353 lines
11 KiB
C++
Executable File
353 lines
11 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2009
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_DHEAP_H
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#define LEMON_DHEAP_H
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///\ingroup heaps
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///\file
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///\brief D-ary heap implementation.
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#include <vector>
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#include <utility>
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#include <functional>
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namespace lemon {
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/// \ingroup heaps
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///
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///\brief D-ary heap data structure.
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///
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/// This class implements the \e D-ary \e heap data structure.
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/// It fully conforms to the \ref concepts::Heap "heap concept".
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///
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/// The \ref DHeap "D-ary heap" is a generalization of the
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/// \ref BinHeap "binary heap" structure, its nodes have at most
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/// \c D children, instead of two.
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/// \ref BinHeap and \ref QuadHeap are specialized implementations
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/// of this structure for <tt>D=2</tt> and <tt>D=4</tt>, respectively.
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///
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/// \tparam PR Type of the priorities of the items.
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/// \tparam IM A read-writable item map with \c int values, used
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/// internally to handle the cross references.
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/// \tparam D The degree of the heap, each node have at most \e D
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/// children. The default is 16. Powers of two are suggested to use
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/// so that the multiplications and divisions needed to traverse the
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/// nodes of the heap could be performed faster.
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/// \tparam CMP A functor class for comparing the priorities.
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/// The default is \c std::less<PR>.
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///
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///\sa BinHeap
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///\sa FouraryHeap
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#ifdef DOXYGEN
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template <typename PR, typename IM, int D, typename CMP>
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#else
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template <typename PR, typename IM, int D = 16,
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typename CMP = std::less<PR> >
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#endif
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class DHeap {
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public:
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/// Type of the item-int map.
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typedef IM ItemIntMap;
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/// Type of the priorities.
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typedef PR Prio;
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/// Type of the items stored in the heap.
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typedef typename ItemIntMap::Key Item;
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/// Type of the item-priority pairs.
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typedef std::pair<Item,Prio> Pair;
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/// Functor type for comparing the priorities.
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typedef CMP Compare;
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/// \brief Type to represent the states of the items.
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///
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/// Each item has a state associated to it. It can be "in heap",
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/// "pre-heap" or "post-heap". The latter two are indifferent from the
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/// heap's point of view, but may be useful to the user.
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///
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/// The item-int map must be initialized in such way that it assigns
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/// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
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enum State {
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IN_HEAP = 0, ///< = 0.
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PRE_HEAP = -1, ///< = -1.
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POST_HEAP = -2 ///< = -2.
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};
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private:
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std::vector<Pair> _data;
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Compare _comp;
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ItemIntMap &_iim;
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public:
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/// \brief Constructor.
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///
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/// Constructor.
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/// \param map A map that assigns \c int values to the items.
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/// It is used internally to handle the cross references.
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/// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
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explicit DHeap(ItemIntMap &map) : _iim(map) {}
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/// \brief Constructor.
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///
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/// Constructor.
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/// \param map A map that assigns \c int values to the items.
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/// It is used internally to handle the cross references.
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/// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
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/// \param comp The function object used for comparing the priorities.
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DHeap(ItemIntMap &map, const Compare &comp)
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: _iim(map), _comp(comp) {}
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/// \brief The number of items stored in the heap.
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///
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/// This function returns the number of items stored in the heap.
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int size() const { return _data.size(); }
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/// \brief Check if the heap is empty.
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///
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/// This function returns \c true if the heap is empty.
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bool empty() const { return _data.empty(); }
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/// \brief Make the heap empty.
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///
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/// This functon makes the heap empty.
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/// It does not change the cross reference map. If you want to reuse
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/// a heap that is not surely empty, you should first clear it and
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/// then you should set the cross reference map to \c PRE_HEAP
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/// for each item.
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void clear() { _data.clear(); }
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private:
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int parent(int i) { return (i-1)/D; }
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int firstChild(int i) { return D*i+1; }
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bool less(const Pair &p1, const Pair &p2) const {
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return _comp(p1.second, p2.second);
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}
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void bubbleUp(int hole, Pair p) {
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int par = parent(hole);
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while( hole>0 && less(p,_data[par]) ) {
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move(_data[par],hole);
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hole = par;
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par = parent(hole);
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}
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move(p, hole);
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}
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void bubbleDown(int hole, Pair p, int length) {
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if( length>1 ) {
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int child = firstChild(hole);
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while( child+D<=length ) {
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int min=child;
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for (int i=1; i<D; ++i) {
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if( less(_data[child+i], _data[min]) )
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min=child+i;
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}
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if( !less(_data[min], p) )
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goto ok;
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move(_data[min], hole);
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hole = min;
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child = firstChild(hole);
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}
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if ( child<length ) {
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int min = child;
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while (++child < length) {
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if( less(_data[child], _data[min]) )
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min=child;
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}
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if( less(_data[min], p) ) {
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move(_data[min], hole);
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hole = min;
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}
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}
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}
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ok:
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move(p, hole);
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}
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void move(const Pair &p, int i) {
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_data[i] = p;
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_iim.set(p.first, i);
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}
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public:
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/// \brief Insert a pair of item and priority into the heap.
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///
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/// This function inserts \c p.first to the heap with priority
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/// \c p.second.
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/// \param p The pair to insert.
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/// \pre \c p.first must not be stored in the heap.
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void push(const Pair &p) {
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int n = _data.size();
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_data.resize(n+1);
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bubbleUp(n, p);
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}
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/// \brief Insert an item into the heap with the given priority.
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///
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/// This function inserts the given item into the heap with the
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/// given priority.
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/// \param i The item to insert.
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/// \param p The priority of the item.
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/// \pre \e i must not be stored in the heap.
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void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
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/// \brief Return the item having minimum priority.
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///
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/// This function returns the item having minimum priority.
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/// \pre The heap must be non-empty.
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Item top() const { return _data[0].first; }
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/// \brief The minimum priority.
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///
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/// This function returns the minimum priority.
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/// \pre The heap must be non-empty.
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Prio prio() const { return _data[0].second; }
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/// \brief Remove the item having minimum priority.
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///
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/// This function removes the item having minimum priority.
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/// \pre The heap must be non-empty.
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void pop() {
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int n = _data.size()-1;
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_iim.set(_data[0].first, POST_HEAP);
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if (n>0) bubbleDown(0, _data[n], n);
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_data.pop_back();
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}
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/// \brief Remove the given item from the heap.
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///
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/// This function removes the given item from the heap if it is
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/// already stored.
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/// \param i The item to delete.
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/// \pre \e i must be in the heap.
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void erase(const Item &i) {
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int h = _iim[i];
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int n = _data.size()-1;
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_iim.set(_data[h].first, POST_HEAP);
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if( h<n ) {
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if( less(_data[parent(h)], _data[n]) )
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bubbleDown(h, _data[n], n);
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else
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bubbleUp(h, _data[n]);
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}
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_data.pop_back();
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}
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/// \brief The priority of the given item.
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///
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/// This function returns the priority of the given item.
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/// \param i The item.
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/// \pre \e i must be in the heap.
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Prio operator[](const Item &i) const {
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int idx = _iim[i];
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return _data[idx].second;
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}
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/// \brief Set the priority of an item or insert it, if it is
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/// not stored in the heap.
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///
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/// This method sets the priority of the given item if it is
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/// already stored in the heap. Otherwise it inserts the given
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/// item into the heap with the given priority.
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/// \param i The item.
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/// \param p The priority.
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void set(const Item &i, const Prio &p) {
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int idx = _iim[i];
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if( idx<0 )
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push(i,p);
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else if( _comp(p, _data[idx].second) )
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bubbleUp(idx, Pair(i,p));
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else
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bubbleDown(idx, Pair(i,p), _data.size());
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}
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/// \brief Decrease the priority of an item to the given value.
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///
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/// This function decreases the priority of an item to the given value.
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/// \param i The item.
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/// \param p The priority.
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/// \pre \e i must be stored in the heap with priority at least \e p.
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void decrease(const Item &i, const Prio &p) {
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int idx = _iim[i];
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bubbleUp(idx, Pair(i,p));
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}
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/// \brief Increase the priority of an item to the given value.
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///
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/// This function increases the priority of an item to the given value.
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/// \param i The item.
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/// \param p The priority.
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/// \pre \e i must be stored in the heap with priority at most \e p.
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void increase(const Item &i, const Prio &p) {
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int idx = _iim[i];
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bubbleDown(idx, Pair(i,p), _data.size());
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}
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/// \brief Return the state of an item.
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///
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/// This method returns \c PRE_HEAP if the given item has never
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/// been in the heap, \c IN_HEAP if it is in the heap at the moment,
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/// and \c POST_HEAP otherwise.
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/// In the latter case it is possible that the item will get back
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/// to the heap again.
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/// \param i The item.
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State state(const Item &i) const {
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int s = _iim[i];
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if (s>=0) s=0;
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return State(s);
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}
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/// \brief Set the state of an item in the heap.
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///
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/// This function sets the state of the given item in the heap.
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/// It can be used to manually clear the heap when it is important
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/// to achive better time complexity.
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/// \param i The item.
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/// \param st The state. It should not be \c IN_HEAP.
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void state(const Item& i, State st) {
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switch (st) {
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case POST_HEAP:
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case PRE_HEAP:
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if (state(i) == IN_HEAP) erase(i);
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_iim[i] = st;
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break;
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case IN_HEAP:
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break;
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}
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}
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/// \brief Replace an item in the heap.
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///
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/// This function replaces item \c i with item \c j.
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/// Item \c i must be in the heap, while \c j must be out of the heap.
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/// After calling this method, item \c i will be out of the
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/// heap and \c j will be in the heap with the same prioriority
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/// as item \c i had before.
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void replace(const Item& i, const Item& j) {
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int idx=_iim[i];
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_iim.set(i, _iim[j]);
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_iim.set(j, idx);
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_data[idx].first=j;
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}
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}; // class DHeap
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} // namespace lemon
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#endif // LEMON_DHEAP_H
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