alpar@209: /* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@100: *
alpar@209: * This file is a part of LEMON, a generic C++ optimization library.
alpar@100: *
alpar@440: * Copyright (C) 2003-2009
alpar@100: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@100: * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@100: *
alpar@100: * Permission to use, modify and distribute this software is granted
alpar@100: * provided that this copyright notice appears in all copies. For
alpar@100: * precise terms see the accompanying LICENSE file.
alpar@100: *
alpar@100: * This software is provided "AS IS" with no warranty of any kind,
alpar@100: * express or implied, and with no claim as to its suitability for any
alpar@100: * purpose.
alpar@100: *
alpar@100: */
alpar@100:
alpar@100: #ifndef LEMON_BIN_HEAP_H
alpar@100: #define LEMON_BIN_HEAP_H
alpar@100:
kpeter@710: ///\ingroup heaps
alpar@100: ///\file
kpeter@709: ///\brief Binary heap implementation.
alpar@100:
alpar@100: #include <vector>
alpar@100: #include <utility>
alpar@100: #include <functional>
alpar@100:
alpar@100: namespace lemon {
alpar@100:
kpeter@710: /// \ingroup heaps
alpar@100: ///
kpeter@709: /// \brief Binary heap data structure.
alpar@100: ///
kpeter@709: /// This class implements the \e binary \e heap data structure.
kpeter@709: /// It fully conforms to the \ref concepts::Heap "heap concept".
deba@683: ///
kpeter@709: /// \tparam PR Type of the priorities of the items.
kpeter@709: /// \tparam IM A read-writable item map with \c int values, used
kpeter@709: /// internally to handle the cross references.
kpeter@709: /// \tparam CMP A functor class for comparing the priorities.
kpeter@709: /// The default is \c std::less<PR>.
kpeter@709: #ifdef DOXYGEN
kpeter@709: template <typename PR, typename IM, typename CMP>
kpeter@709: #else
deba@683: template <typename PR, typename IM, typename CMP = std::less<PR> >
kpeter@709: #endif
alpar@100: class BinHeap {
kpeter@709: public:
alpar@100:
kpeter@709: /// Type of the item-int map.
kpeter@559: typedef IM ItemIntMap;
kpeter@709: /// Type of the priorities.
kpeter@559: typedef PR Prio;
kpeter@709: /// Type of the items stored in the heap.
alpar@100: typedef typename ItemIntMap::Key Item;
kpeter@709: /// Type of the item-priority pairs.
alpar@100: typedef std::pair<Item,Prio> Pair;
kpeter@709: /// Functor type for comparing the priorities.
deba@683: typedef CMP Compare;
alpar@100:
kpeter@709: /// \brief Type to represent the states of the items.
alpar@100: ///
kpeter@709: /// Each item has a state associated to it. It can be "in heap",
kpeter@709: /// "pre-heap" or "post-heap". The latter two are indifferent from the
alpar@100: /// heap's point of view, but may be useful to the user.
alpar@100: ///
kpeter@559: /// The item-int map must be initialized in such way that it assigns
kpeter@559: /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
alpar@100: enum State {
kpeter@584: IN_HEAP = 0, ///< = 0.
kpeter@584: PRE_HEAP = -1, ///< = -1.
kpeter@584: POST_HEAP = -2 ///< = -2.
alpar@100: };
alpar@100:
alpar@100: private:
kpeter@559: std::vector<Pair> _data;
kpeter@559: Compare _comp;
kpeter@559: ItemIntMap &_iim;
alpar@100:
alpar@100: public:
kpeter@709:
kpeter@709: /// \brief Constructor.
alpar@100: ///
kpeter@709: /// Constructor.
kpeter@709: /// \param map A map that assigns \c int values to the items.
kpeter@709: /// It is used internally to handle the cross references.
kpeter@709: /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@559: explicit BinHeap(ItemIntMap &map) : _iim(map) {}
alpar@209:
kpeter@709: /// \brief Constructor.
alpar@100: ///
kpeter@709: /// Constructor.
kpeter@709: /// \param map A map that assigns \c int values to the items.
kpeter@709: /// It is used internally to handle the cross references.
kpeter@709: /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
kpeter@709: /// \param comp The function object used for comparing the priorities.
kpeter@559: BinHeap(ItemIntMap &map, const Compare &comp)
kpeter@559: : _iim(map), _comp(comp) {}
alpar@100:
alpar@100:
kpeter@709: /// \brief The number of items stored in the heap.
alpar@100: ///
kpeter@709: /// This function returns the number of items stored in the heap.
kpeter@559: int size() const { return _data.size(); }
alpar@209:
kpeter@709: /// \brief Check if the heap is empty.
alpar@100: ///
kpeter@709: /// This function returns \c true if the heap is empty.
kpeter@559: bool empty() const { return _data.empty(); }
alpar@100:
kpeter@709: /// \brief Make the heap empty.
alpar@209: ///
kpeter@709: /// This functon makes the heap empty.
kpeter@709: /// It does not change the cross reference map. If you want to reuse
kpeter@709: /// a heap that is not surely empty, you should first clear it and
kpeter@709: /// then you should set the cross reference map to \c PRE_HEAP
kpeter@709: /// for each item.
alpar@209: void clear() {
kpeter@559: _data.clear();
alpar@100: }
alpar@100:
alpar@100: private:
alpar@100: static int parent(int i) { return (i-1)/2; }
alpar@100:
kpeter@711: static int secondChild(int i) { return 2*i+2; }
alpar@100: bool less(const Pair &p1, const Pair &p2) const {
kpeter@559: return _comp(p1.second, p2.second);
alpar@100: }
alpar@100:
kpeter@711: int bubbleUp(int hole, Pair p) {
alpar@100: int par = parent(hole);
kpeter@559: while( hole>0 && less(p,_data[par]) ) {
kpeter@559: move(_data[par],hole);
alpar@209: hole = par;
alpar@209: par = parent(hole);
alpar@100: }
alpar@100: move(p, hole);
alpar@100: return hole;
alpar@100: }
alpar@100:
kpeter@711: int bubbleDown(int hole, Pair p, int length) {
kpeter@711: int child = secondChild(hole);
alpar@100: while(child < length) {
kpeter@559: if( less(_data[child-1], _data[child]) ) {
alpar@209: --child;
alpar@209: }
kpeter@559: if( !less(_data[child], p) )
alpar@209: goto ok;
kpeter@559: move(_data[child], hole);
alpar@209: hole = child;
kpeter@711: child = secondChild(hole);
alpar@100: }
alpar@100: child--;
kpeter@559: if( child<length && less(_data[child], p) ) {
kpeter@559: move(_data[child], hole);
alpar@209: hole=child;
alpar@100: }
alpar@100: ok:
alpar@100: move(p, hole);
alpar@100: return hole;
alpar@100: }
alpar@100:
alpar@100: void move(const Pair &p, int i) {
kpeter@559: _data[i] = p;
kpeter@559: _iim.set(p.first, i);
alpar@100: }
alpar@100:
alpar@100: public:
kpeter@709:
alpar@100: /// \brief Insert a pair of item and priority into the heap.
alpar@100: ///
kpeter@709: /// This function inserts \c p.first to the heap with priority
kpeter@709: /// \c p.second.
alpar@100: /// \param p The pair to insert.
kpeter@709: /// \pre \c p.first must not be stored in the heap.
alpar@100: void push(const Pair &p) {
kpeter@559: int n = _data.size();
kpeter@559: _data.resize(n+1);
kpeter@711: bubbleUp(n, p);
alpar@100: }
alpar@100:
kpeter@709: /// \brief Insert an item into the heap with the given priority.
alpar@209: ///
kpeter@709: /// This function inserts the given item into the heap with the
kpeter@709: /// given priority.
alpar@100: /// \param i The item to insert.
alpar@100: /// \param p The priority of the item.
kpeter@709: /// \pre \e i must not be stored in the heap.
alpar@100: void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
alpar@100:
kpeter@709: /// \brief Return the item having minimum priority.
alpar@100: ///
kpeter@709: /// This function returns the item having minimum priority.
kpeter@709: /// \pre The heap must be non-empty.
alpar@100: Item top() const {
kpeter@559: return _data[0].first;
alpar@100: }
alpar@100:
kpeter@709: /// \brief The minimum priority.
alpar@100: ///
kpeter@709: /// This function returns the minimum priority.
kpeter@709: /// \pre The heap must be non-empty.
alpar@100: Prio prio() const {
kpeter@559: return _data[0].second;
alpar@100: }
alpar@100:
kpeter@709: /// \brief Remove the item having minimum priority.
alpar@100: ///
kpeter@709: /// This function removes the item having minimum priority.
alpar@209: /// \pre The heap must be non-empty.
alpar@100: void pop() {
kpeter@559: int n = _data.size()-1;
kpeter@559: _iim.set(_data[0].first, POST_HEAP);
alpar@100: if (n > 0) {
kpeter@711: bubbleDown(0, _data[n], n);
alpar@100: }
kpeter@559: _data.pop_back();
alpar@100: }
alpar@100:
kpeter@709: /// \brief Remove the given item from the heap.
alpar@100: ///
kpeter@709: /// This function removes the given item from the heap if it is
kpeter@709: /// already stored.
kpeter@709: /// \param i The item to delete.
kpeter@709: /// \pre \e i must be in the heap.
alpar@100: void erase(const Item &i) {
kpeter@559: int h = _iim[i];
kpeter@559: int n = _data.size()-1;
kpeter@559: _iim.set(_data[h].first, POST_HEAP);
alpar@100: if( h < n ) {
kpeter@711: if ( bubbleUp(h, _data[n]) == h) {
kpeter@711: bubbleDown(h, _data[n], n);
alpar@209: }
alpar@100: }
kpeter@559: _data.pop_back();
alpar@100: }
alpar@100:
kpeter@709: /// \brief The priority of the given item.
alpar@100: ///
kpeter@709: /// This function returns the priority of the given item.
kpeter@559: /// \param i The item.
kpeter@709: /// \pre \e i must be in the heap.
alpar@100: Prio operator[](const Item &i) const {
kpeter@559: int idx = _iim[i];
kpeter@559: return _data[idx].second;
alpar@100: }
alpar@100:
kpeter@709: /// \brief Set the priority of an item or insert it, if it is
kpeter@709: /// not stored in the heap.
alpar@100: ///
kpeter@709: /// This method sets the priority of the given item if it is
kpeter@709: /// already stored in the heap. Otherwise it inserts the given
kpeter@709: /// item into the heap with the given priority.
alpar@100: /// \param i The item.
alpar@100: /// \param p The priority.
alpar@100: void set(const Item &i, const Prio &p) {
kpeter@559: int idx = _iim[i];
alpar@100: if( idx < 0 ) {
alpar@209: push(i,p);
alpar@100: }
kpeter@559: else if( _comp(p, _data[idx].second) ) {
kpeter@711: bubbleUp(idx, Pair(i,p));
alpar@100: }
alpar@100: else {
kpeter@711: bubbleDown(idx, Pair(i,p), _data.size());
alpar@100: }
alpar@100: }
alpar@100:
kpeter@709: /// \brief Decrease the priority of an item to the given value.
alpar@100: ///
kpeter@709: /// This function decreases the priority of an item to the given value.
kpeter@559: /// \param i The item.
kpeter@559: /// \param p The priority.
kpeter@709: /// \pre \e i must be stored in the heap with priority at least \e p.
alpar@100: void decrease(const Item &i, const Prio &p) {
kpeter@559: int idx = _iim[i];
kpeter@711: bubbleUp(idx, Pair(i,p));
alpar@100: }
alpar@209:
kpeter@709: /// \brief Increase the priority of an item to the given value.
alpar@100: ///
kpeter@709: /// This function increases the priority of an item to the given value.
kpeter@559: /// \param i The item.
kpeter@559: /// \param p The priority.
kpeter@709: /// \pre \e i must be stored in the heap with priority at most \e p.
alpar@100: void increase(const Item &i, const Prio &p) {
kpeter@559: int idx = _iim[i];
kpeter@711: bubbleDown(idx, Pair(i,p), _data.size());
alpar@100: }
alpar@100:
kpeter@709: /// \brief Return the state of an item.
alpar@100: ///
kpeter@709: /// This method returns \c PRE_HEAP if the given item has never
kpeter@709: /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
kpeter@709: /// and \c POST_HEAP otherwise.
kpeter@709: /// In the latter case it is possible that the item will get back
kpeter@709: /// to the heap again.
alpar@100: /// \param i The item.
alpar@100: State state(const Item &i) const {
kpeter@559: int s = _iim[i];
alpar@100: if( s>=0 )
alpar@209: s=0;
alpar@100: return State(s);
alpar@100: }
alpar@100:
kpeter@709: /// \brief Set the state of an item in the heap.
alpar@100: ///
kpeter@709: /// This function sets the state of the given item in the heap.
kpeter@709: /// It can be used to manually clear the heap when it is important
kpeter@709: /// to achive better time complexity.
alpar@100: /// \param i The item.
alpar@209: /// \param st The state. It should not be \c IN_HEAP.
alpar@100: void state(const Item& i, State st) {
alpar@100: switch (st) {
alpar@100: case POST_HEAP:
alpar@100: case PRE_HEAP:
alpar@100: if (state(i) == IN_HEAP) {
alpar@100: erase(i);
alpar@100: }
kpeter@559: _iim[i] = st;
alpar@100: break;
alpar@100: case IN_HEAP:
alpar@100: break;
alpar@100: }
alpar@100: }
alpar@100:
kpeter@709: /// \brief Replace an item in the heap.
alpar@100: ///
kpeter@709: /// This function replaces item \c i with item \c j.
kpeter@709: /// Item \c i must be in the heap, while \c j must be out of the heap.
kpeter@709: /// After calling this method, item \c i will be out of the
kpeter@709: /// heap and \c j will be in the heap with the same prioriority
kpeter@709: /// as item \c i had before.
alpar@100: void replace(const Item& i, const Item& j) {
kpeter@559: int idx = _iim[i];
kpeter@559: _iim.set(i, _iim[j]);
kpeter@559: _iim.set(j, idx);
kpeter@559: _data[idx].first = j;
alpar@100: }
alpar@100:
alpar@100: }; // class BinHeap
alpar@209:
alpar@100: } // namespace lemon
alpar@100:
alpar@100: #endif // LEMON_BIN_HEAP_H