/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * 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 {

 /**

 \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 at 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 dim2

 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 macro will also save a lot of typing by defining some

 convenience <tt>typedef</tt>s.

 \skipline TYPEDEF

 Actually, the macro above would be equivalent with the following

 <tt>typedef</tt>s.

 \code

 typedef ListGraph::Node Node;

 typedef ListGraph::NodeIt NodeIt;

 typedef ListGraph::Edge Edge;

 typedef ListGraph::EdgeIt EdgeIt;

 typedef ListGraph::OutEdgeIt OutEdgeIt;

 typedef ListGraph::InEdgeIt InEdgeIt;

 \endcode

 \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 one 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 label)

 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 an integer value assigned to each node. We call this "level" and the nodes are on level 0 at the

 beginning of the execution.

 \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 a bool map indicating which edges are reverted.

 Actually this map called \c rev is only

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

 algorithm updates this map, 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 algorithm itself. 

 In each iteration we choose an active node (\c act will do it for us).

 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 and

 stepping 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::Palette "Palette"

 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.)

 */

 }