If sentinel nodes are being used, the list is usually said to be empty when it has only sentinel nodes. The link fields need not be physically part of the nodes. If the data records are stored in an array and referenced by their indices, the link field may be stored in a separate array with the same indices as the data records. Since a reference to the first node gives access to the whole list, that reference is often called the 'address', 'pointer', or 'handle' of the list.
Algorithms that manipulate linked lists usually get such handles to the input lists and return the handles to the resulting lists. In fact, in the context of such algorithms, the word "list" often means "list handle". In some situations, however, it may be convenient to refer to a list by a handle that consists of two links, pointing to its first and last nodes. The alternatives listed above may be arbitrarily combined in almost every way, so one may have circular doubly linked lists without sentinels, circular singly linked lists with sentinels, etc.
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. A dynamic array is a data structure that allocates all elements contiguously in memory, and keeps a count of the current number of elements. If the space reserved for the dynamic array is exceeded, it is reallocated and possibly copied, which is an expensive operation. Linked lists have several advantages over dynamic arrays.
Insertion or deletion of an element at a specific point of a list, assuming that we have indexed a pointer to the node before the one to be removed, or before the insertion point already, is a constant-time operation otherwise without this reference it is O n , whereas insertion in a dynamic array at random locations will require moving half of the elements on average, and all the elements in the worst case. While one can "delete" an element from an array in constant time by somehow marking its slot as "vacant", this causes fragmentation that impedes the performance of iteration. Moreover, arbitrarily many elements may be inserted into a linked list, limited only by the total memory available; while a dynamic array will eventually fill up its underlying array data structure and will have to reallocate—an expensive operation, one that may not even be possible if memory is fragmented, although the cost of reallocation can be averaged over insertions, and the cost of an insertion due to reallocation would still be amortized O 1.
This helps with appending elements at the array's end, but inserting into or removing from middle positions still carries prohibitive costs due to data moving to maintain contiguity. An array from which many elements are removed may also have to be resized in order to avoid wasting too much space. On the other hand, dynamic arrays as well as fixed-size array data structures allow constant-time random access , while linked lists allow only sequential access to elements.
Singly linked lists, in fact, can be easily traversed in only 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 and dynamic arrays is also faster than on linked lists on many machines, because they have optimal locality of reference and thus make good use of data caching. 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 , because the storage overhead for the links may exceed by a factor of two or more the size of the data.
In contrast, a dynamic array requires only the space for the data itself and a very small amount of control data. Some hybrid solutions try to combine the advantages of the two representations.
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 dynamic arrays vs. 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 the n th 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. However, the linked list will be poor at finding the next person to remove and will need to search through the list until it finds that person. A dynamic 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 n th person in the circle by directly referencing them by their position in the array. The list ranking problem concerns the efficient conversion of a linked list representation into an array.
Although trivial for a conventional computer, solving this problem by a parallel algorithm is complicated and has been the subject of much research. A balanced tree has similar memory access patterns and space overhead to a linked list while permitting much more efficient indexing, taking O log n time instead of O n for a random access. However, insertion and deletion operations are more expensive due to the overhead of tree manipulations to maintain balance. Schemes exist for trees to automatically maintain themselves in a balanced state: AVL trees or red-black trees.
While doubly linked and circular lists have advantages over singly linked linear lists, linear lists offer some advantages that make them preferable in some situations. A singly linked linear list is a recursive data structure, because it contains a pointer to a smaller object of the same type. For that reason, many operations on singly linked linear lists such as merging two lists, or enumerating the elements in reverse order often have very simple recursive algorithms, much simpler than any solution using iterative commands. While those recursive solutions can be adapted for doubly linked and circularly linked lists, the procedures generally need extra arguments and more complicated base cases.
Linear singly linked lists also allow tail-sharing , the use of a common final portion of sub-list as the terminal portion of two different lists. In particular, if a new node is added at the beginning of a list, the former list remains available as the tail of the new one—a simple example of a persistent data structure.
Again, this is not true with the other variants: a node may never belong to two different circular or doubly linked lists. In particular, end-sentinel nodes can be shared among singly linked non-circular lists. The same end-sentinel node may be used for every such list. In Lisp , for example, every proper list ends with a link to a special node, denoted by nil or , whose CAR and CDR links point to itself.
The advantages of the fancy variants are often limited to the complexity of the algorithms, not in their efficiency. A circular list, in particular, can usually be emulated by a linear list together with two variables that point to the first and last nodes, at no extra cost. 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 fast and easy sequential access to the list in both directions.
In a doubly linked list, one can insert or delete a node in a constant number of operations given only that node's address. To do the same in a singly linked list, one must have the address of the pointer to that node, which is either the handle for the whole list in case of the first node or the link field in the previous node. Some algorithms require access in both directions. On the other hand, doubly linked lists do not allow tail-sharing and cannot be used as persistent data structures.
A circularly linked list may be a natural option to represent arrays that are naturally circular, e. In these applications, a pointer to any node serves as a handle to the whole list. With a circular list, a pointer to the last node gives easy access also to the first node, by following one link.
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Thus, in applications that require access to both ends of the list e. A circular list can be split into two circular lists, in constant time, by giving the addresses of the last node of each piece.
The operation consists in swapping the contents of the link fields of those two nodes. Applying the same operation to any two nodes in two distinct lists joins the two list into one. This property greatly simplifies some algorithms and data structures, such as the quad-edge and face-edge. The simplest representation for an empty circular list when such a thing makes sense is a null pointer, indicating that the list has no nodes. Without this choice, many algorithms have to test for this special case, and handle it separately.
By contrast, the use of null to denote an empty linear list is more natural and often creates fewer special cases. Sentinel node may simplify certain list operations, by ensuring that the next or previous nodes exist for every element, and that even empty lists have at least one node.
One may also use a sentinel node at the end of the list, with an appropriate data field, to eliminate some end-of-list tests. For example, when scanning the list looking for a node with a given value x , setting the sentinel's data field to x makes it unnecessary to test for end-of-list inside the loop. However, sentinel nodes use up extra space especially in applications that use many short lists , and they may complicate other operations such as the creation of a new empty list. However, if the circular list is used merely to simulate a linear list, one may avoid some of this complexity by adding a single sentinel node to every list, between the last and the first data nodes.
With this convention, an empty list consists of the sentinel node alone, pointing to itself via the next-node link. The list handle should then be a pointer to the last data node, before the sentinel, if the list is not empty; or to the sentinel itself, if the list is empty. The same trick can be used to simplify the handling of a doubly linked linear list, by turning it into a circular doubly linked list with a single sentinel node. However, in this case, the handle should be a single pointer to the dummy node itself. 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. 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. Linked lists can be measured as a form of high-level standpoint as being a series of nodes where each node has at least one single pointer to the next connected node, and in the case of the last node, a null pointer is used for representing that there will be no further nodes in the linked list.
In the data structure, you will be implementing the linked lists which always maintain head and tail pointers for inserting values at either the head or tail of the list is a constant time operation. Randomly inserting of values is excluded using this concept and will follow a linear operation.
As such, linked lists in data structure have some characteristics which are mentioned below: Insertion is O 1 Deletion is O n Searching is O n Linked lists have a few key points that usually make them very efficient for implementing. These are: the list is dynamic and hence can be resized based on the requirement Secondly, the insertion is O 1. The more you respect them, the more you improve the future retrievability of your digital collections online.
Zakrajsek and Vlasta Vodeb focuses on Geographic location, which is a very important attribute of a cultural heritage item.
It can describe provenience, the current institution, as well as the location of the event or other related events. The added value of the geo-coded cultural content is in the browsing of cultural portals efficiently through space and time, and searching for content in a more user friendly way.