namespace lemon {

/**

\ingroup demos

\file graph_orientation.cc

\brief Graph orientation with lower bound requirement on the

in-degree of the nodes.

This demo shows an adaptation of the well-known "preflow push" algorithm to

a simple graph orientation problem.

The input of the problem is a(n undirected) graph and an integer value

<i>f(n)</i> assigned to each node \e n. The task is to find an orientation

of the edges for which the number of edge arriving to each node \e n is at

least least <i>f(n)</i>.

In fact, the algorithm reads a directed graph and computes a set of edges to

be reversed in order to achieve the in-degree requirement.

This input is given using 

\ref graph-io-page ".lgf (Lemon Graph Format)" file. It should contain

three node maps. The one called "f" contains the in-degree requirements, while

"coordinate_x" and "coordinate_y" indicate the position of the nodes. These

latter ones are used to generate the output, which is a <tt>.eps</tt> file.

\section go-alg-dec The C++ source file

Here you find how to solve the problem above using lemon.

\subsection go-alg-head Headers and convenience typedefs

First we include some important headers.

The first one defines \ref lemon::ListGraph "ListGraph",

the "Swiss army knife" graph implementation.

\dontinclude graph_orientation.cc

\skipline list_graph

The next is  to read a \ref graph-io-page ".lgf" (Lemon Graph Format) file.

\skipline reader

This provides us with some special purpose graph \ref maps "maps".

\skipline iterable

The following header defines a simple data structure to store and manipulate

planar coordinates. It will be used to draw the result.

\skipline xy

And finally, this header contains a simple graph drawing utility.

\skipline eps

As we don't want to type in \ref lemon "lemon::" million times, the

following line seems to be useful.

\skipline namespace

The following <tt>typedef</tt>s will also save a lot of typing.

\skip typedef

\until InEdgeIt

\subsection go-alg-main The main() function

Well, we are ready to start <tt>main()</tt>.

\skip main

\until {

First we check whether the program is called with exactly 1 parameter.

If it isn't, we print a short help message end exit.

The vast majority of people would probably skip this block.

\skip if

\until }

Now, we read a graph \c g, and a map \c f containing

the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)"

file. To generate the output picture, we also read the node titles (\c id) and

coordinates (\c coords).

So, first we create the graph

\skipline ListGraph

and the corresponding NodeMaps.

\skipline NodeMap

\until coords

\note The graph must be given to the maps' constructor.

Then, the following block will read these data from the file, or exit if

the file is missing or corrupt.

\skip try

\until }

\until }

The algorithm needs a "level" integer value assigned to each node. In the

beginning, the nodes are on level 0.

\skipline level

The deficiency (\c def) of a node is the in-degree requirement minus the 

actual in-degree.

\skip def

\until subMap

A node is \e active if its deficiency is positive (i.e. if it doesn't meet

the degree requirement).

\skip active

\until def

We also store in a bool map which edges are reverted. Actually this is only

used to draw these edges with different color in the output picture. The

algorithm will update this map called \c rev, but will not use it otherwise.

\skip rev

\until reversed

The variable \c nodeNum will refer to the number of nodes.

\skipline nodeNum

Here comes the algorithms itself. 

In each iteration we choose an active node (\c act will store it). If there is

no such a node, then the orientation is feasible so we are done.

\skip act

\until while

Then we check if there exists an edge leaving this node that steps down exactly

one level.

\skip OutEdge

\until while

If there exists, we decrease the "activity" of the node \c act by reverting

this egde.

Fortunately, \ref lemon::ListGraph "ListGraph"

has a special function \ref lemon::ListGraph::reverseEdge() "reverseEdge()"

that makes this easy.

We also have to update the maps \c def and

\c rev.

\skipline if

\skip if

\until }

Otherwise (i.e. if there is no edge stepping down one level). We lift up the

current active node \c act. If it reaches level \c nodeNum, then there

exists no appropriate orientation so we stop.

\skipline else

\skipline if

\skipline return

\until }

\until }

\until }

Believe it or not, this algorithm works and runs fast.

Finally, we print the obtained orientation. Note, how the different

\c bool values of

\c rev are transformed into different \ref lemon::Color "RGB color"s

using the class

\ref lemon::ColorSet "ColorSet"

and the \ref map_adaptors "map adaptor" called

\ref lemon::ComposeMap "composeMap".

\skip graphToEps

\until run

\until end of main

Finally here are again the list of the used include files (because I can't turn

this section off.)

*/

}