Place-holder page for algorithms.

 \section algo_bfs_dfs Bfs/Dfs

 Both \ref lemon::Bfs "Bfs" and \ref lemon::Dfs "Dfs" are highly adaptable and efficient

 implementations of the well known algorithms. The algorithms are placed most cases in

 separated files named after the algorithm itself but lower case as all other header file names.

 For example the next Bfs class is in the \c lemon/bfs.h.

 \subsection Bfs

 The algorithm is implemented in the \ref lemon::Bfs "Bfs" template class - rather than as function.

 The class has two template parameters: \b GR and \TR.<br>

 GR is the graph the algorithm runs on. It has \ref lemon::ListGraph "ListGraph" as default type.

 TR is a Traits class commonly used to easy the parametrization of templates. In most cases you

 wont need to modify the default type \ref lemon::BfsDefaultTraits "BfsDefaultTraits<GR>".

 To use the class, declare it!

 \code

 Bfs<ListUGraph>  bfs(gr);

 \endcode

 Note the lack of second template argument because of the default parameter.

 It provides a simple but powerful interface to control the execution.

 \code

 int dist = bfs.run(s,t);

 \endcode

 It finds the shortest path from node \c s to node \c t and returns it, or zero

 if there is no path from \c s to \c t.<br>

 If you want the shortest path from a specified node to all other node, just write:

 \code

 bfs.run(s);

 \endcode

 Now the distances and path information are stored in maps which you can access with

 member functions like \ref lemon::Bfs::distMap "distMap()" or \ref lemon::Bfs::predMap "predMap()".<br>

 Or more directly whit other member functions like \c predNode(). Once the algorithm

 is finished (or to be precise reached that node) \ref lemon::Bfs::dist "dist()" or \ref lemon::Bfs::predNode

 "predNode()" can be called.

 For an example let's say we want to print the shortest path of those nodes which

 are in a certain distance.

 \code

 bfs.run(s);

 for( ListUGraph::NodeIt  n(gr); n != INVALID; ++n ) {

   if( bfs.reached(n) && bfs.dist(n) <= max_dist ) {

     std::cout << gr.id(n);

     Node  prev = bfs.prevNode(n);

     while( prev != INVALID ) {

       std::cout << "<-" << gr.id(prev);

       prev = bfs.prevNode(n);

     }

     std::cout << std::endl;

   }

 }

 \endcode

 \subsubsection bfs_adv_control Advanced control

 In the previous code we only used \c run(). Now we introduce the way you can directly

 control the execution of the algorithm.

 First you have to initialize the variables with \ref lemon::Bfs::init "init()".

 \code

   bfs.init();

 \endcode

 Then you add one or more source nodes to the queue. They will be processed, as they would

 be reached by the algorithm before. And yes - you can add more sources during the execution.

 \code

   bfs.addSource(node_1);

   bfs.addSource(node_2);

   ...

 \endcode

 And finally you can start the process with \ref lemon::Bfs::start "start()", or

 you can write your own loop to process the nodes one-by-one.

 \todo demo for bfs advanced control

 \subsection Dfs

 Since Dfs is very similar to Bfs with a few tiny differences we only see a bit more complex example

 to demonstrate Dfs's capabilities.

 We will see a program, which solves the problem of <b>topological ordering</b>.

 We need to know in which order we should put on our clothes. The program will do the following:

 <ol>

 <li>We run the dfs algorithm to all nodes.

 <li>Put every node into a list when processed completely.

 <li>Write out the list in reverse order.

 </ol>

 \dontinclude topological_ordering.cc

 First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering

 will be done through it.

 \skip SerializingWriteMap

 \until };

 The class meets the \ref lemon::WriteMap "WriteMap" concept. In it's \c set() method the only thing

 we need to do is insert the key - that is the node who's processing just finished - into the beginning

 of the list.

 First we declare the needed data structures: the graph and a map to store the nodes' label.

 \skip ListGraph

 \until label

 Now we build a graph. But keep in mind that it must be DAG because cyclic graphs has no topological

 ordering.

 \skip belt

 \until trousers

 We label them...

 \skip label

 \until trousers

 Then add directed edges which represent the precedences between those items.

 \skip trousers, belt

 \until );

 See how easy is to access the internal information of this algorithm trough maps.

 We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap".

 \skip Dfs

 \until run

 And now comes the third part. Write out the list in reverse order. But the list was

 composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it.

 \skip std

 \until endl

 The program is to be found in the \ref demo directory: \ref topological_ordering.cc