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Type of data structure
the byte layout level structure

In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called one dimensional array. For example, an array of ten 32 bit (4 byte) integer variables, with indices 0 through 9, may be stored as ten words at memory addresses 2000, 2004, 2008, , 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, , 0x7F4) so that the element with index i has the address 2000 + (i × 4). The memory address of the first element of an array is called first address, foundation address, or base 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 the more mathematically correct equivalent. Tables are often implemented in the form of arrays, 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, but not always, Array indexing was originally done by self modifying code, and later using index registers and indirect addressing. Some mainframes designed in the 1960s, such as the Burroughs B5000 and its successors, used memory segmentation to perform index bounds checking in hardware. Assembly languages generally have no special support for arrays, other than what the machine itself provides. The earliest high level programming languages, including FORTRAN (1957), Lisp (1958), COBOL (1960), and ALGOL 60 (1960), had support for multi dimensional arrays, and so has C (1972). In C++ (1983), class templates exist for multi dimensional arrays whose dimension is fixed at runtime
1 (one based indexing) The first element of the array is indexed by subscript of 1.
n (n based indexing) The base index of an array can be freely chosen. Usually programming languages allowing n based indexing also allow negative index values and other scalar data types like enumerations, or characters may be used as an array index. Using zero based indexing is the design choice of many influential programming languages, including C, Java and Lisp. This leads to simpler implementation where the subscript refers to an offset from the starting position of an array, so the first element has an offset of zero. Arrays can have multiple dimensions, thus it is not uncommon to access an array using multiple indices. For example, a two dimensional array A with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression A[1][3] in the case of a zero based indexing system. Thus two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array. The number of indices needed to specify an element is called the dimension, dimensionality, or rank of the array. In standard arrays, each index is restricted to a certain range of consecutive integers (or consecutive values of some enumerated type), and the address of an element is computed by a "linear" formula on the indices.

A one dimensional array (or single dimension array) is a type of linear array. Accessing its elements involves a single subscript which can either represent a row or column index. As an example consider the C declaration int anArrayName[10]; which declares a one dimensional array of ten integers. Here, the array can store ten elements of type int This array has indices starting from zero through nine. For example, the expressions anArrayName[0] and anArrayName[9] are the first and last elements respectively. For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride. If the valid element indices begin at 0, the constant B is simply the address of the first element of the array. For this reason, the C programming language specifies that array indices always begin at 0; and many programmers will call that element "zeroth" rather than "first". However, one can choose the index of the first element by an appropriate choice of the base address B. For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by B + 30c, then the indices of those same elements will be 31 to 35. If the numbering does not start at 0, the constant B may not be the address of any element.

The addressing formula is completely defined by the dimension d, the base address B, and the increments c1, c2, , ck. It is often useful to pack these parameters into a record called the array's descriptor or stride vector or dope vector. whereas growable arrays require linear (Θ(n)) time to insert or delete elements at an arbitrary position. Linked lists allow constant time removal and insertion in the middle but take linear time for indexed access. Their memory use is typically worse than arrays, but is still linear. An Iliffe vector is an alternative to a multidimensional array structure. It uses a one dimensional array of references to arrays of one dimension less. For two dimensions, in particular, this alternative structure would be a vector of pointers to vectors, one for each row(pointer on c or c++). Thus an element in row i and column j of an array A would be accessed by double indexing (A[i][j] in typical notation). This alternative structure allows jagged arrays, where each row may have a different size—or, in general, where the valid range of each index depends on the values of all preceding indices. It also saves one multiplication (by the column address increment) replacing it by a bit shift (to index the vector of row pointers) and one extra memory access (fetching the row address), which may be worthwhile in some architectures.

The dimension of an array is the number of indices needed to select an element. Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one dimensional array is a list of data, a two dimensional array is a rectangle of data, a three dimensional array a block of data, etc. This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array. For example, an array with 5 rows and 4 columns is two dimensional, but such matrices form a 20 dimensional space. Similarly, a three dimensional vector can be represented by a one dimensional array of size three.