# Design a data structure for LRU Cache

Design a data structure for LRU Cache. It should support the following operations: get and set.

get(key) – Get the value (will always be positive) of the key if the key exists in the cache, otherwise return -1.

set(key, value) – Set or insert the value if the key is not already present. When the cache reached its capacity, it should invalidate the least recently used item before inserting a new item.

Examples:

// Let’s say we have a LRU cache of capacity 2.
LRUCache cache = new LRUCache(2);

cache.set(1, 10); // it will store a key (1) with value 10 in the cache.
cache.set(2, 20); // it will store a key (1) with value 10 in the cache.
cache.get(1); // returns 10
cache.set(3, 30); // evicts key 2 and store a key (3) with value 30 in the cache.
cache.set(4, 40); // evicts key 1 and store a key (4) with value 40 in the cache.
cache.get(3); // returns 30
cache.get(4); // returns 40

Solution:

1. Brute-force Approach:

We will keep an array of Nodes and each node will contain the following information:

 `class` `Node { ` `    ``int` `key; ` `    ``int` `value; ` ` `  `    ``// it shows the time at which the key is stored. ` `    ``// We will use the timeStamp to find out the  ` `    ``// least recently used (LRU) node. ` `    ``int` `timeStamp;  ` ` `  `    ``public` `Node(``int` `key, ``int` `value) ` `    ``{ ` `        ``this``.key = key; ` `        ``this``.value = value; ` ` `  `        ``// currentTimeStamp from system ` `        ``this``.timeStamp = currentTimeStamp; ` `    ``} ` `} `

The size of the array will be equal to the given capacity of cache.

(a) For get(int key): We can simply iterate over the array and compare the key of each node with the given key and return the value stored in the node for that key. If we don’t find any such node, return simply -1.

Time Complexity: O(n)

(b) For set(int key, int value): If the array if full, we have to delete one node from the array. To find the LRU node, we will iterate through the array and find the node with least timeStamp value. We will simply insert the new node (with new key and value) at the place of the LRU node.

If the array is not full, we can simply insert a new node in the array at the last current index of the array.

Time Complexity: O(n)

2. Optimized Approach:

The key to solve this problem is using a double linked list which enables us to quickly move nodes.
The LRU cache is a hash map of keys and double linked nodes. The hash map makes the time of get() to be O(1). The list of double linked nodes make the nodes adding/removal operations O(1).

Java Code using Doubly Linked List and HashMap:

 `import` `java.util.HashMap; ` ` `  `class` `Node { ` `    ``int` `key; ` `    ``int` `value; ` `    ``Node pre; ` `    ``Node next; ` ` `  `    ``public` `Node(``int` `key, ``int` `value) ` `    ``{ ` `        ``this``.key = key; ` `        ``this``.value = value; ` `    ``} ` `} ` ` `  `class` `LRUCache { ` `    ``private` `HashMap map; ` `    ``private` `int` `capicity, count; ` `    ``private` `Node head, tail; ` ` `  `    ``public` `LRUCache(``int` `capacity) ` `    ``{ ` `        ``this``.capicity = capacity; ` `        ``map = ``new` `HashMap<>(); ` `        ``head = ``new` `Node(``0``, ``0``); ` `        ``tail = ``new` `Node(``0``, ``0``); ` `        ``head.next = tail; ` `        ``tail.pre = head; ` `        ``head.pre = ``null``; ` `        ``tail.next = ``null``; ` `        ``count = ``0``; ` `    ``} ` ` `  `    ``public` `void` `deleteNode(Node node) ` `    ``{ ` `        ``node.pre.next = node.next; ` `        ``node.next.pre = node.pre; ` `    ``} ` ` `  `    ``public` `void` `addToHead(Node node) ` `    ``{ ` `        ``node.next = head.next; ` `        ``node.next.pre = node; ` `        ``node.pre = head; ` `        ``head.next = node; ` `    ``} ` ` `  `    ``// This method works in O(1) ` `    ``public` `int` `get(``int` `key) ` `    ``{ ` `        ``if` `(map.get(key) != ``null``) { ` `            ``Node node = map.get(key); ` `            ``int` `result = node.value; ` `            ``deleteNode(node); ` `            ``addToHead(node); ` `            ``System.out.println(``"Got the value : "` `+ ` `                  ``result + ``" for the key: "` `+ key); ` `            ``return` `result; ` `        ``} ` `        ``System.out.println(``"Did not get any value"` `+ ` `                            ``" for the key: "` `+ key); ` `        ``return` `-``1``; ` `    ``} ` ` `  `    ``// This method works in O(1) ` `    ``public` `void` `set(``int` `key, ``int` `value) ` `    ``{ ` `        ``System.out.println(``"Going to set the (key, "``+  ` `             ``"value) : ("` `+ key + ``", "` `+ value + ``")"``); ` `        ``if` `(map.get(key) != ``null``) { ` `            ``Node node = map.get(key); ` `            ``node.value = value; ` `            ``deleteNode(node); ` `            ``addToHead(node); ` `        ``} ` `        ``else` `{ ` `            ``Node node = ``new` `Node(key, value); ` `            ``map.put(key, node); ` `            ``if` `(count < capicity) { ` `                ``count++; ` `                ``addToHead(node); ` `            ``} ` `            ``else` `{ ` `                ``map.remove(tail.pre.key); ` `                ``deleteNode(tail.pre); ` `                ``addToHead(node); ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `public` `class` `TestLRUCache { ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``System.out.println(``"Going to test the LRU "``+  ` `                           ``" Cache Implementation"``); ` `        ``LRUCache cache = ``new` `LRUCache(``2``); ` `  `  `        ``// it will store a key (1) with value  ` `        ``// 10 in the cache. ` `        ``cache.set(``1``, ``10``);  ` ` `  `        ``// it will store a key (1) with value 10 in the cache. ` `        ``cache.set(``2``, ``20``);  ` `        ``System.out.println(``"Value for the key: 1 is "` `+  ` `                           ``cache.get(``1``)); ``// returns 10 ` ` `  `        ``// evicts key 2 and store a key (3) with ` `        ``// value 30 in the cache. ` `        ``cache.set(``3``, ``30``);  ` ` `  `        ``System.out.println(``"Value for the key: 2 is "` `+  ` `                ``cache.get(``2``)); ``// returns -1 (not found) ` ` `  `        ``// evicts key 1 and store a key (4) with ` `        ``// value 40 in the cache. ` `        ``cache.set(``4``, ``40``);  ` `        ``System.out.println(``"Value for the key: 1 is "` `+ ` `               ``cache.get(``1``)); ``// returns -1 (not found) ` `        ``System.out.println(``"Value for the key: 3 is "` `+  ` `                           ``cache.get(``3``)); ``// returns 30 ` `        ``System.out.println(``"Value for the key: 4 is "` `+ ` `                           ``cache.get(``4``)); ``// return 40 ` `    ``} ` `} `

Output:

```Going to test the LRU  Cache Implementation
Going to set the (key, value) : (1, 10)
Going to set the (key, value) : (2, 20)
Got the value : 10 for the key: 1
Value for the key: 1 is 10
Going to set the (key, value) : (3, 30)
Did not get any value for the key: 2
Value for the key: 2 is -1
Going to set the (key, value) : (4, 40)
Did not get any value for the key: 1
Value for the key: 1 is -1
Got the value : 30 for the key: 3
Value for the key: 3 is 30
Got the value : 40 for the key: 4
Value for the key: 4 is 40
```

Another implementation in Java using LinkedHashMap:
removeEldestEntry() is overridden to impose a policy for removing old mappings when size goes beyond capacity.

 `import` `java.util.LinkedHashMap; ` `import` `java.util.Map; ` ` `  `class` `LRUCache { ` `    ``private` `LinkedHashMap map; ` `    ``private` `final` `int` `CAPACITY; ` `    ``public` `LRUCache(``int` `capacity) ` `    ``{ ` `        ``CAPACITY = capacity; ` `        ``map = ``new` `LinkedHashMap(capacity, ``0``.75f, ``true``) { ` `            ``protected` `boolean` `removeEldestEntry(Map.Entry eldest) ` `            ``{ ` `                ``return` `size() > CAPACITY; ` `            ``} ` `        ``}; ` `    ``} ` ` `  `    ``// This method works in O(1) ` `    ``public` `int` `get(``int` `key) ` `    ``{ ` `        ``System.out.println(``"Going to get the value "` `+  ` `                               ``"for the key : "` `+ key); ` `        ``return` `map.getOrDefault(key, -``1``); ` `    ``} ` ` `  `    ``// This method works in O(1) ` `    ``public` `void` `set(``int` `key, ``int` `value) ` `    ``{ ` `        ``System.out.println(``"Going to set the (key, "` `+  ` `             ``"value) : ("` `+ key + ``", "` `+ value + ``")"``); ` `        ``map.put(key, value); ` `    ``} ` `} ` ` `  `public` `class` `TestLRUCacheWithLinkedHashMap { ` ` `  `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``System.out.println(``"Going to test the LRU "``+  ` `                           ``" Cache Implementation"``); ` `        ``LRUCache cache = ``new` `LRUCache(``2``); ` `  `  `        ``// it will store a key (1) with value  ` `        ``// 10 in the cache. ` `        ``cache.set(``1``, ``10``);  ` ` `  `        ``// it will store a key (1) with value 10 in the cache. ` `        ``cache.set(``2``, ``20``);  ` `        ``System.out.println(``"Value for the key: 1 is "` `+  ` `                           ``cache.get(``1``)); ``// returns 10 ` ` `  `        ``// evicts key 2 and store a key (3) with ` `        ``// value 30 in the cache. ` `        ``cache.set(``3``, ``30``);  ` ` `  `        ``System.out.println(``"Value for the key: 2 is "` `+  ` `                ``cache.get(``2``)); ``// returns -1 (not found) ` ` `  `        ``// evicts key 1 and store a key (4) with ` `        ``// value 40 in the cache. ` `        ``cache.set(``4``, ``40``);  ` `        ``System.out.println(``"Value for the key: 1 is "` `+ ` `               ``cache.get(``1``)); ``// returns -1 (not found) ` `        ``System.out.println(``"Value for the key: 3 is "` `+  ` `                           ``cache.get(``3``)); ``// returns 30 ` `        ``System.out.println(``"Value for the key: 4 is "` `+ ` `                           ``cache.get(``4``)); ``// return 40 ` ` `  `    ``} ` `} `

Output:

```Going to test the LRU  Cache Implementation
Going to set the (key, value) : (1, 10)
Going to set the (key, value) : (2, 20)
Going to get the value for the key : 1
Value for the key: 1 is 10
Going to set the (key, value) : (3, 30)
Going to get the value for the key : 2
Value for the key: 2 is -1
Going to set the (key, value) : (4, 40)
Going to get the value for the key : 1
Value for the key: 1 is -1
Going to get the value for the key : 3
Value for the key: 3 is 30
Going to get the value for the key : 4
Value for the key: 4 is 40
```

You can find the C++ code here

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