1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/edmonds_karp.h Tue Nov 30 20:21:52 2010 +0100
1.3 @@ -0,0 +1,515 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2010
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_EDMONDS_KARP_H
1.23 +#define LEMON_EDMONDS_KARP_H
1.24 +
1.25 +/// \file
1.26 +/// \ingroup max_flow
1.27 +/// \brief Implementation of the Edmonds-Karp algorithm.
1.28 +
1.29 +#include <lemon/tolerance.h>
1.30 +#include <vector>
1.31 +
1.32 +namespace lemon {
1.33 +
1.34 + /// \brief Default traits class of EdmondsKarp class.
1.35 + ///
1.36 + /// Default traits class of EdmondsKarp class.
1.37 + /// \param GR Digraph type.
1.38 + /// \param CAP Type of capacity map.
1.39 + template <typename GR, typename CAP>
1.40 + struct EdmondsKarpDefaultTraits {
1.41 +
1.42 + /// \brief The digraph type the algorithm runs on.
1.43 + typedef GR Digraph;
1.44 +
1.45 + /// \brief The type of the map that stores the arc capacities.
1.46 + ///
1.47 + /// The type of the map that stores the arc capacities.
1.48 + /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
1.49 + typedef CAP CapacityMap;
1.50 +
1.51 + /// \brief The type of the length of the arcs.
1.52 + typedef typename CapacityMap::Value Value;
1.53 +
1.54 + /// \brief The map type that stores the flow values.
1.55 + ///
1.56 + /// The map type that stores the flow values.
1.57 + /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
1.58 + typedef typename Digraph::template ArcMap<Value> FlowMap;
1.59 +
1.60 + /// \brief Instantiates a FlowMap.
1.61 + ///
1.62 + /// This function instantiates a \ref FlowMap.
1.63 + /// \param digraph The digraph, to which we would like to define the flow map.
1.64 + static FlowMap* createFlowMap(const Digraph& digraph) {
1.65 + return new FlowMap(digraph);
1.66 + }
1.67 +
1.68 + /// \brief The tolerance used by the algorithm
1.69 + ///
1.70 + /// The tolerance used by the algorithm to handle inexact computation.
1.71 + typedef lemon::Tolerance<Value> Tolerance;
1.72 +
1.73 + };
1.74 +
1.75 + /// \ingroup max_flow
1.76 + ///
1.77 + /// \brief Edmonds-Karp algorithms class.
1.78 + ///
1.79 + /// This class provides an implementation of the \e Edmonds-Karp \e
1.80 + /// algorithm producing a flow of maximum value in directed
1.81 + /// digraphs. The Edmonds-Karp algorithm is slower than the Preflow
1.82 + /// algorithm but it has an advantage of the step-by-step execution
1.83 + /// control with feasible flow solutions. The \e source node, the \e
1.84 + /// target node, the \e capacity of the arcs and the \e starting \e
1.85 + /// flow value of the arcs should be passed to the algorithm
1.86 + /// through the constructor.
1.87 + ///
1.88 + /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in
1.89 + /// worst case. Always try the preflow algorithm instead of this if
1.90 + /// you just want to compute the optimal flow.
1.91 + ///
1.92 + /// \param GR The digraph type the algorithm runs on.
1.93 + /// \param CAP The capacity map type.
1.94 + /// \param TR Traits class to set various data types used by
1.95 + /// the algorithm. The default traits class is \ref
1.96 + /// EdmondsKarpDefaultTraits. See \ref EdmondsKarpDefaultTraits for the
1.97 + /// documentation of a Edmonds-Karp traits class.
1.98 +
1.99 +#ifdef DOXYGEN
1.100 + template <typename GR, typename CAP, typename TR>
1.101 +#else
1.102 + template <typename GR,
1.103 + typename CAP = typename GR::template ArcMap<int>,
1.104 + typename TR = EdmondsKarpDefaultTraits<GR, CAP> >
1.105 +#endif
1.106 + class EdmondsKarp {
1.107 + public:
1.108 +
1.109 + typedef TR Traits;
1.110 + typedef typename Traits::Digraph Digraph;
1.111 + typedef typename Traits::CapacityMap CapacityMap;
1.112 + typedef typename Traits::Value Value;
1.113 +
1.114 + typedef typename Traits::FlowMap FlowMap;
1.115 + typedef typename Traits::Tolerance Tolerance;
1.116 +
1.117 + private:
1.118 +
1.119 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.120 + typedef typename Digraph::template NodeMap<Arc> PredMap;
1.121 +
1.122 + const Digraph& _graph;
1.123 + const CapacityMap* _capacity;
1.124 +
1.125 + Node _source, _target;
1.126 +
1.127 + FlowMap* _flow;
1.128 + bool _local_flow;
1.129 +
1.130 + PredMap* _pred;
1.131 + std::vector<Node> _queue;
1.132 +
1.133 + Tolerance _tolerance;
1.134 + Value _flow_value;
1.135 +
1.136 + void createStructures() {
1.137 + if (!_flow) {
1.138 + _flow = Traits::createFlowMap(_graph);
1.139 + _local_flow = true;
1.140 + }
1.141 + if (!_pred) {
1.142 + _pred = new PredMap(_graph);
1.143 + }
1.144 + _queue.resize(countNodes(_graph));
1.145 + }
1.146 +
1.147 + void destroyStructures() {
1.148 + if (_local_flow) {
1.149 + delete _flow;
1.150 + }
1.151 + if (_pred) {
1.152 + delete _pred;
1.153 + }
1.154 + }
1.155 +
1.156 + public:
1.157 +
1.158 + ///\name Named template parameters
1.159 +
1.160 + ///@{
1.161 +
1.162 + template <typename T>
1.163 + struct DefFlowMapTraits : public Traits {
1.164 + typedef T FlowMap;
1.165 + static FlowMap *createFlowMap(const Digraph&) {
1.166 + LEMON_ASSERT(false,"Uninitialized parameter.");
1.167 + return 0;
1.168 + }
1.169 + };
1.170 +
1.171 + /// \brief \ref named-templ-param "Named parameter" for setting
1.172 + /// FlowMap type
1.173 + ///
1.174 + /// \ref named-templ-param "Named parameter" for setting FlowMap
1.175 + /// type
1.176 + template <typename T>
1.177 + struct DefFlowMap
1.178 + : public EdmondsKarp<Digraph, CapacityMap, DefFlowMapTraits<T> > {
1.179 + typedef EdmondsKarp<Digraph, CapacityMap, DefFlowMapTraits<T> >
1.180 + Create;
1.181 + };
1.182 +
1.183 +
1.184 + /// @}
1.185 +
1.186 + protected:
1.187 +
1.188 + EdmondsKarp() {}
1.189 +
1.190 + public:
1.191 +
1.192 + /// \brief The constructor of the class.
1.193 + ///
1.194 + /// The constructor of the class.
1.195 + /// \param digraph The digraph the algorithm runs on.
1.196 + /// \param capacity The capacity of the arcs.
1.197 + /// \param source The source node.
1.198 + /// \param target The target node.
1.199 + EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity,
1.200 + Node source, Node target)
1.201 + : _graph(digraph), _capacity(&capacity), _source(source), _target(target),
1.202 + _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
1.203 + {
1.204 + LEMON_ASSERT(_source != _target,"Flow source and target are the same nodes.");
1.205 + }
1.206 +
1.207 + /// \brief Destructor.
1.208 + ///
1.209 + /// Destructor.
1.210 + ~EdmondsKarp() {
1.211 + destroyStructures();
1.212 + }
1.213 +
1.214 + /// \brief Sets the capacity map.
1.215 + ///
1.216 + /// Sets the capacity map.
1.217 + /// \return \c (*this)
1.218 + EdmondsKarp& capacityMap(const CapacityMap& map) {
1.219 + _capacity = ↦
1.220 + return *this;
1.221 + }
1.222 +
1.223 + /// \brief Sets the flow map.
1.224 + ///
1.225 + /// Sets the flow map.
1.226 + /// \return \c (*this)
1.227 + EdmondsKarp& flowMap(FlowMap& map) {
1.228 + if (_local_flow) {
1.229 + delete _flow;
1.230 + _local_flow = false;
1.231 + }
1.232 + _flow = ↦
1.233 + return *this;
1.234 + }
1.235 +
1.236 + /// \brief Returns the flow map.
1.237 + ///
1.238 + /// \return The flow map.
1.239 + const FlowMap& flowMap() const {
1.240 + return *_flow;
1.241 + }
1.242 +
1.243 + /// \brief Sets the source node.
1.244 + ///
1.245 + /// Sets the source node.
1.246 + /// \return \c (*this)
1.247 + EdmondsKarp& source(const Node& node) {
1.248 + _source = node;
1.249 + return *this;
1.250 + }
1.251 +
1.252 + /// \brief Sets the target node.
1.253 + ///
1.254 + /// Sets the target node.
1.255 + /// \return \c (*this)
1.256 + EdmondsKarp& target(const Node& node) {
1.257 + _target = node;
1.258 + return *this;
1.259 + }
1.260 +
1.261 + /// \brief Sets the tolerance used by algorithm.
1.262 + ///
1.263 + /// Sets the tolerance used by algorithm.
1.264 + EdmondsKarp& tolerance(const Tolerance& tolerance) {
1.265 + _tolerance = tolerance;
1.266 + return *this;
1.267 + }
1.268 +
1.269 + /// \brief Returns the tolerance used by algorithm.
1.270 + ///
1.271 + /// Returns the tolerance used by algorithm.
1.272 + const Tolerance& tolerance() const {
1.273 + return _tolerance;
1.274 + }
1.275 +
1.276 + /// \name Execution control
1.277 + /// The simplest way to execute the
1.278 + /// algorithm is to use the \c run() member functions.
1.279 + /// \n
1.280 + /// If you need more control on initial solution or
1.281 + /// execution then you have to call one \ref init() function and then
1.282 + /// the start() or multiple times the \c augment() member function.
1.283 +
1.284 + ///@{
1.285 +
1.286 + /// \brief Initializes the algorithm
1.287 + ///
1.288 + /// Sets the flow to empty flow.
1.289 + void init() {
1.290 + createStructures();
1.291 + for (ArcIt it(_graph); it != INVALID; ++it) {
1.292 + _flow->set(it, 0);
1.293 + }
1.294 + _flow_value = 0;
1.295 + }
1.296 +
1.297 + /// \brief Initializes the algorithm
1.298 + ///
1.299 + /// Initializes the flow to the \c flowMap. The \c flowMap should
1.300 + /// contain a feasible flow, ie. in each node excluding the source
1.301 + /// and the target the incoming flow should be equal to the
1.302 + /// outgoing flow.
1.303 + template <typename FlowMap>
1.304 + void flowInit(const FlowMap& flowMap) {
1.305 + createStructures();
1.306 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.307 + _flow->set(e, flowMap[e]);
1.308 + }
1.309 + _flow_value = 0;
1.310 + for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
1.311 + _flow_value += (*_flow)[jt];
1.312 + }
1.313 + for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
1.314 + _flow_value -= (*_flow)[jt];
1.315 + }
1.316 + }
1.317 +
1.318 + /// \brief Initializes the algorithm
1.319 + ///
1.320 + /// Initializes the flow to the \c flowMap. The \c flowMap should
1.321 + /// contain a feasible flow, ie. in each node excluding the source
1.322 + /// and the target the incoming flow should be equal to the
1.323 + /// outgoing flow.
1.324 + /// \return %False when the given flowMap does not contain
1.325 + /// feasible flow.
1.326 + template <typename FlowMap>
1.327 + bool checkedFlowInit(const FlowMap& flowMap) {
1.328 + createStructures();
1.329 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.330 + _flow->set(e, flowMap[e]);
1.331 + }
1.332 + for (NodeIt it(_graph); it != INVALID; ++it) {
1.333 + if (it == _source || it == _target) continue;
1.334 + Value outFlow = 0;
1.335 + for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) {
1.336 + outFlow += (*_flow)[jt];
1.337 + }
1.338 + Value inFlow = 0;
1.339 + for (InArcIt jt(_graph, it); jt != INVALID; ++jt) {
1.340 + inFlow += (*_flow)[jt];
1.341 + }
1.342 + if (_tolerance.different(outFlow, inFlow)) {
1.343 + return false;
1.344 + }
1.345 + }
1.346 + for (ArcIt it(_graph); it != INVALID; ++it) {
1.347 + if (_tolerance.less((*_flow)[it], 0)) return false;
1.348 + if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
1.349 + }
1.350 + _flow_value = 0;
1.351 + for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
1.352 + _flow_value += (*_flow)[jt];
1.353 + }
1.354 + for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
1.355 + _flow_value -= (*_flow)[jt];
1.356 + }
1.357 + return true;
1.358 + }
1.359 +
1.360 + /// \brief Augment the solution on an arc shortest path.
1.361 + ///
1.362 + /// Augment the solution on an arc shortest path. It searches an
1.363 + /// arc shortest path between the source and the target
1.364 + /// in the residual digraph by the bfs algoritm.
1.365 + /// Then it increases the flow on this path with the minimal residual
1.366 + /// capacity on the path. If there is no such path it gives back
1.367 + /// false.
1.368 + /// \return %False when the augmenting didn't success so the
1.369 + /// current flow is a feasible and optimal solution.
1.370 + bool augment() {
1.371 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.372 + _pred->set(n, INVALID);
1.373 + }
1.374 +
1.375 + int first = 0, last = 1;
1.376 +
1.377 + _queue[0] = _source;
1.378 + _pred->set(_source, OutArcIt(_graph, _source));
1.379 +
1.380 + while (first != last && (*_pred)[_target] == INVALID) {
1.381 + Node n = _queue[first++];
1.382 +
1.383 + for (OutArcIt e(_graph, n); e != INVALID; ++e) {
1.384 + Value rem = (*_capacity)[e] - (*_flow)[e];
1.385 + Node t = _graph.target(e);
1.386 + if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
1.387 + _pred->set(t, e);
1.388 + _queue[last++] = t;
1.389 + }
1.390 + }
1.391 + for (InArcIt e(_graph, n); e != INVALID; ++e) {
1.392 + Value rem = (*_flow)[e];
1.393 + Node t = _graph.source(e);
1.394 + if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
1.395 + _pred->set(t, e);
1.396 + _queue[last++] = t;
1.397 + }
1.398 + }
1.399 + }
1.400 +
1.401 + if ((*_pred)[_target] != INVALID) {
1.402 + Node n = _target;
1.403 + Arc e = (*_pred)[n];
1.404 +
1.405 + Value prem = (*_capacity)[e] - (*_flow)[e];
1.406 + n = _graph.source(e);
1.407 + while (n != _source) {
1.408 + e = (*_pred)[n];
1.409 + if (_graph.target(e) == n) {
1.410 + Value rem = (*_capacity)[e] - (*_flow)[e];
1.411 + if (rem < prem) prem = rem;
1.412 + n = _graph.source(e);
1.413 + } else {
1.414 + Value rem = (*_flow)[e];
1.415 + if (rem < prem) prem = rem;
1.416 + n = _graph.target(e);
1.417 + }
1.418 + }
1.419 +
1.420 + n = _target;
1.421 + e = (*_pred)[n];
1.422 +
1.423 + _flow->set(e, (*_flow)[e] + prem);
1.424 + n = _graph.source(e);
1.425 + while (n != _source) {
1.426 + e = (*_pred)[n];
1.427 + if (_graph.target(e) == n) {
1.428 + _flow->set(e, (*_flow)[e] + prem);
1.429 + n = _graph.source(e);
1.430 + } else {
1.431 + _flow->set(e, (*_flow)[e] - prem);
1.432 + n = _graph.target(e);
1.433 + }
1.434 + }
1.435 +
1.436 + _flow_value += prem;
1.437 + return true;
1.438 + } else {
1.439 + return false;
1.440 + }
1.441 + }
1.442 +
1.443 + /// \brief Executes the algorithm
1.444 + ///
1.445 + /// It runs augmenting phases until the optimal solution is reached.
1.446 + void start() {
1.447 + while (augment()) {}
1.448 + }
1.449 +
1.450 + /// \brief Runs the algorithm.
1.451 + ///
1.452 + /// It is just a shorthand for:
1.453 + ///
1.454 + ///\code
1.455 + /// ek.init();
1.456 + /// ek.start();
1.457 + ///\endcode
1.458 + void run() {
1.459 + init();
1.460 + start();
1.461 + }
1.462 +
1.463 + /// @}
1.464 +
1.465 + /// \name Query Functions
1.466 + /// The result of the Edmonds-Karp algorithm can be obtained using these
1.467 + /// functions.\n
1.468 + /// Before the use of these functions,
1.469 + /// either run() or start() must be called.
1.470 +
1.471 + ///@{
1.472 +
1.473 + /// \brief Returns the value of the maximum flow.
1.474 + ///
1.475 + /// Returns the value of the maximum flow by returning the excess
1.476 + /// of the target node \c t.
1.477 +
1.478 + Value flowValue() const {
1.479 + return _flow_value;
1.480 + }
1.481 +
1.482 +
1.483 + /// \brief Returns the flow on the arc.
1.484 + ///
1.485 + /// Sets the \c flowMap to the flow on the arcs.
1.486 + Value flow(const Arc& arc) const {
1.487 + return (*_flow)[arc];
1.488 + }
1.489 +
1.490 + /// \brief Returns true when the node is on the source side of minimum cut.
1.491 + ///
1.492 +
1.493 + /// Returns true when the node is on the source side of minimum
1.494 + /// cut.
1.495 +
1.496 + bool minCut(const Node& node) const {
1.497 + return ((*_pred)[node] != INVALID) or node == _source;
1.498 + }
1.499 +
1.500 + /// \brief Returns a minimum value cut.
1.501 + ///
1.502 + /// Sets \c cutMap to the characteristic vector of a minimum value cut.
1.503 +
1.504 + template <typename CutMap>
1.505 + void minCutMap(CutMap& cutMap) const {
1.506 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.507 + cutMap.set(n, (*_pred)[n] != INVALID);
1.508 + }
1.509 + cutMap.set(_source, true);
1.510 + }
1.511 +
1.512 + /// @}
1.513 +
1.514 + };
1.515 +
1.516 +}
1.517 +
1.518 +#endif
2.1 --- a/test/CMakeLists.txt Mon Mar 18 18:48:58 2013 +0100
2.2 +++ b/test/CMakeLists.txt Tue Nov 30 20:21:52 2010 +0100
2.3 @@ -25,6 +25,7 @@
2.4 dijkstra_test
2.5 dim_test
2.6 edge_set_test
2.7 + edmonds_karp_test
2.8 error_test
2.9 euler_test
2.10 fractional_matching_test
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/test/edmonds_karp_test.cc Tue Nov 30 20:21:52 2010 +0100
3.3 @@ -0,0 +1,236 @@
3.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
3.5 + *
3.6 + * This file is a part of LEMON, a generic C++ optimization library.
3.7 + *
3.8 + * Copyright (C) 2003-2010
3.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
3.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
3.11 + *
3.12 + * Permission to use, modify and distribute this software is granted
3.13 + * provided that this copyright notice appears in all copies. For
3.14 + * precise terms see the accompanying LICENSE file.
3.15 + *
3.16 + * This software is provided "AS IS" with no warranty of any kind,
3.17 + * express or implied, and with no claim as to its suitability for any
3.18 + * purpose.
3.19 + *
3.20 + */
3.21 +
3.22 +#include<iostream>
3.23 +
3.24 +#include "test_tools.h"
3.25 +#include<lemon/smart_graph.h>
3.26 +#include<lemon/edmonds_karp.h>
3.27 +#include <lemon/concepts/digraph.h>
3.28 +#include <lemon/concepts/maps.h>
3.29 +#include <lemon/lgf_reader.h>
3.30 +
3.31 +using namespace lemon;
3.32 +
3.33 +char test_lgf[] =
3.34 + "@nodes\n"
3.35 + "label\n"
3.36 + "0\n"
3.37 + "1\n"
3.38 + "2\n"
3.39 + "3\n"
3.40 + "4\n"
3.41 + "5\n"
3.42 + "6\n"
3.43 + "7\n"
3.44 + "8\n"
3.45 + "9\n"
3.46 + "@arcs\n"
3.47 + " label capacity\n"
3.48 + "0 1 0 20\n"
3.49 + "0 2 1 0\n"
3.50 + "1 1 2 3\n"
3.51 + "1 2 3 8\n"
3.52 + "1 3 4 8\n"
3.53 + "2 5 5 5\n"
3.54 + "3 2 6 5\n"
3.55 + "3 5 7 5\n"
3.56 + "3 6 8 5\n"
3.57 + "4 3 9 3\n"
3.58 + "5 7 10 3\n"
3.59 + "5 6 11 10\n"
3.60 + "5 8 12 10\n"
3.61 + "6 8 13 8\n"
3.62 + "8 9 14 20\n"
3.63 + "8 1 15 5\n"
3.64 + "9 5 16 5\n"
3.65 + "@attributes\n"
3.66 + "source 1\n"
3.67 + "target 8\n";
3.68 +
3.69 +void checkEdmondKarpCompile() {
3.70 + typedef int VType;
3.71 + typedef concepts::Digraph Digraph;
3.72 +
3.73 + typedef Digraph::Node Node;
3.74 + typedef Digraph::Arc Arc;
3.75 + typedef concepts::ReadMap<Arc,VType> CapMap;
3.76 + typedef concepts::ReadWriteMap<Arc,VType> FlowMap;
3.77 + typedef concepts::WriteMap<Node,bool> CutMap;
3.78 +
3.79 + Digraph g;
3.80 + Node n;
3.81 + Arc e;
3.82 + CapMap cap;
3.83 + FlowMap flow;
3.84 + CutMap cut;
3.85 + VType v;
3.86 + bool b;
3.87 + ignore_unused_variable_warning(v,b);
3.88 + typedef EdmondsKarp<Digraph, CapMap>
3.89 + ::DefFlowMap<FlowMap>
3.90 + ::Create EKType;
3.91 + EKType ek_test(g, cap, n, n);
3.92 + const EKType& const_ek_test = ek_test;
3.93 +
3.94 + EKType::Tolerance tol = const_ek_test.tolerance();
3.95 + ek_test.tolerance(tol);
3.96 +
3.97 + ek_test
3.98 + .capacityMap(cap)
3.99 + .flowMap(flow)
3.100 + .source(n)
3.101 + .target(n);
3.102 +
3.103 + ek_test.init();
3.104 + ek_test.start();
3.105 +
3.106 + v = const_ek_test.flowValue();
3.107 + v = const_ek_test.flow(e);
3.108 +
3.109 + const FlowMap& fm = const_ek_test.flowMap();
3.110 + b = const_ek_test.minCut(n);
3.111 + const_ek_test.minCutMap(cut);
3.112 +
3.113 + ignore_unused_variable_warning(fm);
3.114 +}
3.115 +
3.116 +int cutValue (const SmartDigraph& g,
3.117 + const SmartDigraph::NodeMap<bool>& cut,
3.118 + const SmartDigraph::ArcMap<int>& cap) {
3.119 +
3.120 + int c=0;
3.121 + for(SmartDigraph::ArcIt e(g); e!=INVALID; ++e) {
3.122 + if (cut[g.source(e)] && !cut[g.target(e)]) c+=cap[e];
3.123 + }
3.124 + return c;
3.125 +}
3.126 +
3.127 +bool checkFlow(const SmartDigraph& g,
3.128 + const SmartDigraph::ArcMap<int>& flow,
3.129 + const SmartDigraph::ArcMap<int>& cap,
3.130 + SmartDigraph::Node s, SmartDigraph::Node t) {
3.131 +
3.132 + for (SmartDigraph::ArcIt e(g); e != INVALID; ++e) {
3.133 + if (flow[e] < 0 || flow[e] > cap[e]) return false;
3.134 + }
3.135 +
3.136 + for (SmartDigraph::NodeIt n(g); n != INVALID; ++n) {
3.137 + if (n == s || n == t) continue;
3.138 + int sum = 0;
3.139 + for (SmartDigraph::OutArcIt e(g, n); e != INVALID; ++e) {
3.140 + sum += flow[e];
3.141 + }
3.142 + for (SmartDigraph::InArcIt e(g, n); e != INVALID; ++e) {
3.143 + sum -= flow[e];
3.144 + }
3.145 + if (sum != 0) return false;
3.146 + }
3.147 + return true;
3.148 +}
3.149 +
3.150 +int main() {
3.151 +
3.152 + typedef SmartDigraph Digraph;
3.153 +
3.154 + typedef Digraph::Node Node;
3.155 + typedef Digraph::NodeIt NodeIt;
3.156 + typedef Digraph::ArcIt ArcIt;
3.157 + typedef Digraph::ArcMap<int> CapMap;
3.158 + typedef Digraph::ArcMap<int> FlowMap;
3.159 + typedef Digraph::NodeMap<bool> CutMap;
3.160 +
3.161 + typedef EdmondsKarp<Digraph, CapMap> EKType;
3.162 +
3.163 + Digraph g;
3.164 + Node s, t;
3.165 + CapMap cap(g);
3.166 + std::istringstream input(test_lgf);
3.167 + DigraphReader<Digraph>(g,input).
3.168 + arcMap("capacity", cap).
3.169 + node("source",s).
3.170 + node("target",t).
3.171 + run();
3.172 +
3.173 + EKType ek_test(g, cap, s, t);
3.174 + ek_test.run();
3.175 +
3.176 + check(checkFlow(g, ek_test.flowMap(), cap, s, t),
3.177 + "The flow is not feasible.");
3.178 +
3.179 + CutMap min_cut(g);
3.180 + ek_test.minCutMap(min_cut);
3.181 + int min_cut_value=cutValue(g,min_cut,cap);
3.182 +
3.183 + check(ek_test.flowValue() == min_cut_value,
3.184 + "The max flow value is not equal to the three min cut values.");
3.185 +
3.186 + FlowMap flow(g);
3.187 + for(ArcIt e(g); e!=INVALID; ++e) flow[e] = ek_test.flowMap()[e];
3.188 +
3.189 + int flow_value=ek_test.flowValue();
3.190 +
3.191 + for(ArcIt e(g); e!=INVALID; ++e) cap[e]=2*cap[e];
3.192 + ek_test.flowInit(flow);
3.193 + ek_test.start();
3.194 +
3.195 + CutMap min_cut1(g);
3.196 + ek_test.minCutMap(min_cut1);
3.197 + min_cut_value=cutValue(g,min_cut1,cap);
3.198 +
3.199 + check(ek_test.flowValue() == min_cut_value &&
3.200 + min_cut_value == 2*flow_value,
3.201 + "The max flow value or the min cut value is wrong.");
3.202 +
3.203 + check(checkFlow(g, ek_test.flowMap(), cap, s, t),
3.204 + "The flow is not feasible.");
3.205 +
3.206 + CutMap min_cut2(g);
3.207 + ek_test.minCutMap(min_cut2);
3.208 + min_cut_value=cutValue(g,min_cut2,cap);
3.209 +
3.210 + check(ek_test.flowValue() == min_cut_value &&
3.211 + min_cut_value == 2*flow_value,
3.212 + "The max flow value or the three min cut values were not doubled.");
3.213 +
3.214 +
3.215 + ek_test.flowMap(flow);
3.216 +
3.217 + NodeIt tmp1(g,s);
3.218 + ++tmp1;
3.219 + if ( tmp1 != INVALID ) s=tmp1;
3.220 +
3.221 + NodeIt tmp2(g,t);
3.222 + ++tmp2;
3.223 + if ( tmp2 != INVALID ) t=tmp2;
3.224 +
3.225 + ek_test.source(s);
3.226 + ek_test.target(t);
3.227 +
3.228 + ek_test.run();
3.229 +
3.230 + CutMap min_cut3(g);
3.231 + ek_test.minCutMap(min_cut3);
3.232 + min_cut_value=cutValue(g,min_cut3,cap);
3.233 +
3.234 +
3.235 + check(ek_test.flowValue() == min_cut_value,
3.236 + "The max flow value or the three min cut values are incorrect.");
3.237 +
3.238 + return 0;
3.239 +}