How to implement LRU caching scheme? What data structures should be used?
We are given total possible page numbers that can be referred. We are also given cache (or memory) size (Number of page frames that cache can hold at a time). The LRU caching scheme is to remove the least recently used frame when the cache is full and a new page is referenced which is not there in cache. Please see the Galvin book for more details (see the LRU page replacement slide here).
We use two data structures to implement an LRU Cache.
- Queue which is implemented using a doubly linked list. The maximum size of the queue will be equal to the total number of frames available (cache size).The most recently used pages will be near front end and least recently pages will be near rear end.
- A Hash with page number as key and address of the corresponding queue node as value.
When a page is referenced, the required page may be in the memory. If it is in the memory, we need to detach the node of the list and bring it to the front of the queue.
If the required page is not in the memory, we bring that in memory. In simple words, we add a new node to the front of the queue and update the corresponding node address in the hash. If the queue is full, i.e. all the frames are full, we remove a node from the rear of queue, and add the new node to the front of queue.
Example – Consider the following reference string :
1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5
Find the number of page faults using least recently used (LRU) page replacement algorithm with 3 page frames.
Explanation –
Note: Initially no page is in the memory.
C++ using STL
/* We can use stl container list as a double ended queue to store the cache keys, with the descending time of reference from front to back and a set container to check presence of a key. But to fetch the address of the key in the list using find(), it takes O(N) time. This can be optimized by storing a reference (iterator) to each key in a hash map. */#include <bits/stdc++.h> using namespace std; class LRUCache { // store keys of cache list<int> dq; // store references of key in cache unordered_map<int, list<int>::iterator> ma; int csize; //maximum capacity of cache public: LRUCache(int); void refer(int); void display(); }; LRUCache::LRUCache(int n) { csize = n; } /* Refers key x with in the LRU cache */void LRUCache::refer(int x) { // not present in cache if (ma.find(x) == ma.end()) { // cache is full if (dq.size() == csize) { //delete least recently used element int last = dq.back(); dq.pop_back(); ma.erase(last); } } // present in cache else dq.erase(ma[x]); // update reference dq.push_front(x); ma[x] = dq.begin(); } // display contents of cache void LRUCache::display() { for (auto it = dq.begin(); it != dq.end(); it++) cout << (*it) << " "; cout << endl; } // Driver program to test above functions int main() { LRUCache ca(4); ca.refer(1); ca.refer(2); ca.refer(3); ca.refer(1); ca.refer(4); ca.refer(5); ca.display(); return 0; } // This code is contributed by Satish Srinivas |
C
// A C program to show implementation of LRU cache #include <stdio.h> #include <stdlib.h> // A Queue Node (Queue is implemented using Doubly Linked List) typedef struct QNode { struct QNode *prev, *next; unsigned pageNumber; // the page number stored in this QNode } QNode; // A Queue (A FIFO collection of Queue Nodes) typedef struct Queue { unsigned count; // Number of filled frames unsigned numberOfFrames; // total number of frames QNode *front, *rear; } Queue; // A hash (Collection of pointers to Queue Nodes) typedef struct Hash { int capacity; // how many pages can be there QNode* *array; // an array of queue nodes } Hash; // A utility function to create a new Queue Node. The queue Node // will store the given 'pageNumber' QNode* newQNode( unsigned pageNumber ) { // Allocate memory and assign 'pageNumber' QNode* temp = (QNode *)malloc( sizeof( QNode ) ); temp->pageNumber = pageNumber; // Initialize prev and next as NULL temp->prev = temp->next = NULL; return temp; } // A utility function to create an empty Queue. // The queue can have at most 'numberOfFrames' nodes Queue* createQueue( int numberOfFrames ) { Queue* queue = (Queue *)malloc( sizeof( Queue ) ); // The queue is empty queue->count = 0; queue->front = queue->rear = NULL; // Number of frames that can be stored in memory queue->numberOfFrames = numberOfFrames; return queue; } // A utility function to create an empty Hash of given capacity Hash* createHash( int capacity ) { // Allocate memory for hash Hash* hash = (Hash *) malloc( sizeof( Hash ) ); hash->capacity = capacity; // Create an array of pointers for refering queue nodes hash->array = (QNode **) malloc( hash->capacity * sizeof( QNode* ) ); // Initialize all hash entries as empty int i; for( i = 0; i < hash->capacity; ++i ) hash->array[i] = NULL; return hash; } // A function to check if there is slot available in memory int AreAllFramesFull( Queue* queue ) { return queue->count == queue->numberOfFrames; } // A utility function to check if queue is empty int isQueueEmpty( Queue* queue ) { return queue->rear == NULL; } // A utility function to delete a frame from queue void deQueue( Queue* queue ) { if( isQueueEmpty( queue ) ) return; // If this is the only node in list, then change front if (queue->front == queue->rear) queue->front = NULL; // Change rear and remove the previous rear QNode* temp = queue->rear; queue->rear = queue->rear->prev; if (queue->rear) queue->rear->next = NULL; free( temp ); // decrement the number of full frames by 1 queue->count--; } // A function to add a page with given 'pageNumber' to both queue // and hash void Enqueue( Queue* queue, Hash* hash, unsigned pageNumber ) { // If all frames are full, remove the page at the rear if ( AreAllFramesFull ( queue ) ) { // remove page from hash hash->array[ queue->rear->pageNumber ] = NULL; deQueue( queue ); } // Create a new node with given page number, // And add the new node to the front of queue QNode* temp = newQNode( pageNumber ); temp->next = queue->front; // If queue is empty, change both front and rear pointers if ( isQueueEmpty( queue ) ) queue->rear = queue->front = temp; else // Else change the front { queue->front->prev = temp; queue->front = temp; } // Add page entry to hash also hash->array[ pageNumber ] = temp; // increment number of full frames queue->count++; } // This function is called when a page with given 'pageNumber' is referenced // from cache (or memory). There are two cases: // 1. Frame is not there in memory, we bring it in memory and add to the front // of queue // 2. Frame is there in memory, we move the frame to front of queue void ReferencePage( Queue* queue, Hash* hash, unsigned pageNumber ) { QNode* reqPage = hash->array[ pageNumber ]; // the page is not in cache, bring it if ( reqPage == NULL ) Enqueue( queue, hash, pageNumber ); // page is there and not at front, change pointer else if (reqPage != queue->front) { // Unlink rquested page from its current location // in queue. reqPage->prev->next = reqPage->next; if (reqPage->next) reqPage->next->prev = reqPage->prev; // If the requested page is rear, then change rear // as this node will be moved to front if (reqPage == queue->rear) { queue->rear = reqPage->prev; queue->rear->next = NULL; } // Put the requested page before current front reqPage->next = queue->front; reqPage->prev = NULL; // Change prev of current front reqPage->next->prev = reqPage; // Change front to the requested page queue->front = reqPage; } } // Driver program to test above functions int main() { // Let cache can hold 4 pages Queue* q = createQueue( 4 ); // Let 10 different pages can be requested (pages to be // referenced are numbered from 0 to 9 Hash* hash = createHash( 10 ); // Let us refer pages 1, 2, 3, 1, 4, 5 ReferencePage( q, hash, 1); ReferencePage( q, hash, 2); ReferencePage( q, hash, 3); ReferencePage( q, hash, 1); ReferencePage( q, hash, 4); ReferencePage( q, hash, 5); // Let us print cache frames after the above referenced pages printf ("%d ", q->front->pageNumber); printf ("%d ", q->front->next->pageNumber); printf ("%d ", q->front->next->next->pageNumber); printf ("%d ", q->front->next->next->next->pageNumber); return 0; } |
Java
/* We can use Java inbuilt Deque as a double ended queue to store the cache keys, with the descending time of reference from front to back and a set container to check presence of a key. But remove a key from the Deque using remove() , it takes O(N) time. This can be optimized by storing a reference (iterator) to each key in a hash map. */import java.util.Deque; import java.util.HashSet; import java.util.LinkedList; import java.util.Iterator; public class LRUCache { // store keys of cache static Deque<Integer> dq; // store references of key in cache static HashSet<Integer> map; //maximum capacity of cache static int csize; LRUCache(int n) { dq=new LinkedList<>(); map=new HashSet<>(); csize=n; } /* Refers key x with in the LRU cache */ public void refer(int x) { if(!map.contains(x)) { if(dq.size()==csize) { int last=dq.removeLast(); map.remove(last); } } else { /* The found page may not be always the last element, even if it's an intermediate element that needs to be removed and added to the start of the Queue */ int index =0 , i=0; Iterator<Integer> itr = dq.iterator(); while(itr.hasNext()) { if(itr.next()==x) { index = i; break; } i++; } dq.remove(index); } dq.push(x); map.add(x); } // display contents of cache public void display() { Iterator<Integer> itr = dq.iterator(); while(itr.hasNext()) { System.out.print(itr.next()+" "); } } public static void main(String[] args) { LRUCache ca=new LRUCache(4); ca.refer(1); ca.refer(2); ca.refer(3); ca.refer(1); ca.refer(4); ca.refer(5); ca.display(); } } //This code is contributed by Gaurav Tiwari |
Output:
5 4 1 3
This article is compiled by Aashish Barnwal and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
leave a comment
0 Comments