In

computer science, an

**array data structure**, or simply an

**array**, is a

data structure consisting of a collection of

*elements* (

values or

variables), each identified by at least one

*array index* or

*key*. An array is stored so that the position of each element can be computed from its index

tuple by a mathematical formula.

[1][2][3] The simplest type of data structure is a linear array, also called one-dimensional array.

For example, an array of 10 32-bit integer variables, with indices 0 through 9, may be stored as 10

words at memory addresses 2000, 2004, 2008, ... 2036, so that the element with index

*i* has the address 2000 + 4 ×

*i*.

[4]The memory address of the first element of an array is called first address or foundation address.

Because the mathematical concept of a

matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called matrices. In some cases the term "vector" is used in computing to refer to an array, although

tuples rather than

vectors are more correctly the mathematical equivalent. Arrays are often used to implement

tables, especially

lookup tables; the word

*table* is sometimes used as a synonym of

*array*.

Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as

lists and

strings. They effectively exploit the addressing logic of computers. In most modern computers and many

external storage devices, the memory is a one-dimensional array of words, whose indices are their addresses.

Processors, especially

vector processors, are often optimized for array operations.

Arrays are useful mostly because the element indices can be computed at

run time. Among other things, this feature allows a single iterative

statement to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are required to have the same size and should use the same data representation. The set of valid index tuples and the addresses of the elements (and hence the element addressing formula) are usually,

[3][5] but not always,

[2] fixed while the array is in use.

The term

*array* is often used to mean

array data type, a kind of

data type provided by most

high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time. Array types are often implemented by array structures; however, in some languages they may be implemented by

hash tables,

linked lists,

search trees, or other data structures.

The term is also used, especially in the description of

algorithms, to mean

associative array or "abstract array", a

theoretical computer science model (an

abstract data type or ADT) intended to capture the essential properties of arrays. Arrays have better cache locality as compared to

linked lists.