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kpeter (Peter Kovacs)
kpeter@inf.elte.hu
Small doc fixes and improvements (#359)
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LEMON code without an explicit copyright notice is covered by the following
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copyright/license.
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Copyright (C) 2003-2009 Egervary Jeno Kombinatorikus Optimalizalasi
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Copyright (C) 2003-2010 Egervary Jeno Kombinatorikus Optimalizalasi
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Kutatocsoport (Egervary Combinatorial Optimization Research Group,
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EGRES).
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===========================================================================
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Boost Software License, Version 1.0
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===========================================================================
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Permission is hereby granted, free of charge, to any person or organization
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obtaining a copy of the software and accompanying documentation covered by
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this license (the "Software") to use, reproduce, display, distribute,
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execute, and transmit the Software, and to prepare derivative works of the
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Software, and to permit third-parties to whom the Software is furnished to
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do so, all subject to the following:
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The copyright notices in the Software and this entire statement, including
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the above license grant, this restriction and the following disclaimer,
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must be included in all copies of the Software, in whole or in part, and
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all derivative works of the Software, unless such copies or derivative
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works are solely in the form of machine-executable object code generated by
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a source language processor.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
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SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
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ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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DEALINGS IN THE SOFTWARE.
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2010
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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namespace lemon {
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/**
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@defgroup datas Data Structures
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This group contains the several data structures implemented in LEMON.
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*/
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/**
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@defgroup graphs Graph Structures
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@ingroup datas
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\brief Graph structures implemented in LEMON.
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The implementation of combinatorial algorithms heavily relies on
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efficient graph implementations. LEMON offers data structures which are
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planned to be easily used in an experimental phase of implementation studies,
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and thereafter the program code can be made efficient by small modifications.
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The most efficient implementation of diverse applications require the
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usage of different physical graph implementations. These differences
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appear in the size of graph we require to handle, memory or time usage
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limitations or in the set of operations through which the graph can be
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accessed.  LEMON provides several physical graph structures to meet
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the diverging requirements of the possible users.  In order to save on
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running time or on memory usage, some structures may fail to provide
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some graph features like arc/edge or node deletion.
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Alteration of standard containers need a very limited number of
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operations, these together satisfy the everyday requirements.
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In the case of graph structures, different operations are needed which do
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not alter the physical graph, but gives another view. If some nodes or
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arcs have to be hidden or the reverse oriented graph have to be used, then
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this is the case. It also may happen that in a flow implementation
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the residual graph can be accessed by another algorithm, or a node-set
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is to be shrunk for another algorithm.
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LEMON also provides a variety of graphs for these requirements called
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\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
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in conjunction with other graph representations.
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You are free to use the graph structure that fit your requirements
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the best, most graph algorithms and auxiliary data structures can be used
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with any graph structure.
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<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
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*/
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/**
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@defgroup graph_adaptors Adaptor Classes for Graphs
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@ingroup graphs
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\brief Adaptor classes for digraphs and graphs
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This group contains several useful adaptor classes for digraphs and graphs.
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The main parts of LEMON are the different graph structures, generic
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graph algorithms, graph concepts, which couple them, and graph
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adaptors. While the previous notions are more or less clear, the
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latter one needs further explanation. Graph adaptors are graph classes
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which serve for considering graph structures in different ways.
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A short example makes this much clearer.  Suppose that we have an
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instance \c g of a directed graph type, say ListDigraph and an algorithm
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\code
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template <typename Digraph>
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int algorithm(const Digraph&);
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\endcode
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is needed to run on the reverse oriented graph.  It may be expensive
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(in time or in memory usage) to copy \c g with the reversed
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arcs.  In this case, an adaptor class is used, which (according
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to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
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The adaptor uses the original digraph structure and digraph operations when
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methods of the reversed oriented graph are called.  This means that the adaptor
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have minor memory usage, and do not perform sophisticated algorithmic
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actions.  The purpose of it is to give a tool for the cases when a
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graph have to be used in a specific alteration.  If this alteration is
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obtained by a usual construction like filtering the node or the arc set or
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considering a new orientation, then an adaptor is worthwhile to use.
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To come back to the reverse oriented graph, in this situation
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\code
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template<typename Digraph> class ReverseDigraph;
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\endcode
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template class can be used. The code looks as follows
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\code
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ListDigraph g;
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ReverseDigraph<ListDigraph> rg(g);
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int result = algorithm(rg);
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\endcode
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During running the algorithm, the original digraph \c g is untouched.
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This techniques give rise to an elegant code, and based on stable
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graph adaptors, complex algorithms can be implemented easily.
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In flow, circulation and matching problems, the residual
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graph is of particular importance. Combining an adaptor implementing
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this with shortest path algorithms or minimum mean cycle algorithms,
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a range of weighted and cardinality optimization algorithms can be
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obtained. For other examples, the interested user is referred to the
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detailed documentation of particular adaptors.
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The behavior of graph adaptors can be very different. Some of them keep
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capabilities of the original graph while in other cases this would be
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meaningless. This means that the concepts that they meet depend
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on the graph adaptor, and the wrapped graph.
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For example, if an arc of a reversed digraph is deleted, this is carried
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out by deleting the corresponding arc of the original digraph, thus the
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adaptor modifies the original digraph.
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However in case of a residual digraph, this operation has no sense.
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Let us stand one more example here to simplify your work.
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ReverseDigraph has constructor
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\code
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ReverseDigraph(Digraph& digraph);
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\endcode
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This means that in a situation, when a <tt>const %ListDigraph&</tt>
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reference to a graph is given, then it have to be instantiated with
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<tt>Digraph=const %ListDigraph</tt>.
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\code
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int algorithm1(const ListDigraph& g) {
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  ReverseDigraph<const ListDigraph> rg(g);
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  return algorithm2(rg);
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}
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\endcode
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*/
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/**
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@defgroup maps Maps
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@ingroup datas
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\brief Map structures implemented in LEMON.
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This group contains the map structures implemented in LEMON.
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LEMON provides several special purpose maps and map adaptors that e.g. combine
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new maps from existing ones.
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<b>See also:</b> \ref map_concepts "Map Concepts".
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*/
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/**
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@defgroup graph_maps Graph Maps
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@ingroup maps
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\brief Special graph-related maps.
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This group contains maps that are specifically designed to assign
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values to the nodes and arcs/edges of graphs.
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If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
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\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
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*/
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/**
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\defgroup map_adaptors Map Adaptors
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\ingroup maps
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\brief Tools to create new maps from existing ones
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This group contains map adaptors that are used to create "implicit"
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maps from other maps.
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Most of them are \ref concepts::ReadMap "read-only maps".
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They can make arithmetic and logical operations between one or two maps
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(negation, shifting, addition, multiplication, logical 'and', 'or',
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'not' etc.) or e.g. convert a map to another one of different Value type.
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The typical usage of this classes is passing implicit maps to
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algorithms.  If a function type algorithm is called then the function
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type map adaptors can be used comfortable. For example let's see the
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usage of map adaptors with the \c graphToEps() function.
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\code
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  Color nodeColor(int deg) {
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    if (deg >= 2) {
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      return Color(0.5, 0.0, 0.5);
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    } else if (deg == 1) {
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      return Color(1.0, 0.5, 1.0);
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    } else {
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      return Color(0.0, 0.0, 0.0);
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    }
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  }
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  Digraph::NodeMap<int> degree_map(graph);
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  graphToEps(graph, "graph.eps")
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    .coords(coords).scaleToA4().undirected()
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    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
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    .run();
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\endcode
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The \c functorToMap() function makes an \c int to \c Color map from the
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\c nodeColor() function. The \c composeMap() compose the \c degree_map
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and the previously created map. The composed map is a proper function to
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get the color of each node.
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The usage with class type algorithms is little bit harder. In this
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case the function type map adaptors can not be used, because the
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function map adaptors give back temporary objects.
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\code
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  Digraph graph;
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  typedef Digraph::ArcMap<double> DoubleArcMap;
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  DoubleArcMap length(graph);
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  DoubleArcMap speed(graph);
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  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
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  TimeMap time(length, speed);
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  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
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  dijkstra.run(source, target);
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\endcode
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We have a length map and a maximum speed map on the arcs of a digraph.
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The minimum time to pass the arc can be calculated as the division of
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the two maps which can be done implicitly with the \c DivMap template
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class. We use the implicit minimum time map as the length map of the
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\c Dijkstra algorithm.
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*/
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/**
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@defgroup paths Path Structures
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@ingroup datas
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\brief %Path structures implemented in LEMON.
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This group contains the path structures implemented in LEMON.
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LEMON provides flexible data structures to work with paths.
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All of them have similar interfaces and they can be copied easily with
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assignment operators and copy constructors. This makes it easy and
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efficient to have e.g. the Dijkstra algorithm to store its result in
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any kind of path structure.
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\sa \ref concepts::Path "Path concept"
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*/
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/**
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@defgroup heaps Heap Structures
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@ingroup datas
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\brief %Heap structures implemented in LEMON.
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This group contains the heap structures implemented in LEMON.
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LEMON provides several heap classes. They are efficient implementations
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of the abstract data type \e priority \e queue. They store items with
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specified values called \e priorities in such a way that finding and
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removing the item with minimum priority are efficient.
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The basic operations are adding and erasing items, changing the priority
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of an item, etc.
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Heaps are crucial in several algorithms, such as Dijkstra and Prim.
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The heap implementations have the same interface, thus any of them can be
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used easily in such algorithms.
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\sa \ref concepts::Heap "Heap concept"
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*/
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/**
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@defgroup matrices Matrices
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@ingroup datas
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\brief Two dimensional data storages implemented in LEMON.
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This group contains two dimensional data storages implemented in LEMON.
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*/
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/**
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@defgroup auxdat Auxiliary Data Structures
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@ingroup datas
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\brief Auxiliary data structures implemented in LEMON.
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This group contains some data structures implemented in LEMON in
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order to make it easier to implement combinatorial algorithms.
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*/
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/**
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@defgroup geomdat Geometric Data Structures
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@ingroup auxdat
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\brief Geometric data structures implemented in LEMON.
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This group contains geometric data structures implemented in LEMON.
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 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
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   vector with the usual operations.
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 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
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   rectangular bounding box of a set of \ref lemon::dim2::Point
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   "dim2::Point"'s.
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*/
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/**
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@defgroup matrices Matrices
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@ingroup auxdat
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\brief Two dimensional data storages implemented in LEMON.
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This group contains two dimensional data storages implemented in LEMON.
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*/
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/**
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@defgroup algs Algorithms
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\brief This group contains the several algorithms
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implemented in LEMON.
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309 301
This group contains the several algorithms
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implemented in LEMON.
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*/
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/**
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@defgroup search Graph Search
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@ingroup algs
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\brief Common graph search algorithms.
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This group contains the common graph search algorithms, namely
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\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
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\ref clrs01algorithms.
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*/
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/**
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@defgroup shortest_path Shortest Path Algorithms
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@ingroup algs
326 318
\brief Algorithms for finding shortest paths.
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This group contains the algorithms for finding shortest paths in digraphs
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\ref clrs01algorithms.
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 - \ref Dijkstra algorithm for finding shortest paths from a source node
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   when all arc lengths are non-negative.
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 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
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   from a source node when arc lenghts can be either positive or negative,
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   but the digraph should not contain directed cycles with negative total
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   length.
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 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
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   for solving the \e all-pairs \e shortest \e paths \e problem when arc
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   lenghts can be either positive or negative, but the digraph should
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   not contain directed cycles with negative total length.
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 - \ref Suurballe A successive shortest path algorithm for finding
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   arc-disjoint paths between two nodes having minimum total length.
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*/
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/**
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@defgroup spantree Minimum Spanning Tree Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cost spanning trees and arborescences.
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350 342
This group contains the algorithms for finding minimum cost spanning
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trees and arborescences \ref clrs01algorithms.
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*/
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/**
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@defgroup max_flow Maximum Flow Algorithms
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@ingroup algs
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\brief Algorithms for finding maximum flows.
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This group contains the algorithms for finding maximum flows and
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feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
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The \e maximum \e flow \e problem is to find a flow of maximum value between
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a single source and a single target. Formally, there is a \f$G=(V,A)\f$
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digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
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\f$s, t \in V\f$ source and target nodes.
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A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
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following optimization problem.
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369 361
\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
370 362
\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
371 363
    \quad \forall u\in V\setminus\{s,t\} \f]
372 364
\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
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LEMON contains several algorithms for solving maximum flow problems:
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- \ref EdmondsKarp Edmonds-Karp algorithm
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  \ref edmondskarp72theoretical.
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- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
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  \ref goldberg88newapproach.
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- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
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  \ref dinic70algorithm, \ref sleator83dynamic.
381 373
- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
382 374
  \ref goldberg88newapproach, \ref sleator83dynamic.
383 375

	
384 376
In most cases the \ref Preflow algorithm provides the
385 377
fastest method for computing a maximum flow. All implementations
386 378
also provide functions to query the minimum cut, which is the dual
387 379
problem of maximum flow.
388 380

	
389 381
\ref Circulation is a preflow push-relabel algorithm implemented directly
390 382
for finding feasible circulations, which is a somewhat different problem,
391 383
but it is strongly related to maximum flow.
392 384
For more information, see \ref Circulation.
393 385
*/
394 386

	
395 387
/**
396 388
@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
397 389
@ingroup algs
398 390

	
399 391
\brief Algorithms for finding minimum cost flows and circulations.
400 392

	
401 393
This group contains the algorithms for finding minimum cost flows and
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circulations \ref amo93networkflows. For more information about this
403 395
problem and its dual solution, see \ref min_cost_flow
404 396
"Minimum Cost Flow Problem".
405 397

	
406 398
LEMON contains several algorithms for this problem.
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 - \ref NetworkSimplex Primal Network Simplex algorithm with various
408 400
   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
409 401
 - \ref CostScaling Cost Scaling algorithm based on push/augment and
410 402
   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
411 403
   \ref bunnagel98efficient.
412 404
 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
413 405
   shortest path method \ref edmondskarp72theoretical.
414 406
 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
415 407
   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
416 408

	
417 409
In general NetworkSimplex is the most efficient implementation,
418 410
but in special cases other algorithms could be faster.
419 411
For example, if the total supply and/or capacities are rather small,
420 412
CapacityScaling is usually the fastest algorithm (without effective scaling).
421 413
*/
422 414

	
423 415
/**
424 416
@defgroup min_cut Minimum Cut Algorithms
425 417
@ingroup algs
426 418

	
427 419
\brief Algorithms for finding minimum cut in graphs.
428 420

	
429 421
This group contains the algorithms for finding minimum cut in graphs.
430 422

	
431 423
The \e minimum \e cut \e problem is to find a non-empty and non-complete
432 424
\f$X\f$ subset of the nodes with minimum overall capacity on
433 425
outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
434 426
\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
435 427
cut is the \f$X\f$ solution of the next optimization problem:
436 428

	
437 429
\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
438 430
    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
439 431

	
440 432
LEMON contains several algorithms related to minimum cut problems:
441 433

	
442 434
- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
443 435
  in directed graphs.
444 436
- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
445 437
  calculating minimum cut in undirected graphs.
446 438
- \ref GomoryHu "Gomory-Hu tree computation" for calculating
447 439
  all-pairs minimum cut in undirected graphs.
448 440

	
449 441
If you want to find minimum cut just between two distinict nodes,
450 442
see the \ref max_flow "maximum flow problem".
451 443
*/
452 444

	
453 445
/**
454 446
@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
455 447
@ingroup algs
456 448
\brief Algorithms for finding minimum mean cycles.
457 449

	
458 450
This group contains the algorithms for finding minimum mean cycles
459 451
\ref clrs01algorithms, \ref amo93networkflows.
460 452

	
461 453
The \e minimum \e mean \e cycle \e problem is to find a directed cycle
462 454
of minimum mean length (cost) in a digraph.
463 455
The mean length of a cycle is the average length of its arcs, i.e. the
464 456
ratio between the total length of the cycle and the number of arcs on it.
465 457

	
466 458
This problem has an important connection to \e conservative \e length
467 459
\e functions, too. A length function on the arcs of a digraph is called
468 460
conservative if and only if there is no directed cycle of negative total
469 461
length. For an arbitrary length function, the negative of the minimum
470 462
cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
471 463
arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
472 464
function.
473 465

	
474 466
LEMON contains three algorithms for solving the minimum mean cycle problem:
475
- \ref Karp "Karp"'s original algorithm \ref amo93networkflows,
467
- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
476 468
  \ref dasdan98minmeancycle.
477
- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
469
- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
478 470
  version of Karp's algorithm \ref dasdan98minmeancycle.
479
- \ref Howard "Howard"'s policy iteration algorithm
471
- \ref HowardMmc Howard's policy iteration algorithm
480 472
  \ref dasdan98minmeancycle.
481 473

	
482
In practice, the Howard algorithm proved to be by far the most efficient
483
one, though the best known theoretical bound on its running time is
484
exponential.
485
Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
486
O(n<sup>2</sup>+e), but the latter one is typically faster due to the
487
applied early termination scheme.
474
In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
475
most efficient one, though the best known theoretical bound on its running
476
time is exponential.
477
Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
478
run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
479
typically faster due to the applied early termination scheme.
488 480
*/
489 481

	
490 482
/**
491 483
@defgroup matching Matching Algorithms
492 484
@ingroup algs
493 485
\brief Algorithms for finding matchings in graphs and bipartite graphs.
494 486

	
495 487
This group contains the algorithms for calculating
496 488
matchings in graphs and bipartite graphs. The general matching problem is
497 489
finding a subset of the edges for which each node has at most one incident
498 490
edge.
499 491

	
500 492
There are several different algorithms for calculate matchings in
501 493
graphs.  The matching problems in bipartite graphs are generally
502 494
easier than in general graphs. The goal of the matching optimization
503 495
can be finding maximum cardinality, maximum weight or minimum cost
504 496
matching. The search can be constrained to find perfect or
505 497
maximum cardinality matching.
506 498

	
507 499
The matching algorithms implemented in LEMON:
508 500
- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
509 501
  for calculating maximum cardinality matching in bipartite graphs.
510 502
- \ref PrBipartiteMatching Push-relabel algorithm
511 503
  for calculating maximum cardinality matching in bipartite graphs.
512 504
- \ref MaxWeightedBipartiteMatching
513 505
  Successive shortest path algorithm for calculating maximum weighted
514 506
  matching and maximum weighted bipartite matching in bipartite graphs.
515 507
- \ref MinCostMaxBipartiteMatching
516 508
  Successive shortest path algorithm for calculating minimum cost maximum
517 509
  matching in bipartite graphs.
518 510
- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
519 511
  maximum cardinality matching in general graphs.
520 512
- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
521 513
  maximum weighted matching in general graphs.
522 514
- \ref MaxWeightedPerfectMatching
523 515
  Edmond's blossom shrinking algorithm for calculating maximum weighted
524 516
  perfect matching in general graphs.
525 517
- \ref MaxFractionalMatching Push-relabel algorithm for calculating
526 518
  maximum cardinality fractional matching in general graphs.
527 519
- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
528 520
  maximum weighted fractional matching in general graphs.
529 521
- \ref MaxWeightedPerfectFractionalMatching
530 522
  Augmenting path algorithm for calculating maximum weighted
531 523
  perfect fractional matching in general graphs.
532 524

	
533 525
\image html matching.png
534 526
\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
535 527
*/
536 528

	
537 529
/**
538 530
@defgroup graph_properties Connectivity and Other Graph Properties
539 531
@ingroup algs
540 532
\brief Algorithms for discovering the graph properties
541 533

	
542 534
This group contains the algorithms for discovering the graph properties
543 535
like connectivity, bipartiteness, euler property, simplicity etc.
544 536

	
545 537
\image html connected_components.png
546 538
\image latex connected_components.eps "Connected components" width=\textwidth
547 539
*/
548 540

	
549 541
/**
550 542
@defgroup planar Planarity Embedding and Drawing
551 543
@ingroup algs
552 544
\brief Algorithms for planarity checking, embedding and drawing
553 545

	
554 546
This group contains the algorithms for planarity checking,
555 547
embedding and drawing.
556 548

	
557 549
\image html planar.png
558 550
\image latex planar.eps "Plane graph" width=\textwidth
559 551
*/
560 552

	
561 553
/**
562 554
@defgroup approx Approximation Algorithms
563 555
@ingroup algs
564 556
\brief Approximation algorithms.
565 557

	
566 558
This group contains the approximation and heuristic algorithms
567 559
implemented in LEMON.
568 560
*/
569 561

	
570 562
/**
571 563
@defgroup auxalg Auxiliary Algorithms
572 564
@ingroup algs
573 565
\brief Auxiliary algorithms implemented in LEMON.
574 566

	
575 567
This group contains some algorithms implemented in LEMON
576 568
in order to make it easier to implement complex algorithms.
577 569
*/
578 570

	
579 571
/**
580 572
@defgroup gen_opt_group General Optimization Tools
581 573
\brief This group contains some general optimization frameworks
582 574
implemented in LEMON.
583 575

	
584 576
This group contains some general optimization frameworks
585 577
implemented in LEMON.
586 578
*/
587 579

	
588 580
/**
589 581
@defgroup lp_group LP and MIP Solvers
590 582
@ingroup gen_opt_group
591 583
\brief LP and MIP solver interfaces for LEMON.
592 584

	
593 585
This group contains LP and MIP solver interfaces for LEMON.
594 586
Various LP solvers could be used in the same manner with this
595 587
high-level interface.
596 588

	
597 589
The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
598 590
\ref cplex, \ref soplex.
599 591
*/
600 592

	
601 593
/**
602 594
@defgroup lp_utils Tools for Lp and Mip Solvers
603 595
@ingroup lp_group
604 596
\brief Helper tools to the Lp and Mip solvers.
605 597

	
606 598
This group adds some helper tools to general optimization framework
607 599
implemented in LEMON.
608 600
*/
609 601

	
610 602
/**
611 603
@defgroup metah Metaheuristics
612 604
@ingroup gen_opt_group
613 605
\brief Metaheuristics for LEMON library.
614 606

	
615 607
This group contains some metaheuristic optimization tools.
616 608
*/
617 609

	
618 610
/**
619 611
@defgroup utils Tools and Utilities
620 612
\brief Tools and utilities for programming in LEMON
621 613

	
622 614
Tools and utilities for programming in LEMON.
623 615
*/
624 616

	
625 617
/**
626 618
@defgroup gutils Basic Graph Utilities
627 619
@ingroup utils
628 620
\brief Simple basic graph utilities.
629 621

	
630 622
This group contains some simple basic graph utilities.
631 623
*/
632 624

	
633 625
/**
634 626
@defgroup misc Miscellaneous Tools
635 627
@ingroup utils
636 628
\brief Tools for development, debugging and testing.
637 629

	
638 630
This group contains several useful tools for development,
639 631
debugging and testing.
640 632
*/
641 633

	
642 634
/**
643 635
@defgroup timecount Time Measuring and Counting
644 636
@ingroup misc
645 637
\brief Simple tools for measuring the performance of algorithms.
646 638

	
647 639
This group contains simple tools for measuring the performance
648 640
of algorithms.
649 641
*/
650 642

	
651 643
/**
652 644
@defgroup exceptions Exceptions
653 645
@ingroup utils
654 646
\brief Exceptions defined in LEMON.
655 647

	
656 648
This group contains the exceptions defined in LEMON.
657 649
*/
658 650

	
659 651
/**
660 652
@defgroup io_group Input-Output
661 653
\brief Graph Input-Output methods
662 654

	
663 655
This group contains the tools for importing and exporting graphs
664 656
and graph related data. Now it supports the \ref lgf-format
665 657
"LEMON Graph Format", the \c DIMACS format and the encapsulated
666 658
postscript (EPS) format.
667 659
*/
668 660

	
669 661
/**
670 662
@defgroup lemon_io LEMON Graph Format
671 663
@ingroup io_group
672 664
\brief Reading and writing LEMON Graph Format.
673 665

	
674 666
This group contains methods for reading and writing
675 667
\ref lgf-format "LEMON Graph Format".
676 668
*/
677 669

	
678 670
/**
679 671
@defgroup eps_io Postscript Exporting
680 672
@ingroup io_group
681 673
\brief General \c EPS drawer and graph exporter
682 674

	
683 675
This group contains general \c EPS drawing methods and special
684 676
graph exporting tools.
685 677
*/
686 678

	
687 679
/**
688 680
@defgroup dimacs_group DIMACS Format
689 681
@ingroup io_group
690 682
\brief Read and write files in DIMACS format
691 683

	
692 684
Tools to read a digraph from or write it to a file in DIMACS format data.
693 685
*/
694 686

	
695 687
/**
696 688
@defgroup nauty_group NAUTY Format
697 689
@ingroup io_group
698 690
\brief Read \e Nauty format
699 691

	
700 692
Tool to read graphs from \e Nauty format data.
701 693
*/
702 694

	
703 695
/**
704 696
@defgroup concept Concepts
705 697
\brief Skeleton classes and concept checking classes
706 698

	
707 699
This group contains the data/algorithm skeletons and concept checking
708 700
classes implemented in LEMON.
709 701

	
710 702
The purpose of the classes in this group is fourfold.
711 703

	
712 704
- These classes contain the documentations of the %concepts. In order
713 705
  to avoid document multiplications, an implementation of a concept
714 706
  simply refers to the corresponding concept class.
715 707

	
716 708
- These classes declare every functions, <tt>typedef</tt>s etc. an
717 709
  implementation of the %concepts should provide, however completely
718 710
  without implementations and real data structures behind the
719 711
  interface. On the other hand they should provide nothing else. All
720 712
  the algorithms working on a data structure meeting a certain concept
721 713
  should compile with these classes. (Though it will not run properly,
722 714
  of course.) In this way it is easily to check if an algorithm
723 715
  doesn't use any extra feature of a certain implementation.
724 716

	
725 717
- The concept descriptor classes also provide a <em>checker class</em>
726 718
  that makes it possible to check whether a certain implementation of a
727 719
  concept indeed provides all the required features.
728 720

	
729 721
- Finally, They can serve as a skeleton of a new implementation of a concept.
730 722
*/
731 723

	
732 724
/**
733 725
@defgroup graph_concepts Graph Structure Concepts
734 726
@ingroup concept
735 727
\brief Skeleton and concept checking classes for graph structures
736 728

	
737 729
This group contains the skeletons and concept checking classes of
738 730
graph structures.
739 731
*/
740 732

	
741 733
/**
742 734
@defgroup map_concepts Map Concepts
743 735
@ingroup concept
744 736
\brief Skeleton and concept checking classes for maps
745 737

	
746 738
This group contains the skeletons and concept checking classes of maps.
747 739
*/
748 740

	
749 741
/**
750 742
@defgroup tools Standalone Utility Applications
751 743

	
752 744
Some utility applications are listed here.
753 745

	
754 746
The standard compilation procedure (<tt>./configure;make</tt>) will compile
755 747
them, as well.
756 748
*/
757 749

	
758 750
/**
759 751
\anchor demoprograms
760 752

	
761 753
@defgroup demos Demo Programs
762 754

	
763 755
Some demo programs are listed here. Their full source codes can be found in
764 756
the \c demo subdirectory of the source tree.
765 757

	
766 758
In order to compile them, use the <tt>make demo</tt> or the
767 759
<tt>make check</tt> commands.
768 760
*/
769 761

	
770 762
}
Ignore white space 6 line context
1 1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 2
 *
3 3
 * This file is a part of LEMON, a generic C++ optimization library.
4 4
 *
5 5
 * Copyright (C) 2003-2010
6 6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 8
 *
9 9
 * Permission to use, modify and distribute this software is granted
10 10
 * provided that this copyright notice appears in all copies. For
11 11
 * precise terms see the accompanying LICENSE file.
12 12
 *
13 13
 * This software is provided "AS IS" with no warranty of any kind,
14 14
 * express or implied, and with no claim as to its suitability for any
15 15
 * purpose.
16 16
 *
17 17
 */
18 18

	
19 19
#ifndef LEMON_ARG_PARSER_H
20 20
#define LEMON_ARG_PARSER_H
21 21

	
22 22
#include <vector>
23 23
#include <map>
24 24
#include <list>
25 25
#include <string>
26 26
#include <iostream>
27 27
#include <sstream>
28 28
#include <algorithm>
29 29
#include <lemon/assert.h>
30 30

	
31 31
///\ingroup misc
32 32
///\file
33 33
///\brief A tool to parse command line arguments.
34 34

	
35 35
namespace lemon {
36 36

	
37 37
  ///Exception used by ArgParser
38

	
39
  ///Exception used by ArgParser.
40
  ///
38 41
  class ArgParserException : public Exception {
39 42
  public:
43
    /// Reasons for failure
44

	
45
    /// Reasons for failure.
46
    ///
40 47
    enum Reason {
41
      HELP,         /// <tt>--help</tt> option was given
42
      UNKNOWN_OPT,  /// Unknown option was given
43
      INVALID_OPT   /// Invalid combination of options
48
      HELP,         ///< <tt>--help</tt> option was given.
49
      UNKNOWN_OPT,  ///< Unknown option was given.
50
      INVALID_OPT   ///< Invalid combination of options.
44 51
    };
45 52

	
46 53
  private:
47 54
    Reason _reason;
48 55

	
49 56
  public:
50 57
    ///Constructor
51 58
    ArgParserException(Reason r) throw() : _reason(r) {}
52 59
    ///Virtual destructor
53 60
    virtual ~ArgParserException() throw() {}
54 61
    ///A short description of the exception
55 62
    virtual const char* what() const throw() {
56 63
      switch(_reason)
57 64
        {
58 65
        case HELP:
59 66
          return "lemon::ArgParseException: ask for help";
60 67
          break;
61 68
        case UNKNOWN_OPT:
62 69
          return "lemon::ArgParseException: unknown option";
63 70
          break;
64 71
        case INVALID_OPT:
65 72
          return "lemon::ArgParseException: invalid combination of options";
66 73
          break;
67 74
        }
68 75
      return "";
69 76
    }
70 77
    ///Return the reason for the failure
71 78
    Reason reason() const {return _reason; }
72 79
  };
73 80

	
74 81

	
75 82
  ///Command line arguments parser
76 83

	
77 84
  ///\ingroup misc
78 85
  ///Command line arguments parser.
79 86
  ///
80 87
  ///For a complete example see the \ref arg_parser_demo.cc demo file.
81 88
  class ArgParser {
82 89

	
83 90
    static void _showHelp(void *p);
84 91
  protected:
85 92

	
86 93
    int _argc;
87 94
    const char * const *_argv;
88 95

	
89 96
    enum OptType { UNKNOWN=0, BOOL=1, STRING=2, DOUBLE=3, INTEGER=4, FUNC=5 };
90 97

	
91 98
    class ParData {
92 99
    public:
93 100
      union {
94 101
        bool *bool_p;
95 102
        int *int_p;
96 103
        double *double_p;
97 104
        std::string *string_p;
98 105
        struct {
99 106
          void (*p)(void *);
100 107
          void *data;
101 108
        } func_p;
102 109

	
103 110
      };
104 111
      std::string help;
105 112
      bool mandatory;
106 113
      OptType type;
107 114
      bool set;
108 115
      bool ingroup;
109 116
      bool has_syn;
110 117
      bool syn;
111 118
      bool self_delete;
112 119
      ParData() : mandatory(false), type(UNKNOWN), set(false), ingroup(false),
113 120
                  has_syn(false), syn(false), self_delete(false) {}
114 121
    };
115 122

	
116 123
    typedef std::map<std::string,ParData> Opts;
117 124
    Opts _opts;
118 125

	
119 126
    class GroupData
120 127
    {
121 128
    public:
122 129
      typedef std::list<std::string> Opts;
123 130
      Opts opts;
124 131
      bool only_one;
125 132
      bool mandatory;
126 133
      GroupData() :only_one(false), mandatory(false) {}
127 134
    };
128 135

	
129 136
    typedef std::map<std::string,GroupData> Groups;
130 137
    Groups _groups;
131 138

	
132 139
    struct OtherArg
133 140
    {
134 141
      std::string name;
135 142
      std::string help;
136 143
      OtherArg(std::string n, std::string h) :name(n), help(h) {}
137 144

	
138 145
    };
139 146

	
140 147
    std::vector<OtherArg> _others_help;
141 148
    std::vector<std::string> _file_args;
142 149
    std::string _command_name;
143 150

	
144 151

	
145 152
  private:
146 153
    //Bind a function to an option.
147 154

	
148 155
    //\param name The name of the option. The leading '-' must be omitted.
149 156
    //\param help A help string.
150 157
    //\retval func The function to be called when the option is given. It
151 158
    //  must be of type "void f(void *)"
152 159
    //\param data Data to be passed to \c func
153 160
    ArgParser &funcOption(const std::string &name,
154 161
                    const std::string &help,
155 162
                    void (*func)(void *),void *data);
156 163

	
157 164
    bool _exit_on_problems;
158 165

	
159 166
    void _terminate(ArgParserException::Reason reason) const;
160 167

	
161 168
  public:
162 169

	
163 170
    ///Constructor
164 171
    ArgParser(int argc, const char * const *argv);
165 172

	
166 173
    ~ArgParser();
167 174

	
168 175
    ///\name Options
169 176
    ///
170 177

	
171 178
    ///@{
172 179

	
173 180
    ///Add a new integer type option
174 181

	
175 182
    ///Add a new integer type option.
176 183
    ///\param name The name of the option. The leading '-' must be omitted.
177 184
    ///\param help A help string.
178 185
    ///\param value A default value for the option.
179 186
    ///\param obl Indicate if the option is mandatory.
180 187
    ArgParser &intOption(const std::string &name,
181 188
                    const std::string &help,
182 189
                    int value=0, bool obl=false);
183 190

	
184 191
    ///Add a new floating point type option
185 192

	
186 193
    ///Add a new floating point type option.
187 194
    ///\param name The name of the option. The leading '-' must be omitted.
188 195
    ///\param help A help string.
189 196
    ///\param value A default value for the option.
190 197
    ///\param obl Indicate if the option is mandatory.
191 198
    ArgParser &doubleOption(const std::string &name,
192 199
                      const std::string &help,
193 200
                      double value=0, bool obl=false);
194 201

	
195 202
    ///Add a new bool type option
196 203

	
197 204
    ///Add a new bool type option.
198 205
    ///\param name The name of the option. The leading '-' must be omitted.
199 206
    ///\param help A help string.
200 207
    ///\param value A default value for the option.
201 208
    ///\param obl Indicate if the option is mandatory.
202 209
    ///\note A mandatory bool obtion is of very little use.
203 210
    ArgParser &boolOption(const std::string &name,
204 211
                      const std::string &help,
205 212
                      bool value=false, bool obl=false);
206 213

	
207 214
    ///Add a new string type option
208 215

	
209 216
    ///Add a new string type option.
210 217
    ///\param name The name of the option. The leading '-' must be omitted.
211 218
    ///\param help A help string.
212 219
    ///\param value A default value for the option.
213 220
    ///\param obl Indicate if the option is mandatory.
214 221
    ArgParser &stringOption(const std::string &name,
215 222
                      const std::string &help,
216 223
                      std::string value="", bool obl=false);
217 224

	
218 225
    ///Give help string for non-parsed arguments.
219 226

	
220 227
    ///With this function you can give help string for non-parsed arguments.
221 228
    ///The parameter \c name will be printed in the short usage line, while
222 229
    ///\c help gives a more detailed description.
223 230
    ArgParser &other(const std::string &name,
224 231
                     const std::string &help="");
225 232

	
226 233
    ///@}
227 234

	
228 235
    ///\name Options with External Storage
229 236
    ///Using this functions, the value of the option will be directly written
230 237
    ///into a variable once the option appears in the command line.
231 238

	
232 239
    ///@{
233 240

	
234 241
    ///Add a new integer type option with a storage reference
235 242

	
236 243
    ///Add a new integer type option with a storage reference.
237 244
    ///\param name The name of the option. The leading '-' must be omitted.
238 245
    ///\param help A help string.
239 246
    ///\param obl Indicate if the option is mandatory.
240 247
    ///\retval ref The value of the argument will be written to this variable.
241 248
    ArgParser &refOption(const std::string &name,
242 249
                    const std::string &help,
243 250
                    int &ref, bool obl=false);
244 251

	
245 252
    ///Add a new floating type option with a storage reference
246 253

	
247 254
    ///Add a new floating type option with a storage reference.
248 255
    ///\param name The name of the option. The leading '-' must be omitted.
249 256
    ///\param help A help string.
250 257
    ///\param obl Indicate if the option is mandatory.
251 258
    ///\retval ref The value of the argument will be written to this variable.
252 259
    ArgParser &refOption(const std::string &name,
253 260
                      const std::string &help,
254 261
                      double &ref, bool obl=false);
255 262

	
256 263
    ///Add a new bool type option with a storage reference
257 264

	
258 265
    ///Add a new bool type option with a storage reference.
259 266
    ///\param name The name of the option. The leading '-' must be omitted.
260 267
    ///\param help A help string.
261 268
    ///\param obl Indicate if the option is mandatory.
262 269
    ///\retval ref The value of the argument will be written to this variable.
263 270
    ///\note A mandatory bool obtion is of very little use.
264 271
    ArgParser &refOption(const std::string &name,
265 272
                      const std::string &help,
266 273
                      bool &ref, bool obl=false);
267 274

	
268 275
    ///Add a new string type option with a storage reference
269 276

	
270 277
    ///Add a new string type option with a storage reference.
271 278
    ///\param name The name of the option. The leading '-' must be omitted.
272 279
    ///\param help A help string.
273 280
    ///\param obl Indicate if the option is mandatory.
274 281
    ///\retval ref The value of the argument will be written to this variable.
275 282
    ArgParser &refOption(const std::string &name,
276 283
                      const std::string &help,
277 284
                      std::string &ref, bool obl=false);
278 285

	
279 286
    ///@}
280 287

	
281 288
    ///\name Option Groups and Synonyms
282 289
    ///
283 290

	
284 291
    ///@{
285 292

	
286 293
    ///Bundle some options into a group
287 294

	
288 295
    /// You can group some option by calling this function repeatedly for each
289 296
    /// option to be grouped with the same groupname.
290 297
    ///\param group The group name.
291 298
    ///\param opt The option name.
292 299
    ArgParser &optionGroup(const std::string &group,
293 300
                           const std::string &opt);
294 301

	
295 302
    ///Make the members of a group exclusive
296 303

	
297 304
    ///If you call this function for a group, than at most one of them can be
298 305
    ///given at the same time.
299 306
    ArgParser &onlyOneGroup(const std::string &group);
300 307

	
301 308
    ///Make a group mandatory
302 309

	
303 310
    ///Using this function, at least one of the members of \c group
304 311
    ///must be given.
305 312
    ArgParser &mandatoryGroup(const std::string &group);
306 313

	
307 314
    ///Create synonym to an option
308 315

	
309 316
    ///With this function you can create a synonym \c syn of the
310 317
    ///option \c opt.
311 318
    ArgParser &synonym(const std::string &syn,
312 319
                           const std::string &opt);
313 320

	
314 321
    ///@}
315 322

	
316 323
  private:
317 324
    void show(std::ostream &os,Opts::const_iterator i) const;
318 325
    void show(std::ostream &os,Groups::const_iterator i) const;
319 326
    void showHelp(Opts::const_iterator i) const;
320 327
    void showHelp(std::vector<OtherArg>::const_iterator i) const;
321 328

	
322 329
    void unknownOpt(std::string arg) const;
323 330

	
324 331
    void requiresValue(std::string arg, OptType t) const;
325 332
    void checkMandatories() const;
326 333

	
327 334
    void shortHelp() const;
328 335
    void showHelp() const;
329 336
  public:
330 337

	
331 338
    ///Start the parsing process
332 339
    ArgParser &parse();
333 340

	
334 341
    /// Synonym for parse()
335 342
    ArgParser &run()
336 343
    {
337 344
      return parse();
338 345
    }
339 346

	
340 347
    ///Give back the command name (the 0th argument)
341 348
    const std::string &commandName() const { return _command_name; }
342 349

	
343 350
    ///Check if an opion has been given to the command.
344 351
    bool given(std::string op) const
345 352
    {
346 353
      Opts::const_iterator i = _opts.find(op);
347 354
      return i!=_opts.end()?i->second.set:false;
348 355
    }
349 356

	
350 357

	
351 358
    ///Magic type for operator[]
352 359

	
353 360
    ///This is the type of the return value of ArgParser::operator[]().
354 361
    ///It automatically converts to \c int, \c double, \c bool or
355 362
    ///\c std::string if the type of the option matches, which is checked
356 363
    ///with an \ref LEMON_ASSERT "assertion" (i.e. it performs runtime
357 364
    ///type checking).
358 365
    class RefType
359 366
    {
360 367
      const ArgParser &_parser;
361 368
      std::string _name;
362 369
    public:
363 370
      ///\e
364 371
      RefType(const ArgParser &p,const std::string &n) :_parser(p),_name(n) {}
365 372
      ///\e
366 373
      operator bool()
367 374
      {
368 375
        Opts::const_iterator i = _parser._opts.find(_name);
369 376
        LEMON_ASSERT(i!=_parser._opts.end(),
370 377
                     std::string()+"Unkown option: '"+_name+"'");
371 378
        LEMON_ASSERT(i->second.type==ArgParser::BOOL,
372 379
                     std::string()+"'"+_name+"' is a bool option");
373 380
        return *(i->second.bool_p);
374 381
      }
375 382
      ///\e
376 383
      operator std::string()
377 384
      {
378 385
        Opts::const_iterator i = _parser._opts.find(_name);
379 386
        LEMON_ASSERT(i!=_parser._opts.end(),
380 387
                     std::string()+"Unkown option: '"+_name+"'");
381 388
        LEMON_ASSERT(i->second.type==ArgParser::STRING,
382 389
                     std::string()+"'"+_name+"' is a string option");
383 390
        return *(i->second.string_p);
384 391
      }
385 392
      ///\e
386 393
      operator double()
387 394
      {
388 395
        Opts::const_iterator i = _parser._opts.find(_name);
389 396
        LEMON_ASSERT(i!=_parser._opts.end(),
390 397
                     std::string()+"Unkown option: '"+_name+"'");
391 398
        LEMON_ASSERT(i->second.type==ArgParser::DOUBLE ||
392 399
                     i->second.type==ArgParser::INTEGER,
393 400
                     std::string()+"'"+_name+"' is a floating point option");
394 401
        return i->second.type==ArgParser::DOUBLE ?
395 402
          *(i->second.double_p) : *(i->second.int_p);
396 403
      }
397 404
      ///\e
398 405
      operator int()
399 406
      {
400 407
        Opts::const_iterator i = _parser._opts.find(_name);
401 408
        LEMON_ASSERT(i!=_parser._opts.end(),
402 409
                     std::string()+"Unkown option: '"+_name+"'");
403 410
        LEMON_ASSERT(i->second.type==ArgParser::INTEGER,
404 411
                     std::string()+"'"+_name+"' is an integer option");
405 412
        return *(i->second.int_p);
406 413
      }
407 414

	
408 415
    };
409 416

	
410 417
    ///Give back the value of an option
411 418

	
412 419
    ///Give back the value of an option.
413 420
    ///\sa RefType
414 421
    RefType operator[](const std::string &n) const
415 422
    {
416 423
      return RefType(*this, n);
417 424
    }
418 425

	
419 426
    ///Give back the non-option type arguments.
420 427

	
421 428
    ///Give back a reference to a vector consisting of the program arguments
422 429
    ///not starting with a '-' character.
423 430
    const std::vector<std::string> &files() const { return _file_args; }
424 431

	
425 432
    ///Throw instead of exit in case of problems
426 433
    void throwOnProblems()
427 434
    {
428 435
      _exit_on_problems=false;
429 436
    }
430 437
  };
431 438
}
432 439

	
433 440
#endif // LEMON_ARG_PARSER_H
Ignore white space 3072 line context
1 1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 2
 *
3 3
 * This file is a part of LEMON, a generic C++ optimization library.
4 4
 *
5 5
 * Copyright (C) 2003-2010
6 6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 8
 *
9 9
 * Permission to use, modify and distribute this software is granted
10 10
 * provided that this copyright notice appears in all copies. For
11 11
 * precise terms see the accompanying LICENSE file.
12 12
 *
13 13
 * This software is provided "AS IS" with no warranty of any kind,
14 14
 * express or implied, and with no claim as to its suitability for any
15 15
 * purpose.
16 16
 *
17 17
 */
18 18

	
19 19
#ifndef LEMON_HARTMANN_ORLIN_MMC_H
20 20
#define LEMON_HARTMANN_ORLIN_MMC_H
21 21

	
22 22
/// \ingroup min_mean_cycle
23 23
///
24 24
/// \file
25 25
/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
26 26

	
27 27
#include <vector>
28 28
#include <limits>
29 29
#include <lemon/core.h>
30 30
#include <lemon/path.h>
31 31
#include <lemon/tolerance.h>
32 32
#include <lemon/connectivity.h>
33 33

	
34 34
namespace lemon {
35 35

	
36 36
  /// \brief Default traits class of HartmannOrlinMmc class.
37 37
  ///
38 38
  /// Default traits class of HartmannOrlinMmc class.
39 39
  /// \tparam GR The type of the digraph.
40 40
  /// \tparam CM The type of the cost map.
41
  /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.
41
  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
42 42
#ifdef DOXYGEN
43 43
  template <typename GR, typename CM>
44 44
#else
45 45
  template <typename GR, typename CM,
46 46
    bool integer = std::numeric_limits<typename CM::Value>::is_integer>
47 47
#endif
48 48
  struct HartmannOrlinMmcDefaultTraits
49 49
  {
50 50
    /// The type of the digraph
51 51
    typedef GR Digraph;
52 52
    /// The type of the cost map
53 53
    typedef CM CostMap;
54 54
    /// The type of the arc costs
55 55
    typedef typename CostMap::Value Cost;
56 56

	
57 57
    /// \brief The large cost type used for internal computations
58 58
    ///
59 59
    /// The large cost type used for internal computations.
60 60
    /// It is \c long \c long if the \c Cost type is integer,
61 61
    /// otherwise it is \c double.
62 62
    /// \c Cost must be convertible to \c LargeCost.
63 63
    typedef double LargeCost;
64 64

	
65 65
    /// The tolerance type used for internal computations
66 66
    typedef lemon::Tolerance<LargeCost> Tolerance;
67 67

	
68 68
    /// \brief The path type of the found cycles
69 69
    ///
70 70
    /// The path type of the found cycles.
71 71
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
72 72
    /// and it must have an \c addFront() function.
73 73
    typedef lemon::Path<Digraph> Path;
74 74
  };
75 75

	
76 76
  // Default traits class for integer cost types
77 77
  template <typename GR, typename CM>
78 78
  struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
79 79
  {
80 80
    typedef GR Digraph;
81 81
    typedef CM CostMap;
82 82
    typedef typename CostMap::Value Cost;
83 83
#ifdef LEMON_HAVE_LONG_LONG
84 84
    typedef long long LargeCost;
85 85
#else
86 86
    typedef long LargeCost;
87 87
#endif
88 88
    typedef lemon::Tolerance<LargeCost> Tolerance;
89 89
    typedef lemon::Path<Digraph> Path;
90 90
  };
91 91

	
92 92

	
93 93
  /// \addtogroup min_mean_cycle
94 94
  /// @{
95 95

	
96 96
  /// \brief Implementation of the Hartmann-Orlin algorithm for finding
97 97
  /// a minimum mean cycle.
98 98
  ///
99 99
  /// This class implements the Hartmann-Orlin algorithm for finding
100 100
  /// a directed cycle of minimum mean cost in a digraph
101 101
  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102
  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
102
  /// It is an improved version of \ref KarpMmc "Karp"'s original algorithm,
103 103
  /// it applies an efficient early termination scheme.
104 104
  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
105 105
  ///
106 106
  /// \tparam GR The type of the digraph the algorithm runs on.
107 107
  /// \tparam CM The type of the cost map. The default
108 108
  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
109 109
  /// \tparam TR The traits class that defines various types used by the
110 110
  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
111 111
  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
112 112
  /// In most cases, this parameter should not be set directly,
113 113
  /// consider to use the named template parameters instead.
114 114
#ifdef DOXYGEN
115 115
  template <typename GR, typename CM, typename TR>
116 116
#else
117 117
  template < typename GR,
118 118
             typename CM = typename GR::template ArcMap<int>,
119 119
             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
120 120
#endif
121 121
  class HartmannOrlinMmc
122 122
  {
123 123
  public:
124 124

	
125 125
    /// The type of the digraph
126 126
    typedef typename TR::Digraph Digraph;
127 127
    /// The type of the cost map
128 128
    typedef typename TR::CostMap CostMap;
129 129
    /// The type of the arc costs
130 130
    typedef typename TR::Cost Cost;
131 131

	
132 132
    /// \brief The large cost type
133 133
    ///
134 134
    /// The large cost type used for internal computations.
135 135
    /// By default, it is \c long \c long if the \c Cost type is integer,
136 136
    /// otherwise it is \c double.
137 137
    typedef typename TR::LargeCost LargeCost;
138 138

	
139 139
    /// The tolerance type
140 140
    typedef typename TR::Tolerance Tolerance;
141 141

	
142 142
    /// \brief The path type of the found cycles
143 143
    ///
144 144
    /// The path type of the found cycles.
145 145
    /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",
146 146
    /// it is \ref lemon::Path "Path<Digraph>".
147 147
    typedef typename TR::Path Path;
148 148

	
149 149
    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
150 150
    typedef TR Traits;
151 151

	
152 152
  private:
153 153

	
154 154
    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
155 155

	
156 156
    // Data sturcture for path data
157 157
    struct PathData
158 158
    {
159 159
      LargeCost dist;
160 160
      Arc pred;
161 161
      PathData(LargeCost d, Arc p = INVALID) :
162 162
        dist(d), pred(p) {}
163 163
    };
164 164

	
165 165
    typedef typename Digraph::template NodeMap<std::vector<PathData> >
166 166
      PathDataNodeMap;
167 167

	
168 168
  private:
169 169

	
170 170
    // The digraph the algorithm runs on
171 171
    const Digraph &_gr;
172 172
    // The cost of the arcs
173 173
    const CostMap &_cost;
174 174

	
175 175
    // Data for storing the strongly connected components
176 176
    int _comp_num;
177 177
    typename Digraph::template NodeMap<int> _comp;
178 178
    std::vector<std::vector<Node> > _comp_nodes;
179 179
    std::vector<Node>* _nodes;
180 180
    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
181 181

	
182 182
    // Data for the found cycles
183 183
    bool _curr_found, _best_found;
184 184
    LargeCost _curr_cost, _best_cost;
185 185
    int _curr_size, _best_size;
186 186
    Node _curr_node, _best_node;
187 187
    int _curr_level, _best_level;
188 188

	
189 189
    Path *_cycle_path;
190 190
    bool _local_path;
191 191

	
192 192
    // Node map for storing path data
193 193
    PathDataNodeMap _data;
194 194
    // The processed nodes in the last round
195 195
    std::vector<Node> _process;
196 196

	
197 197
    Tolerance _tolerance;
198 198

	
199 199
    // Infinite constant
200 200
    const LargeCost INF;
201 201

	
202 202
  public:
203 203

	
204 204
    /// \name Named Template Parameters
205 205
    /// @{
206 206

	
207 207
    template <typename T>
208 208
    struct SetLargeCostTraits : public Traits {
209 209
      typedef T LargeCost;
210 210
      typedef lemon::Tolerance<T> Tolerance;
211 211
    };
212 212

	
213 213
    /// \brief \ref named-templ-param "Named parameter" for setting
214 214
    /// \c LargeCost type.
215 215
    ///
216 216
    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
217 217
    /// type. It is used for internal computations in the algorithm.
218 218
    template <typename T>
219 219
    struct SetLargeCost
220 220
      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
221 221
      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
222 222
    };
223 223

	
224 224
    template <typename T>
225 225
    struct SetPathTraits : public Traits {
226 226
      typedef T Path;
227 227
    };
228 228

	
229 229
    /// \brief \ref named-templ-param "Named parameter" for setting
230 230
    /// \c %Path type.
231 231
    ///
232 232
    /// \ref named-templ-param "Named parameter" for setting the \c %Path
233 233
    /// type of the found cycles.
234 234
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
235 235
    /// and it must have an \c addFront() function.
236 236
    template <typename T>
237 237
    struct SetPath
238 238
      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
239 239
      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
240 240
    };
241 241

	
242 242
    /// @}
243 243

	
244 244
  protected:
245 245

	
246 246
    HartmannOrlinMmc() {}
247 247

	
248 248
  public:
249 249

	
250 250
    /// \brief Constructor.
251 251
    ///
252 252
    /// The constructor of the class.
253 253
    ///
254 254
    /// \param digraph The digraph the algorithm runs on.
255 255
    /// \param cost The costs of the arcs.
256 256
    HartmannOrlinMmc( const Digraph &digraph,
257 257
                      const CostMap &cost ) :
258 258
      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
259 259
      _best_found(false), _best_cost(0), _best_size(1),
260 260
      _cycle_path(NULL), _local_path(false), _data(digraph),
261 261
      INF(std::numeric_limits<LargeCost>::has_infinity ?
262 262
          std::numeric_limits<LargeCost>::infinity() :
263 263
          std::numeric_limits<LargeCost>::max())
264 264
    {}
265 265

	
266 266
    /// Destructor.
267 267
    ~HartmannOrlinMmc() {
268 268
      if (_local_path) delete _cycle_path;
269 269
    }
270 270

	
271 271
    /// \brief Set the path structure for storing the found cycle.
272 272
    ///
273 273
    /// This function sets an external path structure for storing the
274 274
    /// found cycle.
275 275
    ///
276 276
    /// If you don't call this function before calling \ref run() or
277 277
    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
278 278
    /// structure. The destuctor deallocates this automatically
279 279
    /// allocated object, of course.
280 280
    ///
281 281
    /// \note The algorithm calls only the \ref lemon::Path::addFront()
282 282
    /// "addFront()" function of the given path structure.
283 283
    ///
284 284
    /// \return <tt>(*this)</tt>
285 285
    HartmannOrlinMmc& cycle(Path &path) {
286 286
      if (_local_path) {
287 287
        delete _cycle_path;
288 288
        _local_path = false;
289 289
      }
290 290
      _cycle_path = &path;
291 291
      return *this;
292 292
    }
293 293

	
294 294
    /// \brief Set the tolerance used by the algorithm.
295 295
    ///
296 296
    /// This function sets the tolerance object used by the algorithm.
297 297
    ///
298 298
    /// \return <tt>(*this)</tt>
299 299
    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
300 300
      _tolerance = tolerance;
301 301
      return *this;
302 302
    }
303 303

	
304 304
    /// \brief Return a const reference to the tolerance.
305 305
    ///
306 306
    /// This function returns a const reference to the tolerance object
307 307
    /// used by the algorithm.
308 308
    const Tolerance& tolerance() const {
309 309
      return _tolerance;
310 310
    }
311 311

	
312 312
    /// \name Execution control
313 313
    /// The simplest way to execute the algorithm is to call the \ref run()
314 314
    /// function.\n
315 315
    /// If you only need the minimum mean cost, you may call
316 316
    /// \ref findCycleMean().
317 317

	
318 318
    /// @{
319 319

	
320 320
    /// \brief Run the algorithm.
321 321
    ///
322 322
    /// This function runs the algorithm.
323 323
    /// It can be called more than once (e.g. if the underlying digraph
324 324
    /// and/or the arc costs have been modified).
325 325
    ///
326 326
    /// \return \c true if a directed cycle exists in the digraph.
327 327
    ///
328 328
    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
329 329
    /// \code
330 330
    ///   return mmc.findCycleMean() && mmc.findCycle();
331 331
    /// \endcode
332 332
    bool run() {
333 333
      return findCycleMean() && findCycle();
334 334
    }
335 335

	
336 336
    /// \brief Find the minimum cycle mean.
337 337
    ///
338 338
    /// This function finds the minimum mean cost of the directed
339 339
    /// cycles in the digraph.
340 340
    ///
341 341
    /// \return \c true if a directed cycle exists in the digraph.
342 342
    bool findCycleMean() {
343 343
      // Initialization and find strongly connected components
344 344
      init();
345 345
      findComponents();
346 346

	
347 347
      // Find the minimum cycle mean in the components
348 348
      for (int comp = 0; comp < _comp_num; ++comp) {
349 349
        if (!initComponent(comp)) continue;
350 350
        processRounds();
351 351

	
352 352
        // Update the best cycle (global minimum mean cycle)
353 353
        if ( _curr_found && (!_best_found ||
354 354
             _curr_cost * _best_size < _best_cost * _curr_size) ) {
355 355
          _best_found = true;
356 356
          _best_cost = _curr_cost;
357 357
          _best_size = _curr_size;
358 358
          _best_node = _curr_node;
359 359
          _best_level = _curr_level;
360 360
        }
361 361
      }
362 362
      return _best_found;
363 363
    }
364 364

	
365 365
    /// \brief Find a minimum mean directed cycle.
366 366
    ///
367 367
    /// This function finds a directed cycle of minimum mean cost
368 368
    /// in the digraph using the data computed by findCycleMean().
369 369
    ///
370 370
    /// \return \c true if a directed cycle exists in the digraph.
371 371
    ///
372 372
    /// \pre \ref findCycleMean() must be called before using this function.
373 373
    bool findCycle() {
374 374
      if (!_best_found) return false;
375 375
      IntNodeMap reached(_gr, -1);
376 376
      int r = _best_level + 1;
377 377
      Node u = _best_node;
378 378
      while (reached[u] < 0) {
379 379
        reached[u] = --r;
380 380
        u = _gr.source(_data[u][r].pred);
381 381
      }
382 382
      r = reached[u];
383 383
      Arc e = _data[u][r].pred;
384 384
      _cycle_path->addFront(e);
385 385
      _best_cost = _cost[e];
386 386
      _best_size = 1;
387 387
      Node v;
388 388
      while ((v = _gr.source(e)) != u) {
389 389
        e = _data[v][--r].pred;
390 390
        _cycle_path->addFront(e);
391 391
        _best_cost += _cost[e];
392 392
        ++_best_size;
393 393
      }
394 394
      return true;
395 395
    }
396 396

	
397 397
    /// @}
398 398

	
399 399
    /// \name Query Functions
400 400
    /// The results of the algorithm can be obtained using these
401 401
    /// functions.\n
402 402
    /// The algorithm should be executed before using them.
403 403

	
404 404
    /// @{
405 405

	
406 406
    /// \brief Return the total cost of the found cycle.
407 407
    ///
408 408
    /// This function returns the total cost of the found cycle.
409 409
    ///
410 410
    /// \pre \ref run() or \ref findCycleMean() must be called before
411 411
    /// using this function.
412 412
    Cost cycleCost() const {
413 413
      return static_cast<Cost>(_best_cost);
414 414
    }
415 415

	
416 416
    /// \brief Return the number of arcs on the found cycle.
417 417
    ///
418 418
    /// This function returns the number of arcs on the found cycle.
419 419
    ///
420 420
    /// \pre \ref run() or \ref findCycleMean() must be called before
421 421
    /// using this function.
422 422
    int cycleSize() const {
423 423
      return _best_size;
424 424
    }
425 425

	
426 426
    /// \brief Return the mean cost of the found cycle.
427 427
    ///
428 428
    /// This function returns the mean cost of the found cycle.
429 429
    ///
430 430
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
431 431
    /// following code.
432 432
    /// \code
433 433
    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
434 434
    /// \endcode
435 435
    ///
436 436
    /// \pre \ref run() or \ref findCycleMean() must be called before
437 437
    /// using this function.
438 438
    double cycleMean() const {
439 439
      return static_cast<double>(_best_cost) / _best_size;
440 440
    }
441 441

	
442 442
    /// \brief Return the found cycle.
443 443
    ///
444 444
    /// This function returns a const reference to the path structure
445 445
    /// storing the found cycle.
446 446
    ///
447 447
    /// \pre \ref run() or \ref findCycle() must be called before using
448 448
    /// this function.
449 449
    const Path& cycle() const {
450 450
      return *_cycle_path;
451 451
    }
452 452

	
453 453
    ///@}
454 454

	
455 455
  private:
456 456

	
457 457
    // Initialization
458 458
    void init() {
459 459
      if (!_cycle_path) {
460 460
        _local_path = true;
461 461
        _cycle_path = new Path;
462 462
      }
463 463
      _cycle_path->clear();
464 464
      _best_found = false;
465 465
      _best_cost = 0;
466 466
      _best_size = 1;
467 467
      _cycle_path->clear();
468 468
      for (NodeIt u(_gr); u != INVALID; ++u)
469 469
        _data[u].clear();
470 470
    }
471 471

	
472 472
    // Find strongly connected components and initialize _comp_nodes
473 473
    // and _out_arcs
474 474
    void findComponents() {
475 475
      _comp_num = stronglyConnectedComponents(_gr, _comp);
476 476
      _comp_nodes.resize(_comp_num);
477 477
      if (_comp_num == 1) {
478 478
        _comp_nodes[0].clear();
479 479
        for (NodeIt n(_gr); n != INVALID; ++n) {
480 480
          _comp_nodes[0].push_back(n);
481 481
          _out_arcs[n].clear();
482 482
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
483 483
            _out_arcs[n].push_back(a);
484 484
          }
485 485
        }
486 486
      } else {
487 487
        for (int i = 0; i < _comp_num; ++i)
488 488
          _comp_nodes[i].clear();
489 489
        for (NodeIt n(_gr); n != INVALID; ++n) {
490 490
          int k = _comp[n];
491 491
          _comp_nodes[k].push_back(n);
492 492
          _out_arcs[n].clear();
493 493
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
494 494
            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
495 495
          }
496 496
        }
497 497
      }
498 498
    }
499 499

	
500 500
    // Initialize path data for the current component
501 501
    bool initComponent(int comp) {
502 502
      _nodes = &(_comp_nodes[comp]);
503 503
      int n = _nodes->size();
504 504
      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
505 505
        return false;
506 506
      }
507 507
      for (int i = 0; i < n; ++i) {
508 508
        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
509 509
      }
510 510
      return true;
511 511
    }
512 512

	
513 513
    // Process all rounds of computing path data for the current component.
514 514
    // _data[v][k] is the cost of a shortest directed walk from the root
515 515
    // node to node v containing exactly k arcs.
516 516
    void processRounds() {
517 517
      Node start = (*_nodes)[0];
518 518
      _data[start][0] = PathData(0);
519 519
      _process.clear();
520 520
      _process.push_back(start);
521 521

	
522 522
      int k, n = _nodes->size();
523 523
      int next_check = 4;
524 524
      bool terminate = false;
525 525
      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
526 526
        processNextBuildRound(k);
527 527
        if (k == next_check || k == n) {
528 528
          terminate = checkTermination(k);
529 529
          next_check = next_check * 3 / 2;
530 530
        }
531 531
      }
532 532
      for ( ; k <= n && !terminate; ++k) {
533 533
        processNextFullRound(k);
534 534
        if (k == next_check || k == n) {
535 535
          terminate = checkTermination(k);
536 536
          next_check = next_check * 3 / 2;
537 537
        }
538 538
      }
539 539
    }
540 540

	
541 541
    // Process one round and rebuild _process
542 542
    void processNextBuildRound(int k) {
543 543
      std::vector<Node> next;
544 544
      Node u, v;
545 545
      Arc e;
546 546
      LargeCost d;
547 547
      for (int i = 0; i < int(_process.size()); ++i) {
548 548
        u = _process[i];
549 549
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
550 550
          e = _out_arcs[u][j];
551 551
          v = _gr.target(e);
552 552
          d = _data[u][k-1].dist + _cost[e];
553 553
          if (_tolerance.less(d, _data[v][k].dist)) {
554 554
            if (_data[v][k].dist == INF) next.push_back(v);
555 555
            _data[v][k] = PathData(d, e);
556 556
          }
557 557
        }
558 558
      }
559 559
      _process.swap(next);
560 560
    }
561 561

	
562 562
    // Process one round using _nodes instead of _process
563 563
    void processNextFullRound(int k) {
564 564
      Node u, v;
565 565
      Arc e;
566 566
      LargeCost d;
567 567
      for (int i = 0; i < int(_nodes->size()); ++i) {
568 568
        u = (*_nodes)[i];
569 569
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
570 570
          e = _out_arcs[u][j];
571 571
          v = _gr.target(e);
572 572
          d = _data[u][k-1].dist + _cost[e];
573 573
          if (_tolerance.less(d, _data[v][k].dist)) {
574 574
            _data[v][k] = PathData(d, e);
575 575
          }
576 576
        }
577 577
      }
578 578
    }
579 579

	
580 580
    // Check early termination
581 581
    bool checkTermination(int k) {
582 582
      typedef std::pair<int, int> Pair;
583 583
      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
584 584
      typename GR::template NodeMap<LargeCost> pi(_gr);
585 585
      int n = _nodes->size();
586 586
      LargeCost cost;
587 587
      int size;
588 588
      Node u;
589 589

	
590 590
      // Search for cycles that are already found
591 591
      _curr_found = false;
592 592
      for (int i = 0; i < n; ++i) {
593 593
        u = (*_nodes)[i];
594 594
        if (_data[u][k].dist == INF) continue;
595 595
        for (int j = k; j >= 0; --j) {
596 596
          if (level[u].first == i && level[u].second > 0) {
597 597
            // A cycle is found
598 598
            cost = _data[u][level[u].second].dist - _data[u][j].dist;
599 599
            size = level[u].second - j;
600 600
            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
601 601
              _curr_cost = cost;
602 602
              _curr_size = size;
603 603
              _curr_node = u;
604 604
              _curr_level = level[u].second;
605 605
              _curr_found = true;
606 606
            }
607 607
          }
608 608
          level[u] = Pair(i, j);
609 609
          if (j != 0) {
610 610
            u = _gr.source(_data[u][j].pred);
611 611
          }
612 612
        }
613 613
      }
614 614

	
615 615
      // If at least one cycle is found, check the optimality condition
616 616
      LargeCost d;
617 617
      if (_curr_found && k < n) {
618 618
        // Find node potentials
619 619
        for (int i = 0; i < n; ++i) {
620 620
          u = (*_nodes)[i];
621 621
          pi[u] = INF;
622 622
          for (int j = 0; j <= k; ++j) {
623 623
            if (_data[u][j].dist < INF) {
624 624
              d = _data[u][j].dist * _curr_size - j * _curr_cost;
625 625
              if (_tolerance.less(d, pi[u])) pi[u] = d;
626 626
            }
627 627
          }
628 628
        }
629 629

	
630 630
        // Check the optimality condition for all arcs
631 631
        bool done = true;
632 632
        for (ArcIt a(_gr); a != INVALID; ++a) {
633 633
          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
634 634
                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
635 635
            done = false;
636 636
            break;
637 637
          }
638 638
        }
639 639
        return done;
640 640
      }
641 641
      return (k == n);
642 642
    }
643 643

	
644 644
  }; //class HartmannOrlinMmc
645 645

	
646 646
  ///@}
647 647

	
648 648
} //namespace lemon
649 649

	
650 650
#endif //LEMON_HARTMANN_ORLIN_MMC_H
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