node);
node.borrow_mut().value = value;
self.remove(&node);
self.push_front(&node);
}
None => {
let node = Rc::new(RefCell::new(Node::new(key, value)));
self.cache.insert(key, Rc::clone(&node));
self.push_front(&node);
if self.cache.len() > self.capacity {
let back_key = self.pop_back().unwrap().borrow().key;
self.cache.remove(&back_key);
}
}
};
}

fn push_front(&mut self, node: &Rc<RefCell<Node>>) {
match self.head.take() {
Some(head) => {
head.borrow_mut().prev = Some(Rc::clone(node));
node.borrow_mut().prev = None;
node.borrow_mut().next = Some(head);
self.head = Some(Rc::clone(node));
}
None => {
self.head = Some(Rc::clone(node));
self.tail = Some(Rc::clone(node));
}
};
}

fn remove(&mut self, node: &Rc<RefCell<Node>>) {
match (node.borrow().prev.as_ref(), node.borrow().next.as_ref()) {
(None, None) => {
self.head = None;
self.tail = None;
}
(None, Some(next)) => {
self.head = Some(Rc::clone(next));
next.borrow_mut().prev = None;
}
(Some(prev), None) => {
self.tail = Some(Rc::clone(prev));
prev.borrow_mut().next = None;
}
(Some(prev), Some(next)) => {
next.borrow_mut().prev = Some(Rc::clone(prev));
prev.borrow_mut().next = Some(Rc::clone(next));
}
};
}

fn pop_back(&mut self) -> Option<Rc<RefCell<Node>>> {
match self.tail.take() {
Some(tail) => {
self.remove(&tail);
Some(tail)
}
None => None,
}
}
}

/**
* Your LRUCache object will be instantiated and called as such:
* let obj = LRUCache::new(capacity);
* let ret_1: i32 = obj.get(key);
* obj.put(key, value);
*/


• class LRUCache {
capacity: number;
map: Map<number, number>;
constructor(capacity: number) {
this.capacity = capacity;
this.map = new Map();
}

get(key: number): number {
if (this.map.has(key)) {
const val = this.map.get(key)!;
this.map.delete(key);
this.map.set(key, val);
return val;
}
return -1;
}

put(key: number, value: number): void {
this.map.delete(key);
this.map.set(key, value);
if (this.map.size > this.capacity) {
this.map.delete(this.map.keys().next().value);
}
}
}

/**
* Your LRUCache object will be instantiated and called as such:
* var obj = new LRUCache(capacity)
* var param_1 = obj.get(key)
* obj.put(key,value)
*/