RhodeCode

/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_BELLMAN_FORD_H

#define LEMON_BELLMAN_FORD_H

/// \ingroup shortest_path

/// \file

/// \brief Bellman-Ford algorithm.

#include <lemon/bits/path_dump.h>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/maps.h>

#include <lemon/path.h>

#include <limits>

namespace lemon {

  /// \brief Default OperationTraits for the BellmanFord algorithm class.

  ///  

  /// This operation traits class defines all computational operations

  /// and constants that are used in the Bellman-Ford algorithm.

  /// The default implementation is based on the \c numeric_limits class.

  /// If the numeric type does not have infinity value, then the maximum

  /// value is used as extremal infinity value.

  template <

    typename V, 

    bool has_inf = std::numeric_limits<V>::has_infinity>

  struct BellmanFordDefaultOperationTraits {

    /// \e

    typedef V Value;

    /// \brief Gives back the zero value of the type.

    static Value zero() {

      return static_cast<Value>(0);

    }

    /// \brief Gives back the positive infinity value of the type.

    static Value infinity() {

      return std::numeric_limits<Value>::infinity();

    }

    /// \brief Gives back the sum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return left + right;

    }

    /// \brief Gives back \c true only if the first value is less than

    /// the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  template <typename V>

  struct BellmanFordDefaultOperationTraits<V, false> {

    typedef V Value;

    static Value zero() {

      return static_cast<Value>(0);

    }

    static Value infinity() {

      return std::numeric_limits<Value>::max();

    }

    static Value plus(const Value& left, const Value& right) {

      if (left == infinity() || right == infinity()) return infinity();

      return left + right;

    }

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  /// \brief Default traits class of BellmanFord class.

  ///

  /// Default traits class of BellmanFord class.

  /// \param GR The type of the digraph.

  /// \param LEN The type of the length map.

  template<typename GR, typename LEN>

  struct BellmanFordDefaultTraits {

    /// The type of the digraph the algorithm runs on. 

    typedef GR Digraph;

    /// \brief The type of the map that stores the arc lengths.

    ///

    /// The type of the map that stores the arc lengths.

    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.

    typedef LEN LengthMap;

    /// The type of the arc lengths.

    typedef typename LEN::Value Value;

    /// \brief Operation traits for Bellman-Ford algorithm.

    ///

    /// It defines the used operations and the infinity value for the

    /// given \c Value type.

    /// \see BellmanFordDefaultOperationTraits

    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last arcs of the 

    /// shortest paths.

    /// 

    /// The type of the map that stores the last

    /// arcs of the shortest paths.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;

    /// \brief Instantiates a \c PredMap.

    /// 

    /// This function instantiates a \ref PredMap. 

    /// \param g is the digraph to which we would like to define the

    /// \ref PredMap.

    static PredMap *createPredMap(const GR& g) {

      return new PredMap(g);

    }

    /// \brief The type of the map that stores the distances of the nodes.

    ///

    /// The type of the map that stores the distances of the nodes.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;

    /// \brief Instantiates a \c DistMap.

    ///

    /// This function instantiates a \ref DistMap. 

    /// \param g is the digraph to which we would like to define the 

    /// \ref DistMap.

    static DistMap *createDistMap(const GR& g) {

      return new DistMap(g);

    }

  };

  /// \brief %BellmanFord algorithm class.

  ///

  /// \ingroup shortest_path

  /// This class provides an efficient implementation of the Bellman-Ford 

  /// algorithm. The maximum time complexity of the algorithm is

  /// <tt>O(ne)</tt>.

  ///

  /// The Bellman-Ford algorithm solves the single-source shortest path

      /// \brief Conversion to \c Node.

      ///

      /// Conversion to \c Node.

      operator Node() const { 

        return _index >= 0 ? _algorithm->_process[_index] : INVALID;

      }

      /// \brief Increment operator.

      ///

      /// Increment operator.

      ActiveIt& operator++() {

        --_index;

        return *this; 

      }

      bool operator==(const ActiveIt& it) const { 

        return static_cast<Node>(*this) == static_cast<Node>(it); 

      }

      bool operator!=(const ActiveIt& it) const { 

        return static_cast<Node>(*this) != static_cast<Node>(it); 

      }

      bool operator<(const ActiveIt& it) const { 

        return static_cast<Node>(*this) < static_cast<Node>(it); 

      }

    private:

      const BellmanFord* _algorithm;

      int _index;

    };

    /// \name Query Functions

    /// The result of the Bellman-Ford algorithm can be obtained using these

    /// functions.\n

    /// Either \ref run() or \ref init() should be called before using them.

    ///@{

    /// \brief The shortest path to the given node.

    ///    

    /// Gives back the shortest path to the given node from the root(s).

    ///

    /// \warning \c t should be reached from the root(s).

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    Path path(Node t) const

    {

      return Path(*_gr, *_pred, t);

    }

    /// \brief The distance of the given node from the root(s).

    ///

    /// Returns the distance of the given node from the root(s).

    ///

    /// \warning If node \c v is not reached from the root(s), then

    /// the return value of this function is undefined.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    Value dist(Node v) const { return (*_dist)[v]; }

    /// \brief Returns the 'previous arc' of the shortest path tree for

    /// the given node.

    ///

    /// This function returns the 'previous arc' of the shortest path

    /// tree for node \c v, i.e. it returns the last arc of a

    /// shortest path from a root to \c v. It is \c INVALID if \c v

    /// is not reached from the root(s) or if \c v is a root.

    ///

    /// The shortest path tree used here is equal to the shortest path

    /// tree used in \ref predNode() and \predMap().

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    Arc predArc(Node v) const { return (*_pred)[v]; }

    /// \brief Returns the 'previous node' of the shortest path tree for

    /// the given node.

    ///

    /// This function returns the 'previous node' of the shortest path

    /// tree for node \c v, i.e. it returns the last but one node of

    /// a shortest path from a root to \c v. It is \c INVALID if \c v

    /// is not reached from the root(s) or if \c v is a root.

    ///

    /// The shortest path tree used here is equal to the shortest path

    /// tree used in \ref predArc() and \predMap().

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    Node predNode(Node v) const { 

      return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]); 

    }

    /// \brief Returns a const reference to the node map that stores the

    /// distances of the nodes.

    ///

    /// Returns a const reference to the node map that stores the distances

    /// of the nodes calculated by the algorithm.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    const DistMap &distMap() const { return *_dist;}

    /// \brief Returns a const reference to the node map that stores the

    /// predecessor arcs.

    ///

    /// Returns a const reference to the node map that stores the predecessor

    /// arcs, which form the shortest path tree (forest).

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    const PredMap &predMap() const { return *_pred; }

    /// \brief Checks if a node is reached from the root(s).

    ///

    /// Returns \c true if \c v is reached from the root(s).

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    bool reached(Node v) const {

      return (*_dist)[v] != OperationTraits::infinity();

    }

    /// \brief Gives back a negative cycle.

    ///    

    /// This function gives back a directed cycle with negative total

    /// length if the algorithm has already found one.

    /// Otherwise it gives back an empty path.

      typename Digraph::template NodeMap<int> state(*_gr, -1);

      lemon::Path<Digraph> cycle;

      for (int i = 0; i < int(_process.size()); ++i) {

        if (state[_process[i]] != -1) continue;

        for (Node v = _process[i]; (*_pred)[v] != INVALID;

             v = _gr->source((*_pred)[v])) {

          if (state[v] == i) {

            cycle.addFront((*_pred)[v]);

            for (Node u = _gr->source((*_pred)[v]); u != v;

                 u = _gr->source((*_pred)[u])) {

              cycle.addFront((*_pred)[u]);

            }

            return cycle;

          }

          else if (state[v] >= 0) {

            break;

          }

          state[v] = i;

        }

      }

      return cycle;

    }

    ///@}

  };

  /// \brief Default traits class of bellmanFord() function.

  ///

  /// Default traits class of bellmanFord() function.

  /// \tparam GR The type of the digraph.

  /// \tparam LEN The type of the length map.

  template <typename GR, typename LEN>

  struct BellmanFordWizardDefaultTraits {

    /// The type of the digraph the algorithm runs on. 

    typedef GR Digraph;

    /// \brief The type of the map that stores the arc lengths.

    ///

    /// The type of the map that stores the arc lengths.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef LEN LengthMap;

    /// The type of the arc lengths.

    typedef typename LEN::Value Value;

    /// \brief Operation traits for Bellman-Ford algorithm.

    ///

    /// It defines the used operations and the infinity value for the

    /// given \c Value type.

    /// \see BellmanFordDefaultOperationTraits

    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the map that stores the last

    /// arcs of the shortest paths.

    /// 

    /// The type of the map that stores the last arcs of the shortest paths.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;

    /// \brief Instantiates a \c PredMap.

    /// 

    /// This function instantiates a \ref PredMap.

    /// \param g is the digraph to which we would like to define the

    /// \ref PredMap.

    static PredMap *createPredMap(const GR &g) {

      return new PredMap(g);

    }

    /// \brief The type of the map that stores the distances of the nodes.

    ///

    /// The type of the map that stores the distances of the nodes.

    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename GR::template NodeMap<Value> DistMap;

    /// \brief Instantiates a \c DistMap.

    ///

    /// This function instantiates a \ref DistMap. 

    /// \param g is the digraph to which we would like to define the

    /// \ref DistMap.

    static DistMap *createDistMap(const GR &g) {

      return new DistMap(g);

    }

    ///The type of the shortest paths.

    ///The type of the shortest paths.

    ///It must meet the \ref concepts::Path "Path" concept.

    typedef lemon::Path<Digraph> Path;

  };

  /// \brief Default traits class used by BellmanFordWizard.

  ///

  /// Default traits class used by BellmanFordWizard.

  /// \tparam GR The type of the digraph.

  /// \tparam LEN The type of the length map.

  template <typename GR, typename LEN>

  class BellmanFordWizardBase 

    : public BellmanFordWizardDefaultTraits<GR, LEN> {

    typedef BellmanFordWizardDefaultTraits<GR, LEN> Base;

  protected:

    // Type of the nodes in the digraph.

    typedef typename Base::Digraph::Node Node;

    // Pointer to the underlying digraph.

    void *_graph;

    // Pointer to the length map

    void *_length;

    // Pointer to the map of predecessors arcs.

    void *_pred;

    // Pointer to the map of distances.

    void *_dist;

    //Pointer to the shortest path to the target node.

    void *_path;

    //Pointer to the distance of the target node.

    void *_di;

    public:

    /// Constructor.

    /// This constructor does not require parameters, it initiates

    /// all of the attributes to default values \c 0.

    BellmanFordWizardBase() :

      _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {}

    /// Constructor.

    /// This constructor requires two parameters,

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2009

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#include <lemon/concepts/digraph.h>

#include <lemon/smart_graph.h>

#include <lemon/list_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/bellman_ford.h>

#include <lemon/path.h>

#include "graph_test.h"

#include "test_tools.h"

using namespace lemon;

char test_lgf[] =

  "@nodes\n"

  "label\n"

  "0\n"

  "1\n"

  "2\n"

  "3\n"

  "4\n"

  "@arcs\n"

  "    length\n"

  "0 1 3\n"

  "1 2 -3\n"

  "1 2 -5\n"

  "1 3 -2\n"

  "0 2 -1\n"

  "1 2 -4\n"

  "0 3 2\n"

  "4 2 -5\n"

  "2 3 1\n"

  "@attributes\n"

  "source 0\n"

  "target 3\n";

void checkBellmanFordCompile()

{

  typedef int Value;

  typedef concepts::Digraph Digraph;

  typedef concepts::ReadMap<Digraph::Arc,Value> LengthMap;

  typedef BellmanFord<Digraph, LengthMap> BF;

  typedef Digraph::Node Node;

  typedef Digraph::Arc Arc;

  Digraph gr;

  Node s, t, n;

  Arc e;

  Value l;

  int k;

  bool b;

  BF::DistMap d(gr);

  BF::PredMap p(gr);

  LengthMap length;

  concepts::Path<Digraph> pp;

  {

    BF bf_test(gr,length);

    const BF& const_bf_test = bf_test;

    bf_test.run(s);

    bf_test.run(s,k);

    bf_test.init();

    bf_test.addSource(s);

    bf_test.addSource(s, 1);

    b = bf_test.processNextRound();

    b = bf_test.processNextWeakRound();

    bf_test.start();

    bf_test.checkedStart();

    bf_test.limitedStart(k);

    l  = const_bf_test.dist(t);

    e  = const_bf_test.predArc(t);

    s  = const_bf_test.predNode(t);

    b  = const_bf_test.reached(t);

    d  = const_bf_test.distMap();

    p  = const_bf_test.predMap();

    pp = const_bf_test.path(t);

    for (BF::ActiveIt it(const_bf_test); it != INVALID; ++it) {}

  }

  {

    BF::SetPredMap<concepts::ReadWriteMap<Node,Arc> >

      ::SetDistMap<concepts::ReadWriteMap<Node,Value> >

      ::SetOperationTraits<BellmanFordDefaultOperationTraits<Value> >

      ::Create bf_test(gr,length);

    LengthMap length_map;

    concepts::ReadWriteMap<Node,Arc> pred_map;

    concepts::ReadWriteMap<Node,Value> dist_map;

    bf_test

      .lengthMap(length_map)

      .predMap(pred_map)

      .distMap(dist_map);

    bf_test.run(s);

    bf_test.run(s,k);

    bf_test.init();

    bf_test.addSource(s);

    bf_test.addSource(s, 1);

    b = bf_test.processNextRound();

    b = bf_test.processNextWeakRound();

    bf_test.start();

    bf_test.checkedStart();

    bf_test.limitedStart(k);

    l  = bf_test.dist(t);

    e  = bf_test.predArc(t);

    s  = bf_test.predNode(t);

    b  = bf_test.reached(t);

    pp = bf_test.path(t);

  }

}

void checkBellmanFordFunctionCompile()

{

  typedef int Value;

  typedef concepts::Digraph Digraph;

  typedef Digraph::Arc Arc;

  typedef Digraph::Node Node;

  typedef concepts::ReadMap<Digraph::Arc,Value> LengthMap;

  Digraph g;

  bool b;

  bellmanFord(g,LengthMap()).run(Node());

  b = bellmanFord(g,LengthMap()).run(Node(),Node());

  bellmanFord(g,LengthMap())

    .predMap(concepts::ReadWriteMap<Node,Arc>())

    .distMap(concepts::ReadWriteMap<Node,Value>())

    .run(Node());

  b=bellmanFord(g,LengthMap())

    .predMap(concepts::ReadWriteMap<Node,Arc>())

    .distMap(concepts::ReadWriteMap<Node,Value>())

    .path(concepts::Path<Digraph>())

    .dist(Value())

    .run(Node(),Node());

}

template <typename Digraph, typename Value>

void checkBellmanFord() {

  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  typedef typename Digraph::template ArcMap<Value> LengthMap;

  Digraph gr;

  Node s, t;

  LengthMap length(gr);

  std::istringstream input(test_lgf);

  digraphReader(gr, input).

    arcMap("length", length).

    node("source", s).

    node("target", t).

    run();

  BellmanFord<Digraph, LengthMap>

    bf(gr, length);

  bf.run(s);

  Path<Digraph> p = bf.path(t);

  check(bf.reached(t) && bf.dist(t) == -1, "Bellman-Ford found a wrong path.");

  check(p.length() == 3, "path() found a wrong path.");

  check(checkPath(gr, p), "path() found a wrong path.");

  check(pathSource(gr, p) == s, "path() found a wrong path.");

  check(pathTarget(gr, p) == t, "path() found a wrong path.");

  ListPath<Digraph> path;

  Value dist;

  bool reached = bellmanFord(gr,length).path(path).dist(dist).run(s,t);

  check(reached && dist == -1, "Bellman-Ford found a wrong path.");

  check(path.length() == 3, "path() found a wrong path.");

  check(checkPath(gr, path), "path() found a wrong path.");

  check(pathSource(gr, path) == s, "path() found a wrong path.");

  check(pathTarget(gr, path) == t, "path() found a wrong path.");

  for(ArcIt e(gr); e!=INVALID; ++e) {

    Node u=gr.source(e);

    Node v=gr.target(e);

    check(!bf.reached(u) || (bf.dist(v) - bf.dist(u) <= length[e]),

          "Wrong output. dist(target)-dist(source)-arc_length=" <<

          bf.dist(v) - bf.dist(u) - length[e]);

  }

  for(NodeIt v(gr); v!=INVALID; ++v) {

    if (bf.reached(v)) {

      check(v==s || bf.predArc(v)!=INVALID, "Wrong tree.");

      if (bf.predArc(v)!=INVALID ) {

        Arc e=bf.predArc(v);

        Node u=gr.source(e);

        check(u==bf.predNode(v),"Wrong tree.");

        check(bf.dist(v) - bf.dist(u) == length[e],

              "Wrong distance! Difference: " <<

              bf.dist(v) - bf.dist(u) - length[e]);

      }

    }

  }

}

void checkBellmanFordNegativeCycle() {

  DIGRAPH_TYPEDEFS(SmartDigraph);

  SmartDigraph gr;

  IntArcMap length(gr);

  Node n1 = gr.addNode();

  Node n2 = gr.addNode();

  Node n3 = gr.addNode();

  Node n4 = gr.addNode();

  Arc a1 = gr.addArc(n1, n2);

  Arc a2 = gr.addArc(n2, n2);

  length[a1] = 2;

  length[a2] = -1;

  {

    BellmanFord<SmartDigraph, IntArcMap> bf(gr, length);

    bf.run(n1);

    StaticPath<SmartDigraph> p = bf.negativeCycle();

    check(p.length() == 1 && p.front() == p.back() && p.front() == a2,

          "Wrong negative cycle.");

  }

  length[a2] = 0;

  {

    BellmanFord<SmartDigraph, IntArcMap> bf(gr, length);

    bf.run(n1);

    check(bf.negativeCycle().empty(),

          "Negative cycle should not be found.");

  }

  length[gr.addArc(n1, n3)] = 5;

  length[gr.addArc(n4, n3)] = 1;

  length[gr.addArc(n2, n4)] = 2;

  length[gr.addArc(n3, n2)] = -4;

  {