/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2010
 * 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 {
/**
[PAGE]sec_basics[PAGE] Basic Concepts

Throughout the tutorial we are working with the \ref lemon namespace.
To save a lot of typing, we assume that a

\code
using namespace lemon;
\endcode

directive is added to the code at the beginning.

[SEC]sec_digraphs[SEC] Directed Graphs

The core features of LEMON are the data structures, algorithms and auxiliary
tools that make it possible to represent graphs and working with them easily
and efficiently.
This section tells you how to work with a directed graph (\e digraph,
for short) in LEMON. Here we use \ref ListDigraph, the most versatile
digraph structure. (The library also provides other digraph types,
see \ref sec_graph_structures "later".)

For using \ref ListDigraph, you must include the header file
\ref list_graph.h like this:

\code
#include <lemon/list_graph.h>
\endcode

The default constructor of the class creates an empty digraph.

\code
  ListDigraph g;
\endcode

The nodes and the arcs of a graph are identified by two data types called
\ref concepts::Digraph::Node "ListDigraph::Node" and \ref concepts::Digraph::Arc
"ListDigraph::Arc". You can add new items to the graph using the member
functions \ref ListDigraph::addNode() "addNode()" and
\ref ListDigraph::addArc() "addArc()", like this:

\code
  ListDigraph::Node x = g.addNode();
  ListDigraph::Node y = g.addNode();
  ListDigraph::Node z = g.addNode();

  g.addArc(x,y);
  g.addArc(y,z);
  g.addArc(z,x);
\endcode

Of course, \ref ListDigraph::addArc() "addArc()" also returns the created arc:

\code
  ListDigraph::Arc arc = g.addArc(x,z);
\endcode

Parallel and loop arcs are also supported.

\code
  ListDigraph::Arc parallel = g.addArc(x,y);
  ListDigraph::Arc loop = g.addArc(x,x);
\endcode

\note Using ListDigraph, you can also remove nodes or arcs with the
\ref ListDigraph::erase() "erase()" function. Moreover, this class provides
several other operations, see its \ref ListDigraph "documentation" for more
information.
However, not all graph structures support the addition and deletion
of graph items (see \ref sec_graph_concepts).

Two important member functions of the directed graphs are
\ref concepts::Digraph::source() "source()"
and \ref concepts::Digraph::target() "target()".
They give back the two end nodes of an arc (as \c Node objects).

\code
  if (g.source(loop) == g.target(loop))
    std::cout << "This is a loop arc" << std::endl;
\endcode

Each graph item has a non-negative integer identifier, which can be obtained
using the \ref concepts::Digraph::id() "id()" function of the graph structure.
These identifiers are unique with respect to a certain item type in a graph,
but a node and an arc may have the same id.

\code
  std::cout << "Arc " << g.id(arc) << " goes from node "
    << g.id(g.source(arc)) << " to node " << g.id(g.target(arc)) << std::endl;
\endcode

\note In fact, the \c Node and \c Arc types are typically simple wrapper
classes for a single \c int value, which is the identifier of the item.


[SEC]sec_digraph_it[SEC] Iterators

Let us assume you want to list the elements of the graph. For this purpose,
the graph structures provide several \e iterators. For example, the following
code will count the number of nodes in a graph.

\code
  int cnt = 0;
  for (ListDigraph::NodeIt n(g); n != INVALID; ++n)
    cnt++;
  std::cout << "Number of nodes: " << cnt << std::endl;
\endcode

\ref concepts::Digraph::NodeIt "ListDigraph::NodeIt"
is an iterator class that lists the nodes.
The name of an iterator type starts with a name that refers to
the iterated objects and ends with 'It'.

Using \ref concepts::Digraph::NodeIt "NodeIt", you must give
the graph object to the constructor and the iterator will be set
to the first node. The next node is obtained by the prefix ++
operator. If there are no more nodes in the graph, the iterator will
be set to \ref INVALID, which is exploited in the stop condition of
the loop.

\note \ref INVALID is a constant in the \ref lemon namespace, which converts to
and compares with each and every iterator and graph item type.
Thus, you can even assign \ref INVALID to a \c Node or \c Arc object.

The iterators convert to the corresponding item types.
For example, the identifiers of the nodes can be printed like this.

\code
  for (ListDigraph::NodeIt n(g); n != INVALID; ++n)
    std::cout << g.id(n) << std::endl;
\endcode

As an other example, the following code adds a full graph to the
existing nodes.

\code
  for (ListDigraph::NodeIt u(g); u != INVALID; ++u)
    for (ListDigraph::NodeIt v(g); v != INVALID; ++v)
      if (u != v) g.addArc(u, v);
\endcode

\note Contrary to the iterators in the C++ Standard Template Library (STL),
LEMON iterators are convertible to the corresponding
item types without having to use \c %operator*(). This is not confusing,
since the program context always indicates whether we refer to the iterator
or to the graph item (they do not have conflicting functionalities).

The graph items are also ordered by the 'less than' operator (with respect to
their integer identifiers). For example, this code will add only one of the
opposite arcs.

\code
  for (ListDigraph::NodeIt u(g); u != INVALID; ++u)
    for (ListDigraph::NodeIt v(g); v != INVALID; ++v)
      if (u < v) g.addArc(u, v);
\endcode

\warning The order in which the iterators visit the items is
undefined. The only thing you may assume that they will list the items
in the same order until the graph is not changed.

Similarly, \ref concepts::Digraph::ArcIt "ListDigraph::ArcIt"
lists the arcs. Its usage is the same as of
\ref concepts::Digraph::NodeIt "ListDigraph::NodeIt".

\code
  int cnt = 0;
  for (ListDigraph::ArcIt a(g); a != INVALID; ++a)
    cnt++;
  std::cout << "Number of arcs: " << cnt << std::endl;
\endcode

Finally, you can also list the arcs starting from or arriving at a
certain node with
\ref concepts::Digraph::OutArcIt "ListDigraph::OutArcIt"
and
\ref concepts::Digraph::InArcIt "ListDigraph::InArcIt".
Their usage is the same, but you must also give the node to the constructor.

\code
  int cnt = 0;
  for (ListDigraph::OutArcIt a(g, x); a != INVALID; ++a)
    cnt++;
  std::cout << "Number of arcs leaving the node 'x': " << cnt << std::endl;
\endcode

\note LEMON provides functions for counting the nodes and arcs of a digraph:
\ref countNodes(), \ref countArcs(), \ref countInArcs(), \ref countOutArcs().
Using them is not just simpler than the above loops, but they could be much
faster, since several graph types support constant time item counting.


[SEC]sec_digraph_maps[SEC] Maps

The concept of "maps" is another fundamental part of LEMON. They allow assigning
values of any type to the nodes or arcs of a graph. The standard maps
provided by the graph structures have a couple of nice properties.

- \e Fast. Accessing (reading/writing) the values is as fast as a
  simple vector reading/writing.
- \e Dynamic. Whenever you need, you
  can allocate new maps in your code, just as a local variable. So when you
  leave its scope, it will be de-allocated automatically.
- \e Automatic. If you add new nodes or arcs to the graph, the storage of the
  existing maps will automatically expanded and the new slots will be
  initialized. On the removal of an item, the corresponding values in the maps
  are properly destructed.
  
By principle, the graph classes represent only the pure structure of
the graph (i.e. the nodes and arcs and their connections).
All data that are assigned to the items of the graph (e.g. node labels,
arc costs or capacities) must be stored separately using maps.

\note These maps must not be confused with \c std::map, since they provide
O(1) time access to the elements instead of O(log n).

So, if you want to assign \c int values to each node, you have to allocate a
\ref concepts::Digraph::NodeMap "NodeMap<int>".

\code
  ListDigraph::NodeMap<int> map(g);
\endcode

As you see, the graph you want to assign a map is given to the
constructor. Then you can access its element as if it were a vector.

\code
  map[x] = 2;
  map[y] = 3;
  map[z] = map[x] + map[y];
\endcode

Any kind of data can be assigned to the graph items (assuming that the type
has a default constructor).

\code
  ListDigraph::NodeMap<std::string> name(g);
  name[x] = "Node A";
  name[y] = "Node B";
\endcode

As a more complex example, let us create a map that assigns \c char labels
to the nodes.

\code
  ListDigraph::NodeMap<char> label(g);
  char ch = 'A';
  for (ListDigraph::NodeIt n(g); n != INVALID; ++n)
    label[n] = ch++;
\endcode

When you create a map, you can also give an initial value of the elements
as a second parameter. For example, the following code puts the number
of outgoing arcs for each node in a map.

\code
  ListDigraph::NodeMap<int> out_deg(g, 0);
  for (ListDigraph::ArcIt a(g); a != INVALID; ++a)
    out_deg[g.source(a)]++;
\endcode

\warning The initial value will apply to the currently existing items only. If
you add new nodes/arcs to the graph, then the corresponding values in the
map will be initialized with the default constructor of the
type.


[SEC]sec_naming_conv[SEC] Naming Conventions

In LEMON, there are some naming conventions you might already notice
in the above examples.

The name of a source file is written lowercase and the words are separated with
underscores (e.g. \ref list_graph.h). All header files are located in the
\c %lemon subdirectory, so you can include them like this.

\code
#include <lemon/header_file.h>
\endcode

The name of a class or any type looks like the following
(e.g. \ref ListDigraph, \ref concepts::Digraph::Node "Node",
\ref concepts::Digraph::NodeIt "NodeIt" etc.).

\code
AllWordsCapitalizedWithoutUnderscores
\endcode

The name of a function looks like the following
(e.g. \ref concepts::Digraph::source() "source()",
\ref concepts::Digraph::source() "target()",
\ref countNodes(), \ref countArcs() etc.).

\code
firstWordLowerCaseRestCapitalizedWithoutUnderscores
\endcode

The names of constants and macros look like the following
(e.g. \ref INVALID).

\code
ALL_UPPER_CASE_WITH_UNDERSCORES
\endcode

For more details, see \ref coding_style.

[TRAILER]
*/
}