/* -*- 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