/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2006

  * 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 graphs.

 ///

 #ifndef LEMON_PATH_H

 #define LEMON_PATH_H

 #include <vector>

 #include <algorithm>

 #include <lemon/path_utils.h>

 #include <lemon/error.h>

 #include <lemon/bits/invalid.h>

 namespace lemon {

   /// \addtogroup paths

   /// @{

   /// \brief A structure for representing directed paths in a graph.

   ///

   /// A structure for representing directed path in a graph.

   /// \param Graph The graph type in which the path is.

   ///

   /// In a sense, the path can be treated as a list of edges. 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(1) time. The front and back

   /// insertion and erasure is amortized O(1) time. The

   /// impelementation is based on two opposite organized vectors.

   template <typename _Graph>

   class Path {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

     /// \brief Default constructor

     ///

     /// Default constructor

     Path() {}

     /// \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>

     Path(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>

     Path& operator=(const CPath& cpath) {

       copyPath(*this, cpath);

       return *this;

     }

     /// \brief Lemon style iterator for path edges

     ///

     /// This class is used to iterate on the edges of the paths.

     class EdgeIt {

       friend class Path;

     public:

       /// \brief Default constructor

       EdgeIt() {}

       /// \brief Invalid constructor

       EdgeIt(Invalid) : path(0), idx(-1) {}

       /// \brief Initializate the constructor to the first edge of path

       EdgeIt(const Path &_path) 

         : path(&_path), idx(_path.empty() ? -1 : 0) {}

     private:

       EdgeIt(const Path &_path, int _idx) 

         : idx(_idx), path(&_path) {}

     public:

       /// \brief Conversion to Edge

       operator const Edge&() const {

         return path->nth(idx);

       }

       /// \brief Next edge

       EdgeIt& operator++() { 

         ++idx;

         if (idx >= path->length()) idx = -1; 

         return *this; 

       }

       /// \brief Comparison operator

       bool operator==(const EdgeIt& e) const { return idx==e.idx; }

       /// \brief Comparison operator

       bool operator!=(const EdgeIt& e) const { return idx!=e.idx; }

       /// \brief Comparison operator

       bool operator<(const EdgeIt& 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 Returns whether the path is empty.

     bool empty() const { return head.empty() && tail.empty(); }

     /// \brief Resets the path to an empty path.

     void clear() { head.clear(); tail.clear(); }

     /// \brief Gives back the nth edge.

     ///

     /// \pre n is in the [0..length() - 1] range

     const Edge& nth(int n) const {

       return n < (int)head.size() ? *(head.rbegin() + n) :

         *(tail.begin() + (n - head.size()));

     }

     /// \brief Initializes edge iterator to point to the nth edge

     ///

     /// \pre n is in the [0..length() - 1] range

     EdgeIt nthIt(int n) const {

       return EdgeIt(*this, n);

     }

     /// \brief Gives back the first edge of the path

     const Edge& front() const {

       return head.empty() ? tail.front() : head.back();

     }

     /// \brief Add a new edge before the current path

     void addFront(const Edge& edge) {

       head.push_back(edge);

     }

     /// \brief Erase the first edge 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 Gives back the last edge of the path

     const Edge& back() const {

       return tail.empty() ? head.front() : tail.back();

     }

     /// \brief Add a new edge behind the current path

     void addBack(const Edge& edge) {

       tail.push_back(edge);

     }

     /// \brief Erase the last edge 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::EdgeIt 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::RevIt it(path); it != INVALID; ++it) {

         head.push_back(it);

       }

     }

   protected:

     typedef std::vector<Edge> Container;

     Container head, tail;

   };

   /// \brief A structure for representing directed paths in a graph.

   ///

   /// A structure for representing directed path in a graph.

   /// \param Graph The graph type in which the path is.

   ///

   /// In a sense, the path can be treated as a list of edges. 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

   /// edges.

   template <typename _Graph>

   class SimplePath {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

     /// \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 edges of the paths

     ///

     /// This class is used to iterate on the edges of the paths

     ///

     /// Of course it converts to Graph::Edge

     class EdgeIt {

       friend class SimplePath;

     public:

       /// Default constructor

       EdgeIt() {}

       /// Invalid constructor

       EdgeIt(Invalid) : path(0), idx(-1) {}

       /// \brief Initializate the constructor to the first edge of path

       EdgeIt(const SimplePath &_path) 

         : path(&_path), idx(_path.empty() ? -1 : 0) {}

     private:

       /// Constructor with starting point

       EdgeIt(const SimplePath &_path, int _idx) 

         : idx(_idx), path(&_path) {}

     public:

       ///Conversion to Graph::Edge

       operator const Edge&() const {

         return path->nth(idx);

       }

       /// Next edge

       EdgeIt& operator++() { 

         ++idx;

         if (idx >= path->length()) idx = -1; 

         return *this; 

       }

       /// Comparison operator

       bool operator==(const EdgeIt& e) const { return idx==e.idx; }

       /// Comparison operator

       bool operator!=(const EdgeIt& e) const { return idx!=e.idx; }

       /// Comparison operator

       bool operator<(const EdgeIt& e) const { return idx<e.idx; }

     private:

       const SimplePath *path;

       int idx;

     };

     /// \brief Length of the path.

     int length() const { return data.size(); }

     /// \brief Returns whether the path is empty.

     bool empty() const { return data.empty(); }

     /// \brief Resets the path to an empty path.

     void clear() { data.clear(); }

     /// \brief Gives back the nth edge.

     ///

     /// \pre n is in the [0..length() - 1] range

     const Edge& nth(int n) const {

       return data[n];

     }

     /// \brief  Initializes edge iterator to point to the nth edge.

     EdgeIt nthIt(int n) const {

       return EdgeIt(*this, n);

     }

     /// \brief Gives back the last edge of the path.

     const Edge& back() const {

       return data.back();

     }

     /// \brief Add a new edge behind the current path.

     void addBack(const Edge& edge) {

       data.push_back(edge);

     }

     /// \brief Erase the last edge 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::EdgeIt 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::RevIt it(path); it != INVALID; ++it) {

         --index;

         data[index] = it;;

       }

     }

   protected:

     typedef std::vector<Edge> Container;

     Container data;

   };

   /// \brief A structure for representing directed paths in a graph.

   ///

   /// A structure for representing directed path in a graph.

   /// \param Graph The graph type in which the path is.

   ///

   /// In a sense, the path can be treated as a list of edges. 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 edge 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 _Graph>

   class ListPath {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

   protected:

     // the std::list<> is incompatible 

     // hard to create invalid iterator

     struct Node {

       Edge edge;

       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 edges of the paths

     ///

     /// This class is used to iterate on the edges of the paths

     ///

     /// Of course it converts to Graph::Edge

     class EdgeIt {

       friend class ListPath;

     public:

       /// Default constructor

       EdgeIt() {}

       /// Invalid constructor

       EdgeIt(Invalid) : path(0), node(0) {}

       /// \brief Initializate the constructor to the first edge of path

       EdgeIt(const ListPath &_path) 

         : path(&_path), node(_path.first) {}

     protected:

       EdgeIt(const ListPath &_path, Node *_node) 

         : path(&_path), node(_node) {}

     public:

       ///Conversion to Graph::Edge

       operator const Edge&() const {

         return node->edge;

       }

       /// Next edge

       EdgeIt& operator++() { 

         node = node->next;

         return *this; 

       }

       /// Comparison operator

       bool operator==(const EdgeIt& e) const { return node==e.node; }

       /// Comparison operator

       bool operator!=(const EdgeIt& e) const { return node!=e.node; }

       /// Comparison operator

       bool operator<(const EdgeIt& e) const { return node<e.node; }

     private:

       const ListPath *path;

       Node *node;

     };

     /// \brief Gives back the nth edge.

     ///

     /// Gives back the nth edge in O(n) time.

     /// \pre n is in the [0..length() - 1] range

     const Edge& nth(int n) const {

       Node *node = first;

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

         node = node->next;

       }

       return node->edge;

     }

     /// \brief Initializes edge iterator to point to the nth edge.

     EdgeIt nthIt(int n) const {

       Node *node = first;

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

         node = node->next;

       }

       return EdgeIt(*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 Returns whether the path is empty.

     bool empty() const { return first == 0; }

     /// \brief Resets the path to an empty path.

     void clear() {

       while (first != 0) {

         last = first->next;

         alloc.destroy(first);

         alloc.deallocate(first, 1);

         first = last;

       }

     }

     /// \brief Gives back the first edge of the path

     const Edge& front() const {

       return first->edge;

     }

     /// \brief Add a new edge before the current path

     void addFront(const Edge& edge) {

       Node *node = alloc.allocate(1);

       alloc.construct(node, Node());

       node->prev = 0;

       node->next = first;

       node->edge = edge;

       if (first) {

         first->prev = node;

         first = node;

       } else {

         first = last = node;

       }

     }

     /// \brief Erase the first edge 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 Gives back the last edge of the path.

     const Edge& back() const {

       return last->edge;

     }

     /// \brief Add a new edge behind the current path.

     void addBack(const Edge& edge) {

       Node *node = alloc.allocate(1);

       alloc.construct(node, Node());

       node->next = 0;

       node->prev = last;

       node->edge = edge;

       if (last) {

         last->next = node;

         last = node;

       } else {

         last = first = node;

       }

     }

     /// \brief Erase the last edge 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 Splicing the given path to the current path.

     ///

     /// It splices the \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 Splicing the given path to the current path.

     ///

     /// It splices the \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 Splicing the given 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(EdgeIt 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 Spliting the current path.

     ///

     /// It splits the current path into two parts. The part before \c

     /// it iterator will remain in the current path and the part from

     /// the it will put into the \c tpath. If the \c tpath had edges

     /// before the operation they will be removed first.  The time

     /// complexity of this function is O(1) plus the clearing of \c

     /// tpath. If the \c it is \c INVALID then it just clears \c

     /// tpath.

     void split(EdgeIt 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::EdgeIt it(path); it != INVALID; ++it) {

         addBack(it);

       }

     }

     template <typename CPath>

     void buildRev(const CPath& path) {

       for (typename CPath::RevIt it(path); it != INVALID; ++it) {

         addFront(it);

       }

     }

   };

   /// \brief A structure for representing directed paths in a graph.

   ///

   /// A structure for representing directed path in a graph.

   /// \param Graph The graph type in which the path is.

   ///

   /// In a sense, the path can be treated as a list of edges. 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 completly static, so it cannot be

   /// modified exclude the assign an other path. It is intented to be

   /// used when you want to store a large number of paths because it is

   /// the most memory efficient path type in the lemon.

   template <typename _Graph>

   class StaticPath {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Edge;

     /// \brief Default constructor

     ///

     /// Default constructor

     StaticPath() : len(0), edges(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>

     StaticPath(const CPath& cpath) : edges(0) {

       copyPath(*this, cpath);

     }

     /// \brief Destructor of the path

     ///

     /// Destructor of the path

     ~StaticPath() {

       if (edges) delete[] edges;

     }

     /// \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>

     StaticPath& operator=(const CPath& cpath) {

       copyPath(*this, cpath);

       return *this;

     }

     /// \brief Iterator class to iterate on the edges of the paths

     ///

     /// This class is used to iterate on the edges of the paths

     ///

     /// Of course it converts to Graph::Edge

     class EdgeIt {

       friend class StaticPath;

     public:

       /// Default constructor

       EdgeIt() {}

       /// Invalid constructor

       EdgeIt(Invalid) : path(0), idx(-1) {}

       /// Initializate the constructor to the first edge of path

       EdgeIt(const StaticPath &_path) 

         : path(&_path), idx(_path.empty() ? -1 : 0) {}

     private:

       /// Constructor with starting point

       EdgeIt(const StaticPath &_path, int _idx) 

         : idx(_idx), path(&_path) {}

     public:

       ///Conversion to Graph::Edge

       operator const Edge&() const {

         return path->nth(idx);

       }

       /// Next edge

       EdgeIt& operator++() { 

         ++idx;

         if (idx >= path->length()) idx = -1; 

         return *this; 

       }

       /// Comparison operator

       bool operator==(const EdgeIt& e) const { return idx==e.idx; }

       /// Comparison operator

       bool operator!=(const EdgeIt& e) const { return idx!=e.idx; }

       /// Comparison operator

       bool operator<(const EdgeIt& e) const { return idx<e.idx; }

     private:

       const StaticPath *path;

       int idx;

     };

     /// \brief Gives back the nth edge.

     ///

     /// \pre n is in the [0..length() - 1] range

     const Edge& nth(int n) const {

       return edges[n];

     }

     /// \brief Initializes edge iterator to point to the nth edge.

     EdgeIt nthIt(int n) const {

       return EdgeIt(*this, n);

     }

     /// \brief Gives back the length of the path.

     int length() const { return len; }

     /// \brief Returns true when the path is empty.

     int empty() const { return len == 0; }

     /// \break Erase all edge in the graph.

     void clear() {

       len = 0;

       if (edges) delete[] edges;

       edges = 0;

     }

     /// \brief Gives back the first edge of the path.

     const Edge& front() const {

       return edges[0];

     }

     /// \brief Gives back the last edge of the path.

     const Edge& back() const {

       return edges[len - 1];

     }

     typedef True BuildTag;

     template <typename CPath>

     void build(const CPath& path) {

       len = path.length();

       edges = new Edge[len];

       int index = 0;

       for (typename CPath::EdgeIt it(path); it != INVALID; ++it) {

         edges[index] = it;

         ++index;

       }

     }

     template <typename CPath>

     void buildRev(const CPath& path) {

       len = path.length();

       edges = new Edge[len];

       int index = len;

       for (typename CPath::RevIt it(path); it != INVALID; ++it) {

         --index;

         edges[index] = it;

       }

     }

   private:

     int len;

     Edge* edges;

   };

   ///@}

 } // namespace lemon

 #endif // LEMON_PATH_H