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I have been trying to understand why LRU caches use doubly link list and not singly link list?
If i go by the time complexities they both have same for insertion , updation and deletion.
Here is the Cheat sheet
Is it because the two ways pointers in DLL is used for easier move of nodes to rear or front ??
The idea behind LRU cache implementation using list (DLL/SLL) is to move the recently used page(node) to the front.
This involves a lot of shifting, say the node is in the middle of the list (DLL/SLL), you'd have to remove the node, rearrange the next pointer of the previous node.
Now in this case, if we use Singly Linked List we'd have to maintain the previous node of the most recently accessed node.
This operation is not necessary if we use Doubly Linked List as it already maintains the previous and next pointer.
The catch here is accessing that latest node, for which we use a hashtable giving us access to that node in O(1).
To remove a targeted node from a linked list, you need to modify the other nodes that point to it.
In a doubly-linked list, the targeted node has pointers to these other nodes, so it's easy to find them.
In a single-linked list, the targeted node does not have a pointer to the other node that points to it. You still need to modify that node, though, so you'd have to search for it.
I'm preparing for coding interviews, and studying Singly Linked Lists, I found 2 books implementing them in 2 different ways:
The HEAD pointer is pointing to a node which element is None and its reference is the actual first node. (If the Linked list is empty, HEAD and TAIL are pointing to this particular node)
The HEAD pointer is pointing to the actual first node directly. (If the Linked list is empty, HEAD and TAIL are pointing to None Object)
So, which is the best implementation to know for coding interviews?
I would prefer to use the second approach. The first approach has one node when actually we have zero entries in the list. For me its easier to understand if a list is empty or not in the second case. If someone asks you in the interview why the choice of that strategy just make sure every edge case is covered in your answer.
Mergesort can be done in-place for list;unlike an array.
However,I have not found a reference yet which explains how this is achieved.
Any pointer is appreciated.
It actually is possible, though not straightforward, to implement an in-place merge sort for arrays. With linked lists the problem becomes quite simple. Each node in a linked list just has a value and a pointer to the next node. It is quite simple to break a linked list in half. Just traverse to the middle node, take its successor as the head of your second list and then set successor to null.
The merge step works just like you would expect. Don't make any new nodes, just relink the nodes from your two lists.
In an interview today I got asked the question.
Apart from answering reversing the list and both forward and backward traversal there was something "fundamental" in it that the interviewer kept stressing. I gave up and of course after interview did a bit of research. It seems that insertion and deletion are more efficient in doubly linked list than singly linked list. I am not quite sure how it can be more efficient for a doubly linked list since it is obvious that more references are required to change.
Can anybody explain the secret behind? I honestly did a quite a bit of research and failed to understand with my main trouble being the fact that a O(n) searching is still needed for the double linked list.
Insertion is clearly less work in a singly-linked list, as long as you are content to always insert at the head or after some known element. (That is, you cannot insert before a known element, but see below.)
Deletion, on the other hand, is trickier because you need to know the element before the element to be deleted.
One way of doing this is to make the delete API work with the predecessor of the element to be deleted. This mirrors the insert API, which takes the element which will be the predecessor of the new element, but it's not very convenient and it's hard to document. It's usually possible, though. Generally speaking, you arrive at an element in a list by traversing the list.
Of course, you could just search the list from the beginning to find the element to be deleted, so that you know what its predecessor was. That assumes that the delete API includes the head of the list, which is also inconvenient. Also, the search is stupidly slow.
The way that hardly anyone uses, but which is actually pretty effective, is to define a singly-linked list iterator to be the pointer to the element preceding the current target of the iterator. This is simple, only one indirection slower than using a pointer directly to the element, and makes both insertion and deletion fast. The downside is that deleting an element may invalidate other iterators to list elements, which is annoying. (It doesn't invalidate the iterator to the element being deleted, which is nice for traversals which delete some elements, but that's not much compensation.)
If deletion is not important, perhaps because the datastructures are immutable, singly-linked lists offer another really useful property: they allow structure-sharing. A singly-linked list can happily be the tail of multiple heads, something which is impossible for a doubly-linked list. For this reason, singly-linked lists have traditionally been the simple datastructure of choice for functional languages.
Here is some code that made it clearer to me... Having:
class Node{
Node next;
Node prev;
}
DELETE a node in a SINGLE LINKED LIST -O(n)-
You don't know which is the preceeding node so you have to traverse the list until you find it:
deleteNode(Node node){
prevNode = tmpNode;
tmpNode = prevNode.next;
while (tmpNode != null) {
if (tmpNode == node) {
prevNode.next = tmpNode.next;
}
prevNode = tmpNode;
tmpNode = prevNode.next;
}
}
DELETE a node in a DOUBLE LINKED LIST -O(1)-
You can simply update the links like this:
deleteNode(Node node){
node.prev.next = node.next;
node.next.prev = node.prev;
}
Here are my thoughts on Doubly-Linked List:
You have ready access\insert on both ends.
it can work as a Queue and a Stack at the same time.
Node deletion requires no additional pointers.
You can apply Hill-Climb traversal since you already have access on both ends.
If you are storing Numerical values, and your list is sorted, you can keep a pointer/variable for median, then Search operation can be highly optimal using Statistical approach.
If you are going to delete an element in a linked list, you will need to link the previous element to the next element. With a doubly linked list you have ready access to both elements because you have links to both of them.
This assumes that you already have a pointer to the element you need to delete and there is no searching involved.
'Apart from answering reversing the list and both forward and backward traversal there was something "fundamental"'.
Nobody seem to have mentioned: in a doubly linked list it is possible to reinsert a deleted element just by having a pointer to the deleted element. See Knuth's Dancing Links paper. I think that's pretty fundamental.
Because doubly linked lists have immediate access to both the front and end
of the list, they can insert data on either side at O(1) as well as delete data on either side at O(1). Because doubly linked lists can insert data at the end in O(1) time and delete data from the front in O(1) time, they make the perfect underlying data structure for a queue. Queeus are lists of items
in which data can only be inserted at the end and removed from the beginning.
queues are an example of an abstract data type, and
that we are able to use an array to implement them under the hood.
Now, since queues insert at the end and delete from the beginning, arrays
are only so good as the underlying data structure. While arrays are O(1) for
insertions at the end, they’re O(N) for deleting from the beginning.
A doubly linked list, on the other hand, is O(1) for both inserting at the end
and for deleting from the beginning. That’s what makes it a perfect fit for
serving as the queue’s underlying data structure.
The doubly linked list is used in LRU cache design since we need to remove the least recently items frequently. The deletion operation is faster. To delete the least recently used item, we just delete if from end, to a new item to add cache, we just append a new node to the beginning of the list
Doubly Linked List is used in navigation systems where front and back navigation is required. It is also used by the browser to implement backward and forward navigation of visited web pages that is a back and forward button.
Singly Linked List vs Doubly Linked List vs Dynamic Arrays:
When comparing the three main data structures, Doubly Linked Lists are most efficient in all major tasks and operations when looking at time complexity. For Doubly Linked Lists, it operates at constant time for all operations except only access by index, where it operated at linear time (n) as it needs to iterate through each node to get to the required index. When it comes to Insert, Remove, First, Last, Concatenation and Count, Doubly Linked list operates at constant time where Dynamic Arrays operate at linear time (n).
In terms of space complexity, Dynamic Arrays stores only elements therefore constant time complexity, singly linked lists stores the successor of each element therefore linear space complexity (n), and worst of all doubly linked list stores the predecessor and successor of each element and therefore also linear space complexity but (2*n).
Unless you have extremely limited resources / space then perhaps either Dynamic arrays or Singly linked lists are better, however, nowadays, space and resources are more and more abundant and so doubly linked lists are far better with the cost of more space.
Doubly Linked list is more effective than the Singly linked list when the location of the element to be deleted is given. Because it is required to operate on "4" pointers only & "2" when the element to be deleted is at the first node or at the last node.
struct Node {
int Value;
struct Node *Fwd;
struct Node *Bwd;
);
Only the below line of code will be enough to delete the element, if the element to be deleted is not in the first or last node.
X->Bwd->Fwd = X->Fwd; X->Fwd->Bwd = X->Bwd;
In what situations should I use each kind of list? What are the advantages of each one?
Plain list:
Stores each item sequentially, so random lookup is extremely fast (i.e. I can instantly say "I want the 657415671567th element, and go straight to it, because we know its memory address will be exactly 657415671567 bigger than the first item). This has little or no memory overhead in storage. However, it has no way of automatically resizing - you have to create a new array, copy across all the values, and then delete the old one. Plain lists are useful when you need to lookup data from anywhere in the list, and you know that your list will not be longer than a certain size.
Linked List:
Each item has a reference to the next item. This means that there is some overhead (to store the reference to the next item). Also, because they're not stored sequentially, you can't immediately go to the 657415671567th element - you have to start at the head (1st element), and then get its reference to go to the 2nd, and then get its reference, to get to the third, ... and then get its reference to get to the 657415671566th, and then get its reference to get to the 657415671567th. In this way, it is very inefficient for random lookup. However, it allows you to modify the length of the list. If your task is to go through each item sequentially, then it's about the same value as a plain list. If you need to change the length of the list, it could be better than a plain list. If you know the 566th element, and you're looking for the 567th, then all you need to do is follow the reference to the next one. However, if you know the 567th and you're looking for the 566th, the only way to find it is to start searching from the 1st element again. This is where Double Linked Lists come in handy...
Double Linked List:
Double linked lists store a reference to the previous element. This means you can traverse the list backwards as well as forwards. This could be very useful in some situations (such as the example given in the Linked List section). Other than that, they have most of the same advantages and disadvantages as a Linked List.
Answer from comments section:
For use as a queue:
You'd have to take all of those advantages and disadvantages into account: Can you say with confidence that your queue will have a maximum size? If your queue could be anywhere from 1 to 10000000000 elements long, then a plain list will just waste memory (and then may not even be big enough). In that case, I'd go with a Linked List. However, rather than storing the index of the front and rear, you should actually store the node.
Recap: A linked list is made up of "nodes", and each node stores the item as well as the reference to the next node
So you should store a reference to the first node, and the last node. Thus, when you enqueue, you stick a new node onto the rear (by linking the old rear one to the new rear one), and remember this new rear node. And, when you dequeue, you remove the front node, and remember the second one as the new "front node". That way, you don't have to worry about any of the middle elements. You can thus ignore the length of the queue (although you can store that too if you really want)
Nobody mentioned my favorite linked list: circularly linked list with a pointer to the last element. You get constant-time insertion and deletion at either end, plus constant-time destructive append. The only cost is that empty lists are a bit tricky. It's a sweet data structure: list, queue, and stack all in one.
One advantage of a doubly-linked list is that removal of a node whose pointer is specified is O(1).
With singly linked lists you can only traverse forwards. With doubly linked lists you can traverse backwards as well as forwards through the list. In general if you are going to use a linked list, there is really no good reason not to use a doubly linked list. I have only used single linked in school.
Doubly-linked list provides several advantages over a singly linked list:
Easier traversal: With a doubly linked list, each node has a pointer to both the previous and next node, allowing for easy traversal in both directions. This is useful for certain types of algorithms that need to move both forwards and backwards through the list.
Faster deletion: In a singly linked list, when you want to delete a node, you need to traverse the list to find the node before it, so that you can update the next pointer. In a doubly linked list, the node you want to delete already has a pointer to the previous node, so you can update the previous node's next pointer directly, making deletion faster.
Easier insertion: Similar to deletion, in a singly linked list, you need to traverse the list to find the node before the one you want to insert. With a doubly linked list, you can insert a new node directly before or after a given node, without the need to traverse the list.
Easier to implement in-place modification: With a doubly linked list, it is easy to move elements around within the list without creating new list elements or destroying old ones.
Easier to implement Queue and Stack : A doubly linked list makes it easy to implement queue and stack data structures.