/* -*- 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