/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 namespace lemon {

 /**

 [PAGE]sec_graph_adaptors[PAGE] Graph Adaptors

 \todo Clarify this section.

 Alteration of standard containers need a very limited number of

 operations, these together satisfy the everyday requirements.

 In the case of graph structures, different operations are needed which do

 not alter the physical graph, but gives another view. If some nodes or

 arcs have to be hidden or the reverse oriented graph have to be used, then

 this is the case. It also may happen that in a flow implementation

 the residual graph can be accessed by another algorithm, or a node-set

 is to be shrunk for another algorithm.

 LEMON also provides a variety of graphs for these requirements called

 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only

 in conjunction with other graph representations.

 The main parts of LEMON are the different graph structures, generic

 graph algorithms, graph concepts, which couple them, and graph

 adaptors. While the previous notions are more or less clear, the

 latter one needs further explanation. Graph adaptors are graph classes

 which serve for considering graph structures in different ways.

 A short example makes this much clearer.  Suppose that we have an

 instance \c g of a directed graph type, say ListDigraph and an algorithm

 \code

 template <typename Digraph>

 int algorithm(const Digraph&);

 \endcode

 is needed to run on the reverse oriented graph.  It may be expensive

 (in time or in memory usage) to copy \c g with the reversed

 arcs.  In this case, an adaptor class is used, which (according

 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.

 The adaptor uses the original digraph structure and digraph operations when

 methods of the reversed oriented graph are called.  This means that the adaptor

 have minor memory usage, and do not perform sophisticated algorithmic

 actions.  The purpose of it is to give a tool for the cases when a

 graph have to be used in a specific alteration.  If this alteration is

 obtained by a usual construction like filtering the node or the arc set or

 considering a new orientation, then an adaptor is worthwhile to use.

 To come back to the reverse oriented graph, in this situation

 \code

 template<typename Digraph> class ReverseDigraph;

 \endcode

 template class can be used. The code looks as follows

 \code

 ListDigraph g;

 ReverseDigraph<ListDigraph> rg(g);

 int result = algorithm(rg);

 \endcode

 During running the algorithm, the original digraph \c g is untouched.

 This techniques give rise to an elegant code, and based on stable

 graph adaptors, complex algorithms can be implemented easily.

 In flow, circulation and matching problems, the residual

 graph is of particular importance. Combining an adaptor implementing

 this with shortest path algorithms or minimum mean cycle algorithms,

 a range of weighted and cardinality optimization algorithms can be

 obtained. For other examples, the interested user is referred to the

 detailed documentation of particular adaptors.

 The behavior of graph adaptors can be very different. Some of them keep

 capabilities of the original graph while in other cases this would be

 meaningless. This means that the concepts that they meet depend

 on the graph adaptor, and the wrapped graph.

 For example, if an arc of a reversed digraph is deleted, this is carried

 out by deleting the corresponding arc of the original digraph, thus the

 adaptor modifies the original digraph.

 However in case of a residual digraph, this operation has no sense.

 Let us stand one more example here to simplify your work.

 ReverseDigraph has constructor

 \code

 ReverseDigraph(Digraph& digraph);

 \endcode

 This means that in a situation, when a <tt>const %ListDigraph&</tt>

 reference to a graph is given, then it have to be instantiated with

 <tt>Digraph=const %ListDigraph</tt>.

 \code

 int algorithm1(const ListDigraph& g) {

   ReverseDigraph<const ListDigraph> rg(g);

   return algorithm2(rg);

 }

 \endcode

 <hr>

 The LEMON graph adaptor classes serve for considering graphs in

 different ways. The adaptors can be used exactly the same as "real"

 graphs (i.e., they conform to the graph concepts), thus all generic

 algorithms can be performed on them. However, the adaptor classes use

 the underlying graph structures and operations when their methods are

 called, thus they have only negligible memory usage and do not perform

 sophisticated algorithmic actions. This technique yields convenient and

 elegant tools for the cases when a graph has to be used in a specific

 alteration, but copying it would be too expensive (in time or in memory

 usage) compared to the algorithm that should be executed on it. The

 following example shows how the \ref ReverseDigraph adaptor can be used

 to run Dijksta's algorithm on the reverse oriented graph. Note that the

 maps of the original graph can be used in connection with the adaptor,

 since the node and arc types of the adaptors convert to the original

 item types. 

 \code

 dijkstra(reverseDigraph(g), length).distMap(dist).run(s);

 \endcode

 Using \ref ReverseDigraph could be as efficient as working with the

 original graph, but not all adaptors can be so fast, of course. For

 example, the subgraph adaptors have to access filter maps for the nodes

 and/or the arcs, thus their iterators are significantly slower than the

 original iterators. LEMON also provides some more complex adaptors, for

 instance, \ref SplitNodes, which can be used for splitting each node in

 a directed graph and \ref ResidualDigraph for modeling the residual

 network for flow and matching problems. 

 Therefore, in cases when rather complex algorithms have to be used

 on a subgraph (e.g. when the nodes and arcs have to be traversed several

 times), it could worth copying the altered graph into an efficient structure

 and run the algorithm on it.

 Note that the adaptor classes can also be used for doing this easily,

 without having to copy the graph manually, as shown in the following

 example.

 \code

   ListDigraph g;

   ListDigraph::NodeMap<bool> filter_map(g);

   // construct the graph and fill the filter map

   {

     SmartDigraph temp_graph;

     ListDigraph::NodeMap<SmartDigraph::Node> node_ref(g);

     digraphCopy(filterNodes(g, filter_map), temp_graph)

       .nodeRef(node_ref).run();

     // use temp_graph

   }

 \endcode

 <hr>

 Another interesting adaptor in LEMON is \ref SplitNodes.

 It can be used for splitting each node into an in-node and an out-node

 in a directed graph. Formally, the adaptor replaces each node

 u in the graph with two nodes, namely node u<sub>in</sub> and node

 u<sub>out</sub>. Each arc (u,c) in the original graph will correspond to an

 arc (u<sub>out</sub>,v<sub>in</sub>). The adaptor also adds an

 additional bind arc (u<sub>in</sub>,u<sub>out</sub>) for each node u

 of the original digraph.

 The aim of this class is to assign costs to the nodes when using

 algorithms which would otherwise consider arc costs only.

 For example, let us suppose that we have a directed graph with costs

 given for both the nodes and the arcs.

 Then Dijkstra's algorithm can be used in connection with \ref SplitNodes

 as follows.

 \code

   typedef SplitNodes<ListDigraph> SplitGraph;

   SplitGraph sg(g);

   SplitGraph::CombinedArcMap<NodeCostMap, ArcCostMap>

     combined_cost(node_cost, arc_cost);

   SplitGraph::NodeMap<double> dist(sg);

   dijkstra(sg, combined_cost).distMap(dist).run(sg.outNode(u));

 \endcode

 Note that this problem can be solved more efficiently with

 map adaptors.

 These techniques help writing compact and elegant code, and makes it possible

 to easily implement complex algorithms based on well tested standard components.

 For instance, in flow and matching problems the residual graph is of

 particular importance.

 Combining \ref ResidualDigraph adaptor with various algorithms, a

 range of weighted and cardinality optimization methods can be obtained

 directly.

 [TRAILER]

 */

 }