/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

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

 *

 * Copyright (C) 2003-2009

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_FIB_HEAP_H

#define LEMON_FIB_HEAP_H

///\file

///\ingroup heaps

///\brief Fibonacci heap implementation.

#include <vector>

#include <utility>

#include <functional>

#include <lemon/math.h>

namespace lemon {

  /// \ingroup heaps

  ///

  /// \brief Fibonacci heap data structure.

  ///

  /// This class implements the \e Fibonacci \e heap data structure.

  /// It fully conforms to the \ref concepts::Heap "heap concept".

  ///

  /// The methods \ref increase() and \ref erase() are not efficient in a

  /// Fibonacci heap. In case of many calls of these operations, it is

  /// better to use other heap structure, e.g. \ref BinHeap "binary heap".

  ///

  /// \tparam PR Type of the priorities of the items.

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  /// \tparam CMP A functor class for comparing the priorities.

  /// The default is \c std::less<PR>.

#ifdef DOXYGEN

  template <typename PR, typename IM, typename CMP>

#else

  template <typename PR, typename IM, typename CMP = std::less<PR> >

#endif

  class FibHeap {

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef PR Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// Type of the item-priority pairs.

    typedef std::pair<Item,Prio> Pair;

    /// Functor type for comparing the priorities.

    typedef CMP Compare;

  private:

    class Store;

    std::vector<Store> _data;

    int _minimum;

    ItemIntMap &_iim;

    Compare _comp;

    int _num;

  public:

    /// \brief Type to represent the states of the items.

    ///

    /// Each item has a state associated to it. It can be "in heap",

    /// "pre-heap" or "post-heap". The latter two are indifferent from the

    /// heap's point of view, but may be useful to the user.

    ///

    /// The item-int map must be initialized in such way that it assigns

    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.

    enum State {

      IN_HEAP = 0,    ///< = 0.

      PRE_HEAP = -1,  ///< = -1.

      POST_HEAP = -2  ///< = -2.

    };

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    explicit FibHeap(ItemIntMap &map)

      : _minimum(0), _iim(map), _num() {}

    /// \brief Constructor.

    ///

    /// Constructor.

    /// \param map A map that assigns \c int values to the items.

    /// It is used internally to handle the cross references.

    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.

    /// \param comp The function object used for comparing the priorities.

    FibHeap(ItemIntMap &map, const Compare &comp)

      : _minimum(0), _iim(map), _comp(comp), _num() {}

    /// \brief The number of items stored in the heap.

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _num; }

    /// \brief Check if the heap is empty.

    ///

    /// This function returns \c true if the heap is empty.

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

    /// \brief Make the heap empty.

    ///

    /// This functon makes the heap empty.

    /// It does not change the cross reference map. If you want to reuse

    /// a heap that is not surely empty, you should first clear it and

    /// then you should set the cross reference map to \c PRE_HEAP

    /// for each item.

    void clear() {

      _data.clear(); _minimum = 0; _num = 0;

    }

    /// \brief Insert an item into the heap with the given priority.

    ///

    /// This function inserts the given item into the heap with the

    /// given priority.

    /// \param item The item to insert.

    /// \param prio The priority of the item.

    /// \pre \e item must not be stored in the heap.

    void push (const Item& item, const Prio& prio) {

      int i=_iim[item];

      if ( i < 0 ) {

        int s=_data.size();

        _iim.set( item, s );

        Store st;

        st.name=item;

        _data.push_back(st);

        i=s;

      } else {

        _data[i].parent=_data[i].child=-1;

        _data[i].degree=0;

        _data[i].in=true;

        _data[i].marked=false;

      }

      if ( _num ) {

        _data[_data[_minimum].right_neighbor].left_neighbor=i;

        _data[i].right_neighbor=_data[_minimum].right_neighbor;

        _data[_minimum].right_neighbor=i;

        _data[i].left_neighbor=_minimum;

        if ( _comp( prio, _data[_minimum].prio) ) _minimum=i;

      } else {

        _data[i].right_neighbor=_data[i].left_neighbor=i;

        _minimum=i;

      }

      _data[i].prio=prio;

      ++_num;

    }

    /// \brief Return the item having minimum priority.

    ///

    /// This function returns the item having minimum priority.

    /// \pre The heap must be non-empty.

    Item top() const { return _data[_minimum].name; }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

    /// \pre The heap must be non-empty.

    Prio prio() const { return _data[_minimum].prio; }

    /// \brief Remove the item having minimum priority.

    ///

    /// This function removes the item having minimum priority.

    /// \pre The heap must be non-empty.

    void pop() {

      /*The first case is that there are only one root.*/

      if ( _data[_minimum].left_neighbor==_minimum ) {

        _data[_minimum].in=false;

        if ( _data[_minimum].degree!=0 ) {

          makeRoot(_data[_minimum].child);

          _minimum=_data[_minimum].child;

          balance();

        }

      } else {

        int right=_data[_minimum].right_neighbor;

        unlace(_minimum);

        _data[_minimum].in=false;

        if ( _data[_minimum].degree > 0 ) {

          int left=_data[_minimum].left_neighbor;

          int child=_data[_minimum].child;

          int last_child=_data[child].left_neighbor;

          makeRoot(child);

          _data[left].right_neighbor=child;

          _data[child].left_neighbor=left;

          _data[right].left_neighbor=last_child;

          _data[last_child].right_neighbor=right;

        }

        _minimum=right;

        balance();

      } // the case where there are more roots

      --_num;

    }

    /// \brief Remove the given item from the heap.

    ///

    /// This function removes the given item from the heap if it is

    /// already stored.

    /// \param item The item to delete.

    /// \pre \e item must be in the heap.

    void erase (const Item& item) {

      int i=_iim[item];

      if ( i >= 0 && _data[i].in ) {

        if ( _data[i].parent!=-1 ) {

          int p=_data[i].parent;

          cut(i,p);

          cascade(p);

        }

        _minimum=i;     //As if its prio would be -infinity

        pop();

      }

    }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param item The item.

    /// \pre \e item must be in the heap.

    Prio operator[](const Item& item) const {

      return _data[_iim[item]].prio;

    }

    /// \brief Set the priority of an item or insert it, if it is

    /// not stored in the heap.

    ///

    /// This method sets the priority of the given item if it is

    /// already stored in the heap. Otherwise it inserts the given

    /// item into the heap with the given priority.

    /// \param item The item.

    /// \param prio The priority.

    void set (const Item& item, const Prio& prio) {

      int i=_iim[item];

      if ( i >= 0 && _data[i].in ) {

        if ( _comp(prio, _data[i].prio) ) decrease(item, prio);

        if ( _comp(_data[i].prio, prio) ) increase(item, prio);

      } else push(item, prio);

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param item The item.

    /// \param prio The priority.

    /// \pre \e item must be stored in the heap with priority at least \e prio.

    void decrease (const Item& item, const Prio& prio) {

      int i=_iim[item];

      _data[i].prio=prio;

      int p=_data[i].parent;

      if ( p!=-1 && _comp(prio, _data[p].prio) ) {

        cut(i,p);

        cascade(p);

      }

      if ( _comp(prio, _data[_minimum].prio) ) _minimum=i;

    }

    /// \brief Increase the priority of an item to the given value.

    ///

    /// This function increases the priority of an item to the given value.

    /// \param item The item.

    /// \param prio The priority.

    /// \pre \e item must be stored in the heap with priority at most \e prio.

    void increase (const Item& item, const Prio& prio) {

      erase(item);

      push(item, prio);

    }

    /// \brief Return the state of an item.

    ///

    /// This method returns \c PRE_HEAP if the given item has never

    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,

    /// and \c POST_HEAP otherwise.

    /// In the latter case it is possible that the item will get back

    /// to the heap again.

    /// \param item The item.

    State state(const Item &item) const {

      int i=_iim[item];

      if( i>=0 ) {

        if ( _data[i].in ) i=0;

        else i=-2;

      }

      return State(i);

    }

    /// \brief Set the state of an item in the heap.

    ///

    /// This function sets the state of the given item in the heap.

    /// It can be used to manually clear the heap when it is important

    /// to achive better time complexity.

    /// \param i The item.

    /// \param st The state. It should not be \c IN_HEAP.

    void state(const Item& i, State st) {

      switch (st) {

      case POST_HEAP:

      case PRE_HEAP:

        if (state(i) == IN_HEAP) {

          erase(i);

        }

        _iim[i] = st;

        break;

      case IN_HEAP:

        break;

      }

    }

  private:

    void balance() {

      int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;

      std::vector<int> A(maxdeg,-1);

      /*

       *Recall that now minimum does not point to the minimum prio element.

       *We set minimum to this during balance().

       */

      int anchor=_data[_minimum].left_neighbor;

      int next=_minimum;

      bool end=false;

      do {

        int active=next;

        if ( anchor==active ) end=true;

        int d=_data[active].degree;

        next=_data[active].right_neighbor;

        while (A[d]!=-1) {

          if( _comp(_data[active].prio, _data[A[d]].prio) ) {

            fuse(active,A[d]);

          } else {

            fuse(A[d],active);

            active=A[d];

          }

          A[d]=-1;

          ++d;

        }

        A[d]=active;

      } while ( !end );

      while ( _data[_minimum].parent >=0 )

        _minimum=_data[_minimum].parent;

      int s=_minimum;

      int m=_minimum;

      do {

        if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;

        s=_data[s].right_neighbor;

      } while ( s != m );

    }

    void makeRoot(int c) {

      int s=c;

      do {

        _data[s].parent=-1;

        s=_data[s].right_neighbor;

      } while ( s != c );

    }

    void cut(int a, int b) {

      /*

       *Replacing a from the children of b.

       */

      --_data[b].degree;

      if ( _data[b].degree !=0 ) {

        int child=_data[b].child;

        if ( child==a )

          _data[b].child=_data[child].right_neighbor;

        unlace(a);

      }

      /*Lacing a to the roots.*/

      int right=_data[_minimum].right_neighbor;

      _data[_minimum].right_neighbor=a;

      _data[a].left_neighbor=_minimum;

      _data[a].right_neighbor=right;

      _data[right].left_neighbor=a;

      _data[a].parent=-1;

      _data[a].marked=false;

    }

    void cascade(int a) {

      if ( _data[a].parent!=-1 ) {

        int p=_data[a].parent;

        if ( _data[a].marked==false ) _data[a].marked=true;

        else {

          cut(a,p);

          cascade(p);

        }

      }

    }

    void fuse(int a, int b) {

      unlace(b);

      /*Lacing b under a.*/

      _data[b].parent=a;

      if (_data[a].degree==0) {

        _data[b].left_neighbor=b;

        _data[b].right_neighbor=b;

        _data[a].child=b;

      } else {

        int child=_data[a].child;

        int last_child=_data[child].left_neighbor;

        _data[child].left_neighbor=b;

        _data[b].right_neighbor=child;

        _data[last_child].right_neighbor=b;

        _data[b].left_neighbor=last_child;

      }

      ++_data[a].degree;

      _data[b].marked=false;

    }

    /*

     *It is invoked only if a has siblings.

     */

    void unlace(int a) {

      int leftn=_data[a].left_neighbor;

      int rightn=_data[a].right_neighbor;

      _data[leftn].right_neighbor=rightn;

      _data[rightn].left_neighbor=leftn;

    }

    class Store {

      friend class FibHeap;

      Item name;

      int parent;

      int left_neighbor;

      int right_neighbor;

      int child;

      int degree;

      bool marked;

      bool in;

      Prio prio;

      Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}

    };

  };

} //namespace lemon

#endif //LEMON_FIB_HEAP_H