namespace lemon {

/**

\page algorithms 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

*/

}