Dynamic array
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 arrays, which have a fixed capacity that needs to be specified at allocation.
A dynamic array is not the same thing as a dynamically allocated array, which is an 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.[1]
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 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-size 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.[2]
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:
- the maximum logical size is unknown, or difficult to calculate, before the array is allocated
- it is considered that a maximum logical size given by a specification is likely to change
- the amortized cost of resizing a dynamic array does not significantly affect performance or responsiveness
Geometric expansion and amortized cost
To avoid incurring the cost of resizing many times, dynamic arrays resize by a large amount, such as doubling in size, and use the reserved space for future expansion. The operation of adding an element to the end might work as follows:
function insertEnd(dynarray a, element e)
if (a.size == a.capacity)
// resize a to twice its current capacity:
a.capacity ← a.capacity * 2
// (copy the contents to the new memory location here)
a[a.size] ← e
a.size ← a.size + 1
As n elements are inserted, the capacities form a geometric progression. Expanding the array by any constant proportion a ensures that inserting n elements takes O(n) time overall, meaning that each insertion takes amortized constant time. Many dynamic arrays also deallocate some of the underlying storage if its size drops below a certain threshold, such as 30% of the capacity. This threshold must be strictly smaller than 1/a in order to provide hysteresis (provide a stable band to avoid repeatedly growing and shrinking) and support mixed sequences of insertions and removals with amortized constant cost.
Dynamic arrays are a common example when teaching amortized analysis.[3][4]
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 about a/(a−1), while the number of wasted cells is bounded above by (a−1)n[citation needed]. If memory allocator uses a first-fit allocation algorithm, then growth factor values such as a=2 can cause dynamic array expansion to run out of memory even though a significant amount of memory may still be available.[5] There have been various discussions on ideal growth factor values, including proposals for the golden ratio as well as the value 1.5.[6] Many textbooks, however, use a = 2 for simplicity and analysis purposes.[3][4]
Below are growth factors used by several popular implementations:
| Implementation | Growth factor (a) |
|---|---|
| Facebook folly/FBVector[7] | 1.5 (3/2) |
| Rust Vec[8] | 2 |
- ^ See, for example, the source code of java.util.ArrayList class from OpenJDK 6.
- ^ Lambert, Kenneth Alfred (2009), "Physical size and logical size", Fundamentals of Python: From First Programs Through Data Structures, Cengage Learning, p. 510, ISBN 978-1423902188
- ^ a b Goodrich, Michael T.; Tamassia, Roberto (2002), "1.5.2 Analyzing an Extendable Array Implementation", Algorithm Design: Foundations, Analysis and Internet Examples, Wiley, pp. 39–41.
- ^ a b Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001) [1990]. "17.4 Dynamic tables". Introduction to Algorithms (2nd ed.). MIT Press and McGraw-Hill. pp. 416–424. ISBN 0-262-03293-7.
- ^ "C++ STL vector: definition, growth factor, member functions". Archived from the original on 2015-08-06. Retrieved 2015-08-05.
- ^ "vector growth factor of 1.5". comp.lang.c++.moderated. Google Groups.
- ^ "facebook/folly". GitHub. Retrieved 2015-08-05.
- ^ "rust-lang/rust". GitHub. Retrieved 2020-06-09.