deba@681: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@681:  *
deba@681:  * This file is a part of LEMON, a generic C++ optimization library.
deba@681:  *
deba@681:  * Copyright (C) 2003-2009
deba@681:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@681:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@681:  *
deba@681:  * Permission to use, modify and distribute this software is granted
deba@681:  * provided that this copyright notice appears in all copies. For
deba@681:  * precise terms see the accompanying LICENSE file.
deba@681:  *
deba@681:  * This software is provided "AS IS" with no warranty of any kind,
deba@681:  * express or implied, and with no claim as to its suitability for any
deba@681:  * purpose.
deba@681:  *
deba@681:  */
deba@681: 
deba@681: #ifndef LEMON_FIB_HEAP_H
deba@681: #define LEMON_FIB_HEAP_H
deba@681: 
deba@681: ///\file
deba@681: ///\ingroup auxdat
deba@681: ///\brief Fibonacci Heap implementation.
deba@681: 
deba@681: #include <vector>
deba@681: #include <functional>
deba@681: #include <lemon/math.h>
deba@681: 
deba@681: namespace lemon {
deba@681: 
deba@681:   /// \ingroup auxdat
deba@681:   ///
deba@681:   ///\brief Fibonacci Heap.
deba@681:   ///
deba@681:   ///This class implements the \e Fibonacci \e heap data structure. A \e heap
deba@681:   ///is a data structure for storing items with specified values called \e
deba@681:   ///priorities in such a way that finding the item with minimum priority is
deba@683:   ///efficient. \c CMP specifies the ordering of the priorities. In a heap
deba@681:   ///one can change the priority of an item, add or erase an item, etc.
deba@681:   ///
deba@681:   ///The methods \ref increase and \ref erase are not efficient in a Fibonacci
deba@681:   ///heap. In case of many calls to these operations, it is better to use a
deba@681:   ///\ref BinHeap "binary heap".
deba@681:   ///
deba@683:   ///\param PRIO Type of the priority of the items.
deba@683:   ///\param IM A read and writable Item int map, used internally
deba@681:   ///to handle the cross references.
deba@683:   ///\param CMP A class for the ordering of the priorities. The
deba@683:   ///default is \c std::less<PRIO>.
deba@681:   ///
deba@681:   ///\sa BinHeap
deba@681:   ///\sa Dijkstra
deba@681: #ifdef DOXYGEN
deba@683:   template <typename PRIO, typename IM, typename CMP>
deba@681: #else
deba@683:   template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
deba@681: #endif
deba@681:   class FibHeap {
deba@681:   public:
deba@681:     ///\e
deba@683:     typedef IM ItemIntMap;
deba@681:     ///\e
deba@683:     typedef PRIO Prio;
deba@681:     ///\e
deba@681:     typedef typename ItemIntMap::Key Item;
deba@681:     ///\e
deba@681:     typedef std::pair<Item,Prio> Pair;
deba@681:     ///\e
deba@683:     typedef CMP Compare;
deba@681: 
deba@681:   private:
deba@683:     class Store;
deba@681: 
deba@683:     std::vector<Store> _data;
deba@683:     int _minimum;
deba@683:     ItemIntMap &_iim;
deba@683:     Compare _comp;
deba@683:     int _num;
deba@681: 
deba@681:   public:
deba@683: 
deba@683:     /// \brief Type to represent the items states.
deba@683:     ///
deba@683:     /// Each Item element have a state associated to it. It may be "in heap",
deba@683:     /// "pre heap" or "post heap". The latter two are indifferent from the
deba@683:     /// heap's point of view, but may be useful to the user.
deba@683:     ///
deba@683:     /// The item-int map must be initialized in such way that it assigns
deba@683:     /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
deba@681:     enum State {
deba@683:       IN_HEAP = 0,    ///< = 0.
deba@683:       PRE_HEAP = -1,  ///< = -1.
deba@683:       POST_HEAP = -2  ///< = -2.
deba@681:     };
deba@681: 
deba@681:     /// \brief The constructor
deba@681:     ///
deba@683:     /// \c map should be given to the constructor, since it is
deba@681:     ///   used internally to handle the cross references.
deba@683:     explicit FibHeap(ItemIntMap &map)
deba@683:       : _minimum(0), _iim(map), _num() {}
deba@681: 
deba@681:     /// \brief The constructor
deba@681:     ///
deba@683:     /// \c map should be given to the constructor, since it is used
deba@683:     /// internally to handle the cross references. \c comp is an
deba@681:     /// object for ordering of the priorities.
deba@683:     FibHeap(ItemIntMap &map, const Compare &comp)
deba@683:       : _minimum(0), _iim(map), _comp(comp), _num() {}
deba@681: 
deba@681:     /// \brief The number of items stored in the heap.
deba@681:     ///
deba@681:     /// Returns the number of items stored in the heap.
deba@683:     int size() const { return _num; }
deba@681: 
deba@681:     /// \brief Checks if the heap stores no items.
deba@681:     ///
deba@681:     ///   Returns \c true if and only if the heap stores no items.
deba@683:     bool empty() const { return _num==0; }
deba@681: 
deba@681:     /// \brief Make empty this heap.
deba@681:     ///
deba@681:     /// Make empty this heap. It does not change the cross reference
deba@681:     /// map.  If you want to reuse a heap what is not surely empty you
deba@681:     /// should first clear the heap and after that you should set the
deba@681:     /// cross reference map for each item to \c PRE_HEAP.
deba@681:     void clear() {
deba@683:       _data.clear(); _minimum = 0; _num = 0;
deba@681:     }
deba@681: 
deba@681:     /// \brief \c item gets to the heap with priority \c value independently
deba@681:     /// if \c item was already there.
deba@681:     ///
deba@681:     /// This method calls \ref push(\c item, \c value) if \c item is not
deba@681:     /// stored in the heap and it calls \ref decrease(\c item, \c value) or
deba@681:     /// \ref increase(\c item, \c value) otherwise.
deba@681:     void set (const Item& item, const Prio& value) {
deba@683:       int i=_iim[item];
deba@683:       if ( i >= 0 && _data[i].in ) {
deba@683:         if ( _comp(value, _data[i].prio) ) decrease(item, value);
deba@683:         if ( _comp(_data[i].prio, value) ) increase(item, value);
deba@681:       } else push(item, value);
deba@681:     }
deba@681: 
deba@681:     /// \brief Adds \c item to the heap with priority \c value.
deba@681:     ///
deba@681:     /// Adds \c item to the heap with priority \c value.
deba@681:     /// \pre \c item must not be stored in the heap.
deba@681:     void push (const Item& item, const Prio& value) {
deba@683:       int i=_iim[item];
deba@681:       if ( i < 0 ) {
deba@683:         int s=_data.size();
deba@683:         _iim.set( item, s );
deba@683:         Store st;
deba@681:         st.name=item;
deba@683:         _data.push_back(st);
deba@681:         i=s;
deba@681:       } else {
deba@683:         _data[i].parent=_data[i].child=-1;
deba@683:         _data[i].degree=0;
deba@683:         _data[i].in=true;
deba@683:         _data[i].marked=false;
deba@681:       }
deba@681: 
deba@683:       if ( _num ) {
deba@683:         _data[_data[_minimum].right_neighbor].left_neighbor=i;
deba@683:         _data[i].right_neighbor=_data[_minimum].right_neighbor;
deba@683:         _data[_minimum].right_neighbor=i;
deba@683:         _data[i].left_neighbor=_minimum;
deba@683:         if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
deba@681:       } else {
deba@683:         _data[i].right_neighbor=_data[i].left_neighbor=i;
deba@683:         _minimum=i;
deba@681:       }
deba@683:       _data[i].prio=value;
deba@683:       ++_num;
deba@681:     }
deba@681: 
deba@681:     /// \brief Returns the item with minimum priority relative to \c Compare.
deba@681:     ///
deba@681:     /// This method returns the item with minimum priority relative to \c
deba@681:     /// Compare.
deba@681:     /// \pre The heap must be nonempty.
deba@683:     Item top() const { return _data[_minimum].name; }
deba@681: 
deba@681:     /// \brief Returns the minimum priority relative to \c Compare.
deba@681:     ///
deba@681:     /// It returns the minimum priority relative to \c Compare.
deba@681:     /// \pre The heap must be nonempty.
deba@683:     const Prio& prio() const { return _data[_minimum].prio; }
deba@681: 
deba@681:     /// \brief Returns the priority of \c item.
deba@681:     ///
deba@681:     /// It returns the priority of \c item.
deba@681:     /// \pre \c item must be in the heap.
deba@681:     const Prio& operator[](const Item& item) const {
deba@683:       return _data[_iim[item]].prio;
deba@681:     }
deba@681: 
deba@681:     /// \brief Deletes the item with minimum priority relative to \c Compare.
deba@681:     ///
deba@681:     /// This method deletes the item with minimum priority relative to \c
deba@681:     /// Compare from the heap.
deba@681:     /// \pre The heap must be non-empty.
deba@681:     void pop() {
deba@681:       /*The first case is that there are only one root.*/
deba@683:       if ( _data[_minimum].left_neighbor==_minimum ) {
deba@683:         _data[_minimum].in=false;
deba@683:         if ( _data[_minimum].degree!=0 ) {
deba@683:           makeroot(_data[_minimum].child);
deba@683:           _minimum=_data[_minimum].child;
deba@681:           balance();
deba@681:         }
deba@681:       } else {
deba@683:         int right=_data[_minimum].right_neighbor;
deba@683:         unlace(_minimum);
deba@683:         _data[_minimum].in=false;
deba@683:         if ( _data[_minimum].degree > 0 ) {
deba@683:           int left=_data[_minimum].left_neighbor;
deba@683:           int child=_data[_minimum].child;
deba@683:           int last_child=_data[child].left_neighbor;
deba@681: 
deba@681:           makeroot(child);
deba@681: 
deba@683:           _data[left].right_neighbor=child;
deba@683:           _data[child].left_neighbor=left;
deba@683:           _data[right].left_neighbor=last_child;
deba@683:           _data[last_child].right_neighbor=right;
deba@681:         }
deba@683:         _minimum=right;
deba@681:         balance();
deba@681:       } // the case where there are more roots
deba@683:       --_num;
deba@681:     }
deba@681: 
deba@681:     /// \brief Deletes \c item from the heap.
deba@681:     ///
deba@681:     /// This method deletes \c item from the heap, if \c item was already
deba@681:     /// stored in the heap. It is quite inefficient in Fibonacci heaps.
deba@681:     void erase (const Item& item) {
deba@683:       int i=_iim[item];
deba@681: 
deba@683:       if ( i >= 0 && _data[i].in ) {
deba@683:         if ( _data[i].parent!=-1 ) {
deba@683:           int p=_data[i].parent;
deba@681:           cut(i,p);
deba@681:           cascade(p);
deba@681:         }
deba@683:         _minimum=i;     //As if its prio would be -infinity
deba@681:         pop();
deba@681:       }
deba@681:     }
deba@681: 
deba@681:     /// \brief Decreases the priority of \c item to \c value.
deba@681:     ///
deba@681:     /// This method decreases the priority of \c item to \c value.
deba@681:     /// \pre \c item must be stored in the heap with priority at least \c
deba@681:     ///   value relative to \c Compare.
deba@681:     void decrease (Item item, const Prio& value) {
deba@683:       int i=_iim[item];
deba@683:       _data[i].prio=value;
deba@683:       int p=_data[i].parent;
deba@681: 
deba@683:       if ( p!=-1 && _comp(value, _data[p].prio) ) {
deba@681:         cut(i,p);
deba@681:         cascade(p);
deba@681:       }
deba@683:       if ( _comp(value, _data[_minimum].prio) ) _minimum=i;
deba@681:     }
deba@681: 
deba@681:     /// \brief Increases the priority of \c item to \c value.
deba@681:     ///
deba@681:     /// This method sets the priority of \c item to \c value. Though
deba@681:     /// there is no precondition on the priority of \c item, this
deba@681:     /// method should be used only if it is indeed necessary to increase
deba@681:     /// (relative to \c Compare) the priority of \c item, because this
deba@681:     /// method is inefficient.
deba@681:     void increase (Item item, const Prio& value) {
deba@681:       erase(item);
deba@681:       push(item, value);
deba@681:     }
deba@681: 
deba@681: 
deba@681:     /// \brief Returns if \c item is in, has already been in, or has never
deba@681:     /// been in the heap.
deba@681:     ///
deba@681:     /// This method returns PRE_HEAP if \c item has never been in the
deba@681:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
deba@681:     /// otherwise. In the latter case it is possible that \c item will
deba@681:     /// get back to the heap again.
deba@681:     State state(const Item &item) const {
deba@683:       int i=_iim[item];
deba@681:       if( i>=0 ) {
deba@683:         if ( _data[i].in ) i=0;
deba@681:         else i=-2;
deba@681:       }
deba@681:       return State(i);
deba@681:     }
deba@681: 
deba@681:     /// \brief Sets the state of the \c item in the heap.
deba@681:     ///
deba@681:     /// Sets the state of the \c item in the heap. It can be used to
deba@681:     /// manually clear the heap when it is important to achive the
deba@683:     /// better time _complexity.
deba@681:     /// \param i The item.
deba@681:     /// \param st The state. It should not be \c IN_HEAP.
deba@681:     void state(const Item& i, State st) {
deba@681:       switch (st) {
deba@681:       case POST_HEAP:
deba@681:       case PRE_HEAP:
deba@681:         if (state(i) == IN_HEAP) {
deba@681:           erase(i);
deba@681:         }
deba@683:         _iim[i] = st;
deba@681:         break;
deba@681:       case IN_HEAP:
deba@681:         break;
deba@681:       }
deba@681:     }
deba@681: 
deba@681:   private:
deba@681: 
deba@681:     void balance() {
deba@681: 
deba@683:       int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
deba@681: 
deba@681:       std::vector<int> A(maxdeg,-1);
deba@681: 
deba@681:       /*
deba@681:        *Recall that now minimum does not point to the minimum prio element.
deba@681:        *We set minimum to this during balance().
deba@681:        */
deba@683:       int anchor=_data[_minimum].left_neighbor;
deba@683:       int next=_minimum;
deba@681:       bool end=false;
deba@681: 
deba@681:       do {
deba@681:         int active=next;
deba@681:         if ( anchor==active ) end=true;
deba@683:         int d=_data[active].degree;
deba@683:         next=_data[active].right_neighbor;
deba@681: 
deba@681:         while (A[d]!=-1) {
deba@683:           if( _comp(_data[active].prio, _data[A[d]].prio) ) {
deba@681:             fuse(active,A[d]);
deba@681:           } else {
deba@681:             fuse(A[d],active);
deba@681:             active=A[d];
deba@681:           }
deba@681:           A[d]=-1;
deba@681:           ++d;
deba@681:         }
deba@681:         A[d]=active;
deba@681:       } while ( !end );
deba@681: 
deba@681: 
deba@683:       while ( _data[_minimum].parent >=0 )
deba@683:         _minimum=_data[_minimum].parent;
deba@683:       int s=_minimum;
deba@683:       int m=_minimum;
deba@681:       do {
deba@683:         if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
deba@683:         s=_data[s].right_neighbor;
deba@681:       } while ( s != m );
deba@681:     }
deba@681: 
deba@681:     void makeroot(int c) {
deba@681:       int s=c;
deba@681:       do {
deba@683:         _data[s].parent=-1;
deba@683:         s=_data[s].right_neighbor;
deba@681:       } while ( s != c );
deba@681:     }
deba@681: 
deba@681:     void cut(int a, int b) {
deba@681:       /*
deba@681:        *Replacing a from the children of b.
deba@681:        */
deba@683:       --_data[b].degree;
deba@681: 
deba@683:       if ( _data[b].degree !=0 ) {
deba@683:         int child=_data[b].child;
deba@681:         if ( child==a )
deba@683:           _data[b].child=_data[child].right_neighbor;
deba@681:         unlace(a);
deba@681:       }
deba@681: 
deba@681: 
deba@681:       /*Lacing a to the roots.*/
deba@683:       int right=_data[_minimum].right_neighbor;
deba@683:       _data[_minimum].right_neighbor=a;
deba@683:       _data[a].left_neighbor=_minimum;
deba@683:       _data[a].right_neighbor=right;
deba@683:       _data[right].left_neighbor=a;
deba@681: 
deba@683:       _data[a].parent=-1;
deba@683:       _data[a].marked=false;
deba@681:     }
deba@681: 
deba@681:     void cascade(int a) {
deba@683:       if ( _data[a].parent!=-1 ) {
deba@683:         int p=_data[a].parent;
deba@681: 
deba@683:         if ( _data[a].marked==false ) _data[a].marked=true;
deba@681:         else {
deba@681:           cut(a,p);
deba@681:           cascade(p);
deba@681:         }
deba@681:       }
deba@681:     }
deba@681: 
deba@681:     void fuse(int a, int b) {
deba@681:       unlace(b);
deba@681: 
deba@681:       /*Lacing b under a.*/
deba@683:       _data[b].parent=a;
deba@681: 
deba@683:       if (_data[a].degree==0) {
deba@683:         _data[b].left_neighbor=b;
deba@683:         _data[b].right_neighbor=b;
deba@683:         _data[a].child=b;
deba@681:       } else {
deba@683:         int child=_data[a].child;
deba@683:         int last_child=_data[child].left_neighbor;
deba@683:         _data[child].left_neighbor=b;
deba@683:         _data[b].right_neighbor=child;
deba@683:         _data[last_child].right_neighbor=b;
deba@683:         _data[b].left_neighbor=last_child;
deba@681:       }
deba@681: 
deba@683:       ++_data[a].degree;
deba@681: 
deba@683:       _data[b].marked=false;
deba@681:     }
deba@681: 
deba@681:     /*
deba@681:      *It is invoked only if a has siblings.
deba@681:      */
deba@681:     void unlace(int a) {
deba@683:       int leftn=_data[a].left_neighbor;
deba@683:       int rightn=_data[a].right_neighbor;
deba@683:       _data[leftn].right_neighbor=rightn;
deba@683:       _data[rightn].left_neighbor=leftn;
deba@681:     }
deba@681: 
deba@681: 
deba@683:     class Store {
deba@681:       friend class FibHeap;
deba@681: 
deba@681:       Item name;
deba@681:       int parent;
deba@681:       int left_neighbor;
deba@681:       int right_neighbor;
deba@681:       int child;
deba@681:       int degree;
deba@681:       bool marked;
deba@681:       bool in;
deba@681:       Prio prio;
deba@681: 
deba@683:       Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
deba@681:     };
deba@681:   };
deba@681: 
deba@681: } //namespace lemon
deba@681: 
deba@681: #endif //LEMON_FIB_HEAP_H
deba@681: