/* -*- 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 auxdat

///\brief Fibonacci Heap implementation.

#include <vector>

#include <functional>

#include <lemon/math.h>

namespace lemon {

  /// \ingroup auxdat

  ///

  ///\brief Fibonacci Heap.

  ///

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

  ///is a data structure for storing items with specified values called \e

  ///priorities in such a way that finding the item with minimum priority is

  ///efficient. \c CMP specifies the ordering of the priorities. In a heap

  ///one can change the priority of an item, add or erase an item, etc.

  ///

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

  ///heap. In case of many calls to these operations, it is better to use a

  ///\ref BinHeap "binary heap".

  ///

  ///\param PRIO Type of the priority of the items.

  ///\param IM A read and writable Item int map, used internally

  ///to handle the cross references.

  ///\param CMP A class for the ordering of the priorities. The

  ///default is \c std::less<PRIO>.

  ///

  ///\sa BinHeap

  ///\sa Dijkstra

#ifdef DOXYGEN

  template <typename PRIO, typename IM, typename CMP>

#else

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

#endif

  class FibHeap {

  public:

    ///\e

    typedef IM ItemIntMap;

    ///\e

    typedef PRIO Prio;

    ///\e

    typedef typename ItemIntMap::Key Item;

    ///\e

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

    ///\e

    typedef CMP Compare;

  private:

    class Store;

    std::vector<Store> _data;

    int _minimum;

    ItemIntMap &_iim;

    Compare _comp;

    int _num;

  public:

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

    ///

    /// Each Item element have a state associated to it. It may 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 The constructor

    ///

    /// \c map should be given to the constructor, since it is

    ///   used internally to handle the cross references.

    explicit FibHeap(ItemIntMap &map)

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

    /// \brief The constructor

    ///

    /// \c map should be given to the constructor, since it is used

    /// internally to handle the cross references. \c comp is an

    /// object for ordering of the priorities.

    FibHeap(ItemIntMap &map, const Compare &comp)

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

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

    ///

    /// Returns the number of items stored in the heap.

    int size() const { return _num; }

    /// \brief Checks if the heap stores no items.

    ///

    ///   Returns \c true if and only if the heap stores no items.

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

    /// \brief Make empty this heap.

    ///

    /// Make empty this heap. It does not change the cross reference

    /// map.  If you want to reuse a heap what is not surely empty you

    /// should first clear the heap and after that you should set the

    /// cross reference map for each item to \c PRE_HEAP.

    void clear() {

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

    }

    /// \brief \c item gets to the heap with priority \c value independently

    /// if \c item was already there.

    ///

    /// This method calls \ref push(\c item, \c value) if \c item is not

    /// stored in the heap and it calls \ref decrease(\c item, \c value) or

    /// \ref increase(\c item, \c value) otherwise.

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

      int i=_iim[item];

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

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

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

      } else push(item, value);

    }

    /// \brief Adds \c item to the heap with priority \c value.

    ///

    /// Adds \c item to the heap with priority \c value.

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

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

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

      } else {

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

        _minimum=i;

      }

      _data[i].prio=value;

      ++_num;

    }

    /// \brief Returns the item with minimum priority relative to \c Compare.

    ///

    /// This method returns the item with minimum priority relative to \c

    /// Compare.

    /// \pre The heap must be nonempty.

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

    /// \brief Returns the minimum priority relative to \c Compare.

    ///

    /// It returns the minimum priority relative to \c Compare.

    /// \pre The heap must be nonempty.

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

    /// \brief Returns the priority of \c item.

    ///

    /// It returns the priority of \c item.

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

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

      return _data[_iim[item]].prio;

    }

    /// \brief Deletes the item with minimum priority relative to \c Compare.

    ///

    /// This method deletes the item with minimum priority relative to \c

    /// Compare from the heap.

    /// \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 Deletes \c item from the heap.

    ///

    /// This method deletes \c item from the heap, if \c item was already

    /// stored in the heap. It is quite inefficient in Fibonacci heaps.

    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 Decreases the priority of \c item to \c value.

    ///

    /// This method decreases the priority of \c item to \c value.

    /// \pre \c item must be stored in the heap with priority at least \c

    ///   value relative to \c Compare.

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

      int i=_iim[item];

      _data[i].prio=value;

      int p=_data[i].parent;

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

        cut(i,p);

        cascade(p);

      }

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

    }

    /// \brief Increases the priority of \c item to \c value.

    ///

    /// This method sets the priority of \c item to \c value. Though

    /// there is no precondition on the priority of \c item, this

    /// method should be used only if it is indeed necessary to increase

    /// (relative to \c Compare) the priority of \c item, because this

    /// method is inefficient.

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

      erase(item);

      push(item, value);

    }

    /// \brief Returns if \c item is in, has already been in, or has never

    /// been in the heap.

    ///

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

    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP

    /// otherwise. In the latter case it is possible that \c item will

    /// get back to the heap again.

    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 Sets the state of the \c item in the heap.

    ///

    /// Sets the state of the \c item in the heap. It can be used to

    /// manually clear the heap when it is important to achive the

    /// 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