Linked data structure
Encyclopedia
In computer science
, a linked data structure is a data structure
which consists of a set of data records
(nodes
) linked together and organized by references
(links or pointers).
In linked data structures, the links are usually treated as special data type
s that can only be dereferenced
or compared for equality. Linked data structures are thus contrasted with arrays and other data structures that require performing arithmetic operations on pointers. This distinction holds even when the nodes are actually implemented as elements of a single array, and the references are actually array indices
: as long as no arithmetic is done on those indices, the data structure is essentially a linked one.
Linking can be done in two ways - Using dynamic allocation and using array index linking.
Linked data structures include linked list
s, search tree
s, expression trees, and many other widely used data structures. They are also key building blocks for many efficient algorithms, such as topological sort and set union-find
.
has a data field and a address field. The Address field contains the address of its successor.
Linked list can be singly, doubly or multiply linked and can either be linear or circular.
Basic Properties
A linked list with three nodes contain two fields each: an integer value and a link to the next node
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, a linked data structure is a data structure
Data structure
In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks...
which consists of a set of data records
Record (computer science)
In computer science, a record is an instance of a product of primitive data types called a tuple. In C it is the compound data in a struct. Records are among the simplest data structures. A record is a value that contains other values, typically in fixed number and sequence and typically indexed...
(nodes
Node (computer science)
A node is a record consisting of one or more fields that are links to other nodes, and a data field. The link and data fields are often implemented by pointers or references although it is also quite common for the data to be embedded directly in the node. Nodes are used to build linked, often...
) linked together and organized by references
Reference (computer science)
In computer science, a reference is a value that enables a program to indirectly access a particular data item, such as a variable or a record, in the computer's memory or in some other storage device. The reference is said to refer to the data item, and accessing those data is called...
(links or pointers).
In linked data structures, the links are usually treated as special data type
Data type
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
s that can only be dereferenced
Reference (computer science)
In computer science, a reference is a value that enables a program to indirectly access a particular data item, such as a variable or a record, in the computer's memory or in some other storage device. The reference is said to refer to the data item, and accessing those data is called...
or compared for equality. Linked data structures are thus contrasted with arrays and other data structures that require performing arithmetic operations on pointers. This distinction holds even when the nodes are actually implemented as elements of a single array, and the references are actually array indices
Index (mathematics)
The word index is used in variety of senses in mathematics.- General :* In perhaps the most frequent sense, an index is a number or other symbol that indicates the location of a variable in a list or array of numbers or other mathematical objects. This type of index is usually written as a...
: as long as no arithmetic is done on those indices, the data structure is essentially a linked one.
Linking can be done in two ways - Using dynamic allocation and using array index linking.
Linked data structures include linked list
Linked list
In computer science, a linked list is a data structure consisting of a group of nodes which together represent a sequence. Under the simplest form, each node is composed of a datum and a reference to the next node in the sequence; more complex variants add additional links...
s, search tree
Search tree
In computer science, a search tree is a binary tree data structure in whose nodes data values are stored from some ordered set, in such a way that in-order traversal of the tree visits the nodes in ascending order of the stored values...
s, expression trees, and many other widely used data structures. They are also key building blocks for many efficient algorithms, such as topological sort and set union-find
Disjoint-set data structure
In computing, a disjoint-set data structure is a data structure that keeps track of a set of elements partitioned into a number of disjoint subsets. A union-find algorithm is an algorithm that performs two useful operations on such a data structure:* Find: Determine which set a particular element...
.
1) Linked Lists
A linked list is a collection of structures ordered not by their physical placement in memory but by logical links that are stored as part of the data in the structure itself. It is not necessary that it should be stored in the adjacent memory locations. Every structureStructure
Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society...
has a data field and a address field. The Address field contains the address of its successor.
Linked list can be singly, doubly or multiply linked and can either be linear or circular.
Basic Properties
- Objects, called nodes, are linked in a linear sequence
- A reference to the first node of the list is always kept. This is called the 'head' or 'front'.
A linked list with three nodes contain two fields each: an integer value and a link to the next node
Example in Java
This is an example of the node class used to store integers in a Java implementation of a linked list.public class IntNode {
public int value;
public IntNode link;
public IntNode(int v) { value = v; }
}
Example in c
This is an example of the node structure used for implementation of linked list in C.struct node
{
int val;
struct node *next;
};
Note: A structure like this which contains a member that points to the same structure is called a self refrential structure.
2) Search Trees
A search tree is a tree data structure in whose nodes data values can be stored from some ordered setOrdered set
In order theory in mathematics, a set with a binary relation R on its elements that is reflexive , antisymmetric and transitive is described as a partially ordered set or poset...
, which is such that in an in-order traversal of the tree the nodes are visited in ascending order of the stored values.
Basic Properties
- Objects, called nodes, are stored in an ordered set.
- In-order traversal provides an ascending readout of the data in the tree
- Sub trees of the tree are in themselves, trees.
Advantages Against Arrays
Compared to arrays, linked data structures allow more flexibility in organizing the data and in allocating space for it. In arrays, the size of the array must be specified precisely at the beginning, this can be a potential waste of memory. A linked data structure is built dynamically and never needs to be bigger than the programmer requires. It also requires no guessing in terms of how much space you must allocate when using a linked data structure. This is a feature that is key in saving wasted memory.In array, the array elements have to be in contiguous(connected and sequential) portion of memory. But in linked data structure, the reference to each node gives us the information where to find out the next one. The nodes of a linked data structure can also be moved individually to different locations without affecting the logical connections between them, unlike arrays. With due care, a process
Process (computing)
In computing, a process is an instance of a computer program that is being executed. It contains the program code and its current activity. Depending on the operating system , a process may be made up of multiple threads of execution that execute instructions concurrently.A computer program is a...
can add or delete nodes to one part of a data structure even while other processes are working on other parts.
On the other hand, access to any particular node in a linked data structure requires following a chain of references that stored in it. If the structure has n nodes, and each node contains at most b links, there will be some nodes that cannot be reached in less than logb n steps. For many structures, some nodes may require worst case
Best, worst and average case
In computer science, best, worst and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively...
up to n−1 steps. In contrast, many array data structures allow access to any element with a constant number of operations, independent of the number of entries.
Broadly the implementation of these linked data structure is through dynamic data structures. It gives us the chance to use particular space again. Memory can be utilized more efficiently by using this data structures. Memory is allocated as per the need and when memory is not further needed, deallocation is done.
General Disadvantages
Linked data structures may also incur in substantial memory allocation overhead (if nodes are allocated individually) and frustrate memory pagingVirtual memory
In computing, virtual memory is a memory management technique developed for multitasking kernels. This technique virtualizes a computer architecture's various forms of computer data storage , allowing a program to be designed as though there is only one kind of memory, "virtual" memory, which...
and processor caching algorithms (since they generally have poor locality of reference
Locality of reference
In computer science, locality of reference, also known as the principle of locality, is the phenomenon of the same value or related storage locations being frequently accessed. There are two basic types of reference locality. Temporal locality refers to the reuse of specific data and/or resources...
). In some cases, linked data structures may also use more memory (for the link fields) than competing array structures. This is because linked data structures are not contiguous. Instances of data can be found all over in memory, unlike arrays.
In arrays, nth element can be accessed immediately, while in a linked data structure we have to follow multiple pointers so element access time varies according to where in the structure the element is.
In some theoretical models of computation
Theoretical computer science
Theoretical computer science is a division or subset of general computer science and mathematics which focuses on more abstract or mathematical aspects of computing....
that enforce the constraints of linked structures, such as the pointer machine
Pointer machine
In theoretical computer science a pointer machine is an "atomistic" abstract computational machine model akin to the Random access machine....
, many problems require more steps than in the unconstrained random access machine
Random access machine
In computer science, random access machine is an abstract machine in the general class of register machines. The RAM is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers...
model.