Dynamic array: Difference between revisions

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{{Short description|List data structure to which elements can be added/removed}}

[[File:Dynamic array.svg|thumb|Several values are inserted at the end of a dynamic array using geometric expansion. Grey cells indicate space reserved for expansion. Most insertions are fast ([[constant time]]), while some are slow due to the need for [[Memory management|reallocation]] (Θ{{math|Θ(''n'')}} time, labelled with turtles). The ''logical size'' and ''capacity'' of the final array are shown.]]

In [[computer science]], a '''dynamic array''', '''growable array''', '''resizable array''', '''dynamic table''', '''mutable array''', or '''array list''' is a [[random access]], variable-size list [[data structure]] that allows elements to be added or removed. It is supplied with standard libraries in many modern mainstream programming languages. Dynamic arrays overcome a limit of static [[array data type|arrays]], which have a fixed capacity that needs to be specified at allocation.

In [[computer science]], a '''dynamic array''', '''growable array''', '''resizable array''', '''dynamic table''', '''mutable array''', or '''array list''' is a [[random access]], variable-size list [[list data structure]] that allows elements to be added or removed. It is supplied with [[standard libraries]] in many modern mainstream [[programming languageslanguage]]s. Dynamic arrays overcome a limit of static [[array data type|arrays]], which have a fixed capacity that needs to be specified at [[Memory management|allocation]].

A dynamic array is not the same thing as a [[dynamic memory allocation|dynamically allocated array]], which is an [[Array data structure|array]] whose size is fixed when the array is allocated, although a dynamic array may use such a fixed-size array as a back end.<ref name="java_util_ArrayList">See, for example, the [http://hg.openjdk.java.net/jdk6/jdk6/jdk/file/e0e25ac28560/src/share/classes/java/util/ArrayList.java source code of java.util.ArrayList class from OpenJDK 6].</ref>

A dynamic array is not the same thing as a [[dynamic memory allocation|dynamically allocated]] array or [[variable-length array]], either of which is an [[Array data structure|array]] whose size is fixed when the array is allocated, although a dynamic array may use such a fixed-size array as a back end.<ref name="java_util_ArrayList">See, for example, the [http://hg.openjdk.java.net/jdk6/jdk6/jdk/file/e0e25ac28560/src/share/classes/java/util/ArrayList.java source code of java.util.ArrayList class from OpenJDK 6].</ref>

== Bounded-size dynamic arrays and capacity ==

A simple dynamic array can be constructed by allocating an array of fixed-size, typically larger than the number of elements immediately required. The elements of the dynamic array are stored contiguously at the start of the underlying array, and the remaining positions towards the end of the underlying array are reserved, or unused. Elements can be added at the end of a dynamic array in [[Time complexity#Constant time|constant time]] by using the reserved space, until this space is completely consumed. When all space is consumed, and an additional element is to be added, then the underlying fixed-sizedsize array needs to be increased in size. Typically resizing is expensive because it involves allocating a new underlying array and copying each element from the original array. Elements can be removed from the end of a dynamic array in constant time, as no resizing is required. The number of elements used by the dynamic array contents is its ''logical size'' or ''size'', while the size of the underlying array is called the dynamic array's ''capacity'' or ''physical size'', which is the maximum possible size without relocating data.<ref>{{citation|author=Lambert, Kenneth Alfred|title=Physical size and logical size|work=Fundamentals of Python: From First Programs Through Data Structures|page=510|url=https://books.google.com/books?id=VtfM3YGW5jYC&pg=PA518&lpg=PA518&dqq=%22logical+size%22+%22dynamic+array%22&sourcepg=bl&ots=9rXJ9tGomJ&sig=D5dRs802ax43NmEpKa1BUWFk1qs&hl=en&sa=X&ei=CC1JUcLqGufLigKTjYGwCA&ved=0CGkQ6AEwBw#v=onepage&q=%22logical%20size%22%20%22dynamic%20array%22&f=falsePA518|publisher=Cengage Learning|year=2009|isbn=1423902181978-1423902188}}</ref>

A fixed-size array will suffice in applications where the maximum logical size is fixed (e.g. by specification), or can be calculated before the array is allocated. A dynamic array might be preferred if:

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== Growth factor ==

The growth factor for the dynamic array depends on several factors including a space-time trade-off and algorithms used in the memory allocator itself. For growth factor ''a'', the average time per insertion operation is {{citation needed span|text=about ''a''/(''a''−1), while the number of wasted cells is bounded above by (''a''−1)''n''|date=January 2018}}. If memory allocator uses a [[First fit algorithm|first-fit allocation]] algorithm, then growth factor values such as ''a=2''=2 can cause dynamic array expansion to run out of memory even though a significant amount of memory may still be available.<ref name=":0">{{Cite web|title = C++ STL vector: definition, growth factor, member functions|url = http://www.gahcep.com/cpp-internals-stl-vector-part-1/|accessdateaccess-date = 2015-08-05|archive-url = https://web.archive.org/web/20150806162750/http://www.gahcep.com/cpp-internals-stl-vector-part-1/|archive-date = 2015-08-06|url-status = dead}}</ref> There have been various discussions on ideal growth factor values, including proposals for the [[golden ratio]] as well as the value 1.5.<ref>{{Cite web|url = https://groups.google.com/forum/#!topic/comp.lang.c++.moderated/asH_VojWKJw%5B1-25%5D|title = vector growth factor of 1.5|date = |accessdate = |website = comp.lang.c++.moderated|publisher = Google Groups|lastaccess-date = 2015-08-05|firstarchive-date = 2011-01-22|archive-url = http://arquivo.pt/wayback/20110122130054/https://groups.google.com/forum/#!topic/comp.lang.c++.moderated/asH_VojWKJw%5B1-25%5D|url-status = dead}}</ref> Many textbooks, however, use ''a''&nbsp;=&nbsp;2 for simplicity and analysis purposes.<ref name="gt-ad">{{citation|first1=Michael T.|last1=Goodrich|author1-link=Michael T. Goodrich|first2=Roberto|last2=Tamassia|author2-link=Roberto Tamassia|title=Algorithm Design: Foundations, Analysis and Internet Examples|publisher=Wiley|year=2002|contribution=1.5.2 Analyzing an Extendable Array Implementation|pages=39–41}}.</ref><ref name="clrs">{{Introduction to Algorithms|chapter=17.4 Dynamic tables|edition=2|pages=416–424}}</ref>

Below are growth factors used by several popular implementations:

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|1.5 (3/2)

|-

|[[Python (programming language)|Python]] PyListObject<ref>[httphttps://svngithub.com/python.org/projectscpython/pythonblob/trunkbace59d8b8e38f5c779ff6296ebdc0527f6db14a/Objects/listobject.c#L58 List object implementation] from pythongithub.orgcom/python/cpython/, retrieved 20112020-0903-2723.</ref>

|~1.125 (n + (n >> 3))

|-

|[[Microsoft Visual C++]] 2013<ref>{{Cite web|title = Dissecting the C++ STL Vector: Part 3 - Capacity & Size|url = https://hadibrais.wordpress.com/2013/11/15/dissecting-the-c-stl-vector-part-3-capacity/|website = Micromysteries|accessdateaccess-date = 2015-08-05|first = Hadi|last = Brais| date=15 November 2013 }}</ref>

|1.5 (3/2)

|-

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|2

|-

|Facebook folly/FBVector<ref>{{Cite web|title = facebook/folly|url = https://github.com/facebook/folly/blob/master/folly/docs/FBVector.md|website = GitHub|accessdateaccess-date = 2015-08-05}}</ref>

|1.5 (3/2)

|-

|[[Unreal Engine]] TArray<ref>{{Cite web |date=2025-02-26 |title=Nested TArrays in structs and memory |url=https://forums.unrealengine.com/t/nested-tarrays-in-structs-and-memory/2357416/3 |access-date=2025-05-26 |website=Epic Developer Community Forums |language=en}}</ref>

|~1.375 (n + ((3 * n) >> 3))

|-

|Rust Vec<ref>{{Cite web|title=rust-lang/rust|url=https://github.com/rust-lang/rust/blob/fd4b177aabb9749dfb562c48e47379cea81dc277/src/liballoc/raw_vec.rs#L443|access-date=2020-06-09|website=GitHub|language=en}}</ref>

|2

|-

|[[Go (programming language)|Go]] slices<ref>{{Cite web|title = golang/go|url = https://github.com/golang/go/blob/master/src/runtime/slice.go#L188|website=GitHub|access-date = 2021-09-14}}</ref>

|between 1.25 and 2

|-

|[[Nim (programming language)|Nim]] sequences<ref>{{Cite web |title=The Nim memory model |url=http://zevv.nl/nim-memory/#_growing_a_seq |access-date=2022-05-24 |website=zevv.nl}}</ref>

|2

|-

|[[Steel Bank Common Lisp|SBCL]] ([[Common Lisp]]) vectors<ref>{{Cite web |title = sbcl/sbcl|url= https://github.com/sbcl/sbcl/blob/master/src/code/array.lisp#L1200-L1204|website=GitHub|access-date=2023-02-15}}</ref>

|2

|-

|[[C Sharp (programming language)|C#]] ([[.NET]] 8) List

|2

|}

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[[Gap buffer]]s are similar to dynamic arrays but allow efficient insertion and deletion operations clustered near the same arbitrary ___location. Some [[deque]] implementations use [[Deque#Implementations|array deques]], which allow amortized constant time insertion/removal at both ends, instead of just one end.

Goodrich<ref>{{Citation | title=Tiered Vectors: Efficient Dynamic Arrays for Rank-Based Sequences | first1=Michael T. | last1=Goodrich | author1-link=Michael T. Goodrich | first2=John G. | last2=Kloss II | year=1999 | url=https://archive.org/details/algorithmsdatast0000wads/page/205 | journal=[[Workshop on Algorithms and Data Structures]] | pages=[https://archive.org/details/algorithmsdatast0000wads/page/205 205–216] | doi=10.1007/3-540-48447-7_21 | volume=1663 | series=Lecture Notes in Computer Science | isbn=978-3-540-66279-2 | url-access=registration }}</ref> presented a dynamic array algorithm called ''tiered vectors'' that providedprovides ''O''(''n''^1/2''k'') performance for order preserving insertions orand deletions from theanywhere middle ofin the array, and ''O''(''k'') get and set, where ''k'' ≥ 2 is a constant parameter.

[[Hashed array tree]] (HAT) is a dynamic array algorithm published by Sitarski in 1996.<ref name="sitarski96">{{Citation | title=HATs: Hashed array trees | department=Algorithm Alley | journal=Dr. Dobb's Journal | date=September 1996 | first1=Edward | last1=Sitarski | volume=21 | issue=11 | url=http://www.ddj.com/architect/184409965?pgno=5}}</ref> Hashed array tree wastes order ''n''^1/2 amount of storage space, where ''n'' is the number of elements in the array. The algorithm has ''O''(1) amortized performance when appending a series of objects to the end of a hashed array tree.

In a 1999 paper,<ref name="brodnik">{{Citation | title=Resizable Arrays in Optimal Time and Space |type=Technical Report CS-99-09 | url=http://www.cs.uwaterloo.ca/research/tr/1999/09/CS-99-09.pdf | year=1999 | first1=Andrej | last1=Brodnik | first2=Svante | last2=Carlsson | first5=ED | last5=Demaine | first4=JI | last4=Munro | first3=Robert | last3=Sedgewick | author3-link=Robert Sedgewick (computer scientist) | publisher=Department of Computer Science, University of Waterloo}}</ref><!-- Defined in {{List data structure comparison}}: {{Citation | title=Resizable Arrays in Optimal Time and Space | date=Technical Report CS-99-09 | url=http://www.cs.uwaterloo.ca/research/tr/1999/09/CS-99-09.pdf | year=1999 | first1=Andrej | last1=Brodnik | first2=Svante | last2=Carlsson | first5=ED | last5=Demaine | first4=JI | last4=Munro | first3=Robert | last3=Sedgewick | author3-link=Robert Sedgewick (computer scientist) | publisher=Department of Computer Science, University of Waterloo}} --> Brodnik et al. describe a tiered dynamic array data structure, which wastes only ''n''^1/2 space for ''n'' elements at any point in time, and they prove a lower bound showing that any dynamic array must waste this much space if the operations are to remain amortized constant time. Additionally, they present a variant where growing and shrinking the buffer has not only amortized but worst-case constant time.

Bagwell (2002)<ref>{{Citation | title=Fast Functional Lists, Hash-Lists, Deques and Variable Length Arrays | first1=Phil | last1=Bagwell | year=2002 | publisher=EPFL | url=http://citeseer.ist.psu.edu/bagwell02fast.html}}</ref> presented the [[VList]] algorithm, which can be adapted to implement a dynamic array.

Naïve resizable arrays -- also called "the worst implementation" of resizable arrays -- keep the allocated size of the array exactly big enough for all the data it contains, perhaps by calling [[realloc]] for each and every item added to the array. Naïve resizable arrays are the simplest way of implementing a resizable array in C. They don't waste any memory, but appending to the end of the array always takes Θ(''n'') time.<ref name="sitarski96" /><ref>

Mike Lam.

[https://w3.cs.jmu.edu/lam2mo/cs240_2015_08/files/04-dyn_arrays.pdf "Dynamic Arrays"].

</ref><ref>

[https://users.cs.northwestern.edu/~jesse/course/cs214-fa19/lec/17-amortized.pdf "Amortized Time"].

</ref><ref>

[https://iq.opengenus.org/hashed-array-tree/ "Hashed Array Tree: Efficient representation of Array"].

</ref><ref>

[https://people.ksp.sk/~kuko/gnarley-trees/Complexity2.html "Different notions of complexity"].

</ref>

Linearly growing arrays pre-allocate ("waste") Θ(1) space every time they re-size the array, making them many times faster than naïve resizable arrays -- appending to the end of the array still takes Θ(''n'') time but with a much smaller constant.

Naïve resizable arrays and linearly growing arrays may be useful when a space-constrained application needs lots of small resizable arrays;

they are also commonly used as an educational example leading to exponentially growing dynamic arrays.<ref>

Peter Kankowski.

[https://www.strchr.com/dynamic_arrays "Dynamic arrays in C"].

</ref>

== Language support ==

[[C++]]'s [[Vector (C++)|<code>std::vector</code>]] and [[Rust (programming language)|Rust]]'s <code>std::vec::Vec</code> are implementations of dynamic arrays, as are the <code>ArrayList</code><ref>Javadoc on {{Javadoc:SE|java/util|ArrayList}}</ref> classes supplied with the [[Java (programming language)|Java]] API<ref name=Bloch>{{cite book | title= "Effective Java: Programming Language Guide" |last=Bloch| first=Joshua| publisher=Addison-Wesley | edition=third | isbn=978-0134685991| year=2018}}</ref>{{rp|236}} and the [[.NET Framework]].<ref>[https://msdn.microsoft.com/en-us/library/system.collections.arraylist ArrayList Class]</ref><ref name=Skeet>{{cite book |last=Skeet|first=Jon|title= C# in Depth |date=23 March 2019 |publisher= Manning |isbn= 978-1617294532}}</ref>{{rp|22}}

The generic <code>List<></code> class supplied with version 2.0 of the .NET Framework is also implemented with dynamic arrays. [[Smalltalk]]'s <code>OrderedCollection</code> is a dynamic array with dynamic start and end-index, making the removal of the first element also O(1).

[[Python (Programming Language)|Python]]'s <code>list</code> datatype implementation is a dynamic array the growth pattern of which is: 0, 4, 8, 16, 24, 32, 40, 52, 64, 76, ...<ref>[https://github.com/python/cpython/blob/bace59d8b8e38f5c779ff6296ebdc0527f6db14a/Objects/listobject.c#L58 listobject.c (github.com)]</ref>

[[Delphi (programming language)|Delphi]] and [[D (programming language)|D]] implement dynamic arrays at the language's core.

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[[Ada (programming language)|Ada]]'s [[wikibooks:Ada Programming/Libraries/Ada.Containers.Vectors|<code>Ada.Containers.Vectors</code>]] generic package provides dynamic array implementation for a given subtype.

Many scripting languages such as [[Perl]] and [[Ruby Ruby_(programming languageprogramming_language)|Ruby]] offer dynamic arrays as a built-in [[primitive data type]].

Several cross-platform frameworks provide dynamic array implementations for [[C (programming language)|C]], including <code>CFArray</code> and <code>CFMutableArray</code> in [[Core Foundation]], and <code>GArray</code> and <code>GPtrArray</code> in [[GLib]].

[[Common Lisp]] provides a rudimentary support for resizable vectors by allowing to configure the built-in <code>array</code> type as ''adjustable'' and the ___location of insertion by the ''fill-pointer''.

== See also ==

* [[Stack (data structure)]]

* [[Queue (data structure)]]

== References ==

<references />

== External links ==

* [https://xlinux.nist.gov/dads/HTML/dynamicarray.html NIST Dictionary of Algorithms and Data Structures: Dynamic array]

* [http://www.bsdua.org/libbsdua.html#vpool VPOOL] - C language implementation of dynamic array.

* [https://web.archive.org/web/20090704095801/http://www.collectionspy.com/ CollectionSpy] &mdash; A Java profiler with explicit support for debugging ArrayList- and Vector-related issues.

* [http://opendatastructures.org/versions/edition-0.1e/ods-java/2_Array_Based_Lists.html Open Data Structures - Chapter 2 - Array-Based Lists], [[Pat Morin]]

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[[Category:Arrays]]

[[Category:Articles with example pseudocode]]

[[Category:Amortized data structures]]