\todo The following contents are ported from the LEMON 0.x tutorial,

 thus they have to thouroughly revised, reorganized and reworked.

 The LEMON maps are not only just storage classes, but also

 they are %concepts of any key--value based data access.

 Beside the standard digraph maps, LEMON contains several "lightweight"

 \e map \e adaptor \e classes, which perform various operations on the

 data of the adapted maps when their access operations are called,

 but without actually copying or modifying the original storage.

 These classes also conform to the map %concepts, thus they can be used

 like standard LEMON maps.

 Let us suppose that we have a traffic network stored in a LEMON digraph

 structure with two arc maps \c length and \c speed, which

 denote the physical length of each arc and the maximum (or average)

 speed that can be achieved on the corresponding road-section,

 respectively. If we are interested in the best traveling times,

 the following code can be used.

 \code

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

 \endcode

 Maps play a central role in LEMON. As their name suggests, they map a

 certain range of \e keys to certain \e values. Each map has two

 <tt>typedef</tt>'s to determine the types of keys and values, like this:

 \code

   typedef Arc Key;

   typedef double Value;

 \endcode

 A map can be 

 \e readable (\ref lemon::concepts::ReadMap "ReadMap", for short),

 \e writable (\ref lemon::concepts::WriteMap "WriteMap") or both

 (\ref lemon::concepts::ReadWriteMap "ReadWriteMap").

 There also exists a special type of

 ReadWrite map called \ref lemon::concepts::ReferenceMap "reference map".

 In addition that you can

 read and write the values of a key, a reference map

 can also give you a reference to the

 value belonging to a key, so you have a direct access to the memory address

 where it is stored.

 Each digraph structure in LEMON provides two standard map templates called

 \c ArcMap and \c NodeMap. Both are reference maps and you can easily

 assign data to the nodes and to the arcs of the digraph. For example if you

 have a digraph \c g defined as

 \code

   ListDigraph g;

 \endcode

 and you want to assign a floating point value to each arc, you can do

 it like this.

 \code

   ListDigraph::ArcMap<double> length(g);

 \endcode

 Note that you must give the underlying digraph to the constructor.

 The value of a readable map can be obtained by <tt>operator[]</tt>.

 \code

   d=length[e];

 \endcode

 where \c e is an instance of \c ListDigraph::Arc.

 (Or anything else

 that converts to \c ListDigraph::Arc, like  \c ListDigraph::ArcIt or

 \c ListDigraph::OutArcIt etc.)

 There are two ways to assign a new value to a key

 - In case of a <em>reference map</em> <tt>operator[]</tt>

 gives you a reference to the

 value, thus you can use this.

 \code

   length[e]=3.5;

 \endcode

 - <em>Writable maps</em> have

 a member function \c set(Key,const Value &)

 for this purpose.

 \code

   length.set(e,3.5);

 \endcode

 The first case is more comfortable and if you store complex structures in your

 map, it might be more efficient. However, there are writable but

 not reference maps, so if you want to write a generic algorithm, you should

 insist on the second way.

 \section how-to-write-your-own-map How to Write Your Own Maps

 \subsection read-maps Readable Maps

 Readable maps are very frequently used as the input of an

 algorithm.  For this purpose the most straightforward way is the use of the

 default maps provided by LEMON's digraph structures.

 Very often however, it is more

 convenient and/or more efficient to write your own readable map.

 You can find some examples below. In these examples \c Digraph is the

 type of the particular digraph structure you use.

 This simple map assigns \f$\pi\f$ to each arc.

 \code

 struct MyMap 

 {

   typedef double Value;

   typedef Digraph::Arc Key;

   double operator[](Key e) const { return PI;}

 };

 \endcode

 An alternative way to define maps is to use \c MapBase

 \code

 struct MyMap : public MapBase<Digraph::Arc,double>

 {

   Value operator[](Key e) const { return PI;}

 };

 \endcode

 Here is a bit more complex example.

 It provides a length function obtained

 from a base length function shifted by a potential difference.

 \code

 class ReducedLengthMap  : public MapBase<Digraph::Arc,double>

 {

   const Digraph &g;

   const Digraph::ArcMap<double> &orig_len;

   const Digraph::NodeMap<double> &pot;

 public:

   Value operator[](Key e) const {

     return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]);

   }

   ReducedLengthMap(const Digraph &_g,

                    const Digraph::ArcMap &_o,

                    const Digraph::NodeMap &_p)

     : g(_g), orig_len(_o), pot(_p) {};

 };

 \endcode

 Then, you can call e.g. Dijkstra algoritm on this map like this:

 \code

   ...

   ReducedLengthMap rm(g,len,pot);

   Dijkstra<Digraph,ReducedLengthMap> dij(g,rm);

   dij.run(s);

   ...

 \endcode

 In the previous section we discussed digraph topology. That is the skeleton a complex

 digraph represented data-set needs. But how to assign the data itself to that skeleton?<br>

 Here come the \b maps in.

 \section maps_intro Introduction to maps

 Maps play a central role in LEMON. As their name suggests, they map a certain range of <i>keys</i> to certain <i>values</i>.

 In LEMON there is many types of maps. Each map has two typedef's to determine the types of keys and values, like this:

 \code

   typedef Arc Key;

   typedef double Value;

 \endcode

 (Except matrix maps, they have two key types.)

 To make easy to use them - especially as template parameters - there are <i>map concepts</i> like by digraph classes.

 <ul>

 <li>\ref concepts::ReadMap "ReadMap" - values can be read out with the \c operator[].

 \code value_typed_variable = map_instance[key_value]; \endcode

 </li>

 <li>\ref concepts::WriteMap "WriteMap" - values can be set with the \c set() member function.

 \code map_instance.set(key_value, value_typed_expression); \endcode

 </li>

 <li>\ref concepts::ReadWriteMap "ReadWriteMap" - it's just a shortcut to indicate that the map is both

 readable and writable. It is delivered from them.

 </li>

 <li>\ref concepts::ReferenceMap "ReferenceMap" - a subclass of ReadWriteMap. It has two additional typedefs

 <i>Reference</i> and <i>ConstReference</i> and two overloads of \c operator[] to

 providing you constant or non-constant reference to the value belonging to a key,

 so you have a direct access to the memory address where it is stored.

 </li>

 <li>And there are the Matrix version of these maps, where the values are assigned to a pair of keys.

 The keys can be different types. (\ref concepts::ReadMatrixMap "ReadMatrixMap", 

 \ref concepts::WriteMatrixMap "WriteMatrixMap", \ref concepts::ReadWriteMatrixMap "ReadWriteMatrixMap",

 \ref concepts::ReferenceMatrixMap "ReferenceMatrixMap")

 </li>

 </ul>

 \section maps_graph Digraphs' maps

 Every \ref MappableDigraphComponent "mappable" digraph class has two public templates: NodeMap<VALUE> and ArcMap<VALUE>

 satisfying the \ref DigraphMap concept.

 If you want to assign data to nodes, just declare a NodeMap with the corresponding

 type. As an example, think of a arc-weighted digraph.

 \code ListDigraph::ArcMap<int>  weight(digraph); \endcode

 You can see that the map needs the digraph whose arcs will mapped, but nothing more.

 If the digraph class is extendable or erasable the map will automatically follow

 the changes you make. If a new node is added a default value is mapped to it.

 You can define the default value by passing a second argument to the map's constructor.

 \code ListDigraph::ArcMap<int>  weight(digraph, 13); \endcode

 But keep in mind that \c VALUE has to have copy constructor.

 Of course \c VALUE can be a rather complex type.

 For practice let's see the following template function (from \ref maps_summary "maps-summary.cc" in the \ref demo directory)!

 \dontinclude maps_summary.cc

 \skip template

 \until }

 The task is simple. We need the summary of some kind of data assigned to a digraph's nodes.

 (Whit a little trick the summary can be calculated only to a sub-digraph without changing

 this code. See \ref SubDigraph techniques - that's LEMON's true potential.)

 And the usage is simpler than the declaration suggests. The compiler deduces the

 template specialization, so the usage is like a simple function call.

 \skip std

 \until ;

 Most of the time you will probably use digraph maps, but keep in mind, that in LEMON maps are more general and can be used widely.

 If you want some 'real-life' examples see the next page, where we discuss \ref algorithms

 (coming soon) and will use maps hardly.

 Or if you want to know more about maps read these \ref maps2 "advanced map techniques".

 Here we discuss some advanced map techniques. Like writing your own maps or how to

 extend/modify a maps functionality with adaptors.

 \section custom_maps Writing Custom ReadMap

 \subsection custom_read_maps Readable Maps

 Readable maps are very frequently used as the input of an

 algorithm.  For this purpose the most straightforward way is the use of the

 default maps provided by LEMON's digraph structures.

 Very often however, it is more

 convenient and/or more efficient to write your own readable map.

 You can find some examples below. In these examples \c Digraph is the

 type of the particular digraph structure you use.

 This simple map assigns \f$\pi\f$ to each arc.

 \code

 struct MyMap 

 {

   typedef double Value;

   typedef Digraph::Arc Key;

   double operator[](const Key &e) const { return PI;}

 };

 \endcode

 An alternative way to define maps is to use MapBase

 \code

 struct MyMap : public MapBase<Digraph::Arc,double>

 {

   Value operator[](const Key& e) const { return PI;}

 };

 \endcode

 Here is a bit more complex example.

 It provides a length function obtained

 from a base length function shifted by a potential difference.

 \code

 class ReducedLengthMap  : public MapBase<Digraph::Arc,double>

 {

   const Digraph &g;

   const Digraph::ArcMap<double> &orig_len;

   const Digraph::NodeMap<double> &pot;

 public:

   Value operator[](Key e) const {

     return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]);

   }

   ReducedLengthMap(const Digraph &_g,

                    const Digraph::ArcMap &_o,

                    const Digraph::NodeMap &_p)

     : g(_g), orig_len(_o), pot(_p) {};

 };

 \endcode

 Then, you can call e.g. Dijkstra algoritm on this map like this:

 \code

   ...

   ReducedLengthMap rm(g,len,pot);

   Dijkstra<Digraph,ReducedLengthMap> dij(g,rm);

   dij.run(s);

   ...

 \endcode