 This article does not cite any references or sources. (February 2007) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed.  Linear data structures  Array Deque Linked list Queue Stack Example of an approximately 40,000 probe spotted oligo microarray with enlarged inset to show detail. ...
A binary tree, a simple type of branching linked data structure. ...
In computer science, a deque (short for doubleended queue) is a data structure for which elements can be added to or removed from the front or back. ...
In computer science, a linked list is one of the fundamental data structures, and can be used to implement other data structures. ...
A queue (pronounced /kuË/) is a particular kind of collection in which the entities in the collection are kept in order and the principal (or only) operations on the collection are the addition of entities to the rear terminal position and removal of entities from the front terminal position. ...
Simple representation of a stack In computer science, a stack is a temporary abstract data type and data structure based on the principle of Last In First Out (LIFO). ...
 In computer science an array is a data structure consisting of a group of elements that are accessed by indexing. In most programming languages each element has the same data type and the array occupies a contiguous area of storage. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
A binary tree, a simple type of branching linked data structure. ...
In mathematics, an element (also called a member) is an object contained in a set (or more generally a class). ...
Index has two distinct meanings in computer science: an integer which identifies an array element, and a data structure which enables sublineartime lookup. ...
A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. ...
In programming languages a data type defines a set of values and the allowable operations on those values[1]. For example, in the Java programming language, the int type represents the set of 32bit integers ranging in value from 2,147,483,648 to 2,147,483,647, and...
The terms storage (U.K.) or memory (U.S.) refer to the parts of a digital computer that retain physical state (data) for some interval of time, possibly even after electrical power to the computer is turned off. ...
Most programming languages have a builtin array data type, although what is called an array in the language documentation is sometimes really an associative array. Conversely, the contiguous storage kind of array discussed here may alternatively be called a vector,^{[1]} list,^{[2]} or table.^{[3]} An associative array (also map, hash, dictionary, finite map, lookup table, and in queryprocessing an index or index file) is an abstract data type composed of a collection of keys and a collection of values, where each key is associated with one value. ...
Tables is a generic name given to a class of board games similar to Backgammon. ...
Some programming languages support array programming (e.g., APL, newer versions of Fortran) which generalises operations and functions to work transparently over arrays as they do with scalars, instead of requiring looping over array members. Array programming languages (also known as vector or multidimensional languages) generalize operations on scalars to apply transparently to vectors, matrices, and higher dimensional arrays. ...
APL (for A Programming Language) is an array programming language based on a notation invented in 1957 by Kenneth E. Iverson while at Harvard University. ...
Fortran (previously FORTRAN[1]) is a generalpurpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ...
Multidimensional arrays are accessed using more than one index: one for each dimension. Arrays can be classified as fixedsized arrays (sometimes known as static arrays) whose size cannot change once their storage has been allocated, or dynamic arrays, which can be resized. A dynamic array, growable array, resizable array, dynamic table, or array list is a data structure, an array which is automatically expanded to accommodate new objects if filled beyond its current size. ...
Properties
Fixedsize arrays permit efficient (constant time, O(1)) random access. They are compact data structures, having a constant memory overhead. And, on CPUs which support caches, sequential iteration over an array has good locality of reference because its elements occupy contiguous memory locations. However, when an array is randomly accessed, for example when probing a hash table, locality of reference may be lost. In computational complexity theory, big O notation is often used to describe how the size of the input data affects an algorithms usage of computational resources (usually running time or memory). ...
Random access compared to sequential access. ...
In computer science, overhead is generally considered any combination of excess or indirect computation time, memory, bandwidth, or other resources that are required to be utilized or expended to enable a particular goal. ...
CPU can stand for: in computing: Central processing unit in journalism: Commonwealth Press Union in law enforcement: Crime prevention unit in software: Critical patch update, a type of software patch distributed by Oracle Corporation in Macleans College is often known as Ash Lim. ...
For other uses, see cache (disambiguation). ...
It has been suggested that this article or section be merged with Memory locality. ...
Random access compared to sequential access. ...
In computer science, a hash table is a data structure that speeds up searching for information by a particular aspect of that information, called a key. ...
Applications Because of their performance characteristics, arrays are used to implement other data structures, such as heaps, hash tables, deques, queues, stacks, strings, and VLists. Example of a complete binary max heap In computer science, a heap is a specialized treebased data structure that satisfies the heap property: if B is a child node of A, then key(A) â‰¥ key(B). ...
In computer science, a hash table is a data structure that speeds up searching for information by a particular aspect of that information, called a key. ...
In computer science, a deque (short for doubleended queue) is a data structure for which elements can be added to or removed from the front or back. ...
A queue (pronounced /kuË/) is a particular kind of collection in which the entities in the collection are kept in order and the principal (or only) operations on the collection are the addition of entities to the rear terminal position and removal of entities from the front terminal position. ...
Simple representation of a stack In computer science, a stack is a temporary abstract data type and data structure based on the principle of Last In First Out (LIFO). ...
In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. ...
If you are seeking the town in the Netherlands, see Vlist. ...
Some algorithms store a variable number of elements in part of a fixedsize array, which is equivalent to using dynamic array with a fixed capacity. See dynamic array for details. A dynamic array, growable array, resizable array, dynamic table, or array list is a data structure, an array which is automatically expanded to accommodate new objects if filled beyond its current size. ...
A dynamic array, growable array, resizable array, dynamic table, or array list is a data structure, an array which is automatically expanded to accommodate new objects if filled beyond its current size. ...
Associative arrays provide a mechanism for arraylike functionality without huge storage overheads when the index values are sparse. Specialized associative arrays with integer keys include Patricia tries and Judy arrays. An associative array (also map, hash, dictionary, finite map, lookup table, and in queryprocessing an index or index file) is an abstract data type composed of a collection of keys and a collection of values, where each key is associated with one value. ...
In computer science, a Patricia trie (also known as a radix tree) is a simple form of compressed trie which merges single child nodes with their parents. ...
In computer science and software engineering, a Judy array is a complex but very fast associative array data structure for storing and looking up values using integer or string keys. ...
Indexing 
The valid index values of each dimension of an array are a bounded set of integers. Programming environments that check indexes for validity are said to perform bounds checking. Index has two distinct meanings in computer science: an integer which identifies an array element, and a data structure which enables sublineartime lookup. ...
In computer programming, bounds checking is the name given to any method of detecting whether or not an index given lies within the limits of an array. ...
Index of the first element The index of the first element (sometimes called the "origin") varies by language. There are three main implementations: zerobased, onebased, and nbased arrays, for which the first element has an index of zero, one, or a programmerspecified value. The zerobased array is more natural in the root machine language and was popularized by the C programming language, in which the abstraction of array is very weak, and an index n of a onedimensional array is simply the offset of the element accessed from the address of the first (or "zero^{th}") element (scaled by the size of the element). Onebased arrays are based on traditional mathematics notation for matrices and most, but not all, mathematical sequences. nbased is made available so the programmer is free to choose the lower bound, which may even be negative, which is most naturally suited for the problem at hand. A system of codes directly understandable by a computers CPU is termed this CPUs native or machine language. ...
C is a generalpurpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...
The word matrix (plural matrices) has several meanings. ...
For other senses of this word, see sequence (disambiguation). ...
The Comparison of programming languages (array), indicates the base index used by various languages. Size can be chosen on initialization/declaration after which it is fixed. ...
Supporters of zerobased indexing sometimes criticize onebased and nbased arrays for being slower. Often this criticism is mistaken when onebased or nbased array accesses are optimized with common subexpression elimination (for single dimensioned arrays) and/or with welldefined dope vectors (for multidimensioned arrays). However, in multidimensional arrays where the net offset into linear memory is computed from all of the indices, zerobased indexing is more natural, simpler, and faster. Edsger W. Dijkstra expressed an opinion in this debate: Why numbering should start at zero. In compiler theory, common subexpression elimination (CSE) is the practice of finding repeated redundant expression evaluations, and replacing them with a single computation assigned to a temporary variable. ...
In computer programming, a dope vector is a data structure used to hold information about an array, especially its memory layout. ...
Edsger Wybe Dijkstra (May 11, 1930 â€“ August 6, 2002); IPA: ) was a Dutch computer scientist. ...
The 0based/1based debate is not limited to just programming languages. For example, the groundfloor of a building is elevator button "0" in France, but elevator button "1" in the USA.
Indexing Methods When the Array is implemented as continuous storage, the indexbased access, e.g. to element n, is simply done (for zerobased indexing) by using the address of the first element and adding n · sizeof(one element). So this is a Θ(1) operation. But there are cases, where continuous storage might be a bad idea:  Insertion and deletion should also be a common operation, but continuous storage requires Θ(n) time for them. Here a balanced tree can be used, giving Θ(log n) for both index access and inserting/deleting. ^{[4]}^{[5]} For example the TextBuffer of GTK+ is implemented on top of a BTree, which has lower overhead compared to a binary tree like the AVL Tree.
 Allowing noninteger indices, which is also called an Associative array. PHP Arrays are indexed by integers, but can also be accessed by string keys.
GTK+, or the GIMP Toolkit, is one of the two most popular widget toolkits for the X Window System for creating graphical user interfaces. ...
Btrees are tree data structures that are most commonly found in databases and filesystem implementations. ...
An example of an unbalanced nonAVL tree In computer science, an AVL tree is a selfbalancing binary search tree, and the first such data structure to be invented. ...
An associative array (also map, hash, dictionary, finite map, lookup table, and in queryprocessing an index or index file) is an abstract data type composed of a collection of keys and a collection of values, where each key is associated with one value. ...
For other uses, see PHP (disambiguation). ...
Multidimensional arrays Ordinary arrays are indexed by a single integer. Also useful, particularly in numerical and graphics applications, is the concept of a multidimensional array, in which we index into the array using an ordered list of integers, such as in a[3,1,5]. The number of integers in the list used to index into the multidimensional array is always the same and is referred to as the array's dimensionality, and the bounds on each of these are called the array's dimensions. An array with dimensionality k is often called kdimensional. Onedimensional arrays correspond to the simple arrays discussed thus far; twodimensional arrays are a particularly common representation for matrices. In practice, the dimensionality of an array rarely exceeds three. Mapping a onedimensional array into memory is obvious, since memory is logically itself a (very large) onedimensional array. When we reach higherdimensional arrays, however, the problem is no longer obvious. Suppose we want to represent this simple twodimensional array: For the square matrix section, see square matrix. ...
It is most common to index this array using the RCconvention, where elements are referred in row, column fashion or , such as: Common ways to index into multidimensional arrays include:  Rowmajor order. Used most notably by staticallydeclared arrays in C. The elements of each row are stored in order.
 Columnmajor order. Used most notably in Fortran. The elements of each column are stored in order.
 Arrays of arrays. Multidimensional arrays are typically represented by onedimensional arrays of references (Iliffe vectors) to other onedimensional arrays. The subarrays can be either the rows or columns.
Rowmajor order describes a way to store a multidimensional array in linear memory. ...
C is a generalpurpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Fortran (previously FORTRAN[1]) is a generalpurpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ...
This article is about a general notion of reference in computing. ...
In computer programming, an Iliffe vector is a data structure used to implement multidimensional arrays. ...
Image File history File links Array_of_array_storage. ...
The first two forms are more compact and have potentially better locality of reference, but are also more limiting; the arrays must be rectangular, meaning that no row can contain more elements than any other. Arrays of arrays, on the other hand, allow the creation of ragged arrays, also called jagged arrays, in which the valid range of one index depends on the value of another, or in this case, simply that different rows can be different sizes. Arrays of arrays are also of value in programming languages that only supply onedimensional arrays as primitives. In many applications, such as numerical applications working with matrices, we iterate over rectangular twodimensional arrays in predictable ways. For example, computing an element of the matrix product AB involves iterating over a row of A and a column of B simultaneously. In mapping the individual array indexes into memory, we wish to exploit locality of reference as much as we can. A compiler can sometimes automatically choose the layout for an array so that sequentially accessed elements are stored sequentially in memory; in our example, it might choose rowmajor order for A, and columnmajor order for B. Even more exotic orderings can be used, for example if we iterate over the main diagonal of a matrix. For the square matrix section, see square matrix. ...
In linear algebra, the main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. ...
References  ^ C calls arrays `vectors'. The term is also common whenever the array is regarded as a mathematical vector.
 ^ Tcl 8 lists are implemented using C vectors.
 ^ This was the practice in some older languages, e.g. COBOL: Using Tables in COBOL
 ^ NIST's Dictionary of Algorithms and Data Structures: Array
 ^ Counted BTree
C is a generalpurpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...
Look up vector in Wiktionary, the free dictionary. ...
Tcl (originally from Tool Command Language, but nonetheless conventionally rendered as Tcl rather than TCL; and pronounced tickle) is a scripting language created by John Ousterhout. ...
C is a generalpurpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...
COBOL (pronounced //) is a Thirdgeneration programming language, and one of the oldest programming languages still in active use. ...
See also Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Webbased project to create a free content dictionary, available in over 151 languages. ...
In computer programming, array slicing is an operation that extracts certain elements from an array and packages them as another array, possibly with different number of indices (or dimensions) and different index ranges. ...
In objectoriented programming, a collection class is any class that is capable of storing other objects. ...
Size can be chosen on initialization/declaration after which it is fixed. ...
A parallel array is a simple data structure for representing arrays of records. ...
In computer science, the set is a collection of certain values without any particular order. ...
A sparse array in computing is an array where most of the elements have the same value (called the default value  usually 0) and only a few elements have a nondefault value. ...
External links  NIST's Dictionary of Algorithms and Data Structures: Array
