/* -*- 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_BINOM_HEAP_H

#define LEMON_BINOM_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 BinomHeap {

  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 BinomHeap(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.

    BinomHeap(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;

        _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); }

      _min = findMin();

      ++_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;

        int prev=-1;

        while( child!=-1 ) {

          neighb=_data[child].right_neighbor;

          _data[child].parent=-1;

          _data[child].right_neighbor=prev;

          head_child=child;

          prev=child;

          child=neighb;

        }

      }

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

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

        _head=head_child;

      }

      // The case where there are more roots.

      else {

        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];

      if( _comp( value,_data[i].prio ) ) {

        _data[i].prio=value;

        int p_loc=_data[i].parent, loc=i;

        int parent, child, neighb;

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

          // parent set for other loc_child

          child=_data[loc].child;

          while( -1!=child ) {

            _data[child].parent=p_loc;

            child=_data[child].right_neighbor;

          }

          // parent set for other p_loc_child

          child=_data[p_loc].child;

          while( -1!=child ) {

            _data[child].parent=loc;

            child=_data[child].right_neighbor;

          }

          child=_data[p_loc].child;

          _data[p_loc].child=_data[loc].child;

          if( child==loc )

            child=p_loc;

          _data[loc].child=child;

          // left_neighb set for p_loc

          if( _data[loc].child!=p_loc ) {

            while( _data[child].right_neighbor!=loc )

              child=_data[child].right_neighbor;

            _data[child].right_neighbor=p_loc;

          }

          // left_neighb set for loc

          parent=_data[p_loc].parent;

          if( -1!=parent ) child=_data[parent].child;

          else child=_head;

          if( child!=p_loc ) {

            while( _data[child].right_neighbor!=p_loc )

              child=_data[child].right_neighbor;

            _data[child].right_neighbor=loc;

          }

          neighb=_data[p_loc].right_neighbor;

          _data[p_loc].right_neighbor=_data[loc].right_neighbor;

          _data[loc].right_neighbor=neighb;

          _data[p_loc].parent=loc;

          _data[loc].parent=parent;

          if( -1!=parent && _data[parent].child==p_loc )

            _data[parent].child=loc;

          /*if new parent will be the first root*/

          if( _head==p_loc )

            _head=loc;

          p_loc=_data[loc].parent;

        }

      }

      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:

    int findMin() {

      int min_loc=-1, min_val;

      int x=_head;

      if( x!=-1 ) {

        min_val=_data[x].prio;

        min_loc=x;

        x=_data[x].right_neighbor;

        while( x!=-1 ) {

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

            min_val=_data[x].prio;

            min_loc=x;

          }

          x=_data[x].right_neighbor;

        }

      }

      return min_loc;

    }

    void merge(int a) {

      interleave(a);

      int x=_head;

      if( -1!=x ) {

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

        while( -1!=x_next ) {

          if( _data[x].degree!=_data[x_next].degree || ( -1!=_data[x_next].right_neighbor && _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {

            x_prev=x;

            x=x_next;

          }

          else {

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

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

              fuse(x_next,x);

            }

            else {

              if( -1==x_prev ) { _head=x_next; }

              else {

                _data[x_prev].right_neighbor=x_next;

              }

              fuse(x,x_next);

              x=x_next;

            }

          }

          x_next=_data[x].right_neighbor;

        }

      }

    }

    void interleave(int a) {

      int other=-1, head_other=-1;

      while( -1!=a || -1!=_head ) {

        if( -1==a ) {

          if( -1==head_other ) {

            head_other=_head;

          }

          else {

            _data[other].right_neighbor=_head;

          }

          _head=-1;

        }

        else if( -1==_head ) {

          if( -1==head_other ) {

            head_other=a;

          }

          else {

            _data[other].right_neighbor=a;

          }

          a=-1;

        }

        else {

          if( _data[a].degree<_data[_head].degree ) {

            if( -1==head_other ) {

              head_other=a;

            }

            else {

              _data[other].right_neighbor=a;

            }

            other=a;

            a=_data[a].right_neighbor;

          }

          else {

            if( -1==head_other ) {

              head_other=_head;

            }

            else {

              _data[other].right_neighbor=_head;

            }

            other=_head;

            _head=_data[_head].right_neighbor;

          }

        }

      }

      _head=head_other;

    }

    // Lacing a under 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;

    }

    // It is invoked only if a 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 BinomHeap;

      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_BINOM_HEAP_H