Array (data type)

In computer science, array is a data type that represents a collection of elements (values or variables), each selected by one or more indices (identifying keys) that can be computed at run time during program execution. Such a collection is usually called an array variable or array value. By analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively. More generally, a multidimensional array (or n-dimensional array) type can be called a tensor type, by analogy with the mathematical concept, tensor.

Language support for array types may include certain built-in array data types, some syntactic constructions (array type constructors) that the programmer may use to define such types and declare array variables, and special notation for indexing array elements. For example, in the Pascal programming language, the declaration A[I,J] := A[N-I,2*J]. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array variable.

In more theoretical contexts, especially in type theory and in the description of abstract algorithms, the terms "array" and "array type" sometimes refer to an abstract data type (ADT) also called abstract array or may refer to an associative array, a mathematical model with the basic operations and behavior of a typical array type in most languagesinta[10];// array 'a' of 10 ints int*p=a;// 'p' points to the first element of 'a' voidfoo(intarr[]){ // the parameter 'arr' is an int[] // 'arr' is decayed to a pointer to its first element }

inta[10][20] or int(*arr)[t][u][v][w]=malloc(sizeof*arr);. The individual elements are accessed by first de-referencing an array pointer followed by indexing, e.g. (*arr)[i][j][k][l]. Alternatively, n-d arrays can be declared as pointers to its first element which is a (n-1) dimensional array, e.g. [foo]

Some languages, such as C, provide only zero-based array types, for which the minimum valid value for any index is 0. This choice is convenient for array implementation and address computations. With a language such as C, a pointer to the interior of any array can be defined that will symbolically act as a pseudo-array that accommodates negative indices. This works only because C does not check an index against bounds when used.

Other languages provide only one-based array types, where each index starts at 1; this is the traditional convention in mathematics for matrices and mathematical sequences. A few languages, such as Pascal and Lua, support n-based array types, whose minimum legal indices are chosen by the programmer. The relative merits of each choice have been the subject of heated debate. Zero-based indexing can avoid off-by-one or fencepost errors.

The relation between numbers appearing in an array declaration and the index of that array's last element also varies by language. In many languages (such as C), one should specify the number of elements contained in the array; whereas in others (such as Pascal and Visual Basic .NET) one should specify the numeric value of the index of the last element. This distinction is not present in languages where the indices start at 1, such as Lua.

Some programming languages support array programming, where operations and functions defined for certain data types are implicitly extended to arrays of elements of those types. Thus one can write A+B to add corresponding elements of two arrays A and B. Usually these languages provide both the element-by-element multiplication and the standard matrix product of linear algebra, and which of these is represented by the * operator varies by language.

Languages providing array programming capabilities have proliferated since the innovations in this area of APL. These are core capabilities of domain-specific languages such as GAUSS, IDL, Matlab, and Mathematica. They are a core facility in newer languages, such as Julia and recent versions of Fortran. These capabilities are also provided via standard extension libraries for other general purpose programming languages (such as the widely used NumPy library for Python).

Many languages provide a built-in string data type, with specialized notation ("string literals") to build values of that type. In some languages (such as C), a string is just an array of characters, or is handled in much the same way. Other languages, like Pascal, may provide vastly different operations for strings and arrays.

Some programming languages provide operations that return the size (number of elements) of a vector, or, more generally, range of each index of an array. In C and C++, arrays do not support the