diff -r cc7e6b8b59bf -r 70f3967ca6eb lemon/path.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/path.h	Thu Mar 20 12:12:24 2008 +0000
@@ -0,0 +1,1079 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+///\ingroup paths
+///\file
+///\brief Classes for representing paths in digraphs.
+///
+
+#ifndef LEMON_PATH_H
+#define LEMON_PATH_H
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/error.h>
+#include <lemon/bits/invalid.h>
+#include <lemon/concepts/path.h>
+
+namespace lemon {
+
+  /// \addtogroup paths
+  /// @{
+
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence, it
+  /// cannot enumerate the nodes of the path and the source node of
+  /// a zero length path is undefined.
+  ///
+  /// This implementation is a back and front insertable and erasable
+  /// path type. It can be indexed in O(1) time. The front and back
+  /// insertion and erase is done in O(1) (amortized) time. The
+  /// implementation uses two vectors for storing the front and back
+  /// insertions.
+  template <typename _Digraph>
+  class Path {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    Path() {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This constuctor initializes the path from any other path type.
+    /// It simply makes a copy of the given path.
+    template <typename CPath>
+    Path(const CPath& cpath) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This operator makes a copy of a path of any other type.
+    template <typename CPath>
+    Path& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Lemon style iterator for path arcs
+    ///
+    /// This class is used to iterate on the arcs of the paths.
+    class ArcIt {
+      friend class Path;
+    public:
+      /// \brief Default constructor
+      ArcIt() {}
+      /// \brief Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// \brief Initializate the iterator to the first arc of path
+      ArcIt(const Path &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      ArcIt(const Path &_path, int _idx) 
+        : path(&_path), idx(_idx) {}
+
+    public:
+
+      /// \brief Conversion to Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// \brief Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// \brief Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// \brief Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// \brief Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const Path *path;
+      int idx;
+    };
+
+    /// \brief Length of the path.
+    int length() const { return head.size() + tail.size(); }
+    /// \brief Return whether the path is empty.
+    bool empty() const { return head.empty() && tail.empty(); }
+
+    /// \brief Reset the path to an empty one.
+    void clear() { head.clear(); tail.clear(); }
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return n < int(head.size()) ? *(head.rbegin() + n) :
+        *(tail.begin() + (n - head.size()));
+    }
+
+    /// \brief Initialize arc iterator to point to the nth arc
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The first arc of the path
+    const Arc& front() const {
+      return head.empty() ? tail.front() : head.back();
+    }
+
+    /// \brief Add a new arc before the current path
+    void addFront(const Arc& arc) {
+      head.push_back(arc);
+    }
+
+    /// \brief Erase the first arc of the path
+    void eraseFront() {
+      if (!head.empty()) {
+        head.pop_back();
+      } else {
+        head.clear();
+        int halfsize = tail.size() / 2;
+        head.resize(halfsize);
+        std::copy(tail.begin() + 1, tail.begin() + halfsize + 1,
+                  head.rbegin());
+        std::copy(tail.begin() + halfsize + 1, tail.end(), tail.begin());
+        tail.resize(tail.size() - halfsize - 1);
+      }
+    }
+
+    /// \brief The last arc of the path
+    const Arc& back() const {
+      return tail.empty() ? head.front() : tail.back();
+    }
+
+    /// \brief Add a new arc behind the current path
+    void addBack(const Arc& arc) {
+      tail.push_back(arc);
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      if (!tail.empty()) {
+        tail.pop_back();
+      } else {
+        int halfsize = head.size() / 2;
+        tail.resize(halfsize);
+        std::copy(head.begin() + 1, head.begin() + halfsize + 1,
+                  tail.rbegin());
+        std::copy(head.begin() + halfsize + 1, head.end(), head.begin());
+        head.resize(head.size() - halfsize - 1);
+      }
+    }
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      int len = path.length();
+      tail.reserve(len);
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        tail.push_back(it);
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      int len = path.length();
+      head.reserve(len);
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        head.push_back(it);
+      }
+    }
+
+  protected:
+    typedef std::vector<Arc> Container;
+    Container head, tail;
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot store the source.
+  ///
+  /// This implementation is a just back insertable and erasable path
+  /// type. It can be indexed in O(1) time. The back insertion and
+  /// erasure is amortized O(1) time. This implementation is faster
+  /// then the \c Path type because it use just one vector for the
+  /// arcs.
+  template <typename _Digraph>
+  class SimplePath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    SimplePath() {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    SimplePath(const CPath& cpath) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    SimplePath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class SimplePath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// \brief Initializate the constructor to the first arc of path
+      ArcIt(const SimplePath &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      /// Constructor with starting point
+      ArcIt(const SimplePath &_path, int _idx) 
+        : idx(_idx), path(&_path) {}
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const SimplePath *path;
+      int idx;
+    };
+
+    /// \brief Length of the path.
+    int length() const { return data.size(); }
+    /// \brief Return true if the path is empty.
+    bool empty() const { return data.empty(); }
+
+    /// \brief Reset the path to an empty one.
+    void clear() { data.clear(); }
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return data[n];
+    }
+
+    /// \brief  Initializes arc iterator to point to the nth arc.
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The first arc of the path.
+    const Arc& front() const {
+      return data.front();
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return data.back();
+    }
+
+    /// \brief Add a new arc behind the current path.
+    void addBack(const Arc& arc) {
+      data.push_back(arc);
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      data.pop_back();
+    }
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      int len = path.length();
+      data.resize(len);
+      int index = 0;
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        data[index] = it;;
+        ++index;
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      int len = path.length();
+      data.resize(len);
+      int index = len;
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        --index;
+        data[index] = it;;
+      }
+    }
+
+  protected:
+    typedef std::vector<Arc> Container;
+    Container data;
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot store the source.
+  ///
+  /// This implementation is a back and front insertable and erasable
+  /// path type. It can be indexed in O(k) time, where k is the rank
+  /// of the arc in the path. The length can be computed in O(n)
+  /// time. The front and back insertion and erasure is O(1) time
+  /// and it can be splited and spliced in O(1) time.
+  template <typename _Digraph>
+  class ListPath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+  protected:
+
+    // the std::list<> is incompatible 
+    // hard to create invalid iterator
+    struct Node {
+      Arc arc;
+      Node *next, *prev;
+    };
+
+    Node *first, *last;
+
+    std::allocator<Node> alloc;
+
+  public:
+ 
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    ListPath() : first(0), last(0) {}
+
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    ListPath(const CPath& cpath) : first(0), last(0) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Destructor of the path
+    ///
+    /// Destructor of the path
+    ~ListPath() {
+      clear();
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be initialized with any other path type. It just
+    /// makes a copy of the given path.
+    template <typename CPath>
+    ListPath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class ListPath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), node(0) {}
+      /// \brief Initializate the constructor to the first arc of path
+      ArcIt(const ListPath &_path) 
+        : path(&_path), node(_path.first) {}
+
+    protected:
+
+      ArcIt(const ListPath &_path, Node *_node) 
+        : path(&_path), node(_node) {}
+
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return node->arc;
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        node = node->next;
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return node==e.node; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return node!=e.node; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return node<e.node; }
+
+    private:
+      const ListPath *path;
+      Node *node;
+    };
+
+    /// \brief The nth arc.
+    ///
+    /// This function looks for the nth arc in O(n) time.
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      Node *node = first;
+      for (int i = 0; i < n; ++i) {
+        node = node->next;
+      }
+      return node->arc;
+    }
+
+    /// \brief Initializes arc iterator to point to the nth arc.
+    ArcIt nthIt(int n) const {
+      Node *node = first;
+      for (int i = 0; i < n; ++i) {
+        node = node->next;
+      }
+      return ArcIt(*this, node);
+    }
+
+    /// \brief Length of the path.
+    int length() const {
+      int len = 0;
+      Node *node = first;
+      while (node != 0) {
+        node = node->next;
+        ++len;
+      }
+      return len;
+    }
+
+    /// \brief Return true if the path is empty.
+    bool empty() const { return first == 0; }
+
+    /// \brief Reset the path to an empty one.
+    void clear() {
+      while (first != 0) {
+        last = first->next;
+        alloc.destroy(first);
+        alloc.deallocate(first, 1);
+        first = last;
+      }
+    }
+
+    /// \brief The first arc of the path
+    const Arc& front() const {
+      return first->arc;
+    }
+
+    /// \brief Add a new arc before the current path
+    void addFront(const Arc& arc) {
+      Node *node = alloc.allocate(1);
+      alloc.construct(node, Node());
+      node->prev = 0;
+      node->next = first;
+      node->arc = arc;
+      if (first) {
+        first->prev = node;
+        first = node;
+      } else {
+        first = last = node;
+      }
+    }
+
+    /// \brief Erase the first arc of the path
+    void eraseFront() {
+      Node *node = first;
+      first = first->next;
+      if (first) {
+        first->prev = 0;
+      } else {
+        last = 0;
+      }
+      alloc.destroy(node);
+      alloc.deallocate(node, 1);
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return last->arc;
+    }
+
+    /// \brief Add a new arc behind the current path.
+    void addBack(const Arc& arc) {
+      Node *node = alloc.allocate(1);
+      alloc.construct(node, Node());
+      node->next = 0;
+      node->prev = last;
+      node->arc = arc;
+      if (last) {
+        last->next = node;
+        last = node;
+      } else {
+        last = first = node;
+      }
+    }
+
+    /// \brief Erase the last arc of the path
+    void eraseBack() {
+      Node *node = last;
+      last = last->prev;
+      if (last) {
+        last->next = 0;
+      } else {
+        first = 0;
+      }
+      alloc.destroy(node);
+      alloc.deallocate(node, 1);
+    }
+
+    /// \brief Splice a path to the back of the current path.
+    ///
+    /// It splices \c tpath to the back of the current path and \c
+    /// tpath becomes empty. The time complexity of this function is
+    /// O(1).
+    void spliceBack(ListPath& tpath) {
+      if (first) {
+        if (tpath.first) {
+          last->next = tpath.first;
+          tpath.first->prev = last;
+          last = tpath.last;
+        }
+      } else {
+        first = tpath.first;
+        last = tpath.last;
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Splice a path to the front of the current path.
+    ///
+    /// It splices \c tpath before the current path and \c tpath
+    /// becomes empty. The time complexity of this function
+    /// is O(1).
+    void spliceFront(ListPath& tpath) {
+      if (first) {
+        if (tpath.first) {
+          first->prev = tpath.last;
+          tpath.last->next = first;
+          first = tpath.first;
+        }
+      } else {
+        first = tpath.first;
+        last = tpath.last;
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Splice a path into the current path.
+    ///
+    /// It splices the \c tpath into the current path before the
+    /// position of \c it iterator and \c tpath becomes empty. The
+    /// time complexity of this function is O(1). If the \c it is
+    /// \c INVALID then it will splice behind the current path.
+    void splice(ArcIt it, ListPath& tpath) {
+      if (it.node) {
+        if (tpath.first) {
+          tpath.first->prev = it.node->prev;
+          if (it.node->prev) {
+            it.node->prev->next = tpath.first;
+          } else {
+            first = tpath.first;
+          }
+          it.node->prev = tpath.last;
+          tpath.last->next = it.node;
+        }
+      } else {
+        if (first) {
+          if (tpath.first) {
+            last->next = tpath.first;
+            tpath.first->prev = last;
+            last = tpath.last;
+          }
+        } else {
+          first = tpath.first;
+          last = tpath.last;
+        }
+      }
+      tpath.first = tpath.last = 0;
+    }
+
+    /// \brief Split the current path.
+    ///
+    /// It splits the current path into two parts. The part before
+    /// the iterator \c it will remain in the current path and the part
+    /// starting with
+    /// \c it will put into \c tpath. If \c tpath have arcs
+    /// before the operation they are removed first.  The time
+    /// complexity of this function is O(1) plus the the time of emtying
+    /// \c tpath. If \c it is \c INVALID then it just clears \c tpath
+    void split(ArcIt it, ListPath& tpath) {
+      tpath.clear();
+      if (it.node) {
+        tpath.first = it.node;
+        tpath.last = last;
+        if (it.node->prev) {
+          last = it.node->prev;
+          last->next = 0;
+        } else {
+          first = last = 0;
+        }
+        it.node->prev = 0;
+      }
+    }
+
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        addBack(it);
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        addFront(it);
+      }
+    }
+
+  };
+
+  /// \brief A structure for representing directed paths in a digraph.
+  ///
+  /// A structure for representing directed path in a digraph.
+  /// \param Digraph The digraph type in which the path is.
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores just this list. As a consequence it
+  /// cannot enumerate the nodes in the path and the source node of
+  /// a zero length path is undefined.
+  ///
+  /// This implementation is completly static, i.e. it can be copy constucted
+  /// or copy assigned from another path, but otherwise it cannot be
+  /// modified.
+  ///
+  /// Being the the most memory efficient path type in LEMON,
+  /// it is intented to be
+  /// used when you want to store a large number of paths.
+  template <typename _Digraph>
+  class StaticPath {
+  public:
+
+    typedef _Digraph Digraph;
+    typedef typename Digraph::Arc Arc;
+
+    /// \brief Default constructor
+    ///
+    /// Default constructor
+    StaticPath() : len(0), arcs(0) {}
+    
+    /// \brief Template copy constructor
+    ///
+    /// This path can be initialized from any other path type.
+    template <typename CPath>
+    StaticPath(const CPath& cpath) : arcs(0) {
+      copyPath(*this, cpath);
+    }
+
+    /// \brief Destructor of the path
+    ///
+    /// Destructor of the path
+    ~StaticPath() {
+      if (arcs) delete[] arcs;
+    }
+
+    /// \brief Template copy assignment
+    ///
+    /// This path can be made equal to any other path type. It simply
+    /// makes a copy of the given path.
+    template <typename CPath>
+    StaticPath& operator=(const CPath& cpath) {
+      copyPath(*this, cpath);
+      return *this;
+    }
+
+    /// \brief Iterator class to iterate on the arcs of the paths
+    ///
+    /// This class is used to iterate on the arcs of the paths
+    ///
+    /// Of course it converts to Digraph::Arc
+    class ArcIt {
+      friend class StaticPath;
+    public:
+      /// Default constructor
+      ArcIt() {}
+      /// Invalid constructor
+      ArcIt(Invalid) : path(0), idx(-1) {}
+      /// Initializate the constructor to the first arc of path
+      ArcIt(const StaticPath &_path) 
+        : path(&_path), idx(_path.empty() ? -1 : 0) {}
+
+    private:
+
+      /// Constructor with starting point
+      ArcIt(const StaticPath &_path, int _idx) 
+        : idx(_idx), path(&_path) {}
+
+    public:
+
+      ///Conversion to Digraph::Arc
+      operator const Arc&() const {
+        return path->nth(idx);
+      }
+
+      /// Next arc
+      ArcIt& operator++() { 
+        ++idx;
+        if (idx >= path->length()) idx = -1; 
+        return *this; 
+      }
+
+      /// Comparison operator
+      bool operator==(const ArcIt& e) const { return idx==e.idx; }
+      /// Comparison operator
+      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }
+      /// Comparison operator
+      bool operator<(const ArcIt& e) const { return idx<e.idx; }
+
+    private:
+      const StaticPath *path;
+      int idx;
+    };
+
+    /// \brief The nth arc.
+    ///
+    /// \pre n is in the [0..length() - 1] range
+    const Arc& nth(int n) const {
+      return arcs[n];
+    }
+
+    /// \brief The arc iterator pointing to the nth arc.
+    ArcIt nthIt(int n) const {
+      return ArcIt(*this, n);
+    }
+
+    /// \brief The length of the path.
+    int length() const { return len; }
+
+    /// \brief Return true when the path is empty.
+    int empty() const { return len == 0; }
+
+    /// \break Erase all arcs in the digraph.
+    void clear() {
+      len = 0;
+      if (arcs) delete[] arcs;
+      arcs = 0;
+    }
+
+    /// \brief The first arc of the path.
+    const Arc& front() const {
+      return arcs[0];
+    }
+
+    /// \brief The last arc of the path.
+    const Arc& back() const {
+      return arcs[len - 1];
+    }
+
+
+    typedef True BuildTag;
+
+    template <typename CPath>
+    void build(const CPath& path) {
+      len = path.length();
+      arcs = new Arc[len];
+      int index = 0;
+      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {
+        arcs[index] = it;
+        ++index;
+      }
+    }
+
+    template <typename CPath>
+    void buildRev(const CPath& path) {
+      len = path.length();
+      arcs = new Arc[len];
+      int index = len;
+      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {
+        --index;
+        arcs[index] = it;
+      }
+    }
+
+  private:
+    int len;
+    Arc* arcs;
+  };
+
+  ///////////////////////////////////////////////////////////////////////
+  // Additional utilities
+  ///////////////////////////////////////////////////////////////////////
+
+  namespace _path_bits {
+
+    template <typename Path, typename Enable = void>
+    struct RevTagIndicator {
+      static const bool value = false;
+    };
+
+    template <typename Digraph>
+    struct RevTagIndicator<
+      Digraph, 
+      typename enable_if<typename Digraph::RevTag, void>::type
+    > {
+      static const bool value = true;
+    };
+
+    template <typename Target, typename Source,
+              typename BuildEnable = void, typename RevEnable = void>
+    struct PathCopySelector {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        for (typename Source::ArcIt it(source); it != INVALID; ++it) {
+          target.addBack(it);
+        }
+      }
+    };
+
+    template <typename Target, typename Source, typename BuildEnable>
+    struct PathCopySelector<
+      Target, Source, BuildEnable, 
+      typename enable_if<typename Source::RevPathTag, void>::type> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        for (typename Source::RevArcIt it(source); it != INVALID; ++it) {
+          target.addFront(it);
+        }
+      }
+    };
+
+    template <typename Target, typename Source, typename RevEnable>
+    struct PathCopySelector<
+      Target, Source, 
+      typename enable_if<typename Target::BuildTag, void>::type, RevEnable> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        target.build(source);
+      }
+    };
+
+    template <typename Target, typename Source>
+    struct PathCopySelector<
+      Target, Source, 
+      typename enable_if<typename Target::BuildTag, void>::type,
+      typename enable_if<typename Source::RevPathTag, void>::type> {
+      static void copy(Target& target, const Source& source) {
+        target.clear();
+        target.buildRev(source);
+      }
+    };
+
+  }
+
+
+  /// \brief Make a copy of a path.
+  ///
+  ///  This function makes a copy of a path.
+  template <typename Target, typename Source>
+  void copyPath(Target& target, const Source& source) {
+    checkConcept<concepts::PathDumper<typename Source::Digraph>, Source>();
+    _path_bits::PathCopySelector<Target, Source>::copy(target, source);
+  }
+
+  /// \brief Check the consistency of a path.
+  ///
+  /// This function checks that the target of each arc is the same
+  /// as the source of the next one. 
+  /// 
+  template <typename Digraph, typename Path>
+  bool checkPath(const Digraph& digraph, const Path& path) {
+    typename Path::ArcIt it(path);
+    if (it == INVALID) return true;
+    typename Digraph::Node node = digraph.target(it);
+    ++it;
+    while (it != INVALID) {
+      if (digraph.source(it) != node) return false;
+      node = digraph.target(it);
+      ++it;
+    }
+    return true;
+  }
+
+  /// \brief The source of a path
+  ///
+  /// This function returns the source of the given path.
+  template <typename Digraph, typename Path>
+  typename Digraph::Node pathSource(const Digraph& digraph, const Path& path) {
+    return digraph.source(path.front());
+  }
+
+  /// \brief The target of a path
+  ///
+  /// This function returns the target of the given path.
+  template <typename Digraph, typename Path>
+  typename Digraph::Node pathTarget(const Digraph& digraph, const Path& path) {
+    return digraph.target(path.back());
+  }
+
+  /// \brief Class which helps to iterate through the nodes of a path
+  ///
+  /// In a sense, the path can be treated as a list of arcs. The
+  /// lemon path type stores only this list. As a consequence, it
+  /// cannot enumerate the nodes in the path and the zero length paths
+  /// cannot have a source node.
+  ///
+  /// This class implements the node iterator of a path structure. To
+  /// provide this feature, the underlying digraph should be passed to
+  /// the constructor of the iterator.
+  template <typename Path>
+  class PathNodeIt {
+  private:
+    const typename Path::Digraph *_digraph;
+    typename Path::ArcIt _it;
+    typename Path::Digraph::Node _nd;
+
+  public:
+
+    typedef typename Path::Digraph Digraph;
+    typedef typename Digraph::Node Node;
+    
+    /// Default constructor
+    PathNodeIt() {}
+    /// Invalid constructor
+    PathNodeIt(Invalid) 
+      : _digraph(0), _it(INVALID), _nd(INVALID) {}
+    /// Constructor
+    PathNodeIt(const Digraph& digraph, const Path& path) 
+      : _digraph(&digraph), _it(path) {
+      _nd = (_it != INVALID ? _digraph->source(_it) : INVALID);
+    }
+    /// Constructor
+    PathNodeIt(const Digraph& digraph, const Path& path, const Node& src) 
+      : _digraph(&digraph), _it(path), _nd(src) {}
+
+    ///Conversion to Digraph::Node
+    operator Node() const {
+      return _nd;
+    }
+
+    /// Next node
+    PathNodeIt& operator++() {
+      if (_it == INVALID) _nd = INVALID;
+      else {
+	_nd = _digraph->target(_it);
+	++_it;
+      }
+      return *this;
+    }
+
+    /// Comparison operator
+    bool operator==(const PathNodeIt& n) const { 
+      return _it == n._it && _nd == n._nd; 
+    }
+    /// Comparison operator
+    bool operator!=(const PathNodeIt& n) const { 
+      return _it != n._it || _nd != n._nd; 
+    }
+    /// Comparison operator
+    bool operator<(const PathNodeIt& n) const { 
+      return (_it < n._it && _nd != INVALID);
+    }
+    
+  };
+  
+  ///@}
+
+} // namespace lemon
+
+#endif // LEMON_PATH_H