RhodeCode

  /// \ingroup heaps

  ///

  /// \brief Binary heap data structure.

  ///

  /// This class implements the \e binary \e heap data structure.

  /// It fully conforms to the \ref concepts::Heap "heap concept".

  ///

  /// \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 BinHeap {

  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;

    /// Type of the item-priority pairs.

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

    /// 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:

    std::vector<Pair> _data;

    Compare _comp;

    ItemIntMap &_iim;

  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 BinHeap(ItemIntMap &map) : _iim(map) {}

    /// \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.

    BinHeap(ItemIntMap &map, const Compare &comp)

      : _iim(map), _comp(comp) {}

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

    ///

    /// This function returns the number of items stored in the heap.

    int size() const { return _data.size(); }

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

    ///

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

    bool empty() const { return _data.empty(); }

    /// \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();

    }

  private:

    static int parent(int i) { return (i-1)/2; }

    bool less(const Pair &p1, const Pair &p2) const {

      return _comp(p1.second, p2.second);

    }

      int par = parent(hole);

      while( hole>0 && less(p,_data[par]) ) {

        move(_data[par],hole);

        hole = par;

        par = parent(hole);

      }

      move(p, hole);

      return hole;

    }

      while(child < length) {

        if( less(_data[child-1], _data[child]) ) {

          --child;

        }

        if( !less(_data[child], p) )

          goto ok;

        move(_data[child], hole);

        hole = child;

      }

      child--;

      if( child<length && less(_data[child], p) ) {

        move(_data[child], hole);

        hole=child;

      }

    ok:

      move(p, hole);

      return hole;

    }

    void move(const Pair &p, int i) {

      _data[i] = p;

      _iim.set(p.first, i);

    }

  public:

    /// \brief Insert a pair of item and priority into the heap.

    ///

    /// This function inserts \c p.first to the heap with priority

    /// \c p.second.

    /// \param p The pair to insert.

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

    void push(const Pair &p) {

      int n = _data.size();

      _data.resize(n+1);

    }

    /// \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 i The item to insert.

    /// \param p The priority of the item.

    /// \pre \e i must not be stored in the heap.

    void push(const Item &i, const Prio &p) { push(Pair(i,p)); }

    /// \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[0].first;

    }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

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

    Prio prio() const {

      return _data[0].second;

    }

    /// \brief Remove the item having minimum priority.

    ///

    /// This function removes the item having minimum priority.

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

    void pop() {

      int n = _data.size()-1;

      _iim.set(_data[0].first, POST_HEAP);

      if (n > 0) {

      }

      _data.pop_back();

    }

    /// \brief Remove the given item from the heap.

    ///

    /// This function removes the given item from the heap if it is

    /// already stored.

    /// \param i The item to delete.

    /// \pre \e i must be in the heap.

    void erase(const Item &i) {

      int h = _iim[i];

      int n = _data.size()-1;

      _iim.set(_data[h].first, POST_HEAP);

      if( h < n ) {

        }

      }

      _data.pop_back();

    }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param i The item.

    /// \pre \e i must be in the heap.

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

      int idx = _iim[i];

      return _data[idx].second;

    }

    /// \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 i The item.

    /// \param p The priority.

    void set(const Item &i, const Prio &p) {

      int idx = _iim[i];

      if( idx < 0 ) {

        push(i,p);

      }

      else if( _comp(p, _data[idx].second) ) {

      }

      else {

      }

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at least \e p.

    void decrease(const Item &i, const Prio &p) {

      int idx = _iim[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 i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at most \e p.

    void increase(const Item &i, const Prio &p) {

      int idx = _iim[i];

    }

    /// \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 i The item.

    State state(const Item &i) const {

      int s = _iim[i];

      if( s>=0 )

        s=0;

      return State(s);

    }

    /// \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;

      }

    }

    /// \brief Replace an item in the heap.

    ///

    /// This function replaces item \c i with item \c j.

    /// Item \c i must be in the heap, while \c j must be out of the heap.

    /// After calling this method, item \c i will be out of the

    /// heap and \c j will be in the heap with the same prioriority

    /// as item \c i had before.

    void replace(const Item& i, const Item& j) {

      int idx = _iim[i];

      _iim.set(i, _iim[j]);

      _iim.set(j, idx);

      _data[idx].first = j;

    }

  }; // class BinHeap

} // namespace lemon

#endif // LEMON_BIN_HEAP_H

      static void increase(int& value) {

        --value;

      }

    };

  }

  /// \ingroup heaps

  ///

  /// \brief Bucket heap data structure.

  ///

  /// This class implements the \e bucket \e heap data structure.

  /// It practically conforms to the \ref concepts::Heap "heap concept",

  /// but it has some limitations.

  ///

  /// The bucket heap is a very simple structure. It can store only

  /// \c int priorities and it maintains a list of items for each priority

  /// in the range <tt>[0..C)</tt>. So it should only be used when the

  /// priorities are small. It is not intended to use as a Dijkstra heap.

  ///

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.

  /// The default is \e min-heap. If this parameter is set to \c false,

  /// then the comparison is reversed, so the top(), prio() and pop()

  /// functions deal with the item having maximum priority instead of the

  /// minimum.

  ///

  /// \sa SimpleBucketHeap

  template <typename IM, bool MIN = true>

  class BucketHeap {

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef int Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// Type of the item-priority pairs.

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

  private:

    typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;

  public:

    /// \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.

    };

  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 BucketHeap(ItemIntMap &map) : _iim(map), _minimum(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 _data.size(); }

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

    ///

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

    bool empty() const { return _data.empty(); }

    /// \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(); _first.clear(); _minimum = 0;

    }

  private:

      if (idx + 1 < int(_data.size())) {

        _data[idx] = _data.back();

        if (_data[idx].prev != -1) {

          _data[_data[idx].prev].next = idx;

        } else {

          _first[_data[idx].value] = idx;

        }

        if (_data[idx].next != -1) {

          _data[_data[idx].next].prev = idx;

        }

        _iim[_data[idx].item] = idx;

      }

      _data.pop_back();

    }

    void unlace(int idx) {

      if (_data[idx].prev != -1) {

        _data[_data[idx].prev].next = _data[idx].next;

      } else {

        _first[_data[idx].value] = _data[idx].next;

      }

      if (_data[idx].next != -1) {

        _data[_data[idx].next].prev = _data[idx].prev;

      }

    }

    void lace(int idx) {

      if (int(_first.size()) <= _data[idx].value) {

        _first.resize(_data[idx].value + 1, -1);

      }

      _data[idx].next = _first[_data[idx].value];

      if (_data[idx].next != -1) {

        _data[_data[idx].next].prev = idx;

      }

      _first[_data[idx].value] = idx;

      _data[idx].prev = -1;

    }

  public:

    /// \brief Insert a pair of item and priority into the heap.

    ///

    /// This function inserts \c p.first to the heap with priority

    /// \c p.second.

    /// \param p The pair to insert.

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

    void push(const Pair& p) {

      push(p.first, p.second);

    }

    /// \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 i The item to insert.

    /// \param p The priority of the item.

    /// \pre \e i must not be stored in the heap.

    void push(const Item &i, const Prio &p) {

      int idx = _data.size();

      _iim[i] = idx;

      _data.push_back(BucketItem(i, p));

      lace(idx);

      if (Direction::less(p, _minimum)) {

        _minimum = p;

      }

    }

    /// \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 {

      while (_first[_minimum] == -1) {

        Direction::increase(_minimum);

      }

      return _data[_first[_minimum]].item;

    }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

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

    Prio prio() const {

      while (_first[_minimum] == -1) {

        Direction::increase(_minimum);

      }

      return _minimum;

    }

    /// \brief Remove the item having minimum priority.

    ///

    /// This function removes the item having minimum priority.

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

    void pop() {

      while (_first[_minimum] == -1) {

        Direction::increase(_minimum);

      }

      int idx = _first[_minimum];

      _iim[_data[idx].item] = -2;

      unlace(idx);

    }

    /// \brief Remove the given item from the heap.

    ///

    /// This function removes the given item from the heap if it is

    /// already stored.

    /// \param i The item to delete.

    /// \pre \e i must be in the heap.

    void erase(const Item &i) {

      int idx = _iim[i];

      _iim[_data[idx].item] = -2;

      unlace(idx);

    }

    /// \brief The priority of the given item.

    ///

    /// This function returns the priority of the given item.

    /// \param i The item.

    /// \pre \e i must be in the heap.

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

      int idx = _iim[i];

      return _data[idx].value;

    }

    /// \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 i The item.

    /// \param p The priority.

    void set(const Item &i, const Prio &p) {

      int idx = _iim[i];

      if (idx < 0) {

        push(i, p);

      } else if (Direction::less(p, _data[idx].value)) {

        decrease(i, p);

      } else {

        increase(i, p);

      }

    }

    /// \brief Decrease the priority of an item to the given value.

    ///

    /// This function decreases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at least \e p.

    void decrease(const Item &i, const Prio &p) {

      int idx = _iim[i];

      unlace(idx);

      _data[idx].value = p;

      if (Direction::less(p, _minimum)) {

        _minimum = p;

      }

      lace(idx);

    }

    /// \brief Increase the priority of an item to the given value.

    ///

    /// This function increases the priority of an item to the given value.

    /// \param i The item.

    /// \param p The priority.

    /// \pre \e i must be stored in the heap with priority at most \e p.

    void increase(const Item &i, const Prio &p) {

      int idx = _iim[i];

      unlace(idx);

      _data[idx].value = p;

      lace(idx);

    }

    /// \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 i The item.

    State state(const Item &i) const {

      int idx = _iim[i];

      if (idx >= 0) idx = 0;

      return State(idx);

    }

    /// \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:

    /// 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 FibHeap(ItemIntMap &map)

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

    /// \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.

    FibHeap(ItemIntMap &map, const Compare &comp)

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

    /// \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; }

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

    ///

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

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

    }

    /// \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 prio The priority of the item.

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

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

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

      } else {

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

        _minimum=i;

      }

      _data[i].prio=prio;

      ++_num;

    }

    /// \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[_minimum].name; }

    /// \brief The minimum priority.

    ///

    /// This function returns the minimum priority.

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

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

      /*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 ) {

          _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;

          _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 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 ) {

        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 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.

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

      return _data[_iim[item]].prio;

    }

    /// \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 prio The priority.

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

      int i=_iim[item];

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

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

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

      } else push(item, prio);

    }

    /// \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 prio The priority.

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

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

      int i=_iim[item];

      _data[i].prio=prio;

      int p=_data[i].parent;

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

        cut(i,p);

        cascade(p);

      }

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

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

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

      erase(item);

      push(item, prio);

    }

    /// \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:

    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 );

    }

      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) {}

    };

  };

/* -*- 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_RADIX_HEAP_H

#define LEMON_RADIX_HEAP_H

///\ingroup heaps

///\file

///\brief Radix heap implementation.

#include <vector>

#include <lemon/error.h>

namespace lemon {

  /// \ingroup heaps

  ///

  /// \brief Radix heap data structure.

  ///

  /// This class implements the \e radix \e heap data structure.

  /// It practically conforms to the \ref concepts::Heap "heap concept",

  /// but it has some limitations due its special implementation.

  /// The type of the priorities must be \c int and the priority of an

  /// item cannot be decreased under the priority of the last removed item.

  ///

  /// \tparam IM A read-writable item map with \c int values, used

  /// internally to handle the cross references.

  template <typename IM>

  class RadixHeap {

  public:

    /// Type of the item-int map.

    typedef IM ItemIntMap;

    /// Type of the priorities.

    typedef int Prio;

    /// Type of the items stored in the heap.

    typedef typename ItemIntMap::Key Item;

    /// \brief Exception thrown by RadixHeap.

    ///

    /// This exception is thrown when an item is inserted into a

    /// RadixHeap with a priority smaller than the last erased one.

    /// \see RadixHeap

    public:

      virtual const char* what() const throw() {

      }

    };

    /// \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 {