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+/* -*- 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_KARP_H
+#define LEMON_KARP_H
+
+/// \ingroup shortest_path
+///
+/// \file
+/// \brief Karp's algorithm for finding a minimum mean cycle.
+
+#include <vector>
+#include <limits>
+#include <lemon/core.h>
+#include <lemon/path.h>
+#include <lemon/tolerance.h>
+#include <lemon/connectivity.h>
+
+namespace lemon {
+
+  /// \brief Default traits class of Karp algorithm.
+  ///
+  /// Default traits class of Karp algorithm.
+  /// \tparam GR The type of the digraph.
+  /// \tparam LEN The type of the length map.
+  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
+#ifdef DOXYGEN
+  template <typename GR, typename LEN>
+#else
+  template <typename GR, typename LEN,
+    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
+#endif
+  struct KarpDefaultTraits
+  {
+    /// The type of the digraph
+    typedef GR Digraph;
+    /// The type of the length map
+    typedef LEN LengthMap;
+    /// The type of the arc lengths
+    typedef typename LengthMap::Value Value;
+
+    /// \brief The large value type used for internal computations
+    ///
+    /// The large value type used for internal computations.
+    /// It is \c long \c long if the \c Value type is integer,
+    /// otherwise it is \c double.
+    /// \c Value must be convertible to \c LargeValue.
+    typedef double LargeValue;
+
+    /// The tolerance type used for internal computations
+    typedef lemon::Tolerance<LargeValue> Tolerance;
+
+    /// \brief The path type of the found cycles
+    ///
+    /// The path type of the found cycles.
+    /// It must conform to the \ref lemon::concepts::Path "Path" concept
+    /// and it must have an \c addBack() function.
+    typedef lemon::Path<Digraph> Path;
+  };
+
+  // Default traits class for integer value types
+  template <typename GR, typename LEN>
+  struct KarpDefaultTraits<GR, LEN, true>
+  {
+    typedef GR Digraph;
+    typedef LEN LengthMap;
+    typedef typename LengthMap::Value Value;
+#ifdef LEMON_HAVE_LONG_LONG
+    typedef long long LargeValue;
+#else
+    typedef long LargeValue;
+#endif
+    typedef lemon::Tolerance<LargeValue> Tolerance;
+    typedef lemon::Path<Digraph> Path;
+  };
+
+
+  /// \addtogroup shortest_path
+  /// @{
+
+  /// \brief Implementation of Karp's algorithm for finding a minimum
+  /// mean cycle.
+  ///
+  /// This class implements Karp's algorithm for finding a directed
+  /// cycle of minimum mean length (cost) in a digraph.
+  ///
+  /// \tparam GR The type of the digraph the algorithm runs on.
+  /// \tparam LEN The type of the length map. The default
+  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
+#ifdef DOXYGEN
+  template <typename GR, typename LEN, typename TR>
+#else
+  template < typename GR,
+             typename LEN = typename GR::template ArcMap<int>,
+             typename TR = KarpDefaultTraits<GR, LEN> >
+#endif
+  class Karp
+  {
+  public:
+
+    /// The type of the digraph
+    typedef typename TR::Digraph Digraph;
+    /// The type of the length map
+    typedef typename TR::LengthMap LengthMap;
+    /// The type of the arc lengths
+    typedef typename TR::Value Value;
+
+    /// \brief The large value type
+    ///
+    /// The large value type used for internal computations.
+    /// Using the \ref KarpDefaultTraits "default traits class",
+    /// it is \c long \c long if the \c Value type is integer,
+    /// otherwise it is \c double.
+    typedef typename TR::LargeValue LargeValue;
+
+    /// The tolerance type
+    typedef typename TR::Tolerance Tolerance;
+
+    /// \brief The path type of the found cycles
+    ///
+    /// The path type of the found cycles.
+    /// Using the \ref KarpDefaultTraits "default traits class",
+    /// it is \ref lemon::Path "Path<Digraph>".
+    typedef typename TR::Path Path;
+
+    /// The \ref KarpDefaultTraits "traits class" of the algorithm
+    typedef TR Traits;
+
+  private:
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+    // Data sturcture for path data
+    struct PathData
+    {
+      bool found;
+      LargeValue dist;
+      Arc pred;
+      PathData(bool f = false, LargeValue d = 0, Arc p = INVALID) :
+        found(f), dist(d), pred(p) {}
+    };
+
+    typedef typename Digraph::template NodeMap<std::vector<PathData> >
+      PathDataNodeMap;
+
+  private:
+
+    // The digraph the algorithm runs on
+    const Digraph &_gr;
+    // The length of the arcs
+    const LengthMap &_length;
+
+    // Data for storing the strongly connected components
+    int _comp_num;
+    typename Digraph::template NodeMap<int> _comp;
+    std::vector<std::vector<Node> > _comp_nodes;
+    std::vector<Node>* _nodes;
+    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
+
+    // Data for the found cycle
+    LargeValue _cycle_length;
+    int _cycle_size;
+    Node _cycle_node;
+
+    Path *_cycle_path;
+    bool _local_path;
+
+    // Node map for storing path data
+    PathDataNodeMap _data;
+    // The processed nodes in the last round
+    std::vector<Node> _process;
+
+    Tolerance _tolerance;
+
+  public:
+
+    /// \name Named Template Parameters
+    /// @{
+
+    template <typename T>
+    struct SetLargeValueTraits : public Traits {
+      typedef T LargeValue;
+      typedef lemon::Tolerance<T> Tolerance;
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// \c LargeValue type.
+    ///
+    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
+    /// type. It is used for internal computations in the algorithm.
+    template <typename T>
+    struct SetLargeValue
+      : public Karp<GR, LEN, SetLargeValueTraits<T> > {
+      typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
+    };
+
+    template <typename T>
+    struct SetPathTraits : public Traits {
+      typedef T Path;
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// \c %Path type.
+    ///
+    /// \ref named-templ-param "Named parameter" for setting the \c %Path
+    /// type of the found cycles.
+    /// It must conform to the \ref lemon::concepts::Path "Path" concept
+    /// and it must have an \c addFront() function.
+    template <typename T>
+    struct SetPath
+      : public Karp<GR, LEN, SetPathTraits<T> > {
+      typedef Karp<GR, LEN, SetPathTraits<T> > Create;
+    };
+
+    /// @}
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// The constructor of the class.
+    ///
+    /// \param digraph The digraph the algorithm runs on.
+    /// \param length The lengths (costs) of the arcs.
+    Karp( const Digraph &digraph,
+          const LengthMap &length ) :
+      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
+      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
+      _cycle_path(NULL), _local_path(false), _data(digraph)
+    {}
+
+    /// Destructor.
+    ~Karp() {
+      if (_local_path) delete _cycle_path;
+    }
+
+    /// \brief Set the path structure for storing the found cycle.
+    ///
+    /// This function sets an external path structure for storing the
+    /// found cycle.
+    ///
+    /// If you don't call this function before calling \ref run() or
+    /// \ref findMinMean(), it will allocate a local \ref Path "path"
+    /// structure. The destuctor deallocates this automatically
+    /// allocated object, of course.
+    ///
+    /// \note The algorithm calls only the \ref lemon::Path::addFront()
+    /// "addFront()" function of the given path structure.
+    ///
+    /// \return <tt>(*this)</tt>
+    Karp& cycle(Path &path) {
+      if (_local_path) {
+        delete _cycle_path;
+        _local_path = false;
+      }
+      _cycle_path = &path;
+      return *this;
+    }
+
+    /// \name Execution control
+    /// The simplest way to execute the algorithm is to call the \ref run()
+    /// function.\n
+    /// If you only need the minimum mean length, you may call
+    /// \ref findMinMean().
+
+    /// @{
+
+    /// \brief Run the algorithm.
+    ///
+    /// This function runs the algorithm.
+    /// It can be called more than once (e.g. if the underlying digraph
+    /// and/or the arc lengths have been modified).
+    ///
+    /// \return \c true if a directed cycle exists in the digraph.
+    ///
+    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
+    /// \code
+    ///   return mmc.findMinMean() && mmc.findCycle();
+    /// \endcode
+    bool run() {
+      return findMinMean() && findCycle();
+    }
+
+    /// \brief Find the minimum cycle mean.
+    ///
+    /// This function finds the minimum mean length of the directed
+    /// cycles in the digraph.
+    ///
+    /// \return \c true if a directed cycle exists in the digraph.
+    bool findMinMean() {
+      // Initialization and find strongly connected components
+      init();
+      findComponents();
+      
+      // Find the minimum cycle mean in the components
+      for (int comp = 0; comp < _comp_num; ++comp) {
+        if (!initComponent(comp)) continue;
+        processRounds();
+        updateMinMean();
+      }
+      return (_cycle_node != INVALID);
+    }
+
+    /// \brief Find a minimum mean directed cycle.
+    ///
+    /// This function finds a directed cycle of minimum mean length
+    /// in the digraph using the data computed by findMinMean().
+    ///
+    /// \return \c true if a directed cycle exists in the digraph.
+    ///
+    /// \pre \ref findMinMean() must be called before using this function.
+    bool findCycle() {
+      if (_cycle_node == INVALID) return false;
+      IntNodeMap reached(_gr, -1);
+      int r = _data[_cycle_node].size();
+      Node u = _cycle_node;
+      while (reached[u] < 0) {
+        reached[u] = --r;
+        u = _gr.source(_data[u][r].pred);
+      }
+      r = reached[u];
+      Arc e = _data[u][r].pred;
+      _cycle_path->addFront(e);
+      _cycle_length = _length[e];
+      _cycle_size = 1;
+      Node v;
+      while ((v = _gr.source(e)) != u) {
+        e = _data[v][--r].pred;
+        _cycle_path->addFront(e);
+        _cycle_length += _length[e];
+        ++_cycle_size;
+      }
+      return true;
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The results of the algorithm can be obtained using these
+    /// functions.\n
+    /// The algorithm should be executed before using them.
+
+    /// @{
+
+    /// \brief Return the total length of the found cycle.
+    ///
+    /// This function returns the total length of the found cycle.
+    ///
+    /// \pre \ref run() or \ref findMinMean() must be called before
+    /// using this function.
+    LargeValue cycleLength() const {
+      return _cycle_length;
+    }
+
+    /// \brief Return the number of arcs on the found cycle.
+    ///
+    /// This function returns the number of arcs on the found cycle.
+    ///
+    /// \pre \ref run() or \ref findMinMean() must be called before
+    /// using this function.
+    int cycleArcNum() const {
+      return _cycle_size;
+    }
+
+    /// \brief Return the mean length of the found cycle.
+    ///
+    /// This function returns the mean length of the found cycle.
+    ///
+    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
+    /// following code.
+    /// \code
+    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
+    /// \endcode
+    ///
+    /// \pre \ref run() or \ref findMinMean() must be called before
+    /// using this function.
+    double cycleMean() const {
+      return static_cast<double>(_cycle_length) / _cycle_size;
+    }
+
+    /// \brief Return the found cycle.
+    ///
+    /// This function returns a const reference to the path structure
+    /// storing the found cycle.
+    ///
+    /// \pre \ref run() or \ref findCycle() must be called before using
+    /// this function.
+    const Path& cycle() const {
+      return *_cycle_path;
+    }
+
+    ///@}
+
+  private:
+
+    // Initialization
+    void init() {
+      if (!_cycle_path) {
+        _local_path = true;
+        _cycle_path = new Path;
+      }
+      _cycle_path->clear();
+      _cycle_length = 0;
+      _cycle_size = 1;
+      _cycle_node = INVALID;
+      for (NodeIt u(_gr); u != INVALID; ++u)
+        _data[u].clear();
+    }
+
+    // Find strongly connected components and initialize _comp_nodes
+    // and _out_arcs
+    void findComponents() {
+      _comp_num = stronglyConnectedComponents(_gr, _comp);
+      _comp_nodes.resize(_comp_num);
+      if (_comp_num == 1) {
+        _comp_nodes[0].clear();
+        for (NodeIt n(_gr); n != INVALID; ++n) {
+          _comp_nodes[0].push_back(n);
+          _out_arcs[n].clear();
+          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
+            _out_arcs[n].push_back(a);
+          }
+        }
+      } else {
+        for (int i = 0; i < _comp_num; ++i)
+          _comp_nodes[i].clear();
+        for (NodeIt n(_gr); n != INVALID; ++n) {
+          int k = _comp[n];
+          _comp_nodes[k].push_back(n);
+          _out_arcs[n].clear();
+          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
+            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
+          }
+        }
+      }
+    }
+
+    // Initialize path data for the current component
+    bool initComponent(int comp) {
+      _nodes = &(_comp_nodes[comp]);
+      int n = _nodes->size();
+      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
+        return false;
+      }      
+      for (int i = 0; i < n; ++i) {
+        _data[(*_nodes)[i]].resize(n + 1);
+      }
+      return true;
+    }
+
+    // Process all rounds of computing path data for the current component.
+    // _data[v][k] is the length of a shortest directed walk from the root
+    // node to node v containing exactly k arcs.
+    void processRounds() {
+      Node start = (*_nodes)[0];
+      _data[start][0] = PathData(true, 0);
+      _process.clear();
+      _process.push_back(start);
+
+      int k, n = _nodes->size();
+      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
+        processNextBuildRound(k);
+      }
+      for ( ; k <= n; ++k) {
+        processNextFullRound(k);
+      }
+    }
+
+    // Process one round and rebuild _process
+    void processNextBuildRound(int k) {
+      std::vector<Node> next;
+      Node u, v;
+      Arc e;
+      LargeValue d;
+      for (int i = 0; i < int(_process.size()); ++i) {
+        u = _process[i];
+        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
+          e = _out_arcs[u][j];
+          v = _gr.target(e);
+          d = _data[u][k-1].dist + _length[e];
+          if (!_data[v][k].found) {
+            next.push_back(v);
+            _data[v][k] = PathData(true, _data[u][k-1].dist + _length[e], e);
+          }
+          else if (_tolerance.less(d, _data[v][k].dist)) {
+            _data[v][k] = PathData(true, d, e);
+          }
+        }
+      }
+      _process.swap(next);
+    }
+
+    // Process one round using _nodes instead of _process
+    void processNextFullRound(int k) {
+      Node u, v;
+      Arc e;
+      LargeValue d;
+      for (int i = 0; i < int(_nodes->size()); ++i) {
+        u = (*_nodes)[i];
+        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
+          e = _out_arcs[u][j];
+          v = _gr.target(e);
+          d = _data[u][k-1].dist + _length[e];
+          if (!_data[v][k].found || _tolerance.less(d, _data[v][k].dist)) {
+            _data[v][k] = PathData(true, d, e);
+          }
+        }
+      }
+    }
+
+    // Update the minimum cycle mean
+    void updateMinMean() {
+      int n = _nodes->size();
+      for (int i = 0; i < n; ++i) {
+        Node u = (*_nodes)[i];
+        if (!_data[u][n].found) continue;
+        LargeValue length, max_length = 0;
+        int size, max_size = 1;
+        bool found_curr = false;
+        for (int k = 0; k < n; ++k) {
+          if (!_data[u][k].found) continue;
+          length = _data[u][n].dist - _data[u][k].dist;
+          size = n - k;
+          if (!found_curr || length * max_size > max_length * size) {
+            found_curr = true;
+            max_length = length;
+            max_size = size;
+          }
+        }
+        if ( found_curr && (_cycle_node == INVALID ||
+             max_length * _cycle_size < _cycle_length * max_size) ) {
+          _cycle_length = max_length;
+          _cycle_size = max_size;
+          _cycle_node = u;
+        }
+      }
+    }
+
+  }; //class Karp
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_KARP_H