Iterator

In computer programming, an iterator is an object that progressively provides access to each item of a collection, in order.

A collection may provide multiple iterators via its interface that provide items in different orders, such as forwards and backwards.

An iterator is often implemented in terms of the structure underlying a collection implementation and is often tightly coupled to the collection to enable the operational semantics of the iterator.

An iterator is behaviorally similar to a database cursor.

Iterators date to the CLU programming language in 1974.

Pattern
An iterator provides access to an element of a collection (element access) and can change its internal state to provide access to the next element (element traversal). It also provides for creation and initialization to a first element and indicates whether all elements have been traversed. In some programming contexts, an iterator provides additional functionality.

An iterator allows a consumer to process each element of a collection while isolating the consumer from the internal structure of the collection. The collection can store elements in any manner while the consumer can access them as a sequence.

In object-oriented programming, an iterator class is usually designed in tight coordination with the corresponding collection class. Usually, the collection provides the methods for creating iterators.

A loop counter is sometimes also referred to as a loop iterator. A loop counter, however, only provides the traversal functionality and not the element access functionality.

Generator
One way of implementing an iterator is via a restricted form of coroutine, known as a generator. By contrast with a subroutine, a generator coroutine can yield values to its caller multiple times, instead of returning just once. Most iterators are naturally expressible as generators, but because generators preserve their local state between invocations, they're particularly well-suited for complicated, stateful iterators, such as tree traversers. There are subtle differences and distinctions in the use of the terms "generator" and "iterator", which vary between authors and languages. In Python, a generator is an iterator constructor: a function that returns an iterator. An example of a Python generator returning an iterator for the Fibonacci numbers using Python's  statement follows:

Internal Iterator
An internal iterator is a higher order function (often taking anonymous functions) that traverses a collection while applying a function to each element. For example, Python's  function applies a caller-defined function to each element:

Implicit iterator
Some object-oriented languages such as C#, C++ (later versions), Delphi (later versions), Go, Java (later versions), Lua, Perl, Python, Ruby provide an intrinsic way of iterating through the elements of a collection without an explicit iterator. An iterator object may exist, but is not  represented in the source code.

An implicit iterator is often manifest in language syntax as.

In Python, a collection object can be iterated directly:

In Ruby, iteration requires accessing an iterator property:

This iteration style is sometimes called "internal iteration" because its code fully executes within the context of the iterable object (that controls all aspects of iteration), and the programmer only provides the operation to execute at each step (using an anonymous function).

Languages that support list comprehensions or similar constructs may also make use of implicit iterators during the construction of the result list, as in Python:

Sometimes the implicit hidden nature is only partial. The C++ language has a few function templates for implicit iteration, such as. These functions still require explicit iterator objects as their initial input, but the subsequent iteration does not expose an iterator object to the user.

Stream
Iterators are a useful abstraction of input streams – they provide a potentially infinite iterable (but not necessarily indexable) object. Several languages, such as Perl and Python, implement streams as iterators. In Python, iterators are objects representing streams of data. Alternative implementations of stream include data-driven languages, such as AWK and sed.

Contrast with indexing
Instead of using an iterator, many languages allow the use of a subscript operator and a loop counter to access each element. Although indexing may be used with collections, the use of iterators may have advantages such as:


 * Counting loops are not suitable to all data structures, in particular to data structures with no or slow random access, like lists or trees.
 * Iterators can provide a consistent way to iterate on data structures of all kinds, and therefore make the code more readable, reusable, and less sensitive to a change in the data structure.
 * An iterator can enforce additional restrictions on access, such as ensuring that elements cannot be skipped or that a previously visited element cannot be accessed a second time.
 * An iterator may allow the collection object to be modified without invalidating the iterator. For instance, once an iterator has advanced beyond the first element it may be possible to insert additional elements into the beginning of the collection with predictable results. With indexing this is problematic since the index numbers must change.

The ability of a collection to be modified while iterating through its elements has become necessary in modern object-oriented programming, where the interrelationships between objects and the effects of operations may not be obvious. By using an iterator one is isolated from these sorts of consequences. This assertion must however be taken with a grain of salt, because more often than not, for efficiency reasons, the iterator implementation is so tightly bound to the collection that it does preclude modification of the underlying collection without invalidating itself.

For collections that may move around their data in memory, the only way to not invalidate the iterator is, for the collection, to somehow keep track of all the currently alive iterators and update them on the fly. Since the number of iterators at a given time may be arbitrarily large in comparison to the size of the tied collection, updating them all will drastically impair the complexity guarantee on the collection's operations.

An alternative way to keep the number of updates bound relatively to the collection size would be to use a kind of handle mechanism, that is a collection of indirect pointers to the collection's elements that must be updated with the collection, and let the iterators point to these handles instead of directly to the data elements. But this approach will negatively impact the iterator performance, since it must effectuate a double pointer following to access the actual data element. This is usually not desirable, because many algorithms using the iterators invoke the iterators data access operation more often than the advance method. It is therefore especially important to have iterators with very efficient data access.

All in all, this is always a trade-off between security (iterators remain always valid) and efficiency. Most of the time, the added security is not worth the efficiency price to pay for it. Using an alternative collection (for example a singly linked list instead of a vector) would be a better choice (globally more efficient) if the stability of the iterators is needed.

Categories
Iterators can be categorised according to their functionality. Here is a (non-exhaustive) list of iterator categories:

Types
Different languages or libraries used with these languages define iterator types. Some of them are

.NET
Iterators in the .NET Framework (i.e. C#) are called "enumerators" and represented by the  interface. provides a  method, which advances to the next element and indicates whether the end of the collection has been reached;    a   property, to obtain the value of the element currently being pointed at. and an optional  method,  to rewind the enumerator back to its initial position. The enumerator initially points to a special value before the first element, so a call to  is required to begin iterating.

Enumerators are typically obtained by calling the  method of an object implementing the   interface. a  property, to obtain the value of the element currently being pointed at;   Container classes typically implement this interface. However, the foreach statement in C# can operate on any object providing such a method, even if it does not implement  (duck typing). Both interfaces were expanded into generic versions in .NET 2.0.

The following shows a simple use of iterators in C# 2.0:

C# 2.0 also supports generators: a method that is declared as returning  (or  ), but uses the " " statement to produce a sequence of elements instead of returning an object instance, will be transformed by the compiler into a new class implementing the appropriate interface.

C++
The C++ language makes wide use of iterators in its Standard Library and describes several categories of iterators differing in the repertoire of operations they allow. These include forward iterators, bidirectional iterators, and random access iterators, in order of increasing possibilities. All of the standard container template types provide iterators of one of these categories. Iterators generalize pointers to elements of an array (which indeed can be used as iterators), and their syntax is designed to resemble that of C pointer arithmetic, where the  and   operators are used to reference the element to which the iterator points and pointer arithmetic operators like   are used to modify iterators in the traversal of a container.

Traversal using iterators usually involves a single varying iterator, and two fixed iterators that serve to delimit a range to be traversed. The distance between the limiting iterators, in terms of the number of applications of the operator  needed to transform the lower limit into the upper one, equals the number of items in the designated range; the number of distinct iterator values involved is one more than that. By convention, the lower limiting iterator "points to" the first element in the range, while the upper limiting iterator does not point to any element in the range, but rather just beyond the end of the range. For traversal of an entire container, the  method provides the lower limit, and   the upper limit. The latter does not reference any element of the container at all but is a valid iterator value that can be compared against.

The following example shows a typical use of an iterator.

Iterator types are separate from the container types they are used with, though the two are often used in concert. The category of the iterator (and thus the operations defined for it) usually depends on the type of container, with for instance arrays or vectors providing random access iterators, but sets (which use a linked structure as implementation) only providing bidirectional iterators. One same container type can have more than one associated iterator type; for instance the  container type allows traversal either using (raw) pointers to its elements (of type  ), or values of a special type , and yet another type is provided for "reverse iterators", whose operations are defined in such a way that an algorithm performing a usual (forward) traversal will actually do traversal in reverse order when called with reverse iterators. Most containers also provide a separate  type, for which operations that would allow changing the values pointed to are intentionally not defined.

Simple traversal of a container object or a range of its elements (including modification of those elements unless a  is used) can be done using iterators alone. But container types may also provide methods like  or   that modify the structure of the container itself; these are methods of the container class, but in addition require one or more iterator values to specify the desired operation. While it is possible to have multiple iterators pointing into the same container simultaneously, structure-modifying operations may invalidate certain iterator values (the standard specifies for each case whether this may be so); using an invalidated iterator is an error that will lead to undefined behavior, and such errors need not be signaled by the run time system.

Implicit iteration is also partially supported by C++ through the use of standard function templates, such as , and .

When used they must be initialized with existing iterators, usually  and , that define the range over which iteration occurs. But no explicit iterator object is subsequently exposed as the iteration proceeds. This example shows the use of.

The same can be achieved using, passing a   value as third iterator:

Since C++11, lambda function syntax can be used to specify to operation to be iterated inline, avoiding the need to define a named function. Here is an example of for-each iteration using a lambda function:

Java
Introduced in the Java JDK 1.2 release, the interface allows the iteration of container classes. Each  provides a  and  method,  and may optionally support a   method. Iterators are created by the corresponding container class, typically by a method named.

The  method advances the iterator and returns the value pointed to by the iterator. The first element is obtained upon the first call to. To determine when all the elements in the container have been visited the  test method is used. The following example shows a simple use of iterators:

To show that  can be called repeatedly, we use it to insert commas between the elements but not after the last element.

This approach does not properly separate the advance operation from the actual data access. If the data element must be used more than once for each advance, it needs to be stored in a temporary variable. When an advance is needed without data access (i.e. to skip a given data element), the access is nonetheless performed, though the returned value is ignored in this case.

For collection types that support it, the  method of the iterator removes the most recently visited element from the container while keeping the iterator usable. Adding or removing elements by calling the methods of the container (also from the same thread) makes the iterator unusable. An attempt to get the next element throws the exception. An exception is also thrown if there are no more elements remaining ( has previously returned false).

Additionally, for there is a  with a similar API but that allows forward and backward iteration, provides its current index in the list and allows setting of the list element at its position.

The J2SE 5.0 release of Java introduced the interface to support an enhanced   (foreach) loop for iterating over collections and arrays. defines the method that returns an. Using the enhanced  loop, the preceding example can be rewritten as

Some containers also use the older (since 1.0)  class. It provides  and   methods but has no methods to modify the container.

Scala
In Scala, iterators have a rich set of methods similar to collections, and can be used directly in for loops. Indeed, both iterators and collections inherit from a common base trait -. However, because of the rich set of methods available in the Scala collections library, such as,  ,   etc., it is often not necessary to deal with iterators directly when programming in Scala.

Java iterators and collections can be automatically converted into Scala iterators and collections, respectively, simply by adding the single line

to the file. The  object provides implicit conversions to do this. Implicit conversions are a feature of Scala: methods that, when visible in the current scope, automatically insert calls to themselves into relevant expressions at the appropriate place to make them typecheck when they otherwise would not.

MATLAB
MATLAB supports both external and internal implicit iteration using either "native" arrays or  arrays. In the case of external iteration where the onus is on the user to advance the traversal and request next elements, one can define a set of elements within an array storage structure and traverse the elements using the -loop construct. For example,

traverses an array of integers using the  keyword.

In the case of internal iteration where the user can supply an operation to the iterator to perform over every element of a collection, many built-in operators and MATLAB functions are overloaded to execute over every element of an array and return a corresponding output array implicitly. Furthermore, the  and   functions can be leveraged for performing custom or user defined operations over "native" arrays and   arrays respectively. For example,

defines a primary function  that implicitly applies custom subfunction   to each element of an array using built-in function.

Alternatively, it may be desirable to abstract the mechanisms of the array storage container from the user by defining a custom object-oriented MATLAB implementation of the Iterator Pattern. Such an implementation supporting external iteration is demonstrated in MATLAB Central File Exchange item Design Pattern: Iterator (Behavioral). This is written in the new class-definition syntax introduced with MATLAB software version 7.6 (R2008a) and features a one-dimensional  array realization of the List Abstract Data Type (ADT) as the mechanism for storing a heterogeneous (in data type) set of elements. It provides the functionality for explicit forward List traversal with the,   and   methods for use in a  -loop.

PHP
PHP's  loop was introduced in version 4.0 and made compatible with objects as values in 4.0 Beta 4. However, support for iterators was added in PHP 5 through the introduction of the internal  interface. The two main interfaces for implementation in PHP scripts that enable objects to be iterated via the  loop are   and. The latter does not require the implementing class to declare all required methods, instead it implements an accessor method that returns an instance of. The Standard PHP Library provides several classes to work with special iterators. PHP also supports Generators since 5.5.

The simplest implementation is by wrapping an array, this can be useful for type hinting and information hiding.

All methods of the example class are used during the execution of a complete foreach loop. The iterator's methods are executed in the following order:
 * 1)   ensures that the internal structure starts from the beginning.
 * 2)   returns true in this example.
 * 3)   returned value is stored in.
 * 4)   returned value is stored in.
 * 5)   advances to the next element in the internal structure.
 * 6)   returns false and the loop is aborted.

The next example illustrates a PHP class that implements the  interface, which could be wrapped in an   class to act upon the data before it is returned to the   loop. The usage together with the  constant allows PHP scripts to iterate result sets with billions of rows with very little memory usage. These features are not exclusive to PHP nor to its MySQL class implementations (e.g. the  class implements the   interface as well).

Python
Iterators in Python are a fundamental part of the language and in many cases go unseen as they are implicitly used in the  (foreach) statement, in list comprehensions, and in generator expressions. All of Python's standard built-in collection types support iteration, as well as many classes that are part of the standard library. The following example shows typical implicit iteration over a sequence:

Python dictionaries (a form of associative array) can also be directly iterated over, when the dictionary keys are returned; or the  method of a dictionary can be iterated over where it yields corresponding key,value pairs as a tuple:

Iterators however can be used and defined explicitly. For any iterable sequence type or class, the built-in function  is used to create an iterator object. The iterator object can then be iterated with the  function, which uses the   method internally, which returns the next element in the container. (The previous statement applies to Python 3.x. In Python 2.x, the  method is equivalent.) A   exception will be raised when no more elements are left. The following example shows an equivalent iteration over a sequence using explicit iterators:

Any user-defined class can support standard iteration (either implicit or explicit) by defining an  method that returns an iterator object. The iterator object then needs to define a  method that returns the next element.

Python's generators implement this iteration protocol.

Raku
Iterators in Raku are a fundamental part of the language, although usually users do not have to care about iterators. Their usage is hidden behind iteration APIs such as the  statement, ,  , list indexing with  , etc.

The following example shows typical implicit iteration over a collection of values:

Raku hashes can also be directly iterated over; this yields key-value  objects. The  method can be invoked on the hash to iterate over the key and values; the   method to iterate over the hash's keys; and the   method to iterate over the hash's values.

Iterators however can be used and defined explicitly. For any iterable type, there are several methods that control different aspects of the iteration process. For example, the  method is supposed to return an   object, and the   method is supposed to produce and return the next value if possible, or return the sentinel value   if no more values could be produced. The following example shows an equivalent iteration over a collection using explicit iterators:

All iterable types in Raku compose the  role,   role, or both. The  is quite simple and only requires the   to be implemented by the composing class. The  is more complex and provides a series of methods such as , which allows for a finer operation of iteration in several contexts such as adding or eliminating items, or skipping over them to access other items. Thus, any user-defined class can support standard iteration by composing these roles and implementing the  and/or   methods.

The  class represents a DNA strand and implements the   by composing the   role. The DNA strand is split into a group of trinucleotides when iterated over:

The  class composes both the   and   roles:

Ruby
Ruby implements iterators quite differently; all iterations are done by means of passing callback closures to container methods - this way Ruby not only implements basic iteration but also several patterns of iteration like function mapping, filters and reducing. Ruby also supports an alternative syntax for the basic iterating method, the following three examples are equivalent:

...and...

or even shorter

Ruby can also iterate over fixed lists by using s and either calling their   method or doing a for each on them, as above.

Rust
Rust makes use of external iterators throughout the standard library, including in its  loop, which implicitly calls the   method of an iterator until it is consumed. The most basic  loop for example iterates over a   type:

Specifically, the  loop will call a value's   method, which returns an iterator that in turn yields the elements to the loop. The  loop (or indeed, any method that consumes the iterator), proceeds until the   method returns a   value (iterations yielding elements return a   value, where   is the element type).

All collections provided by the standard library implement the  trait (meaning they define the   method). Iterators themselves implement the  trait, which requires defining the   method. Furthermore, any type implementing  is automatically provided an implementation for   that returns itself.

Iterators support various adapters (, ,  ,  , etc.) as methods provided automatically by the   trait.

Users can create custom iterators by creating a type implementing the  trait. Custom collections can implement the  trait and return an associated iterator type for their elements, enabling their use directly in   loops. Below, the  type implements a custom, unbounded iterator: