lemon/floyd_warshall.h
author deba
Fri, 04 Nov 2005 16:10:23 +0000
changeset 1769 a67ec111236c
parent 1763 49045f2d28d4
child 1865 dcefd1d1377f
permissions -rw-r--r--
Removed todo
Moved to topology module
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/* -*- C++ -*-
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 * lemon/floyd_warshall.h - Part of LEMON, a generic C++ optimization library
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 *
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 * Copyright (C) 2005 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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#ifndef LEMON_FLOYD_WARSHALL_H
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#define LEMON_FLOYD_WARSHALL_H
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///\ingroup flowalgs
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/// \file
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/// \brief FloydWarshall algorithm.
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///
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#include <lemon/list_graph.h>
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#include <lemon/graph_utils.h>
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#include <lemon/invalid.h>
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#include <lemon/error.h>
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#include <lemon/matrix_maps.h>
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#include <lemon/maps.h>
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#include <limits>
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namespace lemon {
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  /// \brief Default OperationTraits for the FloydWarshall algorithm class.
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  ///  
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  /// It defines all computational operations and constants which are
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  /// used in the Floyd-Warshall algorithm. The default implementation
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  /// is based on the numeric_limits class. If the numeric type does not
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  /// have infinity value then the maximum value is used as extremal
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  /// infinity value.
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  template <
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    typename Value, 
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    bool has_infinity = std::numeric_limits<Value>::has_infinity>
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  struct FloydWarshallDefaultOperationTraits {
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    /// \brief Gives back the zero value of the type.
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    static Value zero() {
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      return static_cast<Value>(0);
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    }
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    /// \brief Gives back the positive infinity value of the type.
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    static Value infinity() {
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      return std::numeric_limits<Value>::infinity();
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    }
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    /// \brief Gives back the sum of the given two elements.
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    static Value plus(const Value& left, const Value& right) {
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      return left + right;
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    }
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    /// \brief Gives back true only if the first value less than the second.
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    static bool less(const Value& left, const Value& right) {
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      return left < right;
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    }
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  };
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  template <typename Value>
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  struct FloydWarshallDefaultOperationTraits<Value, false> {
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    static Value zero() {
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      return static_cast<Value>(0);
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    }
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    static Value infinity() {
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      return std::numeric_limits<Value>::max();
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    }
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    static Value plus(const Value& left, const Value& right) {
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      if (left == infinity() || right == infinity()) return infinity();
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      return left + right;
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    }
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    static bool less(const Value& left, const Value& right) {
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      return left < right;
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    }
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  };
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  /// \brief Default traits class of FloydWarshall class.
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  ///
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  /// Default traits class of FloydWarshall class.
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  /// \param _Graph Graph type.
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  /// \param _LegthMap Type of length map.
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  template<class _Graph, class _LengthMap>
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  struct FloydWarshallDefaultTraits {
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    /// The graph type the algorithm runs on. 
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    typedef _Graph Graph;
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    /// \brief The type of the map that stores the edge lengths.
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    ///
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    /// The type of the map that stores the edge lengths.
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    /// It must meet the \ref concept::ReadMap "ReadMap" concept.
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    typedef _LengthMap LengthMap;
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    // The type of the length of the edges.
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    typedef typename _LengthMap::Value Value;
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    /// \brief Operation traits for belmann-ford algorithm.
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    ///
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    /// It defines the infinity type on the given Value type
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    /// and the used operation.
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    /// \see FloydWarshallDefaultOperationTraits
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    typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;
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    /// \brief The type of the matrix map that stores the last edges of the 
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    /// shortest paths.
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    /// 
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    /// The type of the map that stores the last edges of the shortest paths.
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    /// It must be a matrix map with \c Graph::Edge value type.
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    ///
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    typedef DynamicMatrixMap<Graph, typename Graph::Node, 
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			     typename Graph::Edge> PredMap;
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    /// \brief Instantiates a PredMap.
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    /// 
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    /// This function instantiates a \ref PredMap. 
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    /// \param G is the graph, to which we would like to define the PredMap.
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    /// \todo The graph alone may be insufficient for the initialization
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    static PredMap *createPredMap(const _Graph& graph) {
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      return new PredMap(graph);
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    }
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    /// \brief The type of the map that stores the dists of the nodes.
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    ///
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    /// The type of the map that stores the dists of the nodes.
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    /// It must meet the \ref concept::WriteMatrixMap "WriteMatrixMap" concept.
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    ///
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    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;
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    /// \brief Instantiates a DistMap.
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    ///
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    /// This function instantiates a \ref DistMap. 
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    /// \param G is the graph, to which we would like to define the 
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    /// \ref DistMap
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    static DistMap *createDistMap(const _Graph& graph) {
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      return new DistMap(graph);
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    }
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  };
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  /// \brief %FloydWarshall algorithm class.
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  ///
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  /// \ingroup flowalgs
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  /// This class provides an efficient implementation of \c Floyd-Warshall 
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  /// algorithm. The edge lengths are passed to the algorithm using a
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  /// \ref concept::ReadMap "ReadMap", so it is easy to change it to any 
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  /// kind of length.
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  ///
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  /// The algorithm solves the shortest path problem for each pair
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  /// of node when the edges can have negative length but the graph should
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  /// not contain cycles with negative sum of length. If we can assume
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  /// that all edge is non-negative in the graph then the dijkstra algorithm
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  /// should be used from each node rather and if the graph is sparse and
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  /// there are negative circles then the johnson algorithm.
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  ///
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  /// The complexity of this algorithm is O(n^3 + e).
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  ///
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  /// The type of the length is determined by the
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  /// \ref concept::ReadMap::Value "Value" of the length map.
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  ///
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  /// \param _Graph The graph type the algorithm runs on. The default value
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  /// is \ref ListGraph. The value of _Graph is not used directly by
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  /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.
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  /// \param _LengthMap This read-only EdgeMap determines the lengths of the
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  /// edges. It is read once for each edge, so the map may involve in
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  /// relatively time consuming process to compute the edge length if
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  /// it is necessary. The default map type is \ref
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  /// concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".  The value
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  /// of _LengthMap is not used directly by FloydWarshall, it is only passed 
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  /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set
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  /// various data types used by the algorithm.  The default traits
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  /// class is \ref FloydWarshallDefaultTraits
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  /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>".  See \ref
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  /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall 
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  /// traits class.
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  ///
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  /// \author Balazs Dezso
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#ifdef DOXYGEN
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  template <typename _Graph, typename _LengthMap typename _Traits >
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#else
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  template <typename _Graph=ListGraph,
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	    typename _LengthMap=typename _Graph::template EdgeMap<int>,
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	    typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >
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#endif
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  class FloydWarshall {
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  public:
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    /// \brief \ref Exception for uninitialized parameters.
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    ///
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    /// This error represents problems in the initialization
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    /// of the parameters of the algorithms.
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    class UninitializedParameter : public lemon::UninitializedParameter {
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    public:
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      virtual const char* exceptionName() const {
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	return "lemon::FloydWarshall::UninitializedParameter";
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      }
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    };
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    typedef _Traits Traits;
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    ///The type of the underlying graph.
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    typedef typename _Traits::Graph Graph;
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    typedef typename Graph::Node Node;
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    typedef typename Graph::NodeIt NodeIt;
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    typedef typename Graph::Edge Edge;
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    typedef typename Graph::EdgeIt EdgeIt;
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    /// \brief The type of the length of the edges.
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    typedef typename _Traits::LengthMap::Value Value;
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    /// \brief The type of the map that stores the edge lengths.
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    typedef typename _Traits::LengthMap LengthMap;
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    /// \brief The type of the map that stores the last
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    /// edges of the shortest paths. The type of the PredMap
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    /// is a matrix map for Edges
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    typedef typename _Traits::PredMap PredMap;
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    /// \brief The type of the map that stores the dists of the nodes.
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    /// The type of the DistMap is a matrix map for Values
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    typedef typename _Traits::DistMap DistMap;
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    /// \brief The operation traits.
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    typedef typename _Traits::OperationTraits OperationTraits;
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  private:
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    /// Pointer to the underlying graph.
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    const Graph *graph;
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    /// Pointer to the length map
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    const LengthMap *length;
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    ///Pointer to the map of predecessors edges.
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    PredMap *_pred;
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    ///Indicates if \ref _pred is locally allocated (\c true) or not.
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    bool local_pred;
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    ///Pointer to the map of distances.
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    DistMap *_dist;
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    ///Indicates if \ref _dist is locally allocated (\c true) or not.
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    bool local_dist;
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    /// Creates the maps if necessary.
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    void create_maps() {
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      if(!_pred) {
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	local_pred = true;
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	_pred = Traits::createPredMap(*graph);
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      }
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      if(!_dist) {
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	local_dist = true;
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	_dist = Traits::createDistMap(*graph);
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      }
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    }
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  public :
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    /// \name Named template parameters
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    ///@{
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    template <class T>
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    struct DefPredMapTraits : public Traits {
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      typedef T PredMap;
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      static PredMap *createPredMap(const Graph& graph) {
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	throw UninitializedParameter();
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      }
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting PredMap 
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    /// type
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    /// \ref named-templ-param "Named parameter" for setting PredMap type
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    ///
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    template <class T>
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    struct DefPredMap 
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      : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {
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      typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;
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    };
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    template <class T>
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    struct DefDistMapTraits : public Traits {
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      typedef T DistMap;
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      static DistMap *createDistMap(const Graph& graph) {
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	throw UninitializedParameter();
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      }
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting DistMap 
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    /// type
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    ///
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    /// \ref named-templ-param "Named parameter" for setting DistMap type
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    ///
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    template <class T>
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    struct DefDistMap 
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      : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {
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      typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;
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    };
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    template <class T>
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    struct DefOperationTraitsTraits : public Traits {
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      typedef T OperationTraits;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting 
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    /// OperationTraits type
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    ///
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    /// \ref named-templ-param "Named parameter" for setting PredMap type
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    template <class T>
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    struct DefOperationTraits
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      : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {
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      typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >
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      Create;
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    };
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    ///@}
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  protected:
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    FloydWarshall() {}
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  public:      
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    typedef FloydWarshall Create;
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    /// \brief Constructor.
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    ///
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    /// \param _graph the graph the algorithm will run on.
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    /// \param _length the length map used by the algorithm.
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    FloydWarshall(const Graph& _graph, const LengthMap& _length) :
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      graph(&_graph), length(&_length),
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      _pred(0), local_pred(false),
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      _dist(0), local_dist(false) {}
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    ///Destructor.
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    ~FloydWarshall() {
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      if(local_pred) delete _pred;
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      if(local_dist) delete _dist;
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    }
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    /// \brief Sets the length map.
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    ///
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    /// Sets the length map.
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    /// \return \c (*this)
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    FloydWarshall &lengthMap(const LengthMap &m) {
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      length = &m;
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      return *this;
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    }
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    /// \brief Sets the map storing the predecessor edges.
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    ///
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    /// Sets the map storing the predecessor edges.
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    /// If you don't use this function before calling \ref run(),
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    /// it will allocate one. The destuctor deallocates this
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    /// automatically allocated map, of course.
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    /// \return \c (*this)
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    FloydWarshall &predMap(PredMap &m) {
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      if(local_pred) {
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	delete _pred;
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	local_pred=false;
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      }
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      _pred = &m;
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      return *this;
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    }
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    /// \brief Sets the map storing the distances calculated by the algorithm.
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    ///
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    /// Sets the map storing the distances calculated by the algorithm.
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    /// If you don't use this function before calling \ref run(),
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    /// it will allocate one. The destuctor deallocates this
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    /// automatically allocated map, of course.
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    /// \return \c (*this)
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    FloydWarshall &distMap(DistMap &m) {
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      if(local_dist) {
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	delete _dist;
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	local_dist=false;
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      }
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      _dist = &m;
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      return *this;
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    }
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    ///\name Execution control
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    /// The simplest way to execute the algorithm is to use
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    /// one of the member functions called \c run(...).
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    /// \n
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    /// If you need more control on the execution,
deba@1699
   381
    /// Finally \ref start() will perform the actual path
deba@1699
   382
    /// computation.
deba@1699
   383
deba@1699
   384
    ///@{
deba@1699
   385
deba@1699
   386
    /// \brief Initializes the internal data structures.
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   387
    /// 
deba@1699
   388
    /// Initializes the internal data structures.
deba@1699
   389
    void init() {
deba@1699
   390
      create_maps();
deba@1699
   391
      for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699
   392
	for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699
   393
	  _pred->set(it, jt, INVALID);
deba@1741
   394
	  _dist->set(it, jt, OperationTraits::infinity());
deba@1699
   395
	}
deba@1741
   396
	_dist->set(it, it, OperationTraits::zero());
deba@1699
   397
      }
deba@1699
   398
      for (EdgeIt it(*graph); it != INVALID; ++it) {
deba@1699
   399
	Node source = graph->source(it);
deba@1699
   400
	Node target = graph->target(it);	
deba@1699
   401
	if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {
deba@1699
   402
	  _dist->set(source, target, (*length)[it]);
deba@1699
   403
	  _pred->set(source, target, it);
deba@1699
   404
	}
deba@1699
   405
      }
deba@1699
   406
    }
deba@1699
   407
    
deba@1699
   408
    /// \brief Executes the algorithm.
deba@1699
   409
    ///
deba@1699
   410
    /// This method runs the %FloydWarshall algorithm in order to compute 
deba@1699
   411
    /// the shortest path to each node pairs. The algorithm 
deba@1699
   412
    /// computes 
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   413
    /// - The shortest path tree for each node.
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   414
    /// - The distance between each node pairs.
deba@1699
   415
    void start() {
deba@1699
   416
      for (NodeIt kt(*graph); kt != INVALID; ++kt) {
deba@1699
   417
	for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1699
   418
	  for (NodeIt jt(*graph); jt != INVALID; ++jt) {
deba@1699
   419
	    Value relaxed = OperationTraits::plus((*_dist)(it, kt),
deba@1699
   420
						  (*_dist)(kt, jt));
deba@1699
   421
	    if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {
deba@1699
   422
	      _dist->set(it, jt, relaxed);
deba@1699
   423
	      _pred->set(it, jt, (*_pred)(kt, jt));
deba@1699
   424
	    }
deba@1699
   425
	  }
deba@1699
   426
	}
deba@1699
   427
      }
deba@1699
   428
    }
deba@1741
   429
deba@1754
   430
    /// \brief Executes the algorithm and checks the negative cycles.
deba@1741
   431
    ///
deba@1741
   432
    /// This method runs the %FloydWarshall algorithm in order to compute 
deba@1754
   433
    /// the shortest path to each node pairs. If there is a negative cycle 
deba@1741
   434
    /// in the graph it gives back false. 
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   435
    /// The algorithm computes 
deba@1741
   436
    /// - The shortest path tree for each node.
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   437
    /// - The distance between each node pairs.
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   438
    bool checkedStart() {
deba@1741
   439
      start();
deba@1741
   440
      for (NodeIt it(*graph); it != INVALID; ++it) {
deba@1741
   441
	if (OperationTraits::less((*dist)(it, it), OperationTraits::zero())) {
deba@1741
   442
	  return false;
deba@1741
   443
	}
deba@1741
   444
      }
deba@1741
   445
      return true;
deba@1741
   446
    }
deba@1699
   447
    
deba@1699
   448
    /// \brief Runs %FloydWarshall algorithm.
deba@1699
   449
    ///    
deba@1699
   450
    /// This method runs the %FloydWarshall algorithm from a each node
deba@1699
   451
    /// in order to compute the shortest path to each node pairs. 
deba@1699
   452
    /// The algorithm computes
deba@1699
   453
    /// - The shortest path tree for each node.
deba@1699
   454
    /// - The distance between each node pairs.
deba@1699
   455
    ///
deba@1699
   456
    /// \note d.run(s) is just a shortcut of the following code.
deba@1699
   457
    /// \code
deba@1699
   458
    ///  d.init();
deba@1699
   459
    ///  d.start();
deba@1699
   460
    /// \endcode
deba@1699
   461
    void run() {
deba@1699
   462
      init();
deba@1699
   463
      start();
deba@1699
   464
    }
deba@1699
   465
    
deba@1699
   466
    ///@}
deba@1699
   467
deba@1699
   468
    /// \name Query Functions
deba@1699
   469
    /// The result of the %FloydWarshall algorithm can be obtained using these
deba@1699
   470
    /// functions.\n
deba@1699
   471
    /// Before the use of these functions,
deba@1699
   472
    /// either run() or start() must be called.
deba@1699
   473
    
deba@1699
   474
    ///@{
deba@1699
   475
deba@1699
   476
    /// \brief Copies the shortest path to \c t into \c p
deba@1699
   477
    ///    
deba@1699
   478
    /// This function copies the shortest path to \c t into \c p.
deba@1699
   479
    /// If it \c t is a source itself or unreachable, then it does not
deba@1699
   480
    /// alter \c p.
deba@1699
   481
    /// \return Returns \c true if a path to \c t was actually copied to \c p,
deba@1699
   482
    /// \c false otherwise.
deba@1699
   483
    /// \sa DirPath
deba@1699
   484
    template <typename Path>
deba@1699
   485
    bool getPath(Path &p, Node source, Node target) {
deba@1699
   486
      if (connected(source, target)) {
deba@1699
   487
	p.clear();
deba@1699
   488
	typename Path::Builder b(target);
deba@1763
   489
	for(b.setStartNode(target); predEdge(source, target) != INVALID;
deba@1699
   490
	    target = predNode(target)) {
deba@1763
   491
	  b.pushFront(predEdge(source, target));
deba@1699
   492
	}
deba@1699
   493
	b.commit();
deba@1699
   494
	return true;
deba@1699
   495
      }
deba@1699
   496
      return false;
deba@1699
   497
    }
deba@1699
   498
	  
deba@1699
   499
    /// \brief The distance between two nodes.
deba@1699
   500
    ///
deba@1699
   501
    /// Returns the distance between two nodes.
deba@1699
   502
    /// \pre \ref run() must be called before using this function.
deba@1699
   503
    /// \warning If node \c v in unreachable from the root the return value
deba@1699
   504
    /// of this funcion is undefined.
deba@1699
   505
    Value dist(Node source, Node target) const { 
deba@1699
   506
      return (*_dist)(source, target); 
deba@1699
   507
    }
deba@1699
   508
deba@1699
   509
    /// \brief Returns the 'previous edge' of the shortest path tree.
deba@1699
   510
    ///
deba@1699
   511
    /// For the node \c node it returns the 'previous edge' of the shortest 
deba@1699
   512
    /// path tree to direction of the node \c root 
deba@1699
   513
    /// i.e. it returns the last edge of a shortest path from the node \c root 
deba@1699
   514
    /// to \c node. It is \ref INVALID if \c node is unreachable from the root
deba@1699
   515
    /// or if \c node=root. The shortest path tree used here is equal to the 
deba@1699
   516
    /// shortest path tree used in \ref predNode(). 
deba@1699
   517
    /// \pre \ref run() must be called before using this function.
deba@1763
   518
    Edge predEdge(Node root, Node node) const { 
deba@1699
   519
      return (*_pred)(root, node); 
deba@1699
   520
    }
deba@1699
   521
deba@1699
   522
    /// \brief Returns the 'previous node' of the shortest path tree.
deba@1699
   523
    ///
deba@1699
   524
    /// For a node \c node it returns the 'previous node' of the shortest path 
deba@1699
   525
    /// tree to direction of the node \c root, i.e. it returns the last but 
deba@1699
   526
    /// one node from a shortest path from the \c root to \c node. It is 
deba@1699
   527
    /// INVALID if \c node is unreachable from the root or if \c node=root. 
deba@1699
   528
    /// The shortest path tree used here is equal to the 
deba@1763
   529
    /// shortest path tree used in \ref predEdge().  
deba@1699
   530
    /// \pre \ref run() must be called before using this function.
deba@1699
   531
    Node predNode(Node root, Node node) const { 
deba@1699
   532
      return (*_pred)(root, node) == INVALID ? 
deba@1699
   533
      INVALID : graph->source((*_pred)(root, node)); 
deba@1699
   534
    }
deba@1699
   535
    
deba@1699
   536
    /// \brief Returns a reference to the matrix node map of distances.
deba@1699
   537
    ///
deba@1699
   538
    /// Returns a reference to the matrix node map of distances. 
deba@1699
   539
    ///
deba@1699
   540
    /// \pre \ref run() must be called before using this function.
deba@1699
   541
    const DistMap &distMap() const { return *_dist;}
deba@1699
   542
 
deba@1699
   543
    /// \brief Returns a reference to the shortest path tree map.
deba@1699
   544
    ///
deba@1699
   545
    /// Returns a reference to the matrix node map of the edges of the
deba@1699
   546
    /// shortest path tree.
deba@1699
   547
    /// \pre \ref run() must be called before using this function.
deba@1699
   548
    const PredMap &predMap() const { return *_pred;}
deba@1699
   549
 
deba@1699
   550
    /// \brief Checks if a node is reachable from the root.
deba@1699
   551
    ///
deba@1699
   552
    /// Returns \c true if \c v is reachable from the root.
deba@1699
   553
    /// \pre \ref run() must be called before using this function.
deba@1699
   554
    ///
deba@1699
   555
    bool connected(Node source, Node target) { 
deba@1699
   556
      return (*_dist)(source, target) != OperationTraits::infinity(); 
deba@1699
   557
    }
deba@1699
   558
    
deba@1699
   559
    ///@}
deba@1699
   560
  };
deba@1699
   561
 
deba@1699
   562
} //END OF NAMESPACE LEMON
deba@1699
   563
deba@1699
   564
#endif
deba@1699
   565