Array Element Identifier and Addressing Formulas
When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer. Indices are also called subscripts. An index maps the array value to a stored object.
There are three ways in which the elements of an array can be indexed:
- 0 (zero-based indexing): The first element of the array is indexed by subscript of 0.
- 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.
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 (in a row major language) and A (in a column major language) 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.
Read more about this topic: Array Data Structure
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