/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2010
 * 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_algorithms[PAGE] Algorithms

\todo This page is under construction.

In addition to the graph structures, the most important parts of LEMON are
the various algorithms related to graph theory and combinatorial optimization.
The library probvides quite flexible and efficient implementations
for well-known fundamental algorithms, such as breadth-first
search (BFS), depth-first search (DFS), Dijkstra algorithm, Kruskal algorithm
and methods for discovering graph properties like connectivity, bipartiteness
or Euler property, as well as more complex optimization algorithms for finding
maximum flows, minimum cuts, matchings, minimum cost flows and arc-disjoint
paths.

In this section, we present only some of the most fundamental algorithms.
For a complete overview, see the \ref algs module of the reference manual.

[SEC]sec_graph_search[SEC] Graph Search

\todo The following contents are ported from the LEMON 0.x tutorial,
thus they have to thouroughly revised, reorganized and reworked.

See \ref Bfs, \ref Dfs and \ref graph_properties.

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.

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 \b TR.<br>
GR is the digraph the algorithm runs on. It has \ref lemon::ListDigraph "ListDigraph" 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<ListGraph>  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 with other member functions like \ref lemon::Bfs::predNode "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( ListGraph::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

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.


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 MyOrdererMap
\until };
The class meets the \ref concepts::WriteMap "WriteMap" concept. In it's \c set() method the only thing
we need to do is insert the key - that is the node whose processing just finished - into the beginning
of the list.<br>
Although we implemented this needed helper class ourselves it was not necessary.
The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly
what we needed. To be correct it's more general - and it's all in \c LEMON. But
we wanted to show you, how easy is to add additional functionality.

First we declare the needed data structures: the digraph and a map to store the nodes' label.
\skip ListDigraph
\until label

Now we build a digraph. But keep in mind that it must be DAG because cyclic digraphs has no topological
ordering.
\skip belt
\until trousers
We label them...
\skip label
\until trousers
Then add arcs 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

\todo Check the linking of the demo file, the code samples are missing.

More algorithms are described in the \ref algorithms2 "second part".


[SEC]sec_shortest_paths[SEC] Shortest Paths

See \ref Dijkstra and \ref BellmanFord.


If you want to solve some transportation problems in a network then you
will want to find shortest paths between nodes of a graph. This is
usually solved using Dijkstra's algorithm. A utility that solves this is
the LEMON Dijkstra class. The following code is a simple program using
the LEMON Dijkstra class: it calculates the shortest path between node s
and t in a graph g. We omit the part reading the graph g and the length
map len.

<hr>
 
In LEMON, the algorithms are implemented basically as classes, but
for some of them, function-type interfaces are also available
for the sake of convenience.
For instance, the Dijkstra algorithm is implemented in the \ref Dijkstra
template class, but the \ref dijkstra() function is also defined,
which can still be used quite flexibly due to named parameters.

The original sample code could also use the class interface as follows.

\code
  Dijkstra<ListDigraph> dijktra(g, length);
  dijkstra.distMap(dist);
  dijsktra.init();
  dijkstra.addSource(u);
  dijkstra.start();
\endcode

The previous code is obviously longer than the original, but the
execution can be controlled to a higher extent. While using the function-type
interface, only one source can be added to the algorithm, the class
interface makes it possible to specify several root nodes.
Moreover, the algorithm can also be executed step-by-step. For instance,
the following code can be used instead of \ref dijkstra.start().

\code
  while (!dijkstra.emptyQueue()) {
    ListDigraph::Node n = dijkstra.processNextNode();
    cout << g.id(n) << ' ' << dijkstra.dist(g) << endl;
  }
\endcode


[SEC]sec_max_flow[SEC] Maximum Flows

See \ref Preflow.

[TRAILER]
*/
}