lemon/maps.h
changeset 803 1b89e29c9fc7
parent 786 e20173729589
parent 789 8ddb7deabab9
child 877 141f9c0db4a3
     1.1 --- a/lemon/maps.h	Thu Dec 10 17:05:35 2009 +0100
     1.2 +++ b/lemon/maps.h	Thu Dec 10 17:18:25 2009 +0100
     1.3 @@ -22,6 +22,7 @@
     1.4  #include <iterator>
     1.5  #include <functional>
     1.6  #include <vector>
     1.7 +#include <map>
     1.8  
     1.9  #include <lemon/core.h>
    1.10  
    1.11 @@ -29,8 +30,6 @@
    1.12  ///\ingroup maps
    1.13  ///\brief Miscellaneous property maps
    1.14  
    1.15 -#include <map>
    1.16 -
    1.17  namespace lemon {
    1.18  
    1.19    /// \addtogroup maps
    1.20 @@ -57,7 +56,7 @@
    1.21    /// its type definitions, or if you have to provide a writable map,
    1.22    /// but data written to it is not required (i.e. it will be sent to
    1.23    /// <tt>/dev/null</tt>).
    1.24 -  /// It conforms the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    1.25 +  /// It conforms to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    1.26    ///
    1.27    /// \sa ConstMap
    1.28    template<typename K, typename V>
    1.29 @@ -90,7 +89,7 @@
    1.30    /// value to each key.
    1.31    ///
    1.32    /// In other aspects it is equivalent to \c NullMap.
    1.33 -  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.34 +  /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.35    /// concept, but it absorbs the data written to it.
    1.36    ///
    1.37    /// The simplest way of using this map is through the constMap()
    1.38 @@ -159,7 +158,7 @@
    1.39    /// value to each key.
    1.40    ///
    1.41    /// In other aspects it is equivalent to \c NullMap.
    1.42 -  /// So it conforms the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.43 +  /// So it conforms to the \ref concepts::ReadWriteMap "ReadWriteMap"
    1.44    /// concept, but it absorbs the data written to it.
    1.45    ///
    1.46    /// The simplest way of using this map is through the constMap()
    1.47 @@ -231,10 +230,10 @@
    1.48    ///
    1.49    /// This map is essentially a wrapper for \c std::vector. It assigns
    1.50    /// values to integer keys from the range <tt>[0..size-1]</tt>.
    1.51 -  /// It can be used with some data structures, for example
    1.52 -  /// \c UnionFind, \c BinHeap, when the used items are small
    1.53 -  /// integers. This map conforms the \ref concepts::ReferenceMap
    1.54 -  /// "ReferenceMap" concept.
    1.55 +  /// It can be used together with some data structures, e.g.
    1.56 +  /// heap types and \c UnionFind, when the used items are small
    1.57 +  /// integers. This map conforms to the \ref concepts::ReferenceMap
    1.58 +  /// "ReferenceMap" concept. 
    1.59    ///
    1.60    /// The simplest way of using this map is through the rangeMap()
    1.61    /// function.
    1.62 @@ -341,7 +340,7 @@
    1.63    /// that you can specify a default value for the keys that are not
    1.64    /// stored actually. This value can be different from the default
    1.65    /// contructed value (i.e. \c %Value()).
    1.66 -  /// This type conforms the \ref concepts::ReferenceMap "ReferenceMap"
    1.67 +  /// This type conforms to the \ref concepts::ReferenceMap "ReferenceMap"
    1.68    /// concept.
    1.69    ///
    1.70    /// This map is useful if a default value should be assigned to most of
    1.71 @@ -349,9 +348,9 @@
    1.72    /// keys (i.e. the map is "sparse").
    1.73    /// The name of this type also refers to this important usage.
    1.74    ///
    1.75 -  /// Apart form that this map can be used in many other cases since it
    1.76 +  /// Apart form that, this map can be used in many other cases since it
    1.77    /// is based on \c std::map, which is a general associative container.
    1.78 -  /// However keep in mind that it is usually not as efficient as other
    1.79 +  /// However, keep in mind that it is usually not as efficient as other
    1.80    /// maps.
    1.81    ///
    1.82    /// The simplest way of using this map is through the sparseMap()
    1.83 @@ -707,7 +706,7 @@
    1.84    /// "readable map" to another type using the default conversion.
    1.85    /// The \c Key type of it is inherited from \c M and the \c Value
    1.86    /// type is \c V.
    1.87 -  /// This type conforms the \ref concepts::ReadMap "ReadMap" concept.
    1.88 +  /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
    1.89    ///
    1.90    /// The simplest way of using this map is through the convertMap()
    1.91    /// function.
    1.92 @@ -1786,22 +1785,22 @@
    1.93    ///
    1.94    /// The most important usage of it is storing certain nodes or arcs
    1.95    /// that were marked \c true by an algorithm.
    1.96 -  /// For example it makes easier to store the nodes in the processing
    1.97 +  /// For example, it makes easier to store the nodes in the processing
    1.98    /// order of Dfs algorithm, as the following examples show.
    1.99    /// \code
   1.100    ///   std::vector<Node> v;
   1.101 -  ///   dfs(g,s).processedMap(loggerBoolMap(std::back_inserter(v))).run();
   1.102 +  ///   dfs(g).processedMap(loggerBoolMap(std::back_inserter(v))).run(s);
   1.103    /// \endcode
   1.104    /// \code
   1.105    ///   std::vector<Node> v(countNodes(g));
   1.106 -  ///   dfs(g,s).processedMap(loggerBoolMap(v.begin())).run();
   1.107 +  ///   dfs(g).processedMap(loggerBoolMap(v.begin())).run(s);
   1.108    /// \endcode
   1.109    ///
   1.110    /// \note The container of the iterator must contain enough space
   1.111    /// for the elements or the iterator should be an inserter iterator.
   1.112    ///
   1.113    /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
   1.114 -  /// it cannot be used when a readable map is needed, for example as
   1.115 +  /// it cannot be used when a readable map is needed, for example, as
   1.116    /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
   1.117    ///
   1.118    /// \relates LoggerBoolMap
   1.119 @@ -1818,7 +1817,7 @@
   1.120    /// \brief Provides an immutable and unique id for each item in a graph.
   1.121    ///
   1.122    /// IdMap provides a unique and immutable id for each item of the
   1.123 -  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is 
   1.124 +  /// same type (\c Node, \c Arc or \c Edge) in a graph. This id is
   1.125    ///  - \b unique: different items get different ids,
   1.126    ///  - \b immutable: the id of an item does not change (even if you
   1.127    ///    delete other nodes).
   1.128 @@ -1826,7 +1825,7 @@
   1.129    /// Using this map you get access (i.e. can read) the inner id values of
   1.130    /// the items stored in the graph, which is returned by the \c id()
   1.131    /// function of the graph. This map can be inverted with its member
   1.132 -  /// class \c InverseMap or with the \c operator() member.
   1.133 +  /// class \c InverseMap or with the \c operator()() member.
   1.134    ///
   1.135    /// \tparam GR The graph type.
   1.136    /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.137 @@ -1866,9 +1865,11 @@
   1.138  
   1.139    public:
   1.140  
   1.141 -    /// \brief This class represents the inverse of its owner (IdMap).
   1.142 +    /// \brief The inverse map type of IdMap.
   1.143      ///
   1.144 -    /// This class represents the inverse of its owner (IdMap).
   1.145 +    /// The inverse map type of IdMap. The subscript operator gives back
   1.146 +    /// an item by its id.
   1.147 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   1.148      /// \see inverse()
   1.149      class InverseMap {
   1.150      public:
   1.151 @@ -1883,9 +1884,9 @@
   1.152        /// Constructor for creating an id-to-item map.
   1.153        explicit InverseMap(const IdMap& map) : _graph(map._graph) {}
   1.154  
   1.155 -      /// \brief Gives back the given item from its id.
   1.156 +      /// \brief Gives back an item by its id.
   1.157        ///
   1.158 -      /// Gives back the given item from its id.
   1.159 +      /// Gives back an item by its id.
   1.160        Item operator[](int id) const { return _graph->fromId(id, Item());}
   1.161  
   1.162      private:
   1.163 @@ -1898,16 +1899,34 @@
   1.164      InverseMap inverse() const { return InverseMap(*_graph);}
   1.165    };
   1.166  
   1.167 +  /// \brief Returns an \c IdMap class.
   1.168 +  ///
   1.169 +  /// This function just returns an \c IdMap class.
   1.170 +  /// \relates IdMap
   1.171 +  template <typename K, typename GR>
   1.172 +  inline IdMap<GR, K> idMap(const GR& graph) {
   1.173 +    return IdMap<GR, K>(graph);
   1.174 +  }
   1.175  
   1.176    /// \brief General cross reference graph map type.
   1.177  
   1.178    /// This class provides simple invertable graph maps.
   1.179 -  /// It wraps an arbitrary \ref concepts::ReadWriteMap "ReadWriteMap"
   1.180 -  /// and if a key is set to a new value then store it
   1.181 -  /// in the inverse map.
   1.182 +  /// It wraps a standard graph map (\c NodeMap, \c ArcMap or \c EdgeMap)
   1.183 +  /// and if a key is set to a new value, then stores it in the inverse map.
   1.184 +  /// The graph items can be accessed by their values either using
   1.185 +  /// \c InverseMap or \c operator()(), and the values of the map can be
   1.186 +  /// accessed with an STL compatible forward iterator (\c ValueIt).
   1.187 +  /// 
   1.188 +  /// This map is intended to be used when all associated values are
   1.189 +  /// different (the map is actually invertable) or there are only a few
   1.190 +  /// items with the same value.
   1.191 +  /// Otherwise consider to use \c IterableValueMap, which is more 
   1.192 +  /// suitable and more efficient for such cases. It provides iterators
   1.193 +  /// to traverse the items with the same associated value, but
   1.194 +  /// it does not have \c InverseMap.
   1.195    ///
   1.196 -  /// The values of the map can be accessed
   1.197 -  /// with stl compatible forward iterator.
   1.198 +  /// This type is not reference map, so it cannot be modified with
   1.199 +  /// the subscript operator.
   1.200    ///
   1.201    /// \tparam GR The graph type.
   1.202    /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.203 @@ -1923,7 +1942,7 @@
   1.204      typedef typename ItemSetTraits<GR, K>::
   1.205        template Map<V>::Type Map;
   1.206  
   1.207 -    typedef std::map<V, K> Container;
   1.208 +    typedef std::multimap<V, K> Container;
   1.209      Container _inv_map;
   1.210  
   1.211    public:
   1.212 @@ -1945,54 +1964,66 @@
   1.213  
   1.214      /// \brief Forward iterator for values.
   1.215      ///
   1.216 -    /// This iterator is an stl compatible forward
   1.217 +    /// This iterator is an STL compatible forward
   1.218      /// iterator on the values of the map. The values can
   1.219      /// be accessed in the <tt>[beginValue, endValue)</tt> range.
   1.220 -    class ValueIterator
   1.221 +    /// They are considered with multiplicity, so each value is
   1.222 +    /// traversed for each item it is assigned to.
   1.223 +    class ValueIt
   1.224        : public std::iterator<std::forward_iterator_tag, Value> {
   1.225        friend class CrossRefMap;
   1.226      private:
   1.227 -      ValueIterator(typename Container::const_iterator _it)
   1.228 +      ValueIt(typename Container::const_iterator _it)
   1.229          : it(_it) {}
   1.230      public:
   1.231  
   1.232 -      ValueIterator() {}
   1.233 -
   1.234 -      ValueIterator& operator++() { ++it; return *this; }
   1.235 -      ValueIterator operator++(int) {
   1.236 -        ValueIterator tmp(*this);
   1.237 +      /// Constructor
   1.238 +      ValueIt() {}
   1.239 +
   1.240 +      /// \e
   1.241 +      ValueIt& operator++() { ++it; return *this; }
   1.242 +      /// \e
   1.243 +      ValueIt operator++(int) {
   1.244 +        ValueIt tmp(*this);
   1.245          operator++();
   1.246          return tmp;
   1.247        }
   1.248  
   1.249 +      /// \e
   1.250        const Value& operator*() const { return it->first; }
   1.251 +      /// \e
   1.252        const Value* operator->() const { return &(it->first); }
   1.253  
   1.254 -      bool operator==(ValueIterator jt) const { return it == jt.it; }
   1.255 -      bool operator!=(ValueIterator jt) const { return it != jt.it; }
   1.256 +      /// \e
   1.257 +      bool operator==(ValueIt jt) const { return it == jt.it; }
   1.258 +      /// \e
   1.259 +      bool operator!=(ValueIt jt) const { return it != jt.it; }
   1.260  
   1.261      private:
   1.262        typename Container::const_iterator it;
   1.263      };
   1.264 +    
   1.265 +    /// Alias for \c ValueIt
   1.266 +    typedef ValueIt ValueIterator;
   1.267  
   1.268      /// \brief Returns an iterator to the first value.
   1.269      ///
   1.270 -    /// Returns an stl compatible iterator to the
   1.271 +    /// Returns an STL compatible iterator to the
   1.272      /// first value of the map. The values of the
   1.273      /// map can be accessed in the <tt>[beginValue, endValue)</tt>
   1.274      /// range.
   1.275 -    ValueIterator beginValue() const {
   1.276 -      return ValueIterator(_inv_map.begin());
   1.277 +    ValueIt beginValue() const {
   1.278 +      return ValueIt(_inv_map.begin());
   1.279      }
   1.280  
   1.281      /// \brief Returns an iterator after the last value.
   1.282      ///
   1.283 -    /// Returns an stl compatible iterator after the
   1.284 +    /// Returns an STL compatible iterator after the
   1.285      /// last value of the map. The values of the
   1.286      /// map can be accessed in the <tt>[beginValue, endValue)</tt>
   1.287      /// range.
   1.288 -    ValueIterator endValue() const {
   1.289 -      return ValueIterator(_inv_map.end());
   1.290 +    ValueIt endValue() const {
   1.291 +      return ValueIt(_inv_map.end());
   1.292      }
   1.293  
   1.294      /// \brief Sets the value associated with the given key.
   1.295 @@ -2000,11 +2031,15 @@
   1.296      /// Sets the value associated with the given key.
   1.297      void set(const Key& key, const Value& val) {
   1.298        Value oldval = Map::operator[](key);
   1.299 -      typename Container::iterator it = _inv_map.find(oldval);
   1.300 -      if (it != _inv_map.end() && it->second == key) {
   1.301 -        _inv_map.erase(it);
   1.302 +      typename Container::iterator it;
   1.303 +      for (it = _inv_map.equal_range(oldval).first;
   1.304 +           it != _inv_map.equal_range(oldval).second; ++it) {
   1.305 +        if (it->second == key) {
   1.306 +          _inv_map.erase(it);
   1.307 +          break;
   1.308 +        }
   1.309        }
   1.310 -      _inv_map.insert(make_pair(val, key));
   1.311 +      _inv_map.insert(std::make_pair(val, key));
   1.312        Map::set(key, val);
   1.313      }
   1.314  
   1.315 @@ -2016,13 +2051,24 @@
   1.316        return Map::operator[](key);
   1.317      }
   1.318  
   1.319 -    /// \brief Gives back the item by its value.
   1.320 +    /// \brief Gives back an item by its value.
   1.321      ///
   1.322 -    /// Gives back the item by its value.
   1.323 -    Key operator()(const Value& key) const {
   1.324 -      typename Container::const_iterator it = _inv_map.find(key);
   1.325 +    /// This function gives back an item that is assigned to
   1.326 +    /// the given value or \c INVALID if no such item exists.
   1.327 +    /// If there are more items with the same associated value,
   1.328 +    /// only one of them is returned.
   1.329 +    Key operator()(const Value& val) const {
   1.330 +      typename Container::const_iterator it = _inv_map.find(val);
   1.331        return it != _inv_map.end() ? it->second : INVALID;
   1.332      }
   1.333 +    
   1.334 +    /// \brief Returns the number of items with the given value.
   1.335 +    ///
   1.336 +    /// This function returns the number of items with the given value
   1.337 +    /// associated with it.
   1.338 +    int count(const Value &val) const {
   1.339 +      return _inv_map.count(val);
   1.340 +    }
   1.341  
   1.342    protected:
   1.343  
   1.344 @@ -2032,9 +2078,13 @@
   1.345      /// \c AlterationNotifier.
   1.346      virtual void erase(const Key& key) {
   1.347        Value val = Map::operator[](key);
   1.348 -      typename Container::iterator it = _inv_map.find(val);
   1.349 -      if (it != _inv_map.end() && it->second == key) {
   1.350 -        _inv_map.erase(it);
   1.351 +      typename Container::iterator it;
   1.352 +      for (it = _inv_map.equal_range(val).first;
   1.353 +           it != _inv_map.equal_range(val).second; ++it) {
   1.354 +        if (it->second == key) {
   1.355 +          _inv_map.erase(it);
   1.356 +          break;
   1.357 +        }
   1.358        }
   1.359        Map::erase(key);
   1.360      }
   1.361 @@ -2046,9 +2096,13 @@
   1.362      virtual void erase(const std::vector<Key>& keys) {
   1.363        for (int i = 0; i < int(keys.size()); ++i) {
   1.364          Value val = Map::operator[](keys[i]);
   1.365 -        typename Container::iterator it = _inv_map.find(val);
   1.366 -        if (it != _inv_map.end() && it->second == keys[i]) {
   1.367 -          _inv_map.erase(it);
   1.368 +        typename Container::iterator it;
   1.369 +        for (it = _inv_map.equal_range(val).first;
   1.370 +             it != _inv_map.equal_range(val).second; ++it) {
   1.371 +          if (it->second == keys[i]) {
   1.372 +            _inv_map.erase(it);
   1.373 +            break;
   1.374 +          }
   1.375          }
   1.376        }
   1.377        Map::erase(keys);
   1.378 @@ -2065,10 +2119,12 @@
   1.379  
   1.380    public:
   1.381  
   1.382 -    /// \brief The inverse map type.
   1.383 +    /// \brief The inverse map type of CrossRefMap.
   1.384      ///
   1.385 -    /// The inverse of this map. The subscript operator of the map
   1.386 -    /// gives back the item that was last assigned to the value.
   1.387 +    /// The inverse map type of CrossRefMap. The subscript operator gives
   1.388 +    /// back an item by its value.
   1.389 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   1.390 +    /// \see inverse()
   1.391      class InverseMap {
   1.392      public:
   1.393        /// \brief Constructor
   1.394 @@ -2084,8 +2140,9 @@
   1.395  
   1.396        /// \brief Subscript operator.
   1.397        ///
   1.398 -      /// Subscript operator. It gives back the item
   1.399 -      /// that was last assigned to the given value.
   1.400 +      /// Subscript operator. It gives back an item
   1.401 +      /// that is assigned to the given value or \c INVALID
   1.402 +      /// if no such item exists.
   1.403        Value operator[](const Key& key) const {
   1.404          return _inverted(key);
   1.405        }
   1.406 @@ -2094,20 +2151,20 @@
   1.407        const CrossRefMap& _inverted;
   1.408      };
   1.409  
   1.410 -    /// \brief It gives back the read-only inverse map.
   1.411 +    /// \brief Gives back the inverse of the map.
   1.412      ///
   1.413 -    /// It gives back the read-only inverse map.
   1.414 +    /// Gives back the inverse of the CrossRefMap.
   1.415      InverseMap inverse() const {
   1.416        return InverseMap(*this);
   1.417      }
   1.418  
   1.419    };
   1.420  
   1.421 -  /// \brief Provides continuous and unique ID for the
   1.422 +  /// \brief Provides continuous and unique id for the
   1.423    /// items of a graph.
   1.424    ///
   1.425    /// RangeIdMap provides a unique and continuous
   1.426 -  /// ID for each item of a given type (\c Node, \c Arc or
   1.427 +  /// id for each item of a given type (\c Node, \c Arc or
   1.428    /// \c Edge) in a graph. This id is
   1.429    ///  - \b unique: different items get different ids,
   1.430    ///  - \b continuous: the range of the ids is the set of integers
   1.431 @@ -2118,7 +2175,7 @@
   1.432    /// Thus this id is not (necessarily) the same as what can get using
   1.433    /// the \c id() function of the graph or \ref IdMap.
   1.434    /// This map can be inverted with its member class \c InverseMap,
   1.435 -  /// or with the \c operator() member.
   1.436 +  /// or with the \c operator()() member.
   1.437    ///
   1.438    /// \tparam GR The graph type.
   1.439    /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.440 @@ -2246,16 +2303,16 @@
   1.441        _inv_map[pi] = q;
   1.442      }
   1.443  
   1.444 -    /// \brief Gives back the \e RangeId of the item
   1.445 +    /// \brief Gives back the \e range \e id of the item
   1.446      ///
   1.447 -    /// Gives back the \e RangeId of the item.
   1.448 +    /// Gives back the \e range \e id of the item.
   1.449      int operator[](const Item& item) const {
   1.450        return Map::operator[](item);
   1.451      }
   1.452  
   1.453 -    /// \brief Gives back the item belonging to a \e RangeId
   1.454 -    /// 
   1.455 -    /// Gives back the item belonging to a \e RangeId.
   1.456 +    /// \brief Gives back the item belonging to a \e range \e id
   1.457 +    ///
   1.458 +    /// Gives back the item belonging to the given \e range \e id.
   1.459      Item operator()(int id) const {
   1.460        return _inv_map[id];
   1.461      }
   1.462 @@ -2269,7 +2326,9 @@
   1.463  
   1.464      /// \brief The inverse map type of RangeIdMap.
   1.465      ///
   1.466 -    /// The inverse map type of RangeIdMap.
   1.467 +    /// The inverse map type of RangeIdMap. The subscript operator gives
   1.468 +    /// back an item by its \e range \e id.
   1.469 +    /// This type conforms to the \ref concepts::ReadMap "ReadMap" concept.
   1.470      class InverseMap {
   1.471      public:
   1.472        /// \brief Constructor
   1.473 @@ -2287,7 +2346,7 @@
   1.474        /// \brief Subscript operator.
   1.475        ///
   1.476        /// Subscript operator. It gives back the item
   1.477 -      /// that the descriptor currently belongs to.
   1.478 +      /// that the given \e range \e id currently belongs to.
   1.479        Value operator[](const Key& key) const {
   1.480          return _inverted(key);
   1.481        }
   1.482 @@ -2305,12 +2364,932 @@
   1.483  
   1.484      /// \brief Gives back the inverse of the map.
   1.485      ///
   1.486 -    /// Gives back the inverse of the map.
   1.487 +    /// Gives back the inverse of the RangeIdMap.
   1.488      const InverseMap inverse() const {
   1.489        return InverseMap(*this);
   1.490      }
   1.491    };
   1.492  
   1.493 +  /// \brief Returns a \c RangeIdMap class.
   1.494 +  ///
   1.495 +  /// This function just returns an \c RangeIdMap class.
   1.496 +  /// \relates RangeIdMap
   1.497 +  template <typename K, typename GR>
   1.498 +  inline RangeIdMap<GR, K> rangeIdMap(const GR& graph) {
   1.499 +    return RangeIdMap<GR, K>(graph);
   1.500 +  }
   1.501 +  
   1.502 +  /// \brief Dynamic iterable \c bool map.
   1.503 +  ///
   1.504 +  /// This class provides a special graph map type which can store a
   1.505 +  /// \c bool value for graph items (\c Node, \c Arc or \c Edge).
   1.506 +  /// For both \c true and \c false values it is possible to iterate on
   1.507 +  /// the keys mapped to the value.
   1.508 +  ///
   1.509 +  /// This type is a reference map, so it can be modified with the
   1.510 +  /// subscript operator.
   1.511 +  ///
   1.512 +  /// \tparam GR The graph type.
   1.513 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.514 +  /// \c GR::Edge).
   1.515 +  ///
   1.516 +  /// \see IterableIntMap, IterableValueMap
   1.517 +  /// \see CrossRefMap
   1.518 +  template <typename GR, typename K>
   1.519 +  class IterableBoolMap
   1.520 +    : protected ItemSetTraits<GR, K>::template Map<int>::Type {
   1.521 +  private:
   1.522 +    typedef GR Graph;
   1.523 +
   1.524 +    typedef typename ItemSetTraits<GR, K>::ItemIt KeyIt;
   1.525 +    typedef typename ItemSetTraits<GR, K>::template Map<int>::Type Parent;
   1.526 +
   1.527 +    std::vector<K> _array;
   1.528 +    int _sep;
   1.529 +
   1.530 +  public:
   1.531 +
   1.532 +    /// Indicates that the map is reference map.
   1.533 +    typedef True ReferenceMapTag;
   1.534 +
   1.535 +    /// The key type
   1.536 +    typedef K Key;
   1.537 +    /// The value type
   1.538 +    typedef bool Value;
   1.539 +    /// The const reference type.
   1.540 +    typedef const Value& ConstReference;
   1.541 +
   1.542 +  private:
   1.543 +
   1.544 +    int position(const Key& key) const {
   1.545 +      return Parent::operator[](key);
   1.546 +    }
   1.547 +
   1.548 +  public:
   1.549 +
   1.550 +    /// \brief Reference to the value of the map.
   1.551 +    ///
   1.552 +    /// This class is similar to the \c bool type. It can be converted to
   1.553 +    /// \c bool and it provides the same operators.
   1.554 +    class Reference {
   1.555 +      friend class IterableBoolMap;
   1.556 +    private:
   1.557 +      Reference(IterableBoolMap& map, const Key& key)
   1.558 +        : _key(key), _map(map) {}
   1.559 +    public:
   1.560 +
   1.561 +      Reference& operator=(const Reference& value) {
   1.562 +        _map.set(_key, static_cast<bool>(value));
   1.563 +         return *this;
   1.564 +      }
   1.565 +
   1.566 +      operator bool() const {
   1.567 +        return static_cast<const IterableBoolMap&>(_map)[_key];
   1.568 +      }
   1.569 +
   1.570 +      Reference& operator=(bool value) {
   1.571 +        _map.set(_key, value);
   1.572 +        return *this;
   1.573 +      }
   1.574 +      Reference& operator&=(bool value) {
   1.575 +        _map.set(_key, _map[_key] & value);
   1.576 +        return *this;
   1.577 +      }
   1.578 +      Reference& operator|=(bool value) {
   1.579 +        _map.set(_key, _map[_key] | value);
   1.580 +        return *this;
   1.581 +      }
   1.582 +      Reference& operator^=(bool value) {
   1.583 +        _map.set(_key, _map[_key] ^ value);
   1.584 +        return *this;
   1.585 +      }
   1.586 +    private:
   1.587 +      Key _key;
   1.588 +      IterableBoolMap& _map;
   1.589 +    };
   1.590 +
   1.591 +    /// \brief Constructor of the map with a default value.
   1.592 +    ///
   1.593 +    /// Constructor of the map with a default value.
   1.594 +    explicit IterableBoolMap(const Graph& graph, bool def = false)
   1.595 +      : Parent(graph) {
   1.596 +      typename Parent::Notifier* nf = Parent::notifier();
   1.597 +      Key it;
   1.598 +      for (nf->first(it); it != INVALID; nf->next(it)) {
   1.599 +        Parent::set(it, _array.size());
   1.600 +        _array.push_back(it);
   1.601 +      }
   1.602 +      _sep = (def ? _array.size() : 0);
   1.603 +    }
   1.604 +
   1.605 +    /// \brief Const subscript operator of the map.
   1.606 +    ///
   1.607 +    /// Const subscript operator of the map.
   1.608 +    bool operator[](const Key& key) const {
   1.609 +      return position(key) < _sep;
   1.610 +    }
   1.611 +
   1.612 +    /// \brief Subscript operator of the map.
   1.613 +    ///
   1.614 +    /// Subscript operator of the map.
   1.615 +    Reference operator[](const Key& key) {
   1.616 +      return Reference(*this, key);
   1.617 +    }
   1.618 +
   1.619 +    /// \brief Set operation of the map.
   1.620 +    ///
   1.621 +    /// Set operation of the map.
   1.622 +    void set(const Key& key, bool value) {
   1.623 +      int pos = position(key);
   1.624 +      if (value) {
   1.625 +        if (pos < _sep) return;
   1.626 +        Key tmp = _array[_sep];
   1.627 +        _array[_sep] = key;
   1.628 +        Parent::set(key, _sep);
   1.629 +        _array[pos] = tmp;
   1.630 +        Parent::set(tmp, pos);
   1.631 +        ++_sep;
   1.632 +      } else {
   1.633 +        if (pos >= _sep) return;
   1.634 +        --_sep;
   1.635 +        Key tmp = _array[_sep];
   1.636 +        _array[_sep] = key;
   1.637 +        Parent::set(key, _sep);
   1.638 +        _array[pos] = tmp;
   1.639 +        Parent::set(tmp, pos);
   1.640 +      }
   1.641 +    }
   1.642 +
   1.643 +    /// \brief Set all items.
   1.644 +    ///
   1.645 +    /// Set all items in the map.
   1.646 +    /// \note Constant time operation.
   1.647 +    void setAll(bool value) {
   1.648 +      _sep = (value ? _array.size() : 0);
   1.649 +    }
   1.650 +
   1.651 +    /// \brief Returns the number of the keys mapped to \c true.
   1.652 +    ///
   1.653 +    /// Returns the number of the keys mapped to \c true.
   1.654 +    int trueNum() const {
   1.655 +      return _sep;
   1.656 +    }
   1.657 +
   1.658 +    /// \brief Returns the number of the keys mapped to \c false.
   1.659 +    ///
   1.660 +    /// Returns the number of the keys mapped to \c false.
   1.661 +    int falseNum() const {
   1.662 +      return _array.size() - _sep;
   1.663 +    }
   1.664 +
   1.665 +    /// \brief Iterator for the keys mapped to \c true.
   1.666 +    ///
   1.667 +    /// Iterator for the keys mapped to \c true. It works
   1.668 +    /// like a graph item iterator, it can be converted to
   1.669 +    /// the key type of the map, incremented with \c ++ operator, and
   1.670 +    /// if the iterator leaves the last valid key, it will be equal to
   1.671 +    /// \c INVALID.
   1.672 +    class TrueIt : public Key {
   1.673 +    public:
   1.674 +      typedef Key Parent;
   1.675 +
   1.676 +      /// \brief Creates an iterator.
   1.677 +      ///
   1.678 +      /// Creates an iterator. It iterates on the
   1.679 +      /// keys mapped to \c true.
   1.680 +      /// \param map The IterableBoolMap.
   1.681 +      explicit TrueIt(const IterableBoolMap& map)
   1.682 +        : Parent(map._sep > 0 ? map._array[map._sep - 1] : INVALID),
   1.683 +          _map(&map) {}
   1.684 +
   1.685 +      /// \brief Invalid constructor \& conversion.
   1.686 +      ///
   1.687 +      /// This constructor initializes the iterator to be invalid.
   1.688 +      /// \sa Invalid for more details.
   1.689 +      TrueIt(Invalid) : Parent(INVALID), _map(0) {}
   1.690 +
   1.691 +      /// \brief Increment operator.
   1.692 +      ///
   1.693 +      /// Increment operator.
   1.694 +      TrueIt& operator++() {
   1.695 +        int pos = _map->position(*this);
   1.696 +        Parent::operator=(pos > 0 ? _map->_array[pos - 1] : INVALID);
   1.697 +        return *this;
   1.698 +      }
   1.699 +
   1.700 +    private:
   1.701 +      const IterableBoolMap* _map;
   1.702 +    };
   1.703 +
   1.704 +    /// \brief Iterator for the keys mapped to \c false.
   1.705 +    ///
   1.706 +    /// Iterator for the keys mapped to \c false. It works
   1.707 +    /// like a graph item iterator, it can be converted to
   1.708 +    /// the key type of the map, incremented with \c ++ operator, and
   1.709 +    /// if the iterator leaves the last valid key, it will be equal to
   1.710 +    /// \c INVALID.
   1.711 +    class FalseIt : public Key {
   1.712 +    public:
   1.713 +      typedef Key Parent;
   1.714 +
   1.715 +      /// \brief Creates an iterator.
   1.716 +      ///
   1.717 +      /// Creates an iterator. It iterates on the
   1.718 +      /// keys mapped to \c false.
   1.719 +      /// \param map The IterableBoolMap.
   1.720 +      explicit FalseIt(const IterableBoolMap& map)
   1.721 +        : Parent(map._sep < int(map._array.size()) ?
   1.722 +                 map._array.back() : INVALID), _map(&map) {}
   1.723 +
   1.724 +      /// \brief Invalid constructor \& conversion.
   1.725 +      ///
   1.726 +      /// This constructor initializes the iterator to be invalid.
   1.727 +      /// \sa Invalid for more details.
   1.728 +      FalseIt(Invalid) : Parent(INVALID), _map(0) {}
   1.729 +
   1.730 +      /// \brief Increment operator.
   1.731 +      ///
   1.732 +      /// Increment operator.
   1.733 +      FalseIt& operator++() {
   1.734 +        int pos = _map->position(*this);
   1.735 +        Parent::operator=(pos > _map->_sep ? _map->_array[pos - 1] : INVALID);
   1.736 +        return *this;
   1.737 +      }
   1.738 +
   1.739 +    private:
   1.740 +      const IterableBoolMap* _map;
   1.741 +    };
   1.742 +
   1.743 +    /// \brief Iterator for the keys mapped to a given value.
   1.744 +    ///
   1.745 +    /// Iterator for the keys mapped to a given value. It works
   1.746 +    /// like a graph item iterator, it can be converted to
   1.747 +    /// the key type of the map, incremented with \c ++ operator, and
   1.748 +    /// if the iterator leaves the last valid key, it will be equal to
   1.749 +    /// \c INVALID.
   1.750 +    class ItemIt : public Key {
   1.751 +    public:
   1.752 +      typedef Key Parent;
   1.753 +
   1.754 +      /// \brief Creates an iterator with a value.
   1.755 +      ///
   1.756 +      /// Creates an iterator with a value. It iterates on the
   1.757 +      /// keys mapped to the given value.
   1.758 +      /// \param map The IterableBoolMap.
   1.759 +      /// \param value The value.
   1.760 +      ItemIt(const IterableBoolMap& map, bool value)
   1.761 +        : Parent(value ? 
   1.762 +                 (map._sep > 0 ?
   1.763 +                  map._array[map._sep - 1] : INVALID) :
   1.764 +                 (map._sep < int(map._array.size()) ?
   1.765 +                  map._array.back() : INVALID)), _map(&map) {}
   1.766 +
   1.767 +      /// \brief Invalid constructor \& conversion.
   1.768 +      ///
   1.769 +      /// This constructor initializes the iterator to be invalid.
   1.770 +      /// \sa Invalid for more details.
   1.771 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
   1.772 +
   1.773 +      /// \brief Increment operator.
   1.774 +      ///
   1.775 +      /// Increment operator.
   1.776 +      ItemIt& operator++() {
   1.777 +        int pos = _map->position(*this);
   1.778 +        int _sep = pos >= _map->_sep ? _map->_sep : 0;
   1.779 +        Parent::operator=(pos > _sep ? _map->_array[pos - 1] : INVALID);
   1.780 +        return *this;
   1.781 +      }
   1.782 +
   1.783 +    private:
   1.784 +      const IterableBoolMap* _map;
   1.785 +    };
   1.786 +
   1.787 +  protected:
   1.788 +
   1.789 +    virtual void add(const Key& key) {
   1.790 +      Parent::add(key);
   1.791 +      Parent::set(key, _array.size());
   1.792 +      _array.push_back(key);
   1.793 +    }
   1.794 +
   1.795 +    virtual void add(const std::vector<Key>& keys) {
   1.796 +      Parent::add(keys);
   1.797 +      for (int i = 0; i < int(keys.size()); ++i) {
   1.798 +        Parent::set(keys[i], _array.size());
   1.799 +        _array.push_back(keys[i]);
   1.800 +      }
   1.801 +    }
   1.802 +
   1.803 +    virtual void erase(const Key& key) {
   1.804 +      int pos = position(key);
   1.805 +      if (pos < _sep) {
   1.806 +        --_sep;
   1.807 +        Parent::set(_array[_sep], pos);
   1.808 +        _array[pos] = _array[_sep];
   1.809 +        Parent::set(_array.back(), _sep);
   1.810 +        _array[_sep] = _array.back();
   1.811 +        _array.pop_back();
   1.812 +      } else {
   1.813 +        Parent::set(_array.back(), pos);
   1.814 +        _array[pos] = _array.back();
   1.815 +        _array.pop_back();
   1.816 +      }
   1.817 +      Parent::erase(key);
   1.818 +    }
   1.819 +
   1.820 +    virtual void erase(const std::vector<Key>& keys) {
   1.821 +      for (int i = 0; i < int(keys.size()); ++i) {
   1.822 +        int pos = position(keys[i]);
   1.823 +        if (pos < _sep) {
   1.824 +          --_sep;
   1.825 +          Parent::set(_array[_sep], pos);
   1.826 +          _array[pos] = _array[_sep];
   1.827 +          Parent::set(_array.back(), _sep);
   1.828 +          _array[_sep] = _array.back();
   1.829 +          _array.pop_back();
   1.830 +        } else {
   1.831 +          Parent::set(_array.back(), pos);
   1.832 +          _array[pos] = _array.back();
   1.833 +          _array.pop_back();
   1.834 +        }
   1.835 +      }
   1.836 +      Parent::erase(keys);
   1.837 +    }
   1.838 +
   1.839 +    virtual void build() {
   1.840 +      Parent::build();
   1.841 +      typename Parent::Notifier* nf = Parent::notifier();
   1.842 +      Key it;
   1.843 +      for (nf->first(it); it != INVALID; nf->next(it)) {
   1.844 +        Parent::set(it, _array.size());
   1.845 +        _array.push_back(it);
   1.846 +      }
   1.847 +      _sep = 0;
   1.848 +    }
   1.849 +
   1.850 +    virtual void clear() {
   1.851 +      _array.clear();
   1.852 +      _sep = 0;
   1.853 +      Parent::clear();
   1.854 +    }
   1.855 +
   1.856 +  };
   1.857 +
   1.858 +
   1.859 +  namespace _maps_bits {
   1.860 +    template <typename Item>
   1.861 +    struct IterableIntMapNode {
   1.862 +      IterableIntMapNode() : value(-1) {}
   1.863 +      IterableIntMapNode(int _value) : value(_value) {}
   1.864 +      Item prev, next;
   1.865 +      int value;
   1.866 +    };
   1.867 +  }
   1.868 +
   1.869 +  /// \brief Dynamic iterable integer map.
   1.870 +  ///
   1.871 +  /// This class provides a special graph map type which can store an
   1.872 +  /// integer value for graph items (\c Node, \c Arc or \c Edge).
   1.873 +  /// For each non-negative value it is possible to iterate on the keys
   1.874 +  /// mapped to the value.
   1.875 +  ///
   1.876 +  /// This map is intended to be used with small integer values, for which
   1.877 +  /// it is efficient, and supports iteration only for non-negative values.
   1.878 +  /// If you need large values and/or iteration for negative integers,
   1.879 +  /// consider to use \ref IterableValueMap instead.
   1.880 +  ///
   1.881 +  /// This type is a reference map, so it can be modified with the
   1.882 +  /// subscript operator.
   1.883 +  ///
   1.884 +  /// \note The size of the data structure depends on the largest
   1.885 +  /// value in the map.
   1.886 +  ///
   1.887 +  /// \tparam GR The graph type.
   1.888 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
   1.889 +  /// \c GR::Edge).
   1.890 +  ///
   1.891 +  /// \see IterableBoolMap, IterableValueMap
   1.892 +  /// \see CrossRefMap
   1.893 +  template <typename GR, typename K>
   1.894 +  class IterableIntMap
   1.895 +    : protected ItemSetTraits<GR, K>::
   1.896 +        template Map<_maps_bits::IterableIntMapNode<K> >::Type {
   1.897 +  public:
   1.898 +    typedef typename ItemSetTraits<GR, K>::
   1.899 +      template Map<_maps_bits::IterableIntMapNode<K> >::Type Parent;
   1.900 +
   1.901 +    /// The key type
   1.902 +    typedef K Key;
   1.903 +    /// The value type
   1.904 +    typedef int Value;
   1.905 +    /// The graph type
   1.906 +    typedef GR Graph;
   1.907 +
   1.908 +    /// \brief Constructor of the map.
   1.909 +    ///
   1.910 +    /// Constructor of the map. It sets all values to -1.
   1.911 +    explicit IterableIntMap(const Graph& graph)
   1.912 +      : Parent(graph) {}
   1.913 +
   1.914 +    /// \brief Constructor of the map with a given value.
   1.915 +    ///
   1.916 +    /// Constructor of the map with a given value.
   1.917 +    explicit IterableIntMap(const Graph& graph, int value)
   1.918 +      : Parent(graph, _maps_bits::IterableIntMapNode<K>(value)) {
   1.919 +      if (value >= 0) {
   1.920 +        for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
   1.921 +          lace(it);
   1.922 +        }
   1.923 +      }
   1.924 +    }
   1.925 +
   1.926 +  private:
   1.927 +
   1.928 +    void unlace(const Key& key) {
   1.929 +      typename Parent::Value& node = Parent::operator[](key);
   1.930 +      if (node.value < 0) return;
   1.931 +      if (node.prev != INVALID) {
   1.932 +        Parent::operator[](node.prev).next = node.next;
   1.933 +      } else {
   1.934 +        _first[node.value] = node.next;
   1.935 +      }
   1.936 +      if (node.next != INVALID) {
   1.937 +        Parent::operator[](node.next).prev = node.prev;
   1.938 +      }
   1.939 +      while (!_first.empty() && _first.back() == INVALID) {
   1.940 +        _first.pop_back();
   1.941 +      }
   1.942 +    }
   1.943 +
   1.944 +    void lace(const Key& key) {
   1.945 +      typename Parent::Value& node = Parent::operator[](key);
   1.946 +      if (node.value < 0) return;
   1.947 +      if (node.value >= int(_first.size())) {
   1.948 +        _first.resize(node.value + 1, INVALID);
   1.949 +      }
   1.950 +      node.prev = INVALID;
   1.951 +      node.next = _first[node.value];
   1.952 +      if (node.next != INVALID) {
   1.953 +        Parent::operator[](node.next).prev = key;
   1.954 +      }
   1.955 +      _first[node.value] = key;
   1.956 +    }
   1.957 +
   1.958 +  public:
   1.959 +
   1.960 +    /// Indicates that the map is reference map.
   1.961 +    typedef True ReferenceMapTag;
   1.962 +
   1.963 +    /// \brief Reference to the value of the map.
   1.964 +    ///
   1.965 +    /// This class is similar to the \c int type. It can
   1.966 +    /// be converted to \c int and it has the same operators.
   1.967 +    class Reference {
   1.968 +      friend class IterableIntMap;
   1.969 +    private:
   1.970 +      Reference(IterableIntMap& map, const Key& key)
   1.971 +        : _key(key), _map(map) {}
   1.972 +    public:
   1.973 +
   1.974 +      Reference& operator=(const Reference& value) {
   1.975 +        _map.set(_key, static_cast<const int&>(value));
   1.976 +         return *this;
   1.977 +      }
   1.978 +
   1.979 +      operator const int&() const {
   1.980 +        return static_cast<const IterableIntMap&>(_map)[_key];
   1.981 +      }
   1.982 +
   1.983 +      Reference& operator=(int value) {
   1.984 +        _map.set(_key, value);
   1.985 +        return *this;
   1.986 +      }
   1.987 +      Reference& operator++() {
   1.988 +        _map.set(_key, _map[_key] + 1);
   1.989 +        return *this;
   1.990 +      }
   1.991 +      int operator++(int) {
   1.992 +        int value = _map[_key];
   1.993 +        _map.set(_key, value + 1);
   1.994 +        return value;
   1.995 +      }
   1.996 +      Reference& operator--() {
   1.997 +        _map.set(_key, _map[_key] - 1);
   1.998 +        return *this;
   1.999 +      }
  1.1000 +      int operator--(int) {
  1.1001 +        int value = _map[_key];
  1.1002 +        _map.set(_key, value - 1);
  1.1003 +        return value;
  1.1004 +      }
  1.1005 +      Reference& operator+=(int value) {
  1.1006 +        _map.set(_key, _map[_key] + value);
  1.1007 +        return *this;
  1.1008 +      }
  1.1009 +      Reference& operator-=(int value) {
  1.1010 +        _map.set(_key, _map[_key] - value);
  1.1011 +        return *this;
  1.1012 +      }
  1.1013 +      Reference& operator*=(int value) {
  1.1014 +        _map.set(_key, _map[_key] * value);
  1.1015 +        return *this;
  1.1016 +      }
  1.1017 +      Reference& operator/=(int value) {
  1.1018 +        _map.set(_key, _map[_key] / value);
  1.1019 +        return *this;
  1.1020 +      }
  1.1021 +      Reference& operator%=(int value) {
  1.1022 +        _map.set(_key, _map[_key] % value);
  1.1023 +        return *this;
  1.1024 +      }
  1.1025 +      Reference& operator&=(int value) {
  1.1026 +        _map.set(_key, _map[_key] & value);
  1.1027 +        return *this;
  1.1028 +      }
  1.1029 +      Reference& operator|=(int value) {
  1.1030 +        _map.set(_key, _map[_key] | value);
  1.1031 +        return *this;
  1.1032 +      }
  1.1033 +      Reference& operator^=(int value) {
  1.1034 +        _map.set(_key, _map[_key] ^ value);
  1.1035 +        return *this;
  1.1036 +      }
  1.1037 +      Reference& operator<<=(int value) {
  1.1038 +        _map.set(_key, _map[_key] << value);
  1.1039 +        return *this;
  1.1040 +      }
  1.1041 +      Reference& operator>>=(int value) {
  1.1042 +        _map.set(_key, _map[_key] >> value);
  1.1043 +        return *this;
  1.1044 +      }
  1.1045 +
  1.1046 +    private:
  1.1047 +      Key _key;
  1.1048 +      IterableIntMap& _map;
  1.1049 +    };
  1.1050 +
  1.1051 +    /// The const reference type.
  1.1052 +    typedef const Value& ConstReference;
  1.1053 +
  1.1054 +    /// \brief Gives back the maximal value plus one.
  1.1055 +    ///
  1.1056 +    /// Gives back the maximal value plus one.
  1.1057 +    int size() const {
  1.1058 +      return _first.size();
  1.1059 +    }
  1.1060 +
  1.1061 +    /// \brief Set operation of the map.
  1.1062 +    ///
  1.1063 +    /// Set operation of the map.
  1.1064 +    void set(const Key& key, const Value& value) {
  1.1065 +      unlace(key);
  1.1066 +      Parent::operator[](key).value = value;
  1.1067 +      lace(key);
  1.1068 +    }
  1.1069 +
  1.1070 +    /// \brief Const subscript operator of the map.
  1.1071 +    ///
  1.1072 +    /// Const subscript operator of the map.
  1.1073 +    const Value& operator[](const Key& key) const {
  1.1074 +      return Parent::operator[](key).value;
  1.1075 +    }
  1.1076 +
  1.1077 +    /// \brief Subscript operator of the map.
  1.1078 +    ///
  1.1079 +    /// Subscript operator of the map.
  1.1080 +    Reference operator[](const Key& key) {
  1.1081 +      return Reference(*this, key);
  1.1082 +    }
  1.1083 +
  1.1084 +    /// \brief Iterator for the keys with the same value.
  1.1085 +    ///
  1.1086 +    /// Iterator for the keys with the same value. It works
  1.1087 +    /// like a graph item iterator, it can be converted to
  1.1088 +    /// the item type of the map, incremented with \c ++ operator, and
  1.1089 +    /// if the iterator leaves the last valid item, it will be equal to
  1.1090 +    /// \c INVALID.
  1.1091 +    class ItemIt : public Key {
  1.1092 +    public:
  1.1093 +      typedef Key Parent;
  1.1094 +
  1.1095 +      /// \brief Invalid constructor \& conversion.
  1.1096 +      ///
  1.1097 +      /// This constructor initializes the iterator to be invalid.
  1.1098 +      /// \sa Invalid for more details.
  1.1099 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1100 +
  1.1101 +      /// \brief Creates an iterator with a value.
  1.1102 +      ///
  1.1103 +      /// Creates an iterator with a value. It iterates on the
  1.1104 +      /// keys mapped to the given value.
  1.1105 +      /// \param map The IterableIntMap.
  1.1106 +      /// \param value The value.
  1.1107 +      ItemIt(const IterableIntMap& map, int value) : _map(&map) {
  1.1108 +        if (value < 0 || value >= int(_map->_first.size())) {
  1.1109 +          Parent::operator=(INVALID);
  1.1110 +        } else {
  1.1111 +          Parent::operator=(_map->_first[value]);
  1.1112 +        }
  1.1113 +      }
  1.1114 +
  1.1115 +      /// \brief Increment operator.
  1.1116 +      ///
  1.1117 +      /// Increment operator.
  1.1118 +      ItemIt& operator++() {
  1.1119 +        Parent::operator=(_map->IterableIntMap::Parent::
  1.1120 +                          operator[](static_cast<Parent&>(*this)).next);
  1.1121 +        return *this;
  1.1122 +      }
  1.1123 +
  1.1124 +    private:
  1.1125 +      const IterableIntMap* _map;
  1.1126 +    };
  1.1127 +
  1.1128 +  protected:
  1.1129 +
  1.1130 +    virtual void erase(const Key& key) {
  1.1131 +      unlace(key);
  1.1132 +      Parent::erase(key);
  1.1133 +    }
  1.1134 +
  1.1135 +    virtual void erase(const std::vector<Key>& keys) {
  1.1136 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1137 +        unlace(keys[i]);
  1.1138 +      }
  1.1139 +      Parent::erase(keys);
  1.1140 +    }
  1.1141 +
  1.1142 +    virtual void clear() {
  1.1143 +      _first.clear();
  1.1144 +      Parent::clear();
  1.1145 +    }
  1.1146 +
  1.1147 +  private:
  1.1148 +    std::vector<Key> _first;
  1.1149 +  };
  1.1150 +
  1.1151 +  namespace _maps_bits {
  1.1152 +    template <typename Item, typename Value>
  1.1153 +    struct IterableValueMapNode {
  1.1154 +      IterableValueMapNode(Value _value = Value()) : value(_value) {}
  1.1155 +      Item prev, next;
  1.1156 +      Value value;
  1.1157 +    };
  1.1158 +  }
  1.1159 +
  1.1160 +  /// \brief Dynamic iterable map for comparable values.
  1.1161 +  ///
  1.1162 +  /// This class provides a special graph map type which can store a
  1.1163 +  /// comparable value for graph items (\c Node, \c Arc or \c Edge).
  1.1164 +  /// For each value it is possible to iterate on the keys mapped to
  1.1165 +  /// the value (\c ItemIt), and the values of the map can be accessed
  1.1166 +  /// with an STL compatible forward iterator (\c ValueIt).
  1.1167 +  /// The map stores a linked list for each value, which contains
  1.1168 +  /// the items mapped to the value, and the used values are stored
  1.1169 +  /// in balanced binary tree (\c std::map).
  1.1170 +  ///
  1.1171 +  /// \ref IterableBoolMap and \ref IterableIntMap are similar classes
  1.1172 +  /// specialized for \c bool and \c int values, respectively.
  1.1173 +  ///
  1.1174 +  /// This type is not reference map, so it cannot be modified with
  1.1175 +  /// the subscript operator.
  1.1176 +  ///
  1.1177 +  /// \tparam GR The graph type.
  1.1178 +  /// \tparam K The key type of the map (\c GR::Node, \c GR::Arc or
  1.1179 +  /// \c GR::Edge).
  1.1180 +  /// \tparam V The value type of the map. It can be any comparable
  1.1181 +  /// value type.
  1.1182 +  ///
  1.1183 +  /// \see IterableBoolMap, IterableIntMap
  1.1184 +  /// \see CrossRefMap
  1.1185 +  template <typename GR, typename K, typename V>
  1.1186 +  class IterableValueMap
  1.1187 +    : protected ItemSetTraits<GR, K>::
  1.1188 +        template Map<_maps_bits::IterableValueMapNode<K, V> >::Type {
  1.1189 +  public:
  1.1190 +    typedef typename ItemSetTraits<GR, K>::
  1.1191 +      template Map<_maps_bits::IterableValueMapNode<K, V> >::Type Parent;
  1.1192 +
  1.1193 +    /// The key type
  1.1194 +    typedef K Key;
  1.1195 +    /// The value type
  1.1196 +    typedef V Value;
  1.1197 +    /// The graph type
  1.1198 +    typedef GR Graph;
  1.1199 +
  1.1200 +  public:
  1.1201 +
  1.1202 +    /// \brief Constructor of the map with a given value.
  1.1203 +    ///
  1.1204 +    /// Constructor of the map with a given value.
  1.1205 +    explicit IterableValueMap(const Graph& graph,
  1.1206 +                              const Value& value = Value())
  1.1207 +      : Parent(graph, _maps_bits::IterableValueMapNode<K, V>(value)) {
  1.1208 +      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  1.1209 +        lace(it);
  1.1210 +      }
  1.1211 +    }
  1.1212 +
  1.1213 +  protected:
  1.1214 +
  1.1215 +    void unlace(const Key& key) {
  1.1216 +      typename Parent::Value& node = Parent::operator[](key);
  1.1217 +      if (node.prev != INVALID) {
  1.1218 +        Parent::operator[](node.prev).next = node.next;
  1.1219 +      } else {
  1.1220 +        if (node.next != INVALID) {
  1.1221 +          _first[node.value] = node.next;
  1.1222 +        } else {
  1.1223 +          _first.erase(node.value);
  1.1224 +        }
  1.1225 +      }
  1.1226 +      if (node.next != INVALID) {
  1.1227 +        Parent::operator[](node.next).prev = node.prev;
  1.1228 +      }
  1.1229 +    }
  1.1230 +
  1.1231 +    void lace(const Key& key) {
  1.1232 +      typename Parent::Value& node = Parent::operator[](key);
  1.1233 +      typename std::map<Value, Key>::iterator it = _first.find(node.value);
  1.1234 +      if (it == _first.end()) {
  1.1235 +        node.prev = node.next = INVALID;
  1.1236 +        _first.insert(std::make_pair(node.value, key));
  1.1237 +      } else {
  1.1238 +        node.prev = INVALID;
  1.1239 +        node.next = it->second;
  1.1240 +        if (node.next != INVALID) {
  1.1241 +          Parent::operator[](node.next).prev = key;
  1.1242 +        }
  1.1243 +        it->second = key;
  1.1244 +      }
  1.1245 +    }
  1.1246 +
  1.1247 +  public:
  1.1248 +
  1.1249 +    /// \brief Forward iterator for values.
  1.1250 +    ///
  1.1251 +    /// This iterator is an STL compatible forward
  1.1252 +    /// iterator on the values of the map. The values can
  1.1253 +    /// be accessed in the <tt>[beginValue, endValue)</tt> range.
  1.1254 +    class ValueIt
  1.1255 +      : public std::iterator<std::forward_iterator_tag, Value> {
  1.1256 +      friend class IterableValueMap;
  1.1257 +    private:
  1.1258 +      ValueIt(typename std::map<Value, Key>::const_iterator _it)
  1.1259 +        : it(_it) {}
  1.1260 +    public:
  1.1261 +
  1.1262 +      /// Constructor
  1.1263 +      ValueIt() {}
  1.1264 +
  1.1265 +      /// \e
  1.1266 +      ValueIt& operator++() { ++it; return *this; }
  1.1267 +      /// \e
  1.1268 +      ValueIt operator++(int) {
  1.1269 +        ValueIt tmp(*this);
  1.1270 +        operator++();
  1.1271 +        return tmp;
  1.1272 +      }
  1.1273 +
  1.1274 +      /// \e
  1.1275 +      const Value& operator*() const { return it->first; }
  1.1276 +      /// \e
  1.1277 +      const Value* operator->() const { return &(it->first); }
  1.1278 +
  1.1279 +      /// \e
  1.1280 +      bool operator==(ValueIt jt) const { return it == jt.it; }
  1.1281 +      /// \e
  1.1282 +      bool operator!=(ValueIt jt) const { return it != jt.it; }
  1.1283 +
  1.1284 +    private:
  1.1285 +      typename std::map<Value, Key>::const_iterator it;
  1.1286 +    };
  1.1287 +
  1.1288 +    /// \brief Returns an iterator to the first value.
  1.1289 +    ///
  1.1290 +    /// Returns an STL compatible iterator to the
  1.1291 +    /// first value of the map. The values of the
  1.1292 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1.1293 +    /// range.
  1.1294 +    ValueIt beginValue() const {
  1.1295 +      return ValueIt(_first.begin());
  1.1296 +    }
  1.1297 +
  1.1298 +    /// \brief Returns an iterator after the last value.
  1.1299 +    ///
  1.1300 +    /// Returns an STL compatible iterator after the
  1.1301 +    /// last value of the map. The values of the
  1.1302 +    /// map can be accessed in the <tt>[beginValue, endValue)</tt>
  1.1303 +    /// range.
  1.1304 +    ValueIt endValue() const {
  1.1305 +      return ValueIt(_first.end());
  1.1306 +    }
  1.1307 +
  1.1308 +    /// \brief Set operation of the map.
  1.1309 +    ///
  1.1310 +    /// Set operation of the map.
  1.1311 +    void set(const Key& key, const Value& value) {
  1.1312 +      unlace(key);
  1.1313 +      Parent::operator[](key).value = value;
  1.1314 +      lace(key);
  1.1315 +    }
  1.1316 +
  1.1317 +    /// \brief Const subscript operator of the map.
  1.1318 +    ///
  1.1319 +    /// Const subscript operator of the map.
  1.1320 +    const Value& operator[](const Key& key) const {
  1.1321 +      return Parent::operator[](key).value;
  1.1322 +    }
  1.1323 +
  1.1324 +    /// \brief Iterator for the keys with the same value.
  1.1325 +    ///
  1.1326 +    /// Iterator for the keys with the same value. It works
  1.1327 +    /// like a graph item iterator, it can be converted to
  1.1328 +    /// the item type of the map, incremented with \c ++ operator, and
  1.1329 +    /// if the iterator leaves the last valid item, it will be equal to
  1.1330 +    /// \c INVALID.
  1.1331 +    class ItemIt : public Key {
  1.1332 +    public:
  1.1333 +      typedef Key Parent;
  1.1334 +
  1.1335 +      /// \brief Invalid constructor \& conversion.
  1.1336 +      ///
  1.1337 +      /// This constructor initializes the iterator to be invalid.
  1.1338 +      /// \sa Invalid for more details.
  1.1339 +      ItemIt(Invalid) : Parent(INVALID), _map(0) {}
  1.1340 +
  1.1341 +      /// \brief Creates an iterator with a value.
  1.1342 +      ///
  1.1343 +      /// Creates an iterator with a value. It iterates on the
  1.1344 +      /// keys which have the given value.
  1.1345 +      /// \param map The IterableValueMap
  1.1346 +      /// \param value The value
  1.1347 +      ItemIt(const IterableValueMap& map, const Value& value) : _map(&map) {
  1.1348 +        typename std::map<Value, Key>::const_iterator it =
  1.1349 +          map._first.find(value);
  1.1350 +        if (it == map._first.end()) {
  1.1351 +          Parent::operator=(INVALID);
  1.1352 +        } else {
  1.1353 +          Parent::operator=(it->second);
  1.1354 +        }
  1.1355 +      }
  1.1356 +
  1.1357 +      /// \brief Increment operator.
  1.1358 +      ///
  1.1359 +      /// Increment Operator.
  1.1360 +      ItemIt& operator++() {
  1.1361 +        Parent::operator=(_map->IterableValueMap::Parent::
  1.1362 +                          operator[](static_cast<Parent&>(*this)).next);
  1.1363 +        return *this;
  1.1364 +      }
  1.1365 +
  1.1366 +
  1.1367 +    private:
  1.1368 +      const IterableValueMap* _map;
  1.1369 +    };
  1.1370 +
  1.1371 +  protected:
  1.1372 +
  1.1373 +    virtual void add(const Key& key) {
  1.1374 +      Parent::add(key);
  1.1375 +      unlace(key);
  1.1376 +    }
  1.1377 +
  1.1378 +    virtual void add(const std::vector<Key>& keys) {
  1.1379 +      Parent::add(keys);
  1.1380 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1381 +        lace(keys[i]);
  1.1382 +      }
  1.1383 +    }
  1.1384 +
  1.1385 +    virtual void erase(const Key& key) {
  1.1386 +      unlace(key);
  1.1387 +      Parent::erase(key);
  1.1388 +    }
  1.1389 +
  1.1390 +    virtual void erase(const std::vector<Key>& keys) {
  1.1391 +      for (int i = 0; i < int(keys.size()); ++i) {
  1.1392 +        unlace(keys[i]);
  1.1393 +      }
  1.1394 +      Parent::erase(keys);
  1.1395 +    }
  1.1396 +
  1.1397 +    virtual void build() {
  1.1398 +      Parent::build();
  1.1399 +      for (typename Parent::ItemIt it(*this); it != INVALID; ++it) {
  1.1400 +        lace(it);
  1.1401 +      }
  1.1402 +    }
  1.1403 +
  1.1404 +    virtual void clear() {
  1.1405 +      _first.clear();
  1.1406 +      Parent::clear();
  1.1407 +    }
  1.1408 +
  1.1409 +  private:
  1.1410 +    std::map<Value, Key> _first;
  1.1411 +  };
  1.1412 +
  1.1413    /// \brief Map of the source nodes of arcs in a digraph.
  1.1414    ///
  1.1415    /// SourceMap provides access for the source node of each arc in a digraph,
  1.1416 @@ -2321,9 +3300,9 @@
  1.1417    class SourceMap {
  1.1418    public:
  1.1419  
  1.1420 -    ///\e
  1.1421 +    /// The key type (the \c Arc type of the digraph).
  1.1422      typedef typename GR::Arc Key;
  1.1423 -    ///\e
  1.1424 +    /// The value type (the \c Node type of the digraph).
  1.1425      typedef typename GR::Node Value;
  1.1426  
  1.1427      /// \brief Constructor
  1.1428 @@ -2362,9 +3341,9 @@
  1.1429    class TargetMap {
  1.1430    public:
  1.1431  
  1.1432 -    ///\e
  1.1433 +    /// The key type (the \c Arc type of the digraph).
  1.1434      typedef typename GR::Arc Key;
  1.1435 -    ///\e
  1.1436 +    /// The value type (the \c Node type of the digraph).
  1.1437      typedef typename GR::Node Value;
  1.1438  
  1.1439      /// \brief Constructor
  1.1440 @@ -2404,8 +3383,10 @@
  1.1441    class ForwardMap {
  1.1442    public:
  1.1443  
  1.1444 +    /// The key type (the \c Edge type of the digraph).
  1.1445 +    typedef typename GR::Edge Key;
  1.1446 +    /// The value type (the \c Arc type of the digraph).
  1.1447      typedef typename GR::Arc Value;
  1.1448 -    typedef typename GR::Edge Key;
  1.1449  
  1.1450      /// \brief Constructor
  1.1451      ///
  1.1452 @@ -2444,8 +3425,10 @@
  1.1453    class BackwardMap {
  1.1454    public:
  1.1455  
  1.1456 +    /// The key type (the \c Edge type of the digraph).
  1.1457 +    typedef typename GR::Edge Key;
  1.1458 +    /// The value type (the \c Arc type of the digraph).
  1.1459      typedef typename GR::Arc Value;
  1.1460 -    typedef typename GR::Edge Key;
  1.1461  
  1.1462      /// \brief Constructor
  1.1463      ///
  1.1464 @@ -2480,10 +3463,10 @@
  1.1465    /// in constant time. On the other hand, the values are updated automatically
  1.1466    /// whenever the digraph changes.
  1.1467    ///
  1.1468 -  /// \warning Besides \c addNode() and \c addArc(), a digraph structure 
  1.1469 +  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  1.1470    /// may provide alternative ways to modify the digraph.
  1.1471    /// The correct behavior of InDegMap is not guarantied if these additional
  1.1472 -  /// features are used. For example the functions
  1.1473 +  /// features are used. For example, the functions
  1.1474    /// \ref ListDigraph::changeSource() "changeSource()",
  1.1475    /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1.1476    /// \ref ListDigraph::reverseArc() "reverseArc()"
  1.1477 @@ -2496,7 +3479,7 @@
  1.1478        ::ItemNotifier::ObserverBase {
  1.1479  
  1.1480    public:
  1.1481 -    
  1.1482 +
  1.1483      /// The graph type of InDegMap
  1.1484      typedef GR Graph;
  1.1485      typedef GR Digraph;
  1.1486 @@ -2610,10 +3593,10 @@
  1.1487    /// in constant time. On the other hand, the values are updated automatically
  1.1488    /// whenever the digraph changes.
  1.1489    ///
  1.1490 -  /// \warning Besides \c addNode() and \c addArc(), a digraph structure 
  1.1491 +  /// \warning Besides \c addNode() and \c addArc(), a digraph structure
  1.1492    /// may provide alternative ways to modify the digraph.
  1.1493    /// The correct behavior of OutDegMap is not guarantied if these additional
  1.1494 -  /// features are used. For example the functions
  1.1495 +  /// features are used. For example, the functions
  1.1496    /// \ref ListDigraph::changeSource() "changeSource()",
  1.1497    /// \ref ListDigraph::changeTarget() "changeTarget()" and
  1.1498    /// \ref ListDigraph::reverseArc() "reverseArc()"
  1.1499 @@ -2781,6 +3764,293 @@
  1.1500      return PotentialDifferenceMap<GR, POT>(gr, potential);
  1.1501    }
  1.1502  
  1.1503 +
  1.1504 +  /// \brief Copy the values of a graph map to another map.
  1.1505 +  ///
  1.1506 +  /// This function copies the values of a graph map to another graph map.
  1.1507 +  /// \c To::Key must be equal or convertible to \c From::Key and
  1.1508 +  /// \c From::Value must be equal or convertible to \c To::Value.
  1.1509 +  ///
  1.1510 +  /// For example, an edge map of \c int value type can be copied to
  1.1511 +  /// an arc map of \c double value type in an undirected graph, but
  1.1512 +  /// an arc map cannot be copied to an edge map.
  1.1513 +  /// Note that even a \ref ConstMap can be copied to a standard graph map,
  1.1514 +  /// but \ref mapFill() can also be used for this purpose.
  1.1515 +  ///
  1.1516 +  /// \param gr The graph for which the maps are defined.
  1.1517 +  /// \param from The map from which the values have to be copied.
  1.1518 +  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
  1.1519 +  /// \param to The map to which the values have to be copied.
  1.1520 +  /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
  1.1521 +  template <typename GR, typename From, typename To>
  1.1522 +  void mapCopy(const GR& gr, const From& from, To& to) {
  1.1523 +    typedef typename To::Key Item;
  1.1524 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1525 +    
  1.1526 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1527 +      to.set(it, from[it]);
  1.1528 +    }
  1.1529 +  }
  1.1530 +
  1.1531 +  /// \brief Compare two graph maps.
  1.1532 +  ///
  1.1533 +  /// This function compares the values of two graph maps. It returns 
  1.1534 +  /// \c true if the maps assign the same value for all items in the graph.
  1.1535 +  /// The \c Key type of the maps (\c Node, \c Arc or \c Edge) must be equal
  1.1536 +  /// and their \c Value types must be comparable using \c %operator==().
  1.1537 +  ///
  1.1538 +  /// \param gr The graph for which the maps are defined.
  1.1539 +  /// \param map1 The first map.
  1.1540 +  /// \param map2 The second map.
  1.1541 +  template <typename GR, typename Map1, typename Map2>
  1.1542 +  bool mapCompare(const GR& gr, const Map1& map1, const Map2& map2) {
  1.1543 +    typedef typename Map2::Key Item;
  1.1544 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1545 +    
  1.1546 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1547 +      if (!(map1[it] == map2[it])) return false;
  1.1548 +    }
  1.1549 +    return true;
  1.1550 +  }
  1.1551 +
  1.1552 +  /// \brief Return an item having minimum value of a graph map.
  1.1553 +  ///
  1.1554 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1555 +  /// minimum value of the given graph map.
  1.1556 +  /// If the item set is empty, it returns \c INVALID.
  1.1557 +  ///
  1.1558 +  /// \param gr The graph for which the map is defined.
  1.1559 +  /// \param map The graph map.
  1.1560 +  template <typename GR, typename Map>
  1.1561 +  typename Map::Key mapMin(const GR& gr, const Map& map) {
  1.1562 +    return mapMin(gr, map, std::less<typename Map::Value>());
  1.1563 +  }
  1.1564 +
  1.1565 +  /// \brief Return an item having minimum value of a graph map.
  1.1566 +  ///
  1.1567 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1568 +  /// minimum value of the given graph map.
  1.1569 +  /// If the item set is empty, it returns \c INVALID.
  1.1570 +  ///
  1.1571 +  /// \param gr The graph for which the map is defined.
  1.1572 +  /// \param map The graph map.
  1.1573 +  /// \param comp Comparison function object.
  1.1574 +  template <typename GR, typename Map, typename Comp>
  1.1575 +  typename Map::Key mapMin(const GR& gr, const Map& map, const Comp& comp) {
  1.1576 +    typedef typename Map::Key Item;
  1.1577 +    typedef typename Map::Value Value;
  1.1578 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1579 +
  1.1580 +    ItemIt min_item(gr);
  1.1581 +    if (min_item == INVALID) return INVALID;
  1.1582 +    Value min = map[min_item];
  1.1583 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1584 +      if (comp(map[it], min)) {
  1.1585 +        min = map[it];
  1.1586 +        min_item = it;
  1.1587 +      }
  1.1588 +    }
  1.1589 +    return min_item;
  1.1590 +  }
  1.1591 +
  1.1592 +  /// \brief Return an item having maximum value of a graph map.
  1.1593 +  ///
  1.1594 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1595 +  /// maximum value of the given graph map.
  1.1596 +  /// If the item set is empty, it returns \c INVALID.
  1.1597 +  ///
  1.1598 +  /// \param gr The graph for which the map is defined.
  1.1599 +  /// \param map The graph map.
  1.1600 +  template <typename GR, typename Map>
  1.1601 +  typename Map::Key mapMax(const GR& gr, const Map& map) {
  1.1602 +    return mapMax(gr, map, std::less<typename Map::Value>());
  1.1603 +  }
  1.1604 +
  1.1605 +  /// \brief Return an item having maximum value of a graph map.
  1.1606 +  ///
  1.1607 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1608 +  /// maximum value of the given graph map.
  1.1609 +  /// If the item set is empty, it returns \c INVALID.
  1.1610 +  ///
  1.1611 +  /// \param gr The graph for which the map is defined.
  1.1612 +  /// \param map The graph map.
  1.1613 +  /// \param comp Comparison function object.
  1.1614 +  template <typename GR, typename Map, typename Comp>
  1.1615 +  typename Map::Key mapMax(const GR& gr, const Map& map, const Comp& comp) {
  1.1616 +    typedef typename Map::Key Item;
  1.1617 +    typedef typename Map::Value Value;
  1.1618 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1619 +
  1.1620 +    ItemIt max_item(gr);
  1.1621 +    if (max_item == INVALID) return INVALID;
  1.1622 +    Value max = map[max_item];
  1.1623 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1624 +      if (comp(max, map[it])) {
  1.1625 +        max = map[it];
  1.1626 +        max_item = it;
  1.1627 +      }
  1.1628 +    }
  1.1629 +    return max_item;
  1.1630 +  }
  1.1631 +
  1.1632 +  /// \brief Return the minimum value of a graph map.
  1.1633 +  ///
  1.1634 +  /// This function returns the minimum value of the given graph map.
  1.1635 +  /// The corresponding item set of the graph must not be empty.
  1.1636 +  ///
  1.1637 +  /// \param gr The graph for which the map is defined.
  1.1638 +  /// \param map The graph map.
  1.1639 +  template <typename GR, typename Map>
  1.1640 +  typename Map::Value mapMinValue(const GR& gr, const Map& map) {
  1.1641 +    return map[mapMin(gr, map, std::less<typename Map::Value>())];
  1.1642 +  }
  1.1643 +
  1.1644 +  /// \brief Return the minimum value of a graph map.
  1.1645 +  ///
  1.1646 +  /// This function returns the minimum value of the given graph map.
  1.1647 +  /// The corresponding item set of the graph must not be empty.
  1.1648 +  ///
  1.1649 +  /// \param gr The graph for which the map is defined.
  1.1650 +  /// \param map The graph map.
  1.1651 +  /// \param comp Comparison function object.
  1.1652 +  template <typename GR, typename Map, typename Comp>
  1.1653 +  typename Map::Value
  1.1654 +  mapMinValue(const GR& gr, const Map& map, const Comp& comp) {
  1.1655 +    return map[mapMin(gr, map, comp)];
  1.1656 +  }
  1.1657 +
  1.1658 +  /// \brief Return the maximum value of a graph map.
  1.1659 +  ///
  1.1660 +  /// This function returns the maximum value of the given graph map.
  1.1661 +  /// The corresponding item set of the graph must not be empty.
  1.1662 +  ///
  1.1663 +  /// \param gr The graph for which the map is defined.
  1.1664 +  /// \param map The graph map.
  1.1665 +  template <typename GR, typename Map>
  1.1666 +  typename Map::Value mapMaxValue(const GR& gr, const Map& map) {
  1.1667 +    return map[mapMax(gr, map, std::less<typename Map::Value>())];
  1.1668 +  }
  1.1669 +
  1.1670 +  /// \brief Return the maximum value of a graph map.
  1.1671 +  ///
  1.1672 +  /// This function returns the maximum value of the given graph map.
  1.1673 +  /// The corresponding item set of the graph must not be empty.
  1.1674 +  ///
  1.1675 +  /// \param gr The graph for which the map is defined.
  1.1676 +  /// \param map The graph map.
  1.1677 +  /// \param comp Comparison function object.
  1.1678 +  template <typename GR, typename Map, typename Comp>
  1.1679 +  typename Map::Value
  1.1680 +  mapMaxValue(const GR& gr, const Map& map, const Comp& comp) {
  1.1681 +    return map[mapMax(gr, map, comp)];
  1.1682 +  }
  1.1683 +
  1.1684 +  /// \brief Return an item having a specified value in a graph map.
  1.1685 +  ///
  1.1686 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1687 +  /// the specified assigned value in the given graph map.
  1.1688 +  /// If no such item exists, it returns \c INVALID.
  1.1689 +  ///
  1.1690 +  /// \param gr The graph for which the map is defined.
  1.1691 +  /// \param map The graph map.
  1.1692 +  /// \param val The value that have to be found.
  1.1693 +  template <typename GR, typename Map>
  1.1694 +  typename Map::Key
  1.1695 +  mapFind(const GR& gr, const Map& map, const typename Map::Value& val) {
  1.1696 +    typedef typename Map::Key Item;
  1.1697 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1698 +
  1.1699 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1700 +      if (map[it] == val) return it;
  1.1701 +    }
  1.1702 +    return INVALID;
  1.1703 +  }
  1.1704 +
  1.1705 +  /// \brief Return an item having value for which a certain predicate is
  1.1706 +  /// true in a graph map.
  1.1707 +  ///
  1.1708 +  /// This function returns an item (\c Node, \c Arc or \c Edge) having
  1.1709 +  /// such assigned value for which the specified predicate is true
  1.1710 +  /// in the given graph map.
  1.1711 +  /// If no such item exists, it returns \c INVALID.
  1.1712 +  ///
  1.1713 +  /// \param gr The graph for which the map is defined.
  1.1714 +  /// \param map The graph map.
  1.1715 +  /// \param pred The predicate function object.
  1.1716 +  template <typename GR, typename Map, typename Pred>
  1.1717 +  typename Map::Key
  1.1718 +  mapFindIf(const GR& gr, const Map& map, const Pred& pred) {
  1.1719 +    typedef typename Map::Key Item;
  1.1720 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1721 +
  1.1722 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1723 +      if (pred(map[it])) return it;
  1.1724 +    }
  1.1725 +    return INVALID;
  1.1726 +  }
  1.1727 +
  1.1728 +  /// \brief Return the number of items having a specified value in a
  1.1729 +  /// graph map.
  1.1730 +  ///
  1.1731 +  /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  1.1732 +  /// having the specified assigned value in the given graph map.
  1.1733 +  ///
  1.1734 +  /// \param gr The graph for which the map is defined.
  1.1735 +  /// \param map The graph map.
  1.1736 +  /// \param val The value that have to be counted.
  1.1737 +  template <typename GR, typename Map>
  1.1738 +  int mapCount(const GR& gr, const Map& map, const typename Map::Value& val) {
  1.1739 +    typedef typename Map::Key Item;
  1.1740 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1741 +
  1.1742 +    int cnt = 0;
  1.1743 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1744 +      if (map[it] == val) ++cnt;
  1.1745 +    }
  1.1746 +    return cnt;
  1.1747 +  }
  1.1748 +
  1.1749 +  /// \brief Return the number of items having values for which a certain
  1.1750 +  /// predicate is true in a graph map.
  1.1751 +  ///
  1.1752 +  /// This function returns the number of items (\c Node, \c Arc or \c Edge)
  1.1753 +  /// having such assigned values for which the specified predicate is true
  1.1754 +  /// in the given graph map.
  1.1755 +  ///
  1.1756 +  /// \param gr The graph for which the map is defined.
  1.1757 +  /// \param map The graph map.
  1.1758 +  /// \param pred The predicate function object.
  1.1759 +  template <typename GR, typename Map, typename Pred>
  1.1760 +  int mapCountIf(const GR& gr, const Map& map, const Pred& pred) {
  1.1761 +    typedef typename Map::Key Item;
  1.1762 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1763 +
  1.1764 +    int cnt = 0;
  1.1765 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1766 +      if (pred(map[it])) ++cnt;
  1.1767 +    }
  1.1768 +    return cnt;
  1.1769 +  }
  1.1770 +
  1.1771 +  /// \brief Fill a graph map with a certain value.
  1.1772 +  ///
  1.1773 +  /// This function sets the specified value for all items (\c Node,
  1.1774 +  /// \c Arc or \c Edge) in the given graph map.
  1.1775 +  ///
  1.1776 +  /// \param gr The graph for which the map is defined.
  1.1777 +  /// \param map The graph map. It must conform to the
  1.1778 +  /// \ref concepts::WriteMap "WriteMap" concept.
  1.1779 +  /// \param val The value.
  1.1780 +  template <typename GR, typename Map>
  1.1781 +  void mapFill(const GR& gr, Map& map, const typename Map::Value& val) {
  1.1782 +    typedef typename Map::Key Item;
  1.1783 +    typedef typename ItemSetTraits<GR, Item>::ItemIt ItemIt;
  1.1784 +
  1.1785 +    for (ItemIt it(gr); it != INVALID; ++it) {
  1.1786 +      map.set(it, val);
  1.1787 +    }
  1.1788 +  }
  1.1789 +
  1.1790    /// @}
  1.1791  }
  1.1792