kpeter@701: /* -*- C++ -*-
kpeter@701:  *
kpeter@701:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@701:  *
kpeter@701:  * Copyright (C) 2003-2008
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_KARY_HEAP_H
kpeter@701: #define LEMON_KARY_HEAP_H
kpeter@701: 
kpeter@701: ///\ingroup auxdat
kpeter@701: ///\file
kpeter@701: ///\brief Kary Heap implementation.
kpeter@701: 
kpeter@701: #include <iostream>
kpeter@701: #include <vector>
kpeter@701: #include <utility>
kpeter@701: #include <functional>
kpeter@701: 
kpeter@701: namespace lemon {
kpeter@701: 
kpeter@701:   ///\ingroup auxdat
kpeter@701:   ///
kpeter@701:   ///\brief A Kary Heap implementation.
kpeter@701:   ///
kpeter@701:   ///This class implements the \e Kary \e heap data structure. A \e heap
kpeter@701:   ///is a data structure for storing items with specified values called \e
kpeter@701:   ///priorities in such a way that finding the item with minimum priority is
kpeter@701:   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
kpeter@701:   ///one can change the priority of an item, add or erase an item, etc.
kpeter@701:   ///
kpeter@701:   ///\param _Prio Type of the priority of the items.
kpeter@701:   ///\param _ItemIntMap A read and writable Item int map, used internally
kpeter@701:   ///to handle the cross references.
kpeter@701:   ///\param _Compare A class for the ordering of the priorities. The
kpeter@701:   ///default is \c std::less<_Prio>.
kpeter@701:   ///
kpeter@701:   ///\sa FibHeap
kpeter@701:   ///\sa Dijkstra
kpeter@701:   ///\author Dorian Batha
kpeter@701: 
kpeter@701:   template <typename _Prio, typename _ItemIntMap,
kpeter@701:             typename _Compare = std::less<_Prio> >
kpeter@701: 
kpeter@701:   class KaryHeap {
kpeter@701: 
kpeter@701:   public:
kpeter@701:     ///\e
kpeter@701:     typedef _ItemIntMap ItemIntMap;
kpeter@701:     ///\e
kpeter@701:     typedef _Prio Prio;
kpeter@701:     ///\e
kpeter@701:     typedef typename ItemIntMap::Key Item;
kpeter@701:     ///\e
kpeter@701:     typedef std::pair<Item,Prio> Pair;
kpeter@701:     ///\e
kpeter@701:     typedef _Compare Compare;
kpeter@701:     ///\e
kpeter@701: 
kpeter@701:     /// \brief Type to represent the items states.
kpeter@701:     ///
kpeter@701:     /// Each Item element have a state associated to it. It may be "in heap",
kpeter@701:     /// "pre heap" or "post heap". The latter two are indifferent from the
kpeter@701:     /// heap's point of view, but may be useful to the user.
kpeter@701:     ///
kpeter@701:     /// The ItemIntMap \e should be initialized in such way that it maps
kpeter@701:     /// PRE_HEAP (-1) to any element to be put in the heap...
kpeter@701:     enum State {
kpeter@701:       IN_HEAP = 0,
kpeter@701:       PRE_HEAP = -1,
kpeter@701:       POST_HEAP = -2
kpeter@701:     };
kpeter@701: 
kpeter@701:   private:
kpeter@701:     std::vector<Pair> data;
kpeter@701:     Compare comp;
kpeter@701:     ItemIntMap &iim;
kpeter@701:     int K;
kpeter@701: 
kpeter@701:   public:
kpeter@701:     /// \brief The constructor.
kpeter@701:     ///
kpeter@701:     /// The constructor.
kpeter@701:     /// \param _iim should be given to the constructor, since it is used
kpeter@701:     /// internally to handle the cross references. The value of the map
kpeter@701:     /// should be PRE_HEAP (-1) for each element.
kpeter@701:     explicit KaryHeap(ItemIntMap &_iim, const int &_K=32) : iim(_iim), K(_K) {}
kpeter@701: 
kpeter@701:     /// \brief The constructor.
kpeter@701:     ///
kpeter@701:     /// The constructor.
kpeter@701:     /// \param _iim should be given to the constructor, since it is used
kpeter@701:     /// internally to handle the cross references. The value of the map
kpeter@701:     /// should be PRE_HEAP (-1) for each element.
kpeter@701:     ///
kpeter@701:     /// \param _comp The comparator function object.
kpeter@701:     KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32)
kpeter@701:       : iim(_iim), comp(_comp), K(_K) {}
kpeter@701: 
kpeter@701: 
kpeter@701:     /// The number of items stored in the heap.
kpeter@701:     ///
kpeter@701:     /// \brief Returns the number of items stored in the heap.
kpeter@701:     int size() const { return data.size(); }
kpeter@701: 
kpeter@701:     /// \brief Checks if the heap stores no items.
kpeter@701:     ///
kpeter@701:     /// Returns \c true if and only if the heap stores no items.
kpeter@701:     bool empty() const { return data.empty(); }
kpeter@701: 
kpeter@701:     /// \brief Make empty this heap.
kpeter@701:     ///
kpeter@701:     /// Make empty this heap. It does not change the cross reference map.
kpeter@701:     /// If you want to reuse what is not surely empty you should first clear
kpeter@701:     /// the heap and after that you should set the cross reference map for
kpeter@701:     /// each item to \c PRE_HEAP.
kpeter@701:     void clear() { data.clear(); }
kpeter@701: 
kpeter@701:   private:
kpeter@701:     int parent(int i) { return (i-1)/K; }
kpeter@701:     int first_child(int i) { return K*i+1; }
kpeter@701: 
kpeter@701:     bool less(const Pair &p1, const Pair &p2) const {
kpeter@701:       return comp(p1.second, p2.second);
kpeter@701:     }
kpeter@701: 
kpeter@701:     int find_min(const int child, const int length) {
kpeter@701:       int min=child, i=1;
kpeter@701:       while( i<K && child+i<length ) {
kpeter@701:         if( less(data[child+i], data[min]) )
kpeter@701:           min=child+i;
kpeter@701:         ++i;
kpeter@701:       }
kpeter@701:       return min;
kpeter@701:     }
kpeter@701: 
kpeter@701:     void bubble_up(int hole, Pair p) {
kpeter@701:       int par = parent(hole);
kpeter@701:       while( hole>0 && less(p,data[par]) ) {
kpeter@701:         move(data[par],hole);
kpeter@701:         hole = par;
kpeter@701:         par = parent(hole);
kpeter@701:       }
kpeter@701:       move(p, hole);
kpeter@701:     }
kpeter@701: 
kpeter@701:     void bubble_down(int hole, Pair p, int length) {
kpeter@701:       if( length>1 ) {
kpeter@701:         int child = first_child(hole);
kpeter@701:         while( child<length ) {
kpeter@701:           child = find_min(child, length);
kpeter@701:           if( !less(data[child], p) )
kpeter@701:             goto ok;
kpeter@701:           move(data[child], hole);
kpeter@701:           hole = child;
kpeter@701:           child = first_child(hole);
kpeter@701:         }
kpeter@701:       }
kpeter@701:     ok:
kpeter@701:       move(p, hole);
kpeter@701:     }
kpeter@701: 
kpeter@701:     void move(const Pair &p, int i) {
kpeter@701:       data[i] = p;
kpeter@701:       iim.set(p.first, i);
kpeter@701:     }
kpeter@701: 
kpeter@701:   public:
kpeter@701:     /// \brief Insert a pair of item and priority into the heap.
kpeter@701:     ///
kpeter@701:     /// Adds \c p.first to the heap with priority \c p.second.
kpeter@701:     /// \param p The pair to insert.
kpeter@701:     void push(const Pair &p) {
kpeter@701:       int n = data.size();
kpeter@701:       data.resize(n+1);
kpeter@701:       bubble_up(n, p);
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Insert an item into the heap with the given heap.
kpeter@701:     ///
kpeter@701:     /// Adds \c i to the heap with priority \c p.
kpeter@701:     /// \param i The item to insert.
kpeter@701:     /// \param p The priority of the item.
kpeter@701:     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
kpeter@701: 
kpeter@701:     /// \brief Returns the item with minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// This method returns the item with minimum priority relative to \c
kpeter@701:     /// Compare.
kpeter@701:     /// \pre The heap must be nonempty.
kpeter@701:     Item top() const { return data[0].first; }
kpeter@701: 
kpeter@701:     /// \brief Returns the minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// It returns the minimum priority relative to \c Compare.
kpeter@701:     /// \pre The heap must be nonempty.
kpeter@701:     Prio prio() const { return data[0].second; }
kpeter@701: 
kpeter@701:     /// \brief Deletes the item with minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// This method deletes the item with minimum priority relative to \c
kpeter@701:     /// Compare from the heap.
kpeter@701:     /// \pre The heap must be non-empty.
kpeter@701:     void pop() {
kpeter@701:       int n = data.size()-1;
kpeter@701:       iim.set(data[0].first, POST_HEAP);
kpeter@701:       if (n>0) bubble_down(0, data[n], n);
kpeter@701:       data.pop_back();
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Deletes \c i from the heap.
kpeter@701:     ///
kpeter@701:     /// This method deletes item \c i from the heap.
kpeter@701:     /// \param i The item to erase.
kpeter@701:     /// \pre The item should be in the heap.
kpeter@701:     void erase(const Item &i) {
kpeter@701:       int h = iim[i];
kpeter@701:       int n = data.size()-1;
kpeter@701:       iim.set(data[h].first, POST_HEAP);
kpeter@701:       if( h<n ) {
kpeter@701:         if( less(data[parent(h)], data[n]) )
kpeter@701:           bubble_down(h, data[n], n);
kpeter@701:         else
kpeter@701:           bubble_up(h, data[n]);
kpeter@701:       }
kpeter@701:       data.pop_back();
kpeter@701:     }
kpeter@701: 
kpeter@701: 
kpeter@701:     /// \brief Returns the priority of \c i.
kpeter@701:     ///
kpeter@701:     /// This function returns the priority of item \c i.
kpeter@701:     /// \pre \c i must be in the heap.
kpeter@701:     /// \param i The item.
kpeter@701:     Prio operator[](const Item &i) const {
kpeter@701:       int idx = iim[i];
kpeter@701:       return data[idx].second;
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief \c i gets to the heap with priority \c p independently
kpeter@701:     /// if \c i was already there.
kpeter@701:     ///
kpeter@701:     /// This method calls \ref push(\c i, \c p) if \c i is not stored
kpeter@701:     /// in the heap and sets the priority of \c i to \c p otherwise.
kpeter@701:     /// \param i The item.
kpeter@701:     /// \param p The priority.
kpeter@701:     void set(const Item &i, const Prio &p) {
kpeter@701:       int idx = iim[i];
kpeter@701:       if( idx<0 )
kpeter@701:         push(i,p);
kpeter@701:       else if( comp(p, data[idx].second) )
kpeter@701:         bubble_up(idx, Pair(i,p));
kpeter@701:       else
kpeter@701:         bubble_down(idx, Pair(i,p), data.size());
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Decreases the priority of \c i to \c p.
kpeter@701:     ///
kpeter@701:     /// This method decreases the priority of item \c i to \c p.
kpeter@701:     /// \pre \c i must be stored in the heap with priority at least \c
kpeter@701:     /// p relative to \c Compare.
kpeter@701:     /// \param i The item.
kpeter@701:     /// \param p The priority.
kpeter@701:     void decrease(const Item &i, const Prio &p) {
kpeter@701:       int idx = iim[i];
kpeter@701:       bubble_up(idx, Pair(i,p));
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Increases the priority of \c i to \c p.
kpeter@701:     ///
kpeter@701:     /// This method sets the priority of item \c i to \c p.
kpeter@701:     /// \pre \c i must be stored in the heap with priority at most \c
kpeter@701:     /// p relative to \c Compare.
kpeter@701:     /// \param i The item.
kpeter@701:     /// \param p The priority.
kpeter@701:     void increase(const Item &i, const Prio &p) {
kpeter@701:       int idx = iim[i];
kpeter@701:       bubble_down(idx, Pair(i,p), data.size());
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Returns if \c item is in, has already been in, or has
kpeter@701:     /// never been in the heap.
kpeter@701:     ///
kpeter@701:     /// This method returns PRE_HEAP if \c item has never been in the
kpeter@701:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
kpeter@701:     /// otherwise. In the latter case it is possible that \c item will
kpeter@701:     /// get back to the heap again.
kpeter@701:     /// \param i The item.
kpeter@701:     State state(const Item &i) const {
kpeter@701:       int s = iim[i];
kpeter@701:       if (s>=0) s=0;
kpeter@701:       return State(s);
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Sets the state of the \c item in the heap.
kpeter@701:     ///
kpeter@701:     /// Sets the state of the \c item in the heap. It can be used to
kpeter@701:     /// manually clear the heap when it is important to achive the
kpeter@701:     /// 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@701:         iim[i] = st;
kpeter@701:         break;
kpeter@701:       case IN_HEAP:
kpeter@701:         break;
kpeter@701:       }
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Replaces an item in the heap.
kpeter@701:     ///
kpeter@701:     /// The \c i item is replaced with \c j item. The \c i item should
kpeter@701:     /// be in the heap, while the \c j should be out of the heap. The
kpeter@701:     /// \c i item will out of the heap and \c j will be in the heap
kpeter@701:     /// with the same prioriority as prevoiusly the \c i item.
kpeter@701:     void replace(const Item& i, const Item& j) {
kpeter@701:       int idx=iim[i];
kpeter@701:       iim.set(i, iim[j]);
kpeter@701:       iim.set(j, idx);
kpeter@701:       data[idx].first=j;
kpeter@701:     }
kpeter@701: 
kpeter@701:   }; // class KaryHeap
kpeter@701: 
kpeter@701: } // namespace lemon
kpeter@701: 
kpeter@701: #endif // LEMON_KARY_HEAP_H