namespace lemon{
/*!

\page maps-page Maps

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 Edge Key;
  typedef double Value;
\endcode

A map can be 
\e readable (\ref lemon::concept::ReadMap "ReadMap", for short),
\e writable (\ref lemon::concept::WriteMap "WriteMap") or both
(\ref lemon::concept::ReadWriteMap "ReadWriteMap").
There also exists a special type of
ReadWrite map called \ref lemon::concept::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 graph structure in LEMON provides two standard map templates called
\c EdgeMap and \c NodeMap. Both are reference maps and you can easily
assign data to the nodes and to the edges of the graph. For example if you
have a graph \c g defined as
\code
  ListGraph g;
\endcode
and you want to assign a floating point value to each edge, you can do
it like this.
\code
  ListGraph::EdgeMap<double> length(g);
\endcode
Note that you must give the underlying graph 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 ListGraph::Edge.
(Or anything else
that converts to \c ListGraph::Edge, like  \c ListGraph::EdgeIt or
\c ListGraph::OutEdgeIt 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 graph 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 Graph is the
type of the particular graph structure you use.


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

\code
struct MyMap 
{
  typedef double Value;
  typedef Graph::Edge Key;
  double operator[](Key e) const { return M_PI;}
};
\endcode

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

\code
struct MyMap : public MapBase<Graph::Edge,double>
{
  Value operator[](Key e) const { return M_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<Graph::Edge,double>
{
  const Graph &g;
  const Graph::EdgeMap<double> &orig_len;
  const Graph::NodeMap<double> &pot;
  
public:
  Value operator[](Key e) const {
    return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]);
  }
  
  ReducedLengthMap(const Graph &_g,
                   const Graph::EdgeMap &_o,
                   const Graph::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<Graph,ReducedLengthMap> dij(g,rm);
  dij.run(s);
  ...
\endcode


\subsection write-maps Writable Maps

To be written...

\subsection side-effect-maps Maps with Side Effect

To be written...

*/
}