Array Deque Linked list Queue Stack In computer science, a linked list is one of the fundamental data structures, and can be used to implement other data structures. It consists of a sequence of nodes, each containing arbitrary data fields and one or two references ("links") pointing to the next and/or previous nodes. The principal benefit of a linked list over a conventional array is that the order of the linked items may be different from the order that the data items are stored in memory or on disk, allowing the list of items to be traversed in a different order. A linked list is a self-referential datatype because it contains a pointer or link to another datum of the same type. Linked lists permit insertion and removal of nodes at any point in the list in constant time, but do not allow random access. Several different types of linked list exist: singly-linked lists, doubly-linked lists, and circularly-linked lists.
Linked lists can be implemented in most languages. Languages such as Lisp and Scheme have the data structure built in, along with operations to access the linked list. Procedural or object-oriented languages such as C, C++, and Java typically rely on mutable references to create linked lists.

History

Types of linked lists

Linearly-linked list
The simplest kind of linked list is a singly-linked list (or slist for short), which has one link per node. This link points to the next node in the list, or to a null value or empty list if it is the final node.

Singly-linked list
A more sophisticated kind of linked list is a doubly-linked list or two-way linked list. Each node has two links: one points to the previous node, or points to a null value or empty list if it is the first node; and one points to the next, or points to a null value or empty list if it is the final node.
In some very low level languages, Xor-linking offers a way to implement doubly-linked lists using a single word for both links, although the use of this technique is usually discouraged.

Doubly-linked list
In a circularly-linked list, the first and final nodes are linked together. This can be done for both singly and doubly linked lists. To traverse a circular linked list, you begin at any node and follow the list in either direction until you return to the original node. Viewed another way, circularly-linked lists can be seen as having no beginning or end. This type of list is most useful for managing buffers for data ingest, and in cases where you have one object in a list and wish to see all other objects in the list.
The pointer pointing to the whole list may be called the access pointer.

Circularly-linked list
In a singly-circularly-linked list, each node has one link, similar to an ordinary singly-linked list, except that the next link of the last node points back to the first node. As in a singly-linked list, new nodes can only be efficiently inserted after a node we already have a reference to. For this reason, it's usual to retain a reference to only the last element in a singly-circularly-linked list, as this allows quick insertion at the beginning, and also allows access to the first node through the last node's next pointer.

Singly-circularly-linked list
In a doubly-circularly-linked list, each node has two links, similar to a doubly-linked list, except that the previous link of the first node points to the last node and the next link of the last node points to the first node. As in doubly-linked lists, insertions and removals can be done at any point with access to any nearby node. Although structurally a doubly-circularly-linked list has no beginning or end, an external access pointer may formally establish the pointed node to be the head node or the tail node, and maintain order just as well as a doubly-linked list with sentinel nodes.

Doubly-circularly-linked list
Linked lists sometimes have a special dummy or sentinel node at the beginning and/or at the end of the list, which is not used to store data. Its purpose is to simplify or speed up some operations, by ensuring that every data node always has a previous and/or next node, and that every list (even one that contains no data elements) always has a "first" and "last" node. Lisp has such a design - the special value nil is used to mark the end of a 'proper' singly-linked list, or chain of cons cells as they are called. A list does not have to end in nil, but a list that did not would be termed 'improper'.

Sentinel nodes
Linked lists are used as a building block for many other data structures, such as stacks, queues and their variations.
The "data" field of a node can be another linked list. By this device, one can construct many linked data structures with lists; this practice originated in the Lisp programming language, where linked lists are a primary (though by no means the only) data structure, and is now a common feature of the functional programming style.
Sometimes, linked lists are used to implement associative arrays, and are in this context called association lists. There is very little good to be said about this use of linked lists; they are easily outperformed by other data structures such as self-balancing binary search trees even on small data sets (see the discussion in associative array). However, sometimes a linked list is dynamically created out of a subset of nodes in such a tree, and used to more efficiently traverse that set.

Applications of linked lists
As with most choices in computer programming and design, no method is well suited to all circumstances. A linked list data structure might work well in one case, but cause problems in another. This is a list of some of the common tradeoffs involving linked list structures. In general, if you have a dynamic collection, where elements are frequently being added and deleted, and the location of new elements added to the list is significant, then benefits of a linked list increase.

Tradeoffs
Linked lists have several advantages over arrays. Elements can be inserted into linked lists indefinitely, while an array will eventually either fill up or need to be resized, an expensive operation that may not even be possible if memory is fragmented. Similarly, an array from which many elements are removed may become wastefully empty or need to be made smaller.
Further memory savings can be achieved, in certain cases, by sharing the same "tail" of elements among two or more lists — that is, the lists end in the same sequence of elements. In this way, one can add new elements to the front of the list while keeping a reference to both the new and the old versions — a simple example of a persistent data structure.
On the other hand, arrays allow random access, while linked lists allow only sequential access to elements. Singly-linked lists, in fact, can only be traversed in one direction. This makes linked lists unsuitable for applications where it's useful to look up an element by its index quickly, such as heapsort. Sequential access on arrays is also faster than on linked lists on many machines due to locality of reference and data caches. Linked lists receive almost no benefit from the cache.
Another disadvantage of linked lists is the extra storage needed for references, which often makes them impractical for lists of small data items such as characters or boolean values. It can also be slow, and with a naïve allocator, wasteful, to allocate memory separately for each new element, a problem generally solved using memory pools.
A number of linked list variants exist that aim to ameliorate some of the above problems. Unrolled linked lists store several elements in each list node, increasing cache performance while decreasing memory overhead for references. CDR coding does both these as well, by replacing references with the actual data referenced, which extends off the end of the referencing record.
A good example that highlights the pros and cons of using arrays vs. linked lists is by implementing a program that resolves the Josephus problem. The Josephus problem is an election method that works by having a group of people stand in a circle. Starting at a predetermined person, you count around the circle n times. Once you reach nth person, take them out of the circle and have the members close the circle. Then count around the circle the same n times and repeat the process, until only one person is left. That person wins the election. This shows the strengths and weaknesses of a linked list vs. an array, because if you view the people as connected nodes in a circular linked list then it shows how easily the linked list is able to delete nodes (as it only has to rearrange the links to the different nodes). However, the linked list will be poor at finding the next person to remove and will need to recurse through the list until it finds that person. An array, on the other hand, will be poor at deleting nodes (or elements) as it cannot remove one node without individually shifting all the elements up the list by one. However, it is exceptionally easy to find the nth person in the circle by directly referencing them by their position in the array.

Linked lists vs. arrays
Double-linked lists require more space per node (unless one uses xor-linking), and their elementary operations are more expensive; but they are often easier to manipulate because they allow sequential access to the list in both directions. In particular, one can insert or delete a node in a constant number of operations given only that node's address. (Compared with singly-linked lists, which require the previous node's address in order to correctly insert or delete.) Some algorithms require access in both directions. On the other hand, they do not allow tail-sharing, and cannot be used as persistent data structures.

Doubly-linked vs. singly-linked
Circular linked lists are most useful for describing naturally circular structures, and have the advantage of regular structure and being able to traverse the list starting at any point. They also allow quick access to the first and last records through a single pointer (the address of the last element). Their main disadvantage is the complexity of iteration, which has subtle special cases.

Sentinel nodes (header nodes)
When manipulating linked lists in-place, care must be taken to not use values that you have invalidated in previous assignments. This makes algorithms for inserting or deleting linked list nodes somewhat subtle. This section gives pseudocode for adding or removing nodes from singly, doubly, and circularly linked lists in-place. Throughout we will use null to refer to an end-of-list marker or sentinel, which may be implemented in a number of ways.

Linked list operations

Linearly-linked lists
Our node data structure will have two fields. We also keep a variable firstNode which always points to the first node in the list, or is null for an empty list.
Traversal of a singly-linked list is simple, beginning at the first node and following each next link until we come to the end:
The following code inserts a node after an existing node in a singly linked list. The diagram shows how it works. Inserting a node before an existing one cannot be done; instead, you have to locate it while keeping track of the previous node.
Inserting at the beginning of the list requires a separate function. This requires updating firstNode.
Similarly, we have functions for removing the node after a given node, and for removing a node from the beginning of the list. The diagram demonstrates the former. To find and remove a particular node, one must again keep track of the previous element.
Notice that removeBeginning() sets list.firstNode to null when removing the last node in the list.
Since we can't iterate backwards, efficient "insertBefore" or "removeBefore" operations are not possible.
Appending one linked list to another can be inefficient unless a reference to the tail is kept as part of the List structure, because we must traverse the entire first list in order to find the tail, and then append the second list to this. Thus, if two linearly-linked lists are each of length n, list appending has asymptotic time complexity of O(n). In the Lisp family of languages, list appending is provided by the append procedure.
Many of the special cases of linked list operations can be eliminated by including a dummy element at the front of the list. This ensures that there are no special cases for the beginning of the list and renders both insertBeginning() and removeBeginning() unnecessary. In this case, the first useful data in the list will be found at list.firstNode.next.

Singly-linked lists
With doubly-linked lists there are even more pointers to update, but also less information is needed, since we can use backwards pointers to observe preceding elements in the list. This enables new operations, and eliminates special-case functions. We will add a prev field to our nodes, pointing to the previous element, and a lastNode field to our list structure which always points to the last node in the list. Both list.firstNode and list.lastNode are null for an empty list.
Iterating through a doubly linked list can be done in either direction. In fact, direction can change many times, if desired.
Forwards
Backwards
These symmetric functions add a node either after or before a given node, with the diagram demonstrating after:
We also need a function to insert a node at the beginning of a possibly-empty list:
A symmetric function inserts at the end:
Removing a node is easier, only requiring care with the firstNode and lastNode:
One subtle consequence of this procedure is that deleting the last element of a list sets both firstNode and lastNode to null, and so it handles removing the last node from a one-element list correctly. Notice that we also don't need separate "removeBefore" or "removeAfter" methods, because in a doubly-linked list we can just use "remove(node.prev)" or "remove(node.next)" where these are valid.

Doubly-linked lists
Circularly-linked lists can be either singly or doubly linked. In a circularly linked list, all nodes are linked in a continuous circle, without using null. For lists with a front and a back (such as a queue), one stores a reference to the last node in the list. The next node after the last node is the first node. Elements can be added to the back of the list and removed from the front in constant time.
Both types of circularly-linked lists benefit from the ability to traverse the full list beginning at any given node. This often allows us to avoid storing firstNode and lastNode, although if the list may be empty we need a special representation for the empty list, such as a lastNode variable which points to some node in the list or is null if it's empty; we use such a lastNode here. This representation significantly simplifies adding and removing nodes with a non-empty list, but empty lists are then a special case.

Circularly-linked lists
Assuming that someNode is some node in a non-empty list, this code iterates through that list starting with someNode (any node will do):
Forwards
Backwards
Notice the postponing of the test to the end of the loop. This is important for the case where the list contains only the single node someNode.
This simple function inserts a node into a doubly-linked circularly-linked list after a given element:
To do an "insertBefore", we can simply "insertAfter(node.prev, newNode)". Inserting an element in a possibly empty list requires a special function:
To insert at the beginning we simply "insertAfter(list.lastNode, node)". Finally, removing a node must deal with the case where the list empties:
As in doubly-linked lists, "removeAfter" and "removeBefore" can be implemented with "remove(list, node.prev)" and "remove(list, node.next)".

Doubly-circularly-linked lists
Languages that do not support any type of reference can still create links by replacing pointers with array indices. The approach is to keep an array of records, where each record has integer fields indicating the index of the next (and possibly previous) node in the array. Not all nodes in the array need be used. If records are not supported as well, parallel arrays can often be used instead.
As an example, consider the following linked list record that uses arrays instead of pointers:
By creating an array of these structures, and an integer variable to store the index of the first element, a linked list can be built:
Links between elements are formed by placing the array index of the next (or previous) cell into the Next or Prev field within a given element. For example:
In the above example, ListHead would be set to 2, the location of the first entry in the list. Notice that entry 3 and 5 through 7 are not part of the list. These cells are available for any additions to the list. By creating a ListFree integer variable, a free list could be created to keep track of what cells are available. If all entries are in use, the size of the array would have to be increased or some elements would have to be deleted before new entries could be stored in the list.
The following code would traverse the list and display names and account balance:
When faced with a choice, the advantages of this approach include:
This approach has one main disadvantage, however: it creates and manages a private memory space for its nodes. This leads to the following issues:
For these reasons, this approach is mainly used for languages that do not support dynamic memory allocation. These disadvantages are also mitigated if the maximum size of the list is known at the time the array is created.

The linked list is relocatable, meaning it can be moved about in memory at will, and it can also be quickly and directly serialized for storage on disk or transfer over a network.
Especially for a small list, array indexes can occupy significantly less space than a full pointer on many architectures.
Locality of reference can be improved by keeping the nodes together in memory and by periodically rearranging them, although this can also be done in a general store.
Naïve dynamic memory allocators can produce an excessive amount of overhead storage for each node allocated; almost no allocation overhead is incurred per node in this approach.
Seizing an entry from a pre-allocated array is faster than using dynamic memory allocation for each node, since dynamic memory allocation typically requires a search for a free memory block of the desired size.
It increase complexity of the implementation.
Growing a large array when it is full may be difficult or impossible, whereas finding space for a new linked list node in a large, general memory pool may be easier.
Adding elements to a dynamic array will occasionally (when it is full) unexpectedly take linear (O(n)) instead of constant time (although it's still an amortized constant).
Using a general memory pool leaves more memory for other data if the list is smaller than expected or if many nodes are freed. Linked lists using arrays of nodes
Many programming languages such as Lisp and Scheme have singly linked lists built in. In many functional languages, these lists are constructed from nodes, each called a cons or cons cell. The cons has two fields: the car, a reference to the data for that node, and the cdr, a reference to the next node. Although cons cells can be used to build other data structures, this is their primary purpose.
In languages that support Abstract data types or templates, linked list ADTs or templates are available for building linked lists. In other languages, linked lists are typically built using references together with records. Here is a complete example in C:

Language support
When constructing a linked list, one is faced with the choice of whether to store the data of the list directly in the linked list nodes, called internal storage, or merely to store a reference to the data, called external storage. Internal storage has the advantage of making access to the data more efficient, requiring less storage overall, having better locality of reference, and simplifying memory management for the list (its data is allocated and deallocated at the same time as the list nodes).
External storage, on the other hand, has the advantage of being more generic, in that the same data structure and machine code can be used for a linked list no matter what the size of the data is. It also makes it easy to place the same data in multiple linked lists. Although with internal storage the same data can be placed in multiple lists by including multiple next references in the node data structure, it would then be necessary to create separate routines to add or delete cells based on each field. It is possible to create additional linked lists of elements that use internal storage by using external storage, and having the cells of the additional linked lists store references to the nodes of the linked list containing the data.
In general, if a set of data structures needs to be included in multiple linked lists, external storage is the best approach. If a set of data structures need to be included in only one linked list, then internal storage is slightly better, unless a generic linked list package using external storage is available. Likewise, if different sets of data that can be stored in the same data structure are to be included in a single linked list, then internal storage would be fine.
Another approach that can be used with some languages involves having different data structures, but all have the initial fields, including the next (and prev if double linked list) references in the same location. After defining separate structures for each type of data, a generic structure can be defined that contains the minimum amount of data shared by all the other structures and contained at the top (beginning) of the structures. Then generic routines can be created that use the minimal structure to perform linked list type operations, but separate routines can then handle the specific data. This approach is often used in message parsing routines, where several types of messages are received, but all start with the same set of fields, usually including a field for message type. The generic routines are used to add new messages to a queue when they are received, and remove them from the queue in order to process the message. The message type field is then used to call the correct routine to process the specific type of message.

Internal and external storage
Suppose you wanted to create a linked list of families and their members. Using internal storage, the structure might look like the following:
To print a complete list of families and their members using internal storage, we could write:
Using external storage, we would create the following structures:
To print a complete list of families and their members using external storage, we could write:
Notice that when using external storage, an extra step is needed to extract the record from the node and cast it into the proper data type. This is because both the list of families and the list of members within the family are stored in two linked lists using the same data structure (node), and this language does not have parametric types.
As long as the number of families that a member can belong to is known at compile time, internal storage works fine. If, however, a member needed to be included in an arbitrary number of families, with the specific number known only at run time, external storage would be necessary.

Speeding up search
Both stacks and queues are often implemented using linked lists, and simply restrict the type of operations which are supported.
The skip list is a linked list augmented with layers of pointers for quickly jumping over large numbers of elements, and then descending to the next layer. This process continues down to the bottom layer, which is the actual list.
A binary tree can be seen as a type of linked list where the elements are themselves linked lists of the same nature. The result is that each node may include a reference to the first node of one or two other linked lists, which, together with their contents, form the subtrees below that node.
An unrolled linked list is a linked list in which each node contains an array of data values. This leads to improved cache performance, since more list elements are contiguous in memory, and reduced memory overhead, because less metadata needs to be stored for each element of the list.
A hash table may use linked lists to store the chains of items that hash to the same position in the hash table.