alpar@100: /* -*- C++ -*-
alpar@100:  *
alpar@100:  * This file is a part of LEMON, a generic C++ optimization library
alpar@100:  *
alpar@100:  * Copyright (C) 2003-2008
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: 
alpar@100: ///\ingroup auxdat
alpar@100: ///\file
alpar@100: ///\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: 
alpar@100:   ///\ingroup auxdat
alpar@100:   ///
alpar@100:   ///\brief A Binary Heap implementation.
alpar@100:   ///
alpar@100:   ///This class implements the \e binary \e heap data structure. A \e heap
alpar@100:   ///is a data structure for storing items with specified values called \e
alpar@100:   ///priorities in such a way that finding the item with minimum priority is
alpar@100:   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
alpar@100:   ///one can change the priority of an item, add or erase an item, etc.
alpar@100:   ///
alpar@100:   ///\param _Prio Type of the priority of the items.
alpar@100:   ///\param _ItemIntMap A read and writable Item int map, used internally
alpar@100:   ///to handle the cross references.
alpar@100:   ///\param _Compare A class for the ordering of the priorities. The
alpar@100:   ///default is \c std::less<_Prio>.
alpar@100:   ///
alpar@100:   ///\sa FibHeap
alpar@100:   ///\sa Dijkstra
alpar@100:   template <typename _Prio, typename _ItemIntMap,
alpar@100: 	    typename _Compare = std::less<_Prio> >
alpar@100:   class BinHeap {
alpar@100: 
alpar@100:   public:
alpar@100:     ///\e
alpar@100:     typedef _ItemIntMap ItemIntMap;
alpar@100:     ///\e
alpar@100:     typedef _Prio Prio;
alpar@100:     ///\e
alpar@100:     typedef typename ItemIntMap::Key Item;
alpar@100:     ///\e
alpar@100:     typedef std::pair<Item,Prio> Pair;
alpar@100:     ///\e
alpar@100:     typedef _Compare Compare;
alpar@100: 
alpar@100:     /// \brief Type to represent the items states.
alpar@100:     ///
alpar@100:     /// Each Item element have a state associated to it. It may be "in heap",
alpar@100:     /// "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:     ///
alpar@100:     /// The ItemIntMap \e should be initialized in such way that it maps
alpar@100:     /// PRE_HEAP (-1) to any element to be put in the heap...
alpar@100:     enum State {
alpar@100:       IN_HEAP = 0,
alpar@100:       PRE_HEAP = -1,
alpar@100:       POST_HEAP = -2
alpar@100:     };
alpar@100: 
alpar@100:   private:
alpar@100:     std::vector<Pair> data;
alpar@100:     Compare comp;
alpar@100:     ItemIntMap &iim;
alpar@100: 
alpar@100:   public:
alpar@100:     /// \brief The constructor.
alpar@100:     ///
alpar@100:     /// The constructor.
alpar@100:     /// \param _iim should be given to the constructor, since it is used
alpar@100:     /// internally to handle the cross references. The value of the map
alpar@100:     /// should be PRE_HEAP (-1) for each element.
alpar@100:     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
alpar@100:     
alpar@100:     /// \brief The constructor.
alpar@100:     ///
alpar@100:     /// The constructor.
alpar@100:     /// \param _iim should be given to the constructor, since it is used
alpar@100:     /// internally to handle the cross references. The value of the map
alpar@100:     /// should be PRE_HEAP (-1) for each element.
alpar@100:     ///
alpar@100:     /// \param _comp The comparator function object.
alpar@100:     BinHeap(ItemIntMap &_iim, const Compare &_comp) 
alpar@100:       : iim(_iim), comp(_comp) {}
alpar@100: 
alpar@100: 
alpar@100:     /// The number of items stored in the heap.
alpar@100:     ///
alpar@100:     /// \brief Returns the number of items stored in the heap.
alpar@100:     int size() const { return data.size(); }
alpar@100:     
alpar@100:     /// \brief Checks if the heap stores no items.
alpar@100:     ///
alpar@100:     /// Returns \c true if and only if the heap stores no items.
alpar@100:     bool empty() const { return data.empty(); }
alpar@100: 
alpar@100:     /// \brief Make empty this heap.
alpar@100:     /// 
alpar@100:     /// Make empty this heap. It does not change the cross reference map.
alpar@100:     /// If you want to reuse what is not surely empty you should first clear
alpar@100:     /// the heap and after that you should set the cross reference map for
alpar@100:     /// each item to \c PRE_HEAP.
alpar@100:     void clear() { 
alpar@100:       data.clear(); 
alpar@100:     }
alpar@100: 
alpar@100:   private:
alpar@100:     static int parent(int i) { return (i-1)/2; }
alpar@100: 
alpar@100:     static int second_child(int i) { return 2*i+2; }
alpar@100:     bool less(const Pair &p1, const Pair &p2) const {
alpar@100:       return comp(p1.second, p2.second);
alpar@100:     }
alpar@100: 
alpar@100:     int bubble_up(int hole, Pair p) {
alpar@100:       int par = parent(hole);
alpar@100:       while( hole>0 && less(p,data[par]) ) {
alpar@100: 	move(data[par],hole);
alpar@100: 	hole = par;
alpar@100: 	par = parent(hole);
alpar@100:       }
alpar@100:       move(p, hole);
alpar@100:       return hole;
alpar@100:     }
alpar@100: 
alpar@100:     int bubble_down(int hole, Pair p, int length) {
alpar@100:       int child = second_child(hole);
alpar@100:       while(child < length) {
alpar@100: 	if( less(data[child-1], data[child]) ) {
alpar@100: 	  --child;
alpar@100: 	}
alpar@100: 	if( !less(data[child], p) )
alpar@100: 	  goto ok;
alpar@100: 	move(data[child], hole);
alpar@100: 	hole = child;
alpar@100: 	child = second_child(hole);
alpar@100:       }
alpar@100:       child--;
alpar@100:       if( child<length && less(data[child], p) ) {
alpar@100: 	move(data[child], hole);
alpar@100: 	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) {
alpar@100:       data[i] = p;
alpar@100:       iim.set(p.first, i);
alpar@100:     }
alpar@100: 
alpar@100:   public:
alpar@100:     /// \brief Insert a pair of item and priority into the heap.
alpar@100:     ///
alpar@100:     /// Adds \c p.first to the heap with priority \c p.second.
alpar@100:     /// \param p The pair to insert.
alpar@100:     void push(const Pair &p) {
alpar@100:       int n = data.size();
alpar@100:       data.resize(n+1);
alpar@100:       bubble_up(n, p);
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Insert an item into the heap with the given heap.
alpar@100:     ///    
alpar@100:     /// Adds \c i to the heap with priority \c p. 
alpar@100:     /// \param i The item to insert.
alpar@100:     /// \param p The priority of the item.
alpar@100:     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
alpar@100: 
alpar@100:     /// \brief Returns the item with minimum priority relative to \c Compare.
alpar@100:     ///
alpar@100:     /// This method returns the item with minimum priority relative to \c
alpar@100:     /// Compare.  
alpar@100:     /// \pre The heap must be nonempty.  
alpar@100:     Item top() const {
alpar@100:       return data[0].first;
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Returns the minimum priority relative to \c Compare.
alpar@100:     ///
alpar@100:     /// It returns the minimum priority relative to \c Compare.
alpar@100:     /// \pre The heap must be nonempty.
alpar@100:     Prio prio() const {
alpar@100:       return data[0].second;
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Deletes the item with minimum priority relative to \c Compare.
alpar@100:     ///
alpar@100:     /// This method deletes the item with minimum priority relative to \c
alpar@100:     /// Compare from the heap.  
alpar@100:     /// \pre The heap must be non-empty.  
alpar@100:     void pop() {
alpar@100:       int n = data.size()-1;
alpar@100:       iim.set(data[0].first, POST_HEAP);
alpar@100:       if (n > 0) {
alpar@100: 	bubble_down(0, data[n], n);
alpar@100:       }
alpar@100:       data.pop_back();
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Deletes \c i from the heap.
alpar@100:     ///
alpar@100:     /// This method deletes item \c i from the heap.
alpar@100:     /// \param i The item to erase.
alpar@100:     /// \pre The item should be in the heap.
alpar@100:     void erase(const Item &i) {
alpar@100:       int h = iim[i];
alpar@100:       int n = data.size()-1;
alpar@100:       iim.set(data[h].first, POST_HEAP);
alpar@100:       if( h < n ) {
alpar@100: 	if ( bubble_up(h, data[n]) == h) {
alpar@100: 	  bubble_down(h, data[n], n);
alpar@100: 	}
alpar@100:       }
alpar@100:       data.pop_back();
alpar@100:     }
alpar@100: 
alpar@100:     
alpar@100:     /// \brief Returns the priority of \c i.
alpar@100:     ///
alpar@100:     /// This function returns the priority of item \c i.  
alpar@100:     /// \pre \c i must be in the heap.
alpar@100:     /// \param i The item.
alpar@100:     Prio operator[](const Item &i) const {
alpar@100:       int idx = iim[i];
alpar@100:       return data[idx].second;
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief \c i gets to the heap with priority \c p independently 
alpar@100:     /// if \c i was already there.
alpar@100:     ///
alpar@100:     /// This method calls \ref push(\c i, \c p) if \c i is not stored
alpar@100:     /// in the heap and sets the priority of \c i to \c p otherwise.
alpar@100:     /// \param i The item.
alpar@100:     /// \param p The priority.
alpar@100:     void set(const Item &i, const Prio &p) {
alpar@100:       int idx = iim[i];
alpar@100:       if( idx < 0 ) {
alpar@100: 	push(i,p);
alpar@100:       }
alpar@100:       else if( comp(p, data[idx].second) ) {
alpar@100: 	bubble_up(idx, Pair(i,p));
alpar@100:       }
alpar@100:       else {
alpar@100: 	bubble_down(idx, Pair(i,p), data.size());
alpar@100:       }
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Decreases the priority of \c i to \c p.
alpar@100:     ///
alpar@100:     /// This method decreases the priority of item \c i to \c p.
alpar@100:     /// \pre \c i must be stored in the heap with priority at least \c
alpar@100:     /// p relative to \c Compare.
alpar@100:     /// \param i The item.
alpar@100:     /// \param p The priority.
alpar@100:     void decrease(const Item &i, const Prio &p) {
alpar@100:       int idx = iim[i];
alpar@100:       bubble_up(idx, Pair(i,p));
alpar@100:     }
alpar@100:     
alpar@100:     /// \brief Increases the priority of \c i to \c p.
alpar@100:     ///
alpar@100:     /// This method sets the priority of item \c i to \c p. 
alpar@100:     /// \pre \c i must be stored in the heap with priority at most \c
alpar@100:     /// p relative to \c Compare.
alpar@100:     /// \param i The item.
alpar@100:     /// \param p The priority.
alpar@100:     void increase(const Item &i, const Prio &p) {
alpar@100:       int idx = iim[i];
alpar@100:       bubble_down(idx, Pair(i,p), data.size());
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Returns if \c item is in, has already been in, or has 
alpar@100:     /// never been in the heap.
alpar@100:     ///
alpar@100:     /// This method returns PRE_HEAP if \c item has never been in the
alpar@100:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
alpar@100:     /// otherwise. In the latter case it is possible that \c item will
alpar@100:     /// get back to the heap again.
alpar@100:     /// \param i The item.
alpar@100:     State state(const Item &i) const {
alpar@100:       int s = iim[i];
alpar@100:       if( s>=0 )
alpar@100: 	s=0;
alpar@100:       return State(s);
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Sets the state of the \c item in the heap.
alpar@100:     ///
alpar@100:     /// Sets the state of the \c item in the heap. It can be used to
alpar@100:     /// manually clear the heap when it is important to achive the
alpar@100:     /// better time complexity.
alpar@100:     /// \param i The item.
alpar@100:     /// \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:         }
alpar@100:         iim[i] = st;
alpar@100:         break;
alpar@100:       case IN_HEAP:
alpar@100:         break;
alpar@100:       }
alpar@100:     }
alpar@100: 
alpar@100:     /// \brief Replaces an item in the heap.
alpar@100:     ///
alpar@100:     /// The \c i item is replaced with \c j item. The \c i item should
alpar@100:     /// be in the heap, while the \c j should be out of the heap. The
alpar@100:     /// \c i item will out of the heap and \c j will be in the heap
alpar@100:     /// with the same prioriority as prevoiusly the \c i item.
alpar@100:     void replace(const Item& i, const Item& j) {
alpar@100:       int idx = iim[i];
alpar@100:       iim.set(i, iim[j]);
alpar@100:       iim.set(j, idx);
alpar@100:       data[idx].first = j;
alpar@100:     }
alpar@100: 
alpar@100:   }; // class BinHeap
alpar@100:   
alpar@100: } // namespace lemon
alpar@100: 
alpar@100: #endif // LEMON_BIN_HEAP_H