Array (data structure)

« Back to Glossary Index

History and Applications of Arrays
– First array-sorting program (merge sort) written by John von Neumann in 1945
– Early array indexing done by self-modifying code
– Some mainframes in the 1960s used memory segmentation for index-bounds checking
– High-level programming languages like FORTRAN, Lisp, COBOL, and ALGOL 60 had support for multi-dimensional arrays
– C++ introduced class templates for fixed and runtime-flexible multi-dimensional arrays
– Arrays used for mathematical vectors, matrices, and rectangular tables
– Many databases consist of one-dimensional arrays with record elements
– Arrays used to implement other data structures like lists, heaps, hash tables, queues, stacks, and strings
– Arrays used for in-program dynamic memory allocation
– Arrays used as control tables to determine program control flow

Element Identifier and Addressing Formulas
– Indexes (subscripts) used to select individual objects in an array
– Three ways to index elements: zero-based indexing, one-based indexing, and n-based indexing
– Zero-based indexing is a design choice in influential programming languages like C, Java, and Lisp
– Arrays can have multiple dimensions, requiring multiple indices for access
– The number of indices needed to specify an element is called the dimensionality or rank of the array

One-dimensional Arrays
– One-dimensional arrays are linear arrays with a single subscript for element access
– Subscript can represent a row or column index
– Accessing elements in a one-dimensional array is straightforward
– One-dimensional arrays are commonly used in various applications
– Can be implemented efficiently with little space overhead

Array Data Type
– Array data type provided by high-level programming languages
– Collection of values or variables selected by one or more run-time indices
– Array types often implemented by array structures, hash tables, linked lists, search trees, etc.
– Array data type can be implemented using various data structures
– Array data type is an abstract data type capturing essential properties of arrays

Multidimensional Arrays and Efficiency
– Addressing formula for element with indices: [row][column]
– Formula: base address + (row * row address increment) + (column * column address increment)
– Example: int a[2][3]
– Array has 2 rows and 3 columns
– Elements stored linearly, starting from first row to second row
– Static arrays have a fixed size and do not allow insertion or removal of elements
– Dynamic arrays can be implemented by allocating a new array and copying contents
– Insertions at the end of the array require amortized constant time
– Store and select operations on arrays take constant time
– Arrays take linear space in the number of elements they hold
– Sequential iteration over an array is faster due to locality of reference
– Arrays have no per-element overhead and are memory-wise compact
– Optimized routines like memcpy can significantly speed up copying array elements

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, fixed while the array is in use.

The term "array" may also refer to an 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.

« Back to Glossary Index

Submit your RFP

We can't wait to read about your project. Use the form below to submit your RFP!

Gabrielle Buff
Gabrielle Buff

Just left us a 5 star review

Great customer service and was able to walk us through the various options available to us in a way that made sense. Would definitely recommend!

Stoute Web Solutions has been a valuable resource for our business. Their attention to detail, expertise, and willingness to help at a moment's notice make them an essential support system for us.

Paul and the team are very professional, courteous, and efficient. They always respond immediately even to my minute concerns. Also, their SEO consultation is superb. These are good people!

Paul Stoute & his team are top notch! You will not find a more honest, hard working group whose focus is the success of your business. If you’re ready to work with the best to create the best for your business, go Stoute Web Solutions; you’ll definitely be glad you did!

Wonderful people that understand our needs and make it happen!

Paul is the absolute best! Always there with solutions in high pressure situations. A steady hand; always there when needed; I would recommend Paul to anyone!

Vince Fogliani

The team over at Stoute web solutions set my business up with a fantastic new website, could not be happier

Steve Sacre

If You are looking for Website design & creativity look no further. Paul & his team are the epitome of excellence.Don't take my word just refer to my website ""that Stoute Web Solutions created.This should convince anyone that You have finally found Your perfect fit

Jamie Hill

Paul and the team at Stoute Web are amazing. They are super fast to answer questions. Super easy to work with, and knows their stuff. 10,000 stars.

Paul and the team from Stoute Web solutions are awesome to work with. They're super intuitive on what best suits your needs and the end product is even better. We will be using them exclusively for our web design and hosting.

Dean Eardley

Beautifully functional websites from professional, knowledgeable team.

Along with hosting most of my url's Paul's business has helped me with website development, graphic design and even a really cool back end database app! I highly recommend him as your 360 solution to making your business more visible in today's social media driven marketplace.

I hate dealing with domain/site hosts. After terrible service for over a decade from Dreamhost, I was desperate to find a new one. I was lucky enough to win...

Paul Stoute has been extremely helpful in helping me choose the best package to suite my needs. Any time I had a technical issue he was there to help me through it. Superb customer service at a great value. I would recommend his services to anyone that wants a hassle free and quality experience for their website needs.

Paul is the BEST! I am a current customer and happy to say he has never let me down. Always responds quickly and if he cant fix the issue right away, if available, he provides you a temporary work around while researching the correct fix! Thanks for being an honest and great company!!

Paul Stoute is absolutely wonderful. Paul always responds to my calls and emails right away. He is truly the backbone of my business. From my fantastic website to popping right up on Google when people search for me and designing my business cards, Paul has been there every step of the way. I would recommend this company to anyone.

I can't say enough great things about Green Tie Hosting. Paul was wonderful in helping me get my website up and running quickly. I have stayed with Green...