/* -*- 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_maps[PAGE] Maps

\todo This page is under construction.

\todo The following contents are ported from the LEMON 0.x tutorial,

thus they have to be thoroughly revised and reworked.

\warning Currently, this section may contain old or faulty contents.

The LEMON maps are not only just storage classes, but also

they are %concepts of any key--value based data access.

Beside the standard digraph maps, LEMON contains several "lightweight"

\e map \e adaptor \e classes, which perform various operations on the

data of the adapted maps when their access operations are called,

but without actually copying or modifying the original storage.

These classes also conform to the map %concepts, thus they can be used

like standard LEMON maps.

Maps play a central role in LEMON. As their name suggests, they map a

certain range of \e keys to certain \e values. Each map has two

<tt>typedef</tt>'s to determine the types of keys and values, like this:

\code

  typedef Arc Key;

  typedef double Value;

\endcode

A map can be 

\e readable (\ref lemon::concepts::ReadMap "ReadMap", for short),

\e writable (\ref lemon::concepts::WriteMap "WriteMap") or both

(\ref lemon::concepts::ReadWriteMap "ReadWriteMap").

There also exists a special type of

ReadWrite map called \ref lemon::concepts::ReferenceMap "reference map".

In addition that you can

read and write the values of a key, a reference map

can also give you a reference to the

value belonging to a key, so you have a direct access to the memory address

where it is stored.

Each digraph structure in LEMON provides two standard map templates called

\c ArcMap and \c NodeMap. Both are reference maps and you can easily

assign data to the nodes and to the arcs of the digraph. For example if you

have a digraph \c g defined as

\code

  ListDigraph g;

\endcode

and you want to assign a floating point value to each arc, you can do

it like this.

\code

  ListDigraph::ArcMap<double> length(g);

\endcode

Note that you must give the underlying digraph to the constructor.

The value of a readable map can be obtained by <tt>operator[]</tt>.

\code

  d=length[e];

\endcode

where \c e is an instance of \c ListDigraph::Arc.

(Or anything else

that converts to \c ListDigraph::Arc, like  \c ListDigraph::ArcIt or

\c ListDigraph::OutArcIt etc.)

There are two ways to assign a new value to a key

- In case of a <em>reference map</em> <tt>operator[]</tt>

gives you a reference to the

value, thus you can use this.

\code

  length[e]=3.5;

\endcode

- <em>Writable maps</em> have

a member function \c set(Key,const Value &)

for this purpose.

\code

  length.set(e,3.5);

\endcode

The first case is more comfortable and if you store complex structures in your

map, it might be more efficient. However, there are writable but

not reference maps, so if you want to write a generic algorithm, you should

insist on the second way.

\section how-to-write-your-own-map How to Write Your Own Maps

\subsection read-maps Readable Maps

Readable maps are very frequently used as the input of an

algorithm.  For this purpose the most straightforward way is the use of the

default maps provided by LEMON's digraph structures.

Very often however, it is more

convenient and/or more efficient to write your own readable map.

You can find some examples below. In these examples \c Digraph is the

type of the particular digraph structure you use.

This simple map assigns \f$\pi\f$ to each arc.

\code

struct MyMap 

{

  typedef double Value;

  typedef Digraph::Arc Key;

  double operator[](Key e) const { return PI;}

};

\endcode

An alternative way to define maps is to use \c MapBase

\code

struct MyMap : public MapBase<Digraph::Arc,double>

{

  Value operator[](Key e) const { return PI;}

};

\endcode

Here is a bit more complex example.

It provides a length function obtained

from a base length function shifted by a potential difference.

\code

class ReducedLengthMap  : public MapBase<Digraph::Arc,double>

{

  const Digraph &g;

  const Digraph::ArcMap<double> &orig_len;

  const Digraph::NodeMap<double> &pot;

public:

  Value operator[](Key e) const {

    return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]);

  }

  ReducedLengthMap(const Digraph &_g,

                   const Digraph::ArcMap &_o,

                   const Digraph::NodeMap &_p)

    : g(_g), orig_len(_o), pot(_p) {};

};

\endcode

Then, you can call e.g. Dijkstra algoritm on this map like this:

\code

  ...

  ReducedLengthMap rm(g,len,pot);

  Dijkstra<Digraph,ReducedLengthMap> dij(g,rm);

  dij.run(s);

  ...

\endcode

In the previous section we discussed digraph topology. That is the skeleton a complex

digraph represented data-set needs. But how to assign the data itself to that skeleton?<br>

Here come the \b maps in.

\section maps_intro Introduction to maps

Maps play a central role in LEMON. As their name suggests, they map a certain range of <i>keys</i> to certain <i>values</i>.

In LEMON there is many types of maps. Each map has two typedef's to determine the types of keys and values, like this:

\code

  typedef Arc Key;

  typedef double Value;

\endcode

(Except matrix maps, they have two key types.)

To make easy to use them - especially as template parameters - there are <i>map concepts</i> like by digraph classes.

<ul>

<li>\ref concepts::ReadMap "ReadMap" - values can be read out with the \c operator[].

\code value_typed_variable = map_instance[key_value]; \endcode

</li>

<li>\ref concepts::WriteMap "WriteMap" - values can be set with the \c set() member function.

\code map_instance.set(key_value, value_typed_expression); \endcode

</li>

<li>\ref concepts::ReadWriteMap "ReadWriteMap" - it's just a shortcut to indicate that the map is both

readable and writable. It is delivered from them.

</li>

<li>\ref concepts::ReferenceMap "ReferenceMap" - a subclass of ReadWriteMap. It has two additional typedefs

<i>Reference</i> and <i>ConstReference</i> and two overloads of \c operator[] to

providing you constant or non-constant reference to the value belonging to a key,

so you have a direct access to the memory address where it is stored.

</li>

<li>And there are the Matrix version of these maps, where the values are assigned to a pair of keys.

The keys can be different types. (\ref concepts::ReadMatrixMap "ReadMatrixMap", 

\ref concepts::WriteMatrixMap "WriteMatrixMap", \ref concepts::ReadWriteMatrixMap "ReadWriteMatrixMap",

\ref concepts::ReferenceMatrixMap "ReferenceMatrixMap")

</li>

</ul>

\section maps_graph Digraphs' maps

Every \ref MappableDigraphComponent "mappable" digraph class has two public templates: NodeMap<VALUE> and ArcMap<VALUE>

satisfying the \ref DigraphMap concept.

If you want to assign data to nodes, just declare a NodeMap with the corresponding

type. As an example, think of a arc-weighted digraph.

\code ListDigraph::ArcMap<int>  weight(digraph); \endcode

You can see that the map needs the digraph whose arcs will mapped, but nothing more.

If the digraph class is extendable or erasable the map will automatically follow

the changes you make. If a new node is added a default value is mapped to it.

You can define the default value by passing a second argument to the map's constructor.

\code ListDigraph::ArcMap<int>  weight(digraph, 13); \endcode

But keep in mind that \c VALUE has to have copy constructor.

Of course \c VALUE can be a rather complex type.

For practice let's see the following template function (from \ref maps_summary "maps-summary.cc" in the \ref demo directory)!

\dontinclude maps_summary.cc

\skip template

\until }

The task is simple. We need the summary of some kind of data assigned to a digraph's nodes.

(Whit a little trick the summary can be calculated only to a sub-digraph without changing

this code. See \ref SubDigraph techniques - that's LEMON's true potential.)

And the usage is simpler than the declaration suggests. The compiler deduces the

template specialization, so the usage is like a simple function call.

\skip std

\until ;

Most of the time you will probably use digraph maps, but keep in mind, that in LEMON maps are more general and can be used widely.

If you want some 'real-life' examples see the next page, where we discuss \ref algorithms

(coming soon) and will use maps hardly.

Or if you want to know more about maps read these \ref maps2 "advanced map techniques".

Here we discuss some advanced map techniques. Like writing your own maps or how to

extend/modify a maps functionality with adaptors.

\section custom_maps Writing Custom ReadMap

\subsection custom_read_maps Readable Maps

Readable maps are very frequently used as the input of an

algorithm.  For this purpose the most straightforward way is the use of the

default maps provided by LEMON's digraph structures.

Very often however, it is more

convenient and/or more efficient to write your own readable map.

You can find some examples below. In these examples \c Digraph is the

type of the particular digraph structure you use.

This simple map assigns \f$\pi\f$ to each arc.

\code

struct MyMap 

{

  typedef double Value;

  typedef Digraph::Arc Key;

  double operator[](const Key &e) const { return PI;}

};

\endcode

An alternative way to define maps is to use MapBase

\code

struct MyMap : public MapBase<Digraph::Arc,double>

{

  Value operator[](const Key& e) const { return PI;}

};

\endcode

Here is a bit more complex example.

It provides a length function obtained

from a base length function shifted by a potential difference.

\code

class ReducedLengthMap  : public MapBase<Digraph::Arc,double>

{

  const Digraph &g;

  const Digraph::ArcMap<double> &orig_len;

  const Digraph::NodeMap<double> &pot;

public:

  Value operator[](Key e) const {

    return orig_len[e]-(pot[g.target(e)]-pot[g.source(e)]);

  }

  ReducedLengthMap(const Digraph &_g,

                   const Digraph::ArcMap &_o,

                   const Digraph::NodeMap &_p)

    : g(_g), orig_len(_o), pot(_p) {};

};

\endcode

Then, you can call e.g. Dijkstra algoritm on this map like this:

\code

  ...

  ReducedLengthMap rm(g,len,pot);

  Dijkstra<Digraph,ReducedLengthMap> dij(g,rm);

  dij.run(s);

  ...

\endcode

[SEC]sec_map_concepts[SEC] Map Concepts

...

[SEC]sec_own_maps[SEC] Creating Own Maps

...

[SEC]sec_map_adaptors[SEC] Map Adaptors

See \ref map_adaptors in the reference manual.

[SEC]sec_algs_with_maps[SEC] Using Algorithms with Special Maps

The basic functionality of the algorithms can be highly extended using

special purpose map types for their internal data structures.

For example, the \ref Dijkstra class stores a 

ef ProcessedMap,

which has to be a writable node map of \ref bool value type.

The assigned value of each node is set to \ref true when the node is

processed, i.e., its actual distance is found.

Applying a special map, \ref LoggerBoolMap, the processed order of

the nodes can easily be stored in a standard container.

Such specific map types can be passed to the algorithms using the technique of

named template parameters. Similarly to the named function parameters,

they allow specifying any subset of the parameters and in arbitrary order.

Let us suppose that we have a traffic network stored in a LEMON digraph

structure with two arc maps \c length and \c speed, which

denote the physical length of each arc and the maximum (or average)

speed that can be achieved on the corresponding road-section,

respectively. If we are interested in the best traveling times,

the following code can be used.

\code

  dijkstra(g, divMap(length, speed)).distMap(dist).run(s);

\endcode

\code

  typedef vector<ListDigraph::Node> Container;

  typedef back_insert_iterator<Container> InsertIterator;

  typedef LoggerBoolMap<InsertIterator> ProcessedMap;

  Dijkstra<ListDigraph>

    ::SetProcessedMap<ProcessedMap>

    ::Create dijktra(g, length);

  Container container;

  InsertIterator iterator(container);

  ProcessedMap processed(iterator);

  dijkstra.processedMap(processed).run(s);

\endcode

The function-type interfaces are considerably simpler, but they can be

used in almost all practical cases. Surprisingly, even the above example

can also be implemented using the \ref dijkstra() function and

named parameters, as follows.

Note that the function-type interface has the major advantage

that temporary objects can be passed as parameters.

\code

  vector<ListDigraph::Node> process_order;

  dijkstra(g, length)

    .processedMap(loggerBoolMap(back_inserter(process_order)))

    .run(s);

\endcode

Let us see a bit more complex example to demonstrate Dfs's capabilities.

We will see a program, which solves the problem of <b>topological ordering</b>.

We need to know in which order we should put on our clothes. The program will do the following:

<ol>

<li>We run the dfs algorithm to all nodes.

<li>Put every node into a list when processed completely.

<li>Write out the list in reverse order.

</ol>

\dontinclude topological_ordering.cc

First of all we will need an own \ref lemon::Dfs::ProcessedMap "ProcessedMap". The ordering

will be done through it.

\skip MyOrdererMap

\until };

The class meets the \ref concepts::WriteMap "WriteMap" concept. In it's \c set() method the only thing

we need to do is insert the key - that is the node whose processing just finished - into the beginning

of the list.<br>

Although we implemented this needed helper class ourselves it was not necessary.

The \ref lemon::FrontInserterBoolMap "FrontInserterBoolMap" class does exactly

what we needed. To be correct it's more general - and it's all in \c LEMON. But

we wanted to show you, how easy is to add additional functionality.

First we declare the needed data structures: the digraph and a map to store the nodes' label.

\skip ListDigraph

\until label

Now we build a digraph. But keep in mind that it must be DAG because cyclic digraphs has no topological

ordering.

\skip belt

\until trousers

We label them...

\skip label

\until trousers

Then add arcs which represent the precedences between those items.

\skip trousers, belt

\until );

See how easy is to access the internal information of this algorithm trough maps.

We only need to set our own map as the class's \ref lemon::Dfs::ProcessedMap "ProcessedMap".

\skip Dfs

\until run

And now comes the third part. Write out the list in reverse order. But the list was

composed in reverse way (with \c push_front() instead of \c push_back() so we just iterate it.

\skip std

\until endl

The program is to be found in the \ref demo directory: \ref topological_ordering.cc

LEMON also contains visitor based algorithm classes for

BFS and DFS.

Skeleton visitor classes are defined for both BFS and DFS, the concrete

implementations can be inherited from them.

\code

  template <typename GR>

  struct DfsVisitor {

    void start(const typename GR::Node& node) {}

    void stop(const typename GR::Node& node) {}

    void reach(const typename GR::Node& node) {}

    void leave(const typename GR::Node& node) {}

    void discover(const typename GR::Arc& arc) {}

    void examine(const typename GR::Arc& arc) {}

    void backtrack(const typename GR::Arc& arc) {}

  };

\endcode

In the following example, the \ref discover()} and \code{examine()

events are processed and the DFS tree is stored in an arc map.

The values of this map indicate whether the corresponding arc

reaches a new node or its target node is already reached.

\code

  template <typename GR>

  struct TreeVisitor : public DfsVisitor<GR> {

    TreeVisitor(typename GR::ArcMap<bool>& tree)

      : _tree(tree) {}

    void discover(const typename GR::Arc& arc)

      { _tree[arc] = true; }

    void examine(const typename GR::Arc& arc)

      { _tree[arc] = false; }

    typename GR::ArcMap<bool>& _tree;

  };

\endcode

[TRAILER]

*/

}