3: Arrays

An array is a collection, mainly of similar data types, stored into a common variable. The collection forms a data structure where objects are stored linearly, one after another in memory. Sometimes arrays are even replicated into the memory hardware.

The structure can also be defined as a particular method of storing elements of indexed data. Elements of data are logically stored sequentially in blocks within the array. Each element is referenced by an index, or subscripts.

The index is usually a number used to address an element in the array. For example, if you were storing information about each day in August, you would create an array with an index capable of addressing 31 values—one for each day of the month. Indexing rules are language dependent, however most languages use either 0 or 1 as the first element of an array.

The concept of an array can be daunting to the uninitiated, but it is really quite simple. Think of a notebook with pages numbered 1 through 12. Each page may or may not contain information on it. The notebook is an array of pages. Each page is an element of the array 'notebook'. Programmatically, you would retrieve information from a page by referring to its number or subscript, i.e., notebook(4) would refer to the contents of page 4 of the array notebook.

Arrays can also be multidimensional - instead of accessing an element of a one-dimensional list, elements are accessed by two or more indices, as from a matrix or tensor.

Multidimensional arrays are as simple as our notebook example above. To envision a multidimensional array, think of a calendar. Each page of the calendar, 1 through 12, is an element, representing a month, which contains approximately 30 elements, which represent days. Each day may or may not have information in it. Programmatically then, calendar(4,15) would refer to the 4th month, 15th day. Thus we have a two-dimensional array. To envision a three-dimensional array, break each day up into 24 hours. Now calendar(4,15,9) would refer to 4th month, 15th day, 9th hour.

Arrays guarantee constant time read and write access, \(O(1)\), however many lookup operations (find_min, find_max, find_index) of an instance of an element are linear time, \(O(n)\). Arrays are very efficient in most languages, as operations compute the address of an element via a simple formula based on the base address element of the array.

Array implementations differ greatly between languages: some languages allow arrays to be re-sized automatically, or to even contain elements of differing types (such as Perl). Other languages are very strict and require the type and length information of an array to be known at run time (such as C).

Arrays typically map directly to contiguous storage locations within your computer's memory and are therefore the "natural" storage structure for most higher level languages.

Simple linear arrays are the basis for most of the other data structures. Many languages do not allow you to allocate any structure except an array, everything else must be implemented on top of the array. The exception is the linked list, that is typically implemented as individually allocated objects, but it is possible to implement a linked list within an array.