kpeter@703: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@701: *
kpeter@703: * This file is a part of LEMON, a generic C++ optimization library.
kpeter@701: *
kpeter@703: * Copyright (C) 2003-2009
kpeter@701: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@701: * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@701: *
kpeter@701: * Permission to use, modify and distribute this software is granted
kpeter@701: * provided that this copyright notice appears in all copies. For
kpeter@701: * precise terms see the accompanying LICENSE file.
kpeter@701: *
kpeter@701: * This software is provided "AS IS" with no warranty of any kind,
kpeter@701: * express or implied, and with no claim as to its suitability for any
kpeter@701: * purpose.
kpeter@701: *
kpeter@701: */
kpeter@701:
kpeter@701: #ifndef LEMON_PAIRING_HEAP_H
kpeter@701: #define LEMON_PAIRING_HEAP_H
kpeter@701:
kpeter@701: ///\file
kpeter@703: ///\ingroup heaps
kpeter@703: ///\brief Pairing heap implementation.
kpeter@701:
kpeter@701: #include <vector>
kpeter@703: #include <utility>
kpeter@701: #include <functional>
kpeter@701: #include <lemon/math.h>
kpeter@701:
kpeter@701: namespace lemon {
kpeter@701:
kpeter@703: /// \ingroup heaps
kpeter@701: ///
kpeter@701: ///\brief Pairing Heap.
kpeter@701: ///
kpeter@703: /// This class implements the \e pairing \e heap data structure.
kpeter@703: /// It fully conforms to the \ref concepts::Heap "heap concept".
kpeter@701: ///
kpeter@703: /// The methods \ref increase() and \ref erase() are not efficient
kpeter@703: /// in a pairing heap. In case of many calls of these operations,
kpeter@703: /// it is better to use other heap structure, e.g. \ref BinHeap
kpeter@703: /// "binary heap".
kpeter@701: ///
kpeter@703: /// \tparam PR Type of the priorities of the items.
kpeter@703: /// \tparam IM A read-writable item map with \c int values, used
kpeter@703: /// internally to handle the cross references.
kpeter@703: /// \tparam CMP A functor class for comparing the priorities.
kpeter@703: /// The default is \c std::less<PR>.
kpeter@701: #ifdef DOXYGEN
kpeter@703: template <typename PR, typename IM, typename CMP>
kpeter@701: #else
kpeter@703: template <typename PR, typename IM, typename CMP = std::less<PR> >
kpeter@701: #endif
kpeter@701: class PairingHeap {
kpeter@701: public:
kpeter@703: /// Type of the item-int map.
kpeter@703: typedef IM ItemIntMap;
kpeter@703: /// Type of the priorities.
kpeter@703: typedef PR Prio;
kpeter@703: /// Type of the items stored in the heap.
kpeter@701: typedef typename ItemIntMap::Key Item;
kpeter@703: /// Functor type for comparing the priorities.
kpeter@703: typedef CMP Compare;
kpeter@703:
kpeter@703: /// \brief Type to represent the states of the items.
kpeter@703: ///
kpeter@703: /// Each item has a state associated to it. It can be "in heap",
kpeter@703: /// "pre-heap" or "post-heap". The latter two are indifferent from the
kpeter@703: /// heap's point of view, but may be useful to the user.
kpeter@703: ///
kpeter@703: /// The item-int map must be initialized in such way that it assigns
kpeter@703: /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
kpeter@703: enum State {
kpeter@703: IN_HEAP = 0, ///< = 0.
kpeter@703: PRE_HEAP = -1, ///< = -1.
kpeter@703: POST_HEAP = -2 ///< = -2.
kpeter@703: };
kpeter@701:
kpeter@701: private:
kpeter@701: class store;
kpeter@701:
kpeter@703: std::vector<store> _data;
kpeter@703: int _min;
kpeter@703: ItemIntMap &_iim;
kpeter@703: Compare _comp;
kpeter@703: int _num_items;
kpeter@701:
kpeter@701: public:
kpeter@703: /// \brief Constructor.
kpeter@703: ///
kpeter@703: /// Constructor.
kpeter@703: /// \param map A map that assigns \c int values to the items.
kpeter@703: /// It is used internally to handle the cross references.
kpeter@703: /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@703: explicit PairingHeap(ItemIntMap &map)
kpeter@703: : _min(0), _iim(map), _num_items(0) {}
kpeter@701:
kpeter@703: /// \brief Constructor.
kpeter@701: ///
kpeter@703: /// Constructor.
kpeter@703: /// \param map A map that assigns \c int values to the items.
kpeter@703: /// It is used internally to handle the cross references.
kpeter@703: /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@703: /// \param comp The function object used for comparing the priorities.
kpeter@703: PairingHeap(ItemIntMap &map, const Compare &comp)
kpeter@703: : _min(0), _iim(map), _comp(comp), _num_items(0) {}
kpeter@701:
kpeter@701: /// \brief The number of items stored in the heap.
kpeter@701: ///
kpeter@703: /// This function returns the number of items stored in the heap.
kpeter@703: int size() const { return _num_items; }
kpeter@701:
kpeter@703: /// \brief Check if the heap is empty.
kpeter@701: ///
kpeter@703: /// This function returns \c true if the heap is empty.
kpeter@703: bool empty() const { return _num_items==0; }
kpeter@701:
kpeter@703: /// \brief Make the heap empty.
kpeter@701: ///
kpeter@703: /// This functon makes the heap empty.
kpeter@703: /// It does not change the cross reference map. If you want to reuse
kpeter@703: /// a heap that is not surely empty, you should first clear it and
kpeter@703: /// then you should set the cross reference map to \c PRE_HEAP
kpeter@703: /// for each item.
kpeter@701: void clear() {
kpeter@703: _data.clear();
kpeter@703: _min = 0;
kpeter@703: _num_items = 0;
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Set the priority of an item or insert it, if it is
kpeter@703: /// not stored in the heap.
kpeter@701: ///
kpeter@703: /// This method sets the priority of the given item if it is
kpeter@703: /// already stored in the heap. Otherwise it inserts the given
kpeter@703: /// item into the heap with the given priority.
kpeter@703: /// \param item The item.
kpeter@703: /// \param value The priority.
kpeter@701: void set (const Item& item, const Prio& value) {
kpeter@703: int i=_iim[item];
kpeter@703: if ( i>=0 && _data[i].in ) {
kpeter@703: if ( _comp(value, _data[i].prio) ) decrease(item, value);
kpeter@703: if ( _comp(_data[i].prio, value) ) increase(item, value);
kpeter@701: } else push(item, value);
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Insert an item into the heap with the given priority.
kpeter@701: ///
kpeter@703: /// This function inserts the given item into the heap with the
kpeter@703: /// given priority.
kpeter@703: /// \param item The item to insert.
kpeter@703: /// \param value The priority of the item.
kpeter@703: /// \pre \e item must not be stored in the heap.
kpeter@701: void push (const Item& item, const Prio& value) {
kpeter@703: int i=_iim[item];
kpeter@701: if( i<0 ) {
kpeter@703: int s=_data.size();
kpeter@703: _iim.set(item, s);
kpeter@701: store st;
kpeter@701: st.name=item;
kpeter@703: _data.push_back(st);
kpeter@701: i=s;
kpeter@701: } else {
kpeter@703: _data[i].parent=_data[i].child=-1;
kpeter@703: _data[i].left_child=false;
kpeter@703: _data[i].degree=0;
kpeter@703: _data[i].in=true;
kpeter@701: }
kpeter@701:
kpeter@703: _data[i].prio=value;
kpeter@701:
kpeter@703: if ( _num_items!=0 ) {
kpeter@703: if ( _comp( value, _data[_min].prio) ) {
kpeter@703: fuse(i,_min);
kpeter@703: _min=i;
kpeter@701: }
kpeter@703: else fuse(_min,i);
kpeter@701: }
kpeter@703: else _min=i;
kpeter@701:
kpeter@703: ++_num_items;
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Return the item having minimum priority.
kpeter@701: ///
kpeter@703: /// This function returns the item having minimum priority.
kpeter@703: /// \pre The heap must be non-empty.
kpeter@703: Item top() const { return _data[_min].name; }
kpeter@701:
kpeter@703: /// \brief The minimum priority.
kpeter@701: ///
kpeter@703: /// This function returns the minimum priority.
kpeter@703: /// \pre The heap must be non-empty.
kpeter@703: const Prio& prio() const { return _data[_min].prio; }
kpeter@701:
kpeter@703: /// \brief The priority of the given item.
kpeter@701: ///
kpeter@703: /// This function returns the priority of the given item.
kpeter@703: /// \param item The item.
kpeter@703: /// \pre \e item must be in the heap.
kpeter@701: const Prio& operator[](const Item& item) const {
kpeter@703: return _data[_iim[item]].prio;
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Remove the item having minimum priority.
kpeter@701: ///
kpeter@703: /// This function removes the item having minimum priority.
kpeter@701: /// \pre The heap must be non-empty.
kpeter@701: void pop() {
kpeter@705: std::vector<int> trees;
kpeter@705: int i=0, child_right = 0;
kpeter@703: _data[_min].in=false;
kpeter@701:
kpeter@703: if( -1!=_data[_min].child ) {
kpeter@703: i=_data[_min].child;
kpeter@705: trees.push_back(i);
kpeter@703: _data[i].parent = -1;
kpeter@703: _data[_min].child = -1;
kpeter@701:
kpeter@701: int ch=-1;
kpeter@703: while( _data[i].child!=-1 ) {
kpeter@703: ch=_data[i].child;
kpeter@703: if( _data[ch].left_child && i==_data[ch].parent ) {
kpeter@705: break;
kpeter@701: } else {
kpeter@703: if( _data[ch].left_child ) {
kpeter@703: child_right=_data[ch].parent;
kpeter@703: _data[ch].parent = i;
kpeter@703: --_data[i].degree;
kpeter@701: }
kpeter@701: else {
kpeter@701: child_right=ch;
kpeter@703: _data[i].child=-1;
kpeter@703: _data[i].degree=0;
kpeter@701: }
kpeter@703: _data[child_right].parent = -1;
kpeter@705: trees.push_back(child_right);
kpeter@701: i = child_right;
kpeter@701: }
kpeter@701: }
kpeter@701:
kpeter@705: int num_child = trees.size();
kpeter@701: int other;
kpeter@701: for( i=0; i<num_child-1; i+=2 ) {
kpeter@705: if ( !_comp(_data[trees[i]].prio, _data[trees[i+1]].prio) ) {
kpeter@705: other=trees[i];
kpeter@705: trees[i]=trees[i+1];
kpeter@705: trees[i+1]=other;
kpeter@701: }
kpeter@705: fuse( trees[i], trees[i+1] );
kpeter@701: }
kpeter@701:
kpeter@701: i = (0==(num_child % 2)) ? num_child-2 : num_child-1;
kpeter@701: while(i>=2) {
kpeter@705: if ( _comp(_data[trees[i]].prio, _data[trees[i-2]].prio) ) {
kpeter@705: other=trees[i];
kpeter@705: trees[i]=trees[i-2];
kpeter@705: trees[i-2]=other;
kpeter@701: }
kpeter@705: fuse( trees[i-2], trees[i] );
kpeter@701: i-=2;
kpeter@701: }
kpeter@705: _min = trees[0];
kpeter@701: }
kpeter@705: else {
kpeter@703: _min = _data[_min].child;
kpeter@701: }
kpeter@701:
kpeter@703: if (_min >= 0) _data[_min].left_child = false;
kpeter@703: --_num_items;
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Remove the given item from the heap.
kpeter@701: ///
kpeter@703: /// This function removes the given item from the heap if it is
kpeter@703: /// already stored.
kpeter@703: /// \param item The item to delete.
kpeter@703: /// \pre \e item must be in the heap.
kpeter@701: void erase (const Item& item) {
kpeter@703: int i=_iim[item];
kpeter@703: if ( i>=0 && _data[i].in ) {
kpeter@703: decrease( item, _data[_min].prio-1 );
kpeter@701: pop();
kpeter@701: }
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Decrease the priority of an item to the given value.
kpeter@701: ///
kpeter@703: /// This function decreases the priority of an item to the given value.
kpeter@703: /// \param item The item.
kpeter@703: /// \param value The priority.
kpeter@703: /// \pre \e item must be stored in the heap with priority at least \e value.
kpeter@701: void decrease (Item item, const Prio& value) {
kpeter@703: int i=_iim[item];
kpeter@703: _data[i].prio=value;
kpeter@703: int p=_data[i].parent;
kpeter@701:
kpeter@703: if( _data[i].left_child && i!=_data[p].child ) {
kpeter@703: p=_data[p].parent;
kpeter@701: }
kpeter@701:
kpeter@703: if ( p!=-1 && _comp(value,_data[p].prio) ) {
kpeter@701: cut(i,p);
kpeter@703: if ( _comp(_data[_min].prio,value) ) {
kpeter@703: fuse(_min,i);
kpeter@701: } else {
kpeter@703: fuse(i,_min);
kpeter@703: _min=i;
kpeter@701: }
kpeter@701: }
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Increase the priority of an item to the given value.
kpeter@701: ///
kpeter@703: /// This function increases the priority of an item to the given value.
kpeter@703: /// \param item The item.
kpeter@703: /// \param value The priority.
kpeter@703: /// \pre \e item must be stored in the heap with priority at most \e value.
kpeter@701: void increase (Item item, const Prio& value) {
kpeter@701: erase(item);
kpeter@701: push(item,value);
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Return the state of an item.
kpeter@701: ///
kpeter@703: /// This method returns \c PRE_HEAP if the given item has never
kpeter@703: /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@703: /// and \c POST_HEAP otherwise.
kpeter@703: /// In the latter case it is possible that the item will get back
kpeter@703: /// to the heap again.
kpeter@703: /// \param item The item.
kpeter@701: State state(const Item &item) const {
kpeter@703: int i=_iim[item];
kpeter@701: if( i>=0 ) {
kpeter@703: if( _data[i].in ) i=0;
kpeter@701: else i=-2;
kpeter@701: }
kpeter@701: return State(i);
kpeter@701: }
kpeter@701:
kpeter@703: /// \brief Set the state of an item in the heap.
kpeter@701: ///
kpeter@703: /// This function sets the state of the given item in the heap.
kpeter@703: /// It can be used to manually clear the heap when it is important
kpeter@703: /// to achive better time complexity.
kpeter@701: /// \param i The item.
kpeter@701: /// \param st The state. It should not be \c IN_HEAP.
kpeter@701: void state(const Item& i, State st) {
kpeter@701: switch (st) {
kpeter@701: case POST_HEAP:
kpeter@701: case PRE_HEAP:
kpeter@701: if (state(i) == IN_HEAP) erase(i);
kpeter@703: _iim[i]=st;
kpeter@701: break;
kpeter@701: case IN_HEAP:
kpeter@701: break;
kpeter@701: }
kpeter@701: }
kpeter@701:
kpeter@701: private:
kpeter@701:
kpeter@701: void cut(int a, int b) {
kpeter@701: int child_a;
kpeter@703: switch (_data[a].degree) {
kpeter@701: case 2:
kpeter@703: child_a = _data[_data[a].child].parent;
kpeter@703: if( _data[a].left_child ) {
kpeter@703: _data[child_a].left_child=true;
kpeter@703: _data[b].child=child_a;
kpeter@703: _data[child_a].parent=_data[a].parent;
kpeter@701: }
kpeter@701: else {
kpeter@703: _data[child_a].left_child=false;
kpeter@703: _data[child_a].parent=b;
kpeter@703: if( a!=_data[b].child )
kpeter@703: _data[_data[b].child].parent=child_a;
kpeter@701: else
kpeter@703: _data[b].child=child_a;
kpeter@701: }
kpeter@703: --_data[a].degree;
kpeter@703: _data[_data[a].child].parent=a;
kpeter@701: break;
kpeter@701:
kpeter@701: case 1:
kpeter@703: child_a = _data[a].child;
kpeter@703: if( !_data[child_a].left_child ) {
kpeter@703: --_data[a].degree;
kpeter@703: if( _data[a].left_child ) {
kpeter@703: _data[child_a].left_child=true;
kpeter@703: _data[child_a].parent=_data[a].parent;
kpeter@703: _data[b].child=child_a;
kpeter@701: }
kpeter@701: else {
kpeter@703: _data[child_a].left_child=false;
kpeter@703: _data[child_a].parent=b;
kpeter@703: if( a!=_data[b].child )
kpeter@703: _data[_data[b].child].parent=child_a;
kpeter@701: else
kpeter@703: _data[b].child=child_a;
kpeter@701: }
kpeter@703: _data[a].child=-1;
kpeter@701: }
kpeter@701: else {
kpeter@703: --_data[b].degree;
kpeter@703: if( _data[a].left_child ) {
kpeter@703: _data[b].child =
kpeter@703: (1==_data[b].degree) ? _data[a].parent : -1;
kpeter@701: } else {
kpeter@703: if (1==_data[b].degree)
kpeter@703: _data[_data[b].child].parent=b;
kpeter@701: else
kpeter@703: _data[b].child=-1;
kpeter@701: }
kpeter@701: }
kpeter@701: break;
kpeter@701:
kpeter@701: case 0:
kpeter@703: --_data[b].degree;
kpeter@703: if( _data[a].left_child ) {
kpeter@703: _data[b].child =
kpeter@703: (0!=_data[b].degree) ? _data[a].parent : -1;
kpeter@701: } else {
kpeter@703: if( 0!=_data[b].degree )
kpeter@703: _data[_data[b].child].parent=b;
kpeter@701: else
kpeter@703: _data[b].child=-1;
kpeter@701: }
kpeter@701: break;
kpeter@701: }
kpeter@703: _data[a].parent=-1;
kpeter@703: _data[a].left_child=false;
kpeter@701: }
kpeter@701:
kpeter@701: void fuse(int a, int b) {
kpeter@703: int child_a = _data[a].child;
kpeter@703: int child_b = _data[b].child;
kpeter@703: _data[a].child=b;
kpeter@703: _data[b].parent=a;
kpeter@703: _data[b].left_child=true;
kpeter@701:
kpeter@701: if( -1!=child_a ) {
kpeter@703: _data[b].child=child_a;
kpeter@703: _data[child_a].parent=b;
kpeter@703: _data[child_a].left_child=false;
kpeter@703: ++_data[b].degree;
kpeter@701:
kpeter@701: if( -1!=child_b ) {
kpeter@703: _data[b].child=child_b;
kpeter@703: _data[child_b].parent=child_a;
kpeter@701: }
kpeter@701: }
kpeter@703: else { ++_data[a].degree; }
kpeter@701: }
kpeter@701:
kpeter@701: class store {
kpeter@701: friend class PairingHeap;
kpeter@701:
kpeter@701: Item name;
kpeter@701: int parent;
kpeter@701: int child;
kpeter@701: bool left_child;
kpeter@701: int degree;
kpeter@701: bool in;
kpeter@701: Prio prio;
kpeter@701:
kpeter@701: store() : parent(-1), child(-1), left_child(false), degree(0), in(true) {}
kpeter@701: };
kpeter@701: };
kpeter@701:
kpeter@701: } //namespace lemon
kpeter@701:
kpeter@701: #endif //LEMON_PAIRING_HEAP_H
kpeter@701: