/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2007

  * 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_MIN_MEAN_CYCLE_H

 #define LEMON_MIN_MEAN_CYCLE_H

 /// \ingroup shortest_path

 ///

 /// \file

 /// \brief Karp's algorithm for finding a minimum mean (directed) cycle.

 #include <vector>

 #include <lemon/graph_utils.h>

 #include <lemon/topology.h>

 #include <lemon/path.h>

 namespace lemon {

   /// \addtogroup shortest_path

   /// @{

   /// \brief Implementation of Karp's algorithm for finding a

   /// minimum mean (directed) cycle.

   ///

   /// The \ref lemon::MinMeanCycle "MinMeanCycle" implements Karp's

   /// algorithm for finding a minimum mean (directed) cycle.

   ///

   /// \param Graph The directed graph type the algorithm runs on.

   /// \param LengthMap The type of the length (cost) map.

   ///

   /// \author Peter Kovacs

   template <typename Graph,

     typename LengthMap = typename Graph::template EdgeMap<int> >

   class MinMeanCycle

   {

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename LengthMap::Value Length;

     typedef typename Graph::template NodeMap<int> IntNodeMap;

     typedef typename Graph::template NodeMap<Edge> PredNodeMap;

     typedef Path<Graph> Path;

     typedef std::vector<Node> NodeVector;

   protected:

     /// \brief Data structure for path data.

     struct PathData

     {

       bool found;

       Length dist;

       Edge pred;

       PathData(bool _found = false, Length _dist = 0) :

 	found(_found), dist(_dist), pred(INVALID) {}

       PathData(bool _found, Length _dist, Edge _pred) :

 	found(_found), dist(_dist), pred(_pred) {}

     };

   private:

     typedef typename Graph::template NodeMap<std::vector<PathData> >

       PathDataNodeMap;

   protected:

     /// \brief Node map for storing path data.

     ///

     /// Node map for storing path data of all nodes in the current

     /// component. dmap[v][k] is the length of a shortest directed walk

     /// to node v from the starting node containing exactly k edges.

     PathDataNodeMap dmap;

     /// \brief The directed graph the algorithm runs on.

     const Graph &graph;

     /// \brief The length of the edges.

     const LengthMap &length;

     /// \brief The total length of the found cycle.

     Length cycle_length;

     /// \brief The number of edges in the found cycle.

     int cycle_size;

     /// \brief A node for obtaining a minimum mean cycle.

     Node cycle_node;

     /// \brief The found cycle.

     Path *cycle_path;

     /// \brief The algorithm uses local \ref lemon::Path "Path"

     /// structure to store the found cycle.

     bool local_path;

     /// \brief Node map for identifying strongly connected components.

     IntNodeMap comp;

     /// \brief The number of strongly connected components.

     int comp_num;

     /// \brief Counter for identifying the current component.

     int comp_cnt;

     /// \brief Nodes of the current component.

     NodeVector nodes;

     /// \brief The processed nodes in the last round.

     NodeVector process;

   public :

     /// \brief The constructor of the class.

     ///

     /// The constructor of the class.

     ///

     /// \param _graph The directed graph the algorithm runs on.

     /// \param _length The length (cost) of the edges.

     MinMeanCycle( const Graph &_graph,

 		  const LengthMap &_length ) :

       graph(_graph), length(_length), dmap(_graph), comp(_graph),

       cycle_length(0), cycle_size(-1), cycle_node(INVALID),

       cycle_path(NULL), local_path(false)

     { }

     /// \brief The destructor of the class.

     ~MinMeanCycle() {

       if (local_path) delete cycle_path;

     }

   protected:

     /// \brief Initializes the internal data structures for the current

     /// component.

     void initCurrent() {

       nodes.clear();

       // Finding the nodes of the current component

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

 	if (comp[v] == comp_cnt) nodes.push_back(v);

       }

       // Creating vectors for all nodes

       int n = nodes.size();

       for (int i = 0; i < n; ++i) {

 	dmap[nodes[i]].resize(n + 1);

       }

     }

     /// \brief Processes all rounds of computing required path data for

     /// the current component.

     void processRounds() {

       dmap[nodes[0]][0] = PathData(true, 0);

       process.clear();

       // Processing the first round

       for (OutEdgeIt e(graph, nodes[0]); e != INVALID; ++e) {

 	Node v = graph.target(e);

 	if (comp[v] != comp_cnt || v == nodes[0]) continue;

 	dmap[v][1] = PathData(true, length[e], e);

 	process.push_back(v);

       }

       // Processing other rounds

       int n = nodes.size(), k;

       for (k = 2; k <= n && process.size() < n; ++k)

 	processNextBuildRound(k);

       for ( ; k <= n; ++k)

 	processNextFullRound(k);

     }

     /// \brief Processes one round of computing required path data and

     /// rebuilds \ref process vector.

     void processNextBuildRound(int k) {

       NodeVector next;

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

 	for (OutEdgeIt e(graph, process[i]); e != INVALID; ++e) {

 	  Node v = graph.target(e);

 	  if (comp[v] != comp_cnt) continue;

 	  if (!dmap[v][k].found) {

 	    next.push_back(v);

 	    dmap[v][k] = PathData(true, dmap[process[i]][k-1].dist + length[e], e);

 	  }

 	  else if (dmap[process[i]][k-1].dist + length[e] < dmap[v][k].dist) {

 	    dmap[v][k] = PathData(true, dmap[process[i]][k-1].dist + length[e], e);

 	  }

 	}

       }

       process.swap(next);

     }

     /// \brief Processes one round of computing required path data

     /// using \ref nodes vector instead of \ref process vector.

     void processNextFullRound(int k) {

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

 	for (OutEdgeIt e(graph, nodes[i]); e != INVALID; ++e) {

 	  Node v = graph.target(e);

 	  if (comp[v] != comp_cnt) continue;

 	  if ( !dmap[v][k].found ||

 	       dmap[nodes[i]][k-1].dist + length[e] < dmap[v][k].dist ) {

 	    dmap[v][k] = PathData(true, dmap[nodes[i]][k-1].dist + length[e], e);

 	  }

 	}

       }

     }

     /// \brief Finds the minimum cycle mean value in the current

     /// component.

     bool findCurrentMin(Length &min_length, int &min_size, Node &min_node) {

       bool found_min = false;

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

 	int n = nodes.size();

 	if (!dmap[nodes[i]][n].found) continue;

 	Length len;

 	int size;

 	bool found_one = false;

 	for (int k = 0; k < n; ++k) {

 	  if (!dmap[nodes[i]][k].found) continue;

 	  Length _len = dmap[nodes[i]][n].dist - dmap[nodes[i]][k].dist;

 	  int _size = n - k;

 	  if (!found_one || len * _size < _len * size) {

 	    found_one = true;

 	    len = _len;

 	    size = _size;

 	  }

 	}

 	if ( found_one &&

 	     (!found_min || len * min_size < min_length * size) ) {

 	  found_min = true;

 	  min_length = len;

 	  min_size = size;

 	  min_node = nodes[i];

 	}

       }

       return found_min;

     }

   public:

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm.

     ///

     /// \return \c true if a cycle exists in the graph.

     ///

     /// \note Apart from the return value, <tt>m.run()</tt> is just a

     /// shortcut of the following code.

     /// \code

     ///   m.init();

     ///   m.findMinMean();

     ///   m.findCycle();

     /// \endcode

     bool run() {

       init();

       findMinMean();

       return findCycle();

     }

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures.

     ///

     /// \sa reset()

     void init() {

       comp_num = stronglyConnectedComponents(graph, comp);

       if (!cycle_path) {

 	local_path = true;

 	cycle_path = new Path;

       }

     }

     /// \brief Finds the minimum cycle mean value in the graph.

     ///

     /// Computes all the required path data and finds the minimum cycle

     /// mean value in the graph.

     ///

     /// \return \c true if a cycle exists in the graph.

     ///

     /// \pre \ref init() must be called before using this function.

     bool findMinMean() {

       cycle_node = INVALID;

       for (comp_cnt = 0; comp_cnt < comp_num; ++comp_cnt) {

 	initCurrent();

 	processRounds();

 	Length min_length;

 	int min_size;

 	Node min_node;

 	bool found_min = findCurrentMin(min_length, min_size, min_node);

 	if ( found_min && (cycle_node == INVALID ||

 	     min_length * cycle_size < cycle_length * min_size) ) {

 	  cycle_length = min_length;

 	  cycle_size = min_size;

 	  cycle_node = min_node;

 	}

       }

       return (cycle_node != INVALID);

     }

     /// \brief Finds a critical (minimum mean) cycle.

     ///

     /// Finds a critical (minimum mean) cycle using the path data

     /// stored in \ref dmap.

     ///

     /// \return \c true if a cycle exists in the graph.

     ///

     /// \pre \ref init() and \ref findMinMean() must be called before

     /// using this function.

     bool findCycle() {

       if (cycle_node == INVALID) return false;

       cycle_length = 0;

       cycle_size = 0;

       IntNodeMap reached(graph, -1);

       int r = reached[cycle_node] = dmap[cycle_node].size() - 1;

       Node u = graph.source(dmap[cycle_node][r].pred);

       while (reached[u] < 0) {

 	reached[u] = --r;

 	u = graph.source(dmap[u][r].pred);

       }

       r = reached[u];

       Edge e = dmap[u][r].pred;

       cycle_path->addFront(e);

       cycle_length = cycle_length + length[e];

       ++cycle_size;

       Node v;

       while ((v = graph.source(e)) != u) {

 	e = dmap[v][--r].pred;

 	cycle_path->addFront(e);

 	cycle_length = cycle_length + length[e];

 	++cycle_size;

       }

       return true;

     }

     /// \brief Resets the internal data structures.

     ///

     /// Resets the internal data structures so that \ref findMinMean()

     /// and \ref findCycle() can be called again (e.g. when the

     /// underlaying graph has been modified).

     ///

     /// \sa init()

     void reset() {

       for (NodeIt u(graph); u != INVALID; ++u)

 	dmap[u].clear();

       cycle_node = INVALID;

       if (cycle_path) cycle_path->clear();

       comp_num = stronglyConnectedComponents(graph, comp);

     }

     /// \brief Returns the total length of the found cycle.

     ///

     /// Returns the total length of the found cycle.

     ///

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

     /// using this function. If only \ref findMinMean() is called,

     /// the return value is not valid.

     Length cycleLength() const {

       return cycle_length;

     }

     /// \brief Returns the number of edges in the found cycle.

     ///

     /// Returns the number of edges in the found cycle.

     ///

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

     /// using this function. If only \ref findMinMean() is called,

     /// the return value is not valid.

     int cycleEdgeNum() const {

       return cycle_size;

     }

     /// \brief Returns the mean length of the found cycle.

     ///

     /// Returns the mean length of the found cycle.

     ///

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

     /// using this function.

     ///

     /// \warning LengthMap::Value must be convertible to double.

     ///

     /// \note <tt>m.minMean()</tt> is just a shortcut of the following

     /// code.

     /// \code

     ///   return m.cycleLength() / double(m.cycleEdgeNum());

     /// \endcode

     /// However if only \ref findMinMean() is called before using this

     /// function, <tt>m.cycleLength()</tt> and <tt>m.cycleEdgeNum()</tt>

     /// are not valid alone, only their ratio is valid.

     double minMean() const {

       return cycle_length / (double)cycle_size;

     }

     /// \brief Returns a const reference to the \ref lemon::Path "Path"

     /// structure of the found cycle.

     ///

     /// Returns a const reference to the \ref lemon::Path "Path"

     /// structure of the found cycle.

     ///

     /// \pre \ref run() must be called before using this function.

     ///

     /// \sa \ref cyclePath()

     const Path& cycle() const {

       return *cycle_path;

     }

     /// \brief Sets the \ref lemon::Path "Path" structure storing the

     /// found cycle.

     ///

     /// Sets the \ref lemon::Path "Path" structure storing the found

     /// cycle. If you don't use this function before calling

     /// \ref run(), it will allocate one. The destuctor deallocates

     /// this automatically allocated map, of course.

     ///

     /// \note The algorithm calls only the \ref lemon::Path::addFront()

     /// "addFront()" method of the given \ref lemon::Path "Path"

     /// structure.

     ///

     /// \return \c (*this)

     MinMeanCycle& cyclePath(Path &path) {

       if (local_path) {

 	delete cycle_path;

 	local_path = false;

       }

       cycle_path = &path;

       return *this;

     }

   }; //class MinMeanCycle

   ///@}

 } //namespace lemon

 #endif //LEMON_MIN_MEAN_CYCLE_H