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Subsections
Iterators are a powerful technique in object-oriented programming and one
of the fundamental design patterns [35]. Roughly speaking, an
iterator is a small, light-weight object, which is associated with a specific
kind of linear sequence. An iterator can be used to access all items in a
linear sequence step-by-step. In this section, different iterator classes are
introduced for traversing the nodes and the edges of a graph, and
for traversing all ingoing and/or outgoing edges of a single node.
Iterators are an alternative to the iteration macros introduced in
sect. Graphs.3.(i).
For example, consider the following iteration pattern:
node v;
forall_nodes (n, G) { ... }
Using the class NodeIt introduced in sect. Node Iterators, this
iteration can be re-written as follows:
for (NodeIt it (G); it.valid(); ++it) { ... }
The crucial differences are:
- No macros are used.
- Iterators are not bound to a loop, which means that the user has finer
control over the iteration process. For example, the continuation condition
it.valid() in the above loop could be replaced by another condition to
terminate the loop once a specific node has been found (and the loop may be
re-started at the same position later on).
- The meaning of iteration may be modified seamlessly. For example, the
filter iterators defined in sect. Filter Node Iterator
restrict the iteration to a subset that is specified by an
arbitrary logical condition (predicate). In other words, the nodes or
edges that do not fulfill this predicate are filtered out automatically during
iteration.
- The functionality of iteration may be extended seamlessly. For example,
the observer iterators defined in sect. Observer Node Iterator
can be used to record details of the
iteration. A concrete example is given in sect. Observer Node Iterator:
an observer iterator can be initialized such that it records the number of
iterations performed by the iterator.
- The safe iterator classes
(see the graph iterator LEDA extension package - they are documented here)
provide a safe access to the nodes and edges of a graph. This means that
the behavior of an iterator is well-defined even if its node or edge is
removed through another iterator.
- Iterator-based implementations of algorithms can be easily
integrated into environments that are implemented according to the STL
style [63], (this style has been adopted for the standard C++
library). For this purpose, sect. STL Iterator Wrapper define adapters,
which convert graph iterators into STL iterators.
Data accessors are a novel technique [48], which allows one
to implement an algorithm for attributed graphs such that the implementation
does not depend on a specific organization of the attributes.
Roughly speaking, an attributed graph consists of a (directed or undirected)
graph and an arbitrary number of node and edge attributes. For example, the
nodes of a graph are often assigned attributes such as names, flags, and
coordinates, and likewise, the edges are assigned attributes such as lengths,
costs, and capacities.
More formally, an attribute a of a set S has a certain type T
and assigns a value of T to every element of S (in other words, a
may be viewed as a function a:S-> T). An attributed set
A=(S,a_1,...,a_m) consists of a set S and attributes a_1,...,a_m.
An attributed graph is a (directed or undirected) graph G=(V,E) such that
the node set V and the edge set E are attributed.
Basically, LEDA provides two features to define attributes for graphs:
- Classes GRAPH and UGRAPH
(sects. Parameterized Graphs and Parameterized Ugraphs) are
templates with two arguments, vtype and etype, which are
reserved for a node and an edge attribute, respectively. To attach several
attributes to nodes and edges, vtype and etype must be
instantiated by structs whose members are the attributes.
- A node array (sect. Node Arrays)
or node map (sect. Node Maps)
represents a node attribute, and analogously, edge arrays
(sect. Edge Arrays)
and edge maps (sect. Edge Maps),
represent edge attributes. Several
attributes can be attached to nodes and edges by instantiating several arrays
or maps.
Data accessors provide a uniform interface to access attributes, and the
concrete organization of the attributes is hidden behind this interface.
Hence, if an implementation of an algorithm does not access attributes
directly, but solely in terms of data accessors, it may be applied to any
organization of the attributes
(in contrast, the algorithms in sect. Graph Algorithms
require an organization of all attributes as node and edge arrays).
Every data accessor class DA comes with a function template
get:
T get(DA da, Iter it);
This function returns the value of the attribute managed by the data accessor
da for the node or edge marked by the iterator it. Moreover,
most data accessor classes also come with a function template set:
void set(DA da, Iter it, T value);
This function overwrites the value of the attribute managed by the data
accessor da for the node or edge marked by the iterator it by
value.
The data accessor classes that do not provide a function template
set realize attributes in such a way that a function set does
not make sense or is even impossible. The constant accessor in
sect. Constant Accessors is a concrete example: it realizes an attribute
that is constant over the whole attributed set and over the whole time
of the program. Hence, it does not make sense to provide a function
set. Moreover, since the constant accessor class organizes its attribute
in a non-materialized fashion, an overwriting function set is even
impossible.
Example: The following trivial algorithm may serve as an example to
demonstrate the usage of data accessors and their interplay with various
iterator types. The first, nested loop accesses all edges once. More
specifically, the outer loop iterates over all nodes of the graph, and the
inner loop iterates over all edges leaving the current node of the outer loop.
Hence, for each edge, the value of the attribute managed by the data accessor
da is overwritten by t. In the second loop, a linear edge iterator
is used to check whether the first loop has set all values correctly.
template <class T, class DA>
void set_and_check (graph& G, DA da, T t)
{
for (NodeIt nit(G); nit.valid(); ++nit)
for (OutAdjIt oait(nit); oait.valid(); ++oait)
set (da, eit, t);
for (EdgeIt eit(G); eit.valid(); ++eit)
if (get(da,it) != t) cout << "Error!" << endl;
}
To demonstrate the application of function set_and_check, we first
consider the case that G is an object of the class GRAPH derived
from graph (sect. Graphs), that the template argument vtype
is instantiated by a struct type attributes, and that the
int-member my_attr of attributes shall be processed by
set_and_check with value 1. Then DA can be instantiated as a
node_member_da:
node_member_da<attributes,int> da (&attributes::my_attr);
set_and_check (G, da, 1);
Now we consider the case that the attribute to be processed is stored in an
edge_array<int> named my_attr_array:
node_array_da<int> da (my_attr_array);
set_and_check (G, da, 1);
Hence, all differences between these two cases are factored out into a single
declaration statement.
Several basic graph algorithms were re-implemented to use only
graph iterators and data accessors. Moreover they share three design
decisions:
- 1.
- algorithms are instances of classes
- 2.
- algorithm instances have the ability to ``advance''
- 3.
- algorithm instances provide access to their internal states
An example for an algorithm that supports the first two decisions is:
class Algorithm {
int state, endstate;
public:
Algorithm(int max) : endstate(max), state(0) { }
void next() { state++; }
bool finished() { return state>=endstate; }
};
With this class Algorithm we can easily instantiate an
algorithm object:
Algorithm alg(5);
while (!alg.finished()) alg.next();
This small piece of code creates an algorithm object and invokes
``next()'' until it has reached an end state.
An advantage of this design is that we can write basic algorithms, which
can be used in a standardized way and if needed, inspection of
internal states and variables can be provided without writing complex
code.
Additionally, it makes it possible to write persistent algorithms,
if the member variables are persistent.
Actually, those algorithms are quite more flexible than ordinary
written algorithm functions:
template<class Alg>
class OutputAlg {
Alg alg;
public:
OutputAlg(int m) : alg(m) {
cout << "max state: " << m << endl; }
void next() {
cout << "old state: " << alg.state;
alg.next();
cout << " new state: " << alg.state << endl; }
bool finished() { return alg.finished(); }
};
This wrapper algorithm can be used like this:
OutputAlg<Algorithm> alg(5);
while (!alg.finished()) alg.next();
In addition to the algorithm mentioned earlier
this wrapper writes the internal states to the
standard output.
This is as efficient as rewriting the ``Algorithm''-class
with an output mechanism, but provides more flexibility.
Next: Node Iterators (NodeIt)
Up: Graphs and Iterators
Previous: Graphs and Iterators
LEDA research project
1998-07-07