/*!

\page graphs How to use graphs

The following program demonstrates the basic features of HugoLib's graph
structures.

\code
#include <iostream>
#include <hugo/list_graph.h>

using namespace hugo;

int main()
{
  typedef ListGraph Graph;
\endcode

ListGraph is one of HugoLib's graph classes. It is based on linked lists,
therefore iterating throuh its edges and nodes is fast.

\code
  typedef Graph::Edge Edge;
  typedef Graph::InEdgeIt InEdgeIt;
  typedef Graph::OutEdgeIt OutEdgeIt;
  typedef Graph::EdgeIt EdgeIt;
  typedef Graph::Node Node;
  typedef Graph::NodeIt NodeIt;

  Graph g;
  
  for (int i = 0; i < 3; i++)
    g.addNode();
  
  for (NodeIt i(g); g.valid(i); g.next(i))
    for (NodeIt j(g); g.valid(j); g.next(j))
      if (i != j) g.addEdge(i, j);
\endcode

After some convenience typedefs we create a graph and add three nodes to it.
Then we add edges to it to form a full graph.

\code
  std::cout << "Nodes:";
  for (NodeIt i(g); g.valid(i); g.next(i))
    std::cout << " " << g.id(i);
  std::cout << std::endl;
\endcode

Here we iterate through all nodes of the graph. We use a constructor of the
node iterator to initialize it to the first node. The next member function is
used to step to the next node, and valid is used to check if we have passed the
last one.

\code
  std::cout << "Nodes:";
  NodeIt n;
  for (g.first(n); n != INVALID; g.next(n))
    std::cout << " " << g.id(n);
  std::cout << std::endl;
\endcode

Here you can see an alternative way to iterate through all nodes. Here we use a
member function of the graph to initialize the node iterator to the first node
of the graph. Using next on the iterator pointing to the last node invalidates
the iterator i.e. sets its value to INVALID. Checking for this value is
equivalent to using the valid member function.

Both of the previous code fragments print out the same:

\code
Nodes: 2 1 0
\endcode

\code
  std::cout << "Edges:";
  for (EdgeIt i(g); g.valid(i); g.next(i))
    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
  std::cout << std::endl;
\endcode

\code
Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
\endcode

We can also iterate through all edges of the graph very similarly. The head and
tail member functions can be used to access the endpoints of an edge.

\code
  NodeIt first_node(g);

  std::cout << "Out-edges of node " << g.id(first_node) << ":";
  for (OutEdgeIt i(g, first_node); g.valid(i); g.next(i))
    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; 
  std::cout << std::endl;

  std::cout << "In-edges of node " << g.id(first_node) << ":";
  for (InEdgeIt i(g, first_node); g.valid(i); g.next(i))
    std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; 
  std::cout << std::endl;
\endcode

\code
Out-edges of node 2: (2,0) (2,1)
In-edges of node 2: (0,2) (1,2)
\endcode

We can also iterate through the in and out-edges of a node. In the above
example we print out the in and out-edges of the first node of the graph.

\code
  Graph::EdgeMap<int> m(g);

  for (EdgeIt e(g); g.valid(e); g.next(e))
    m.set(e, 10 - g.id(e));
  
  std::cout << "Id Edge  Value" << std::endl;
  for (EdgeIt e(g); g.valid(e); g.next(e))
    std::cout << g.id(e) << "  (" << g.id(g.tail(e)) << "," << g.id(g.head(e))
      << ") " << m[e] << std::endl;
\endcode

\code
Id Edge  Value
4  (0,2) 6
2  (1,2) 8
5  (0,1) 5
0  (2,1) 10
3  (1,0) 7
1  (2,0) 9
\endcode

In generic graph optimization programming graphs are not containers rather
incidence structures which are iterable in many ways. HugoLib introduces
concepts that allow us to attach containers to graphs. These containers are
called maps.

In the example above we create an EdgeMap which assigns an int value to all
edges of the graph. We use the set member function of the map to write values
into the map and the operator[] to retrieve them.

Here we used the maps provided by the ListGraph class, but you can also write
your own maps. You can read more about using maps \ref maps "here".

*/