alpar@906: /* -*- C++ -*-
klao@39:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@2553:  * Copyright (C) 2003-2008
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
klao@39:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
klao@39:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
klao@39:  *
klao@39:  */
klao@39: 
alpar@921: #ifndef LEMON_BIN_HEAP_H
alpar@921: #define LEMON_BIN_HEAP_H
klao@37: 
klao@491: ///\ingroup auxdat
klao@274: ///\file
klao@274: ///\brief Binary Heap implementation.
klao@274: 
klao@37: #include <vector>
klao@37: #include <utility>
klao@37: #include <functional>
klao@37: 
alpar@921: namespace lemon {
klao@37: 
deba@2529:   ///\ingroup auxdat
deba@2529:   ///
deba@2529:   ///\brief A Binary Heap implementation.
deba@2529:   ///
jacint@1270:   ///This class implements the \e binary \e heap data structure. A \e heap
jacint@1270:   ///is a data structure for storing items with specified values called \e
jacint@1270:   ///priorities in such a way that finding the item with minimum priority is
jacint@1270:   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
jacint@1270:   ///one can change the priority of an item, add or erase an item, etc.
jacint@1270:   ///
deba@2547:   ///\param _Prio Type of the priority of the items.
deba@2547:   ///\param _ItemIntMap A read and writable Item int map, used internally
jacint@1270:   ///to handle the cross references.
deba@2547:   ///\param _Compare A class for the ordering of the priorities. The
deba@2547:   ///default is \c std::less<_Prio>.
alpar@967:   ///
alpar@967:   ///\sa FibHeap
alpar@967:   ///\sa Dijkstra
deba@2547:   template <typename _Prio, typename _ItemIntMap,
deba@2547: 	    typename _Compare = std::less<_Prio> >
klao@37:   class BinHeap {
klao@37: 
klao@37:   public:
deba@2548:     ///\e
deba@2547:     typedef _ItemIntMap ItemIntMap;
deba@2548:     ///\e
deba@2547:     typedef _Prio Prio;
deba@2548:     ///\e
deba@2547:     typedef typename ItemIntMap::Key Item;
deba@2548:     ///\e
deba@2547:     typedef std::pair<Item,Prio> Pair;
deba@2548:     ///\e
deba@2547:     typedef _Compare Compare;
klao@37: 
deba@1331:     /// \brief Type to represent the items states.
klao@274:     ///
deba@1331:     /// Each Item element have a state associated to it. It may be "in heap",
alpar@1336:     /// "pre heap" or "post heap". The latter two are indifferent from the
deba@1331:     /// heap's point of view, but may be useful to the user.
deba@1331:     ///
alpar@1336:     /// The ItemIntMap \e should be initialized in such way that it maps
deba@1331:     /// PRE_HEAP (-1) to any element to be put in the heap...
deba@2547:     enum State {
klao@37:       IN_HEAP = 0,
klao@37:       PRE_HEAP = -1,
klao@37:       POST_HEAP = -2
klao@37:     };
klao@37: 
klao@37:   private:
deba@2547:     std::vector<Pair> data;
klao@37:     Compare comp;
klao@172:     ItemIntMap &iim;
klao@37: 
klao@37:   public:
deba@1331:     /// \brief The constructor.
deba@1331:     ///
deba@1331:     /// The constructor.
deba@1331:     /// \param _iim should be given to the constructor, since it is used
deba@1331:     /// internally to handle the cross references. The value of the map
deba@1331:     /// should be PRE_HEAP (-1) for each element.
deba@1185:     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {}
jacint@1270:     
deba@1331:     /// \brief The constructor.
deba@1331:     ///
deba@1331:     /// The constructor.
deba@1331:     /// \param _iim should be given to the constructor, since it is used
deba@1331:     /// internally to handle the cross references. The value of the map
deba@1331:     /// should be PRE_HEAP (-1) for each element.
deba@1331:     ///
deba@1331:     /// \param _comp The comparator function object.
deba@1191:     BinHeap(ItemIntMap &_iim, const Compare &_comp) 
deba@1185:       : iim(_iim), comp(_comp) {}
klao@37: 
klao@37: 
deba@1331:     /// The number of items stored in the heap.
deba@1331:     ///
deba@1331:     /// \brief Returns the number of items stored in the heap.
klao@37:     int size() const { return data.size(); }
jacint@1270:     
deba@1331:     /// \brief Checks if the heap stores no items.
deba@1331:     ///
deba@1331:     /// Returns \c true if and only if the heap stores no items.
klao@41:     bool empty() const { return data.empty(); }
klao@37: 
deba@1717:     /// \brief Make empty this heap.
deba@1717:     /// 
deba@2050:     /// Make empty this heap. It does not change the cross reference map.
deba@2050:     /// If you want to reuse what is not surely empty you should first clear
deba@2050:     /// the heap and after that you should set the cross reference map for
deba@2050:     /// each item to \c PRE_HEAP.
deba@1717:     void clear() { 
deba@1717:       data.clear(); 
deba@1717:     }
deba@1717: 
klao@37:   private:
klao@37:     static int parent(int i) { return (i-1)/2; }
deba@2546: 
klao@37:     static int second_child(int i) { return 2*i+2; }
deba@2547:     bool less(const Pair &p1, const Pair &p2) const {
klao@37:       return comp(p1.second, p2.second);
klao@37:     }
klao@37: 
deba@2547:     int bubble_up(int hole, Pair p) {
deba@2546:       int par = parent(hole);
deba@2546:       while( hole>0 && less(p,data[par]) ) {
deba@2546: 	move(data[par],hole);
deba@2546: 	hole = par;
deba@2546: 	par = parent(hole);
deba@2546:       }
deba@2546:       move(p, hole);
deba@2546:       return hole;
deba@2546:     }
deba@2546: 
deba@2547:     int bubble_down(int hole, Pair p, int length) {
deba@2546:       int child = second_child(hole);
deba@2546:       while(child < length) {
deba@2546: 	if( less(data[child-1], data[child]) ) {
deba@2546: 	  --child;
deba@2546: 	}
deba@2546: 	if( !less(data[child], p) )
deba@2546: 	  goto ok;
deba@2546: 	move(data[child], hole);
deba@2546: 	hole = child;
deba@2546: 	child = second_child(hole);
deba@2546:       }
deba@2546:       child--;
deba@2546:       if( child<length && less(data[child], p) ) {
deba@2546: 	move(data[child], hole);
deba@2546: 	hole=child;
deba@2546:       }
deba@2546:     ok:
deba@2546:       move(p, hole);
deba@2546:       return hole;
deba@2546:     }
klao@37: 
deba@2547:     void move(const Pair &p, int i) {
klao@37:       data[i] = p;
klao@172:       iim.set(p.first, i);
klao@37:     }
klao@37: 
klao@37:   public:
deba@1331:     /// \brief Insert a pair of item and priority into the heap.
deba@1331:     ///
deba@1331:     /// Adds \c p.first to the heap with priority \c p.second.
deba@1331:     /// \param p The pair to insert.
deba@2547:     void push(const Pair &p) {
klao@37:       int n = data.size();
klao@37:       data.resize(n+1);
klao@37:       bubble_up(n, p);
klao@37:     }
jacint@1270: 
deba@1331:     /// \brief Insert an item into the heap with the given heap.
deba@1331:     ///    
deba@1331:     /// Adds \c i to the heap with priority \c p. 
deba@1331:     /// \param i The item to insert.
deba@1331:     /// \param p The priority of the item.
deba@2547:     void push(const Item &i, const Prio &p) { push(Pair(i,p)); }
klao@37: 
deba@1331:     /// \brief Returns the item with minimum priority relative to \c Compare.
deba@1331:     ///
deba@1331:     /// This method returns the item with minimum priority relative to \c
deba@1331:     /// Compare.  
deba@1331:     /// \pre The heap must be nonempty.  
deba@2547:     Item top() const {
klao@37:       return data[0].first;
klao@37:     }
jacint@1270: 
deba@1331:     /// \brief Returns the minimum priority relative to \c Compare.
deba@1331:     ///
deba@1331:     /// It returns the minimum priority relative to \c Compare.
deba@1331:     /// \pre The heap must be nonempty.
klao@274:     Prio prio() const {
klao@37:       return data[0].second;
klao@37:     }
klao@37: 
deba@1331:     /// \brief Deletes the item with minimum priority relative to \c Compare.
deba@1331:     ///
deba@1331:     /// This method deletes the item with minimum priority relative to \c
deba@1331:     /// Compare from the heap.  
deba@1331:     /// \pre The heap must be non-empty.  
klao@37:     void pop() {
deba@2546:       int n = data.size()-1;
deba@2546:       iim.set(data[0].first, POST_HEAP);
deba@2546:       if (n > 0) {
deba@2546: 	bubble_down(0, data[n], n);
deba@2546:       }
deba@2546:       data.pop_back();
klao@41:     }
klao@41: 
deba@1331:     /// \brief Deletes \c i from the heap.
deba@1331:     ///
deba@2546:     /// This method deletes item \c i from the heap.
deba@2546:     /// \param i The item to erase.
deba@2546:     /// \pre The item should be in the heap.
deba@2547:     void erase(const Item &i) {
deba@2546:       int h = iim[i];
deba@2546:       int n = data.size()-1;
deba@2546:       iim.set(data[h].first, POST_HEAP);
deba@2546:       if( h < n ) {
deba@2546: 	if ( bubble_up(h, data[n]) == h) {
deba@2546: 	  bubble_down(h, data[n], n);
deba@2546: 	}
deba@2546:       }
deba@2546:       data.pop_back();
klao@37:     }
klao@37: 
jacint@1270:     
deba@1331:     /// \brief Returns the priority of \c i.
deba@1331:     ///
deba@1331:     /// This function returns the priority of item \c i.  
deba@1331:     /// \pre \c i must be in the heap.
deba@1331:     /// \param i The item.
deba@2547:     Prio operator[](const Item &i) const {
jacint@221:       int idx = iim[i];
klao@37:       return data[idx].second;
klao@37:     }
klao@274: 
deba@1331:     /// \brief \c i gets to the heap with priority \c p independently 
deba@1331:     /// if \c i was already there.
deba@1331:     ///
deba@1331:     /// This method calls \ref push(\c i, \c p) if \c i is not stored
deba@1331:     /// in the heap and sets the priority of \c i to \c p otherwise.
deba@1331:     /// \param i The item.
deba@1331:     /// \param p The priority.
deba@2547:     void set(const Item &i, const Prio &p) {
jacint@221:       int idx = iim[i];
klao@37:       if( idx < 0 ) {
klao@172: 	push(i,p);
klao@37:       }
klao@172:       else if( comp(p, data[idx].second) ) {
deba@2547: 	bubble_up(idx, Pair(i,p));
klao@37:       }
klao@37:       else {
deba@2547: 	bubble_down(idx, Pair(i,p), data.size());
klao@37:       }
klao@37:     }
klao@37: 
deba@1331:     /// \brief Decreases the priority of \c i to \c p.
deba@2529:     ///
deba@1331:     /// This method decreases the priority of item \c i to \c p.
deba@1331:     /// \pre \c i must be stored in the heap with priority at least \c
deba@1331:     /// p relative to \c Compare.
deba@1331:     /// \param i The item.
deba@1331:     /// \param p The priority.
deba@2547:     void decrease(const Item &i, const Prio &p) {
jacint@221:       int idx = iim[i];
deba@2547:       bubble_up(idx, Pair(i,p));
klao@37:     }
jacint@1270:     
deba@1331:     /// \brief Increases the priority of \c i to \c p.
deba@1331:     ///
deba@1331:     /// This method sets the priority of item \c i to \c p. 
deba@1331:     /// \pre \c i must be stored in the heap with priority at most \c
deba@1331:     /// p relative to \c Compare.
deba@1331:     /// \param i The item.
deba@1331:     /// \param p The priority.
deba@2547:     void increase(const Item &i, const Prio &p) {
jacint@221:       int idx = iim[i];
deba@2547:       bubble_down(idx, Pair(i,p), data.size());
klao@37:     }
klao@37: 
deba@1331:     /// \brief Returns if \c item is in, has already been in, or has 
deba@1331:     /// never been in the heap.
deba@1331:     ///
deba@1331:     /// This method returns PRE_HEAP if \c item has never been in the
deba@1331:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
deba@1331:     /// otherwise. In the latter case it is possible that \c item will
deba@1331:     /// get back to the heap again.
deba@1331:     /// \param i The item.
deba@2547:     State state(const Item &i) const {
jacint@221:       int s = iim[i];
klao@39:       if( s>=0 )
klao@39: 	s=0;
deba@2547:       return State(s);
klao@39:     }
klao@39: 
deba@1902:     /// \brief Sets the state of the \c item in the heap.
deba@1902:     ///
deba@1902:     /// Sets the state of the \c item in the heap. It can be used to
deba@1902:     /// manually clear the heap when it is important to achive the
deba@1902:     /// better time complexity.
deba@1902:     /// \param i The item.
deba@1902:     /// \param st The state. It should not be \c IN_HEAP. 
deba@2547:     void state(const Item& i, State st) {
deba@1902:       switch (st) {
deba@1902:       case POST_HEAP:
deba@1902:       case PRE_HEAP:
deba@1902:         if (state(i) == IN_HEAP) {
deba@1902:           erase(i);
deba@1902:         }
deba@1903:         iim[i] = st;
deba@1902:         break;
deba@1906:       case IN_HEAP:
deba@1906:         break;
deba@1902:       }
deba@1902:     }
deba@1902: 
deba@2548:     /// \brief Replaces an item in the heap.
deba@2548:     ///
deba@2548:     /// The \c i item is replaced with \c j item. The \c i item should
deba@2548:     /// be in the heap, while the \c j should be out of the heap. The
deba@2548:     /// \c i item will out of the heap and \c j will be in the heap
deba@2548:     /// with the same prioriority as prevoiusly the \c i item.
deba@2548:     void replace(const Item& i, const Item& j) {
deba@2548:       int idx = iim[i];
deba@2548:       iim.set(i, iim[j]);
deba@2548:       iim.set(j, idx);
deba@2548:       data[idx].first = j;
deba@2548:     }
deba@2548: 
klao@37:   }; // class BinHeap
klao@37:   
alpar@921: } // namespace lemon
klao@37: 
alpar@921: #endif // LEMON_BIN_HEAP_H