/**

\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".

Some examples are the following (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 getsart How to start using LEMON):

<ul>

<li> First we give two examples that show how to instantiate a graph. The

first one shows the methods that add nodes and edges, but one will

usually use the second way which reads a graph from a stream (file).

<ol>

<li>The following code fragment shows how to fill a graph with data. It creates a complete graph on 4 nodes. The type Listgraph is one of the LEMON graph types: the typedefs in the beginning are for convenience and we will suppose them later as well.

 \code

  typedef ListGraph Graph;

  typedef Graph::NodeIt NodeIt;

  Graph g;

  for (int i = 0; i < 3; i++)

    g.addNode();

  for (NodeIt i(g); i!=INVALID; ++i)

    for (NodeIt j(g); j!=INVALID; ++j)

      if (i != j) g.addEdge(i, j);

 \endcode 

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

    If you want to read more on the LEMON graph structures and concepts, read the page about \ref graphs "graphs". 

<li> The following code shows how to read a graph from a stream (e.g. a file). LEMON supports the DIMACS file format: it can read a graph instance from a file 

in that format (find the documentation of the DIMACS file format 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 in DIMACS format and use 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" and it also shows how to define a map on the edges (the length

function):

\code

    typedef ListGraph Graph;

    typedef Graph::Node Node;

    typedef Graph::Edge Edge;

    typedef Graph::EdgeMap<int> LengthMap;

    Graph g;

    //An example from Ahuja's book

    Node s=g.addNode();

    Node v2=g.addNode();

    Node v3=g.addNode();

    Node v4=g.addNode();

    Node v5=g.addNode();

    Node t=g.addNode();

    Edge s_v2=g.addEdge(s, v2);

    Edge s_v3=g.addEdge(s, v3);

    Edge v2_v4=g.addEdge(v2, v4);

    Edge v2_v5=g.addEdge(v2, v5);

    Edge v3_v5=g.addEdge(v3, v5);

    Edge v4_t=g.addEdge(v4, t);

    Edge v5_t=g.addEdge(v5, t);

    LengthMap len(g);

    len.set(s_v2, 10);

    len.set(s_v3, 10);

    len.set(v2_v4, 5);

    len.set(v2_v5, 8);

    len.set(v3_v5, 5);

    len.set(v4_t, 8);

    len.set(v5_t, 8);

    std::cout << "The id of s is " << g.id(s)<< std::endl;

    std::cout <<"The id of t is " << g.id(t)<<"."<<std::endl;

    std::cout << "Dijkstra algorithm test..." << std::endl;

    Dijkstra<Graph, LengthMap> dijkstra_test(g,len);

    dijkstra_test.run(s);

    std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;

    std::cout << "The shortest path from s to t goes through the following nodes" <<std::endl;

 std::cout << " (the first one is t, the last one is s): "<<std::endl;

    for (Node v=t;v != s; v=dijkstra_test.predNode(v)){

	std::cout << g.id(v) << "<-";

    }

    std::cout << g.id(s) << std::endl;	

\endcode

See the whole program in \ref dijkstra_demo.cc.

The first part of the code is self-explanatory: we build the graph and set the

length values of the edges. Then we instantiate a member of the Dijkstra class

and 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 

class \ref lemon::Kruskal "LEMON Kruskal class" does this job for you.

The following code fragment shows an example:

Ide Zsuzska fog irni!

<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 CLPLEX (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.

\code

  //A default solver is taken

  LpDefault lp;

  typedef LpDefault::Row Row;

  typedef LpDefault::Col Col;

  //This will be a maximization

  lp.max();

  //We add coloumns (variables) to our problem

  Col x1 = lp.addCol();

  Col x2 = lp.addCol();

  Col x3 = lp.addCol();

  //Constraints

  lp.addRow(x1+x2+x3 <=100);  

  lp.addRow(10*x1+4*x2+5*x3<=600);  

  lp.addRow(2*x1+2*x2+6*x3<=300);  

  //Nonnegativity of the variables

  lp.colLowerBound(x1, 0);

  lp.colLowerBound(x2, 0);

  lp.colLowerBound(x3, 0);

  //Objective function

  lp.setObj(10*x1+6*x2+4*x3);

  //Call the routine of the underlying LP solver

  lp.solve();

  //Print results

  if (lp.primalStatus()==LpSolverBase::OPTIMAL){

    printf("Z = %g; x1 = %g; x2 = %g; x3 = %g\n", 

	   lp.primalValue(), 

	   lp.primal(x1), lp.primal(x2), lp.primal(x3));

  }

  else{

    std::cout<<"Optimal solution not found!"<<std::endl;

  }

\endcode

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.

\code

  //Define a map on the edges for the variables of the LP problem

  typename G::template EdgeMap<LpDefault::Col> x(g);

  lp.addColSet(x);

  //Nonnegativity and capacity constraints

  for(EdgeIt e(g);e!=INVALID;++e) {

    lp.colUpperBound(x[e],cap[e]);

    lp.colLowerBound(x[e],0);

  }

  //Flow conservation constraints for the nodes (except for 's' and 't')

  for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {

    LpDefault::Expr ex;

    for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];

    for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];

    lp.addRow(ex==0);

  }

  //Objective function: the flow value entering 't'

  {

    LpDefault::Expr ex;

    for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];

    for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];

    lp.setObj(ex);

  }

  //Maximization

  lp.max();

  //Solve with the underlying solver

  lp.solve();

\endcode

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

<tt>./lp_maxflow_demo < ?????????.lgf</tt>

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

See the whole code in \ref lp_demo.cc.

</ol>

</ul>

*/