/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2007

  * 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.

  *

  */

 /**

 \page quicktour Quick Tour to LEMON

 Let us first answer the question <b>"What do I want to use LEMON for?"</b>. 

 LEMON is a C++ library, so you can use it if you want to write C++ 

 programs. What kind of tasks does the library LEMON help to solve? 

 It helps to write programs that solve optimization problems that arise

 frequently when <b>designing and testing certain networks</b>, for example

 in telecommunication, computer networks, and other areas that I cannot

 think of now. A very natural way of modelling these networks is by means

 of a <b> graph</b> (we will always mean a directed graph by that and say

 <b> undirected graph </b> otherwise). 

 So if you want to write a program that works with 

 graphs then you might find it useful to use our library LEMON. LEMON 

 defines various graph concepts depending on what you want to do with the 

 graph: a very good description can be found in the page

 about \ref graphs "graphs".

 You will also want to assign data to the edges or nodes of the graph, for

 example a length or capacity function defined on the edges. You can do this in

 LEMON using so called \b maps. You can define a map on the nodes or on the edges of the graph and the value of the map (the range of the function) can be practically almost of any type. Read more about maps \ref maps-page "here".

 In this quick tour we want to show you some facilities LEMON library can provide through examples (simple demo programs). The examples will only show part of the functionality, but links will always be given to reach complete details. 

 You will find links next to the code fragments that help to download full demo programs: save them on your computer and compile them according to the description in the page about \ref getstart "How to start using LEMON". 

 Have fun!

 <ul> <li> The first thing to discuss is the way one can create data structures

 like graphs and maps in a program using LEMON. 

 //There are more graph types

 //implemented in LEMON and you can implement your own graph type just as well:

 //read more about this in the already mentioned page on \ref graphs "graphs".

 First we show how to add nodes and edges to a graph manually. We will also

 define a map on the edges of the graph. After this we show the way one can

 read a graph (and perhaps maps on it) from a stream (e.g. a file). Of course

 we also have routines that write a graph (and perhaps maps) to a stream

 (file): this will also be shown. LEMON supports the DIMACS file formats to

 read network optimization problems, but more importantly we also have our own

 file format that gives a more flexible way to store data related to network

 optimization.

 <ol> <li>The following code shows how to build a graph from scratch

 and iterate on its nodes and edges.  This example also shows how to

 give a map on the edges of the graph.  The type Listgraph is one of

 the LEMON graph types: the typedefs in the beginning are for

 convenience and we will assume them later as well.

 \dontinclude hello_lemon.cc

 \skip include

 \until }

 See the whole program in file \ref hello_lemon.cc in the \c demo subdir of

 LEMON package.

     If you want to read more on the LEMON graph structures and

 concepts, read the page about \ref graphs "graphs".

 <li>LEMON has an own file format for storing graphs, maps on edges/nodes and some other things. Instead of any explanation let us give a

 short example file in this format: read the detailed description of the LEMON

 graph file format and input-output routines here: \ref graph-io-page.

 So here is a file describing a graph of 6 nodes (0 to 5), two nodemaps

 (called \c coordinates_x and \c coordinates_y), several edges, an edge map

 called \c capacity and two designated nodes (called \c source and \c target).

 \verbatim

 @nodeset

 id      coordinates_x   coordinates_y

 5       796.398 208.035

 4       573.002 63.002

 3       568.549 401.748

 2       277.889 68.476

 1       288.248 397.327

 0       102.239 257.532

 @edgeset

                 id      capacity

 4       5       6       8

 3       5       5       8

 2       4       4       5

 1       4       3       8

 1       3       2       5

 0       2       1       10

 0       1       0       10

 #This is a comment here

 @nodes

 source 0

 target 5

 @edges 

 @attributes 

 author "Attila BERNATH"

 @end

 \endverbatim

 Finally let us give a simple example that reads a graph from a file and writes

 it to the standard output.

 \dontinclude reader_writer_demo.cc

 \skip include

 \until return

 \until }

 See the whole program in file \ref reader_writer_demo.cc.

 <li> The following code shows how to read a graph from a stream

 (e.g. a file) in the DIMACS file format (find the documentation of the

 DIMACS file formats on the web).

 \code

 Graph g;

 std::ifstream f("graph.dim");

 readDimacs(f, g);

 \endcode

 One can also store network (graph+capacity on the edges) instances and

 other things (minimum cost flow instances etc.) in DIMACS format and

 read these in LEMON: to see the details read the documentation of the

 \ref dimacs.h "Dimacs file format reader". 

 </ol>

 <li> 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 \ref lemon::Dijkstra "LEMON Dijkstra class".

 The following code is a simple program using the 

 \ref lemon::Dijkstra "LEMON Dijkstra class": it calculates the shortest path between node \c s and \c t in a graph \c g.

 We omit the part reading the graph  \c g and the length map \c len.

 \dontinclude dijkstra_demo.cc

 \skip ListGraph

 \until Graph g

 ...

 \skip Dijkstra algorithm

 \until std::cout << g.id(s)

 See the whole program in \ref dijkstra_demo.cc.

 Some explanation: after instantiating a member of the Dijkstra class

 we run the Dijkstra algorithm from node \c s. After this we read some

 of the results.  You can do much more with the Dijkstra class, for

 example you can run it step by step and gain full control of the

 execution. For a detailed description, see the documentation of the

 \ref lemon::Dijkstra "LEMON Dijkstra class".

 <li> If you want to design a network and want to minimize the total

 length of wires then you might be looking for a <b>minimum spanning

 tree</b> in an undirected graph. This can be found using the Kruskal

 algorithm: the function \ref lemon::kruskal "LEMON Kruskal " does this

 job for you.  

 First make a graph \c g and a cost map \c

 edge_cost_map, then make a bool edgemap \c tree_map or a vector \c

 tree_edge_vec for the algorithm output. After calling the function it

 gives back the weight of the minimum spanning tree and the \c tree_map or

 the \c tree_edge_vec contains the edges of the tree.

 If you want to store the edges in a bool edgemap, then use the

 function as follows:

 \dontinclude kruskal_demo.cc

 \skip Kruskal with boolmap; 

 \until  std::endl

 And if you rather use a vector instead of a bool map:

 \skip Kruskal with vector; 

 \until std::endl

 See the whole program in \ref kruskal_demo.cc.

 <li>Many problems in network optimization can be formalized by means

 of a linear programming problem (LP problem, for short). In our

 library we decided not to write an LP solver, since such packages are

 available in the commercial world just as well as in the open source

 world, and it is also a difficult task to compete these. Instead we

 decided to develop an interface that makes it easier to use these

 solvers together with LEMON. The advantage of this approach is

 twofold. Firstly our C++ interface is more comfortable than the

 solvers' native interface. Secondly, changing the underlying solver in

 a certain software using LEMON's LP interface needs zero effort. So,

 for example, one may try his idea using a free solver, demonstrate its

 usability for a customer and if it works well, but the performance

 should be improved, then one may decide to purchase and use a better

 commercial solver.

 So far we have an

 interface for the commercial LP solver software \b CPLEX (developed by ILOG)

 and for the open source solver \b GLPK (a shorthand for Gnu Linear Programming

 Toolkit).

 We will show two examples, the first one shows how simple it is to formalize

 and solve an LP problem in LEMON, while the second one shows how LEMON

 facilitates solving network optimization problems using LP solvers.

 <ol>

 <li>The following code shows how to solve an LP problem using the LEMON lp

 interface. The code together with the comments is self-explanatory.

 \dontinclude lp_demo.cc

 \skip A default solver is taken

 \until End of LEMON style code

 See the whole code in \ref lp_demo.cc.

 <li>The second example shows how easy it is to formalize a max-flow

 problem as an LP problem using the LEMON LP interface: we are looking

 for a real valued function defined on the edges of the digraph

 satisfying the nonnegativity-, the capacity constraints and the

 flow-conservation constraints and giving the largest flow value

 between to designated nodes.

 In the following code we suppose that we already have the graph \c g,

 the capacity map \c cap, the source node \c s and the target node \c t

 in the memory. We will also omit the typedefs.

 \dontinclude lp_maxflow_demo.cc

 \skip Define a map on the edges for the variables of the LP problem

 \until lp.max();

 \skip Solve with the underlying solver

 \until lp.solve();

 The complete program can be found in file \ref lp_maxflow_demo.cc. After compiling run it in the form:

 <tt>./lp_maxflow_demo < sample.lgf</tt>

 where sample.lgf is a file in the lemon format containing a maxflow instance (designated "source", "target" nodes and "capacity" map on the edges).

 </ol>

 </ul>

 */