/* -*- 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_BINOMIAL_HEAP_H

 #define LEMON_BINOMIAL_HEAP_H

 ///\file

 ///\ingroup heaps

 ///\brief Binomial Heap implementation.

 #include <vector>

 #include <utility>

 #include <functional>

 #include <lemon/math.h>

 #include <lemon/counter.h>

 namespace lemon {

   /// \ingroup heaps

   ///

   ///\brief Binomial heap data structure.

   ///

   /// This class implements the \e binomial \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 binomial 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 BinomialHeap {

   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;

     /// Functor type for comparing the priorities.

     typedef CMP Compare;

     /// \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.

     };

   private:

     class Store;

     std::vector<Store> _data;

     int _min, _head;

     ItemIntMap &_iim;

     Compare _comp;

     int _num_items;

   public:

     /// \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 BinomialHeap(ItemIntMap &map)

       : _min(0), _head(-1), _iim(map), _num_items(0) {}

     /// \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.

     BinomialHeap(ItemIntMap &map, const Compare &comp)

       : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}

     /// \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_items; }

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

     ///

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

     bool empty() const { return _num_items==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(); _min=0; _num_items=0; _head=-1;

     }

     /// \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 value The priority.

     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 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 value The priority of the item.

     /// \pre \e 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;

         st.prio=value;

         _data.push_back(st);

         i=s;

       }

       else {

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

         _data[i].degree=0;

         _data[i].in=true;

         _data[i].prio=value;

       }

       if( 0==_num_items ) {

         _head=i;

         _min=i;

       } else {

         merge(i);

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

       }

       ++_num_items;

     }

     /// \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[_min].name; }

     /// \brief The minimum priority.

     ///

     /// This function returns the minimum priority.

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

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

     /// \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.

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

       return _data[_iim[item]].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() {

       _data[_min].in=false;

       int head_child=-1;

       if ( _data[_min].child!=-1 ) {

         int child=_data[_min].child;

         int neighb;

         while( child!=-1 ) {

           neighb=_data[child].right_neighbor;

           _data[child].parent=-1;

           _data[child].right_neighbor=head_child;

           head_child=child;

           child=neighb;

         }

       }

       if ( _data[_head].right_neighbor==-1 ) {

         // there was only one root

         _head=head_child;

       }

       else {

         // there were more roots

         if( _head!=_min )  { unlace(_min); }

         else { _head=_data[_head].right_neighbor; }

         merge(head_child);

       }

       _min=findMin();

       --_num_items;

     }

     /// \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 ) {

         decrease( item, _data[_min].prio-1 );

         pop();

       }

     }

     /// \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 value The priority.

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

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

       int i=_iim[item];

       int p=_data[i].parent;

       _data[i].prio=value;

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

         _data[i].name=_data[p].name;

         _data[i].prio=_data[p].prio;

         _data[p].name=item;

         _data[p].prio=value;

         _iim[_data[i].name]=i;

         i=p;

         p=_data[p].parent;

       }

       _iim[item]=i;

       if ( _comp(value, _data[_min].prio) ) _min=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 value The priority.

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

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

       erase(item);

       push(item, value);

     }

     /// \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:

     // Find the minimum of the roots

     int findMin() {

       if( _head!=-1 ) {

         int min_loc=_head, min_val=_data[_head].prio;

         for( int x=_data[_head].right_neighbor; x!=-1;

              x=_data[x].right_neighbor ) {

           if( _comp( _data[x].prio,min_val ) ) {

             min_val=_data[x].prio;

             min_loc=x;

           }

         }

         return min_loc;

       }

       else return -1;

     }

     // Merge the heap with another heap starting at the given position

     void merge(int a) {

       if( _head==-1 || a==-1 ) return;

       if( _data[a].right_neighbor==-1 &&

           _data[a].degree<=_data[_head].degree ) {

         _data[a].right_neighbor=_head;

         _head=a;

       } else {

         interleave(a);

       }

       if( _data[_head].right_neighbor==-1 ) return;

       int x=_head;

       int x_prev=-1, x_next=_data[x].right_neighbor;

       while( x_next!=-1 ) {

         if( _data[x].degree!=_data[x_next].degree ||

             ( _data[x_next].right_neighbor!=-1 &&

               _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {

           x_prev=x;

           x=x_next;

         }

         else {

           if( _comp(_data[x_next].prio,_data[x].prio) ) {

             if( x_prev==-1 ) {

               _head=x_next;

             } else {

               _data[x_prev].right_neighbor=x_next;

             }

             fuse(x,x_next);

             x=x_next;

           }

           else {

             _data[x].right_neighbor=_data[x_next].right_neighbor;

             fuse(x_next,x);

           }

         }

         x_next=_data[x].right_neighbor;

       }

     }

     // Interleave the elements of the given list into the list of the roots

     void interleave(int a) {

       int p=_head, q=a;

       int curr=_data.size();

       _data.push_back(Store());

       while( p!=-1 || q!=-1 ) {

         if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {

           _data[curr].right_neighbor=p;

           curr=p;

           p=_data[p].right_neighbor;

         }

         else {

           _data[curr].right_neighbor=q;

           curr=q;

           q=_data[q].right_neighbor;

         }

       }

       _head=_data.back().right_neighbor;

       _data.pop_back();

     }

     // Lace node a under node b

     void fuse(int a, int b) {

       _data[a].parent=b;

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

       _data[b].child=a;

       ++_data[b].degree;

     }

     // Unlace node a (if it has siblings)

     void unlace(int a) {

       int neighb=_data[a].right_neighbor;

       int other=_head;

       while( _data[other].right_neighbor!=a )

         other=_data[other].right_neighbor;

       _data[other].right_neighbor=neighb;

     }

   private:

     class Store {

       friend class BinomialHeap;

       Item name;

       int parent;

       int right_neighbor;

       int child;

       int degree;

       bool in;

       Prio prio;

       Store() : parent(-1), right_neighbor(-1), child(-1), degree(0),

         in(true) {}

     };

   };

 } //namespace lemon

 #endif //LEMON_BINOMIAL_HEAP_H