alpar@255: // -*- C++ -*-
alpar@255: 
jacint@373: #ifndef HUGO_FIB_HEAP_H
jacint@373: #define HUGO_FIB_HEAP_H
alpar@255: 
alpar@430: ///ingroup auxdat
alpar@255: ///\file
alpar@255: ///\brief Fibonacci Heap implementation.
alpar@255: 
alpar@255: #include <vector>
alpar@255: #include <functional>
alpar@255: #include <math.h>
alpar@255: 
alpar@255: namespace hugo {
alpar@255:   
alpar@430:   /// \addtogroup auxdat
alpar@430:   /// @{
alpar@430: 
jacint@373:   /// An implementation of the Fibonacci Heap.
jacint@373: 
jacint@373:   /**
jacint@387:      This class implements the \e Fibonacci \e heap data structure. A \e heap
jacint@387:      is a data structure for storing items with specified values called \e
jacint@387:      priorities, such that finding the item with minimum priority with respect
jacint@387:      to \e Compare is efficient. In a heap one can change the priority of an
jacint@387:      item, add or erase an item, etc.
jacint@373: 
jacint@387:      The methods \ref increase and \ref erase are not efficient in a Fibonacci
jacint@387:      heap. In case of many calls to these operations, it is better to use a
jacint@387:      \e binary \e heap.
jacint@373:      
jacint@387:      \param Item The type of the items to be stored.  
jacint@387:      \param Prio The type of the priority of the items.
jacint@387:      \param ItemIntMap A read and writable Item int map, for the usage of
jacint@373:      the heap.
jacint@387:      \param Compare A class for the comparison of the priorities. The
jacint@373:      default is \c std::less<Prio>.
jacint@373: 
jacint@373:   */
jacint@373: 
jacint@373: #ifdef DOXYGEN
jacint@373:   template <typename Item, 
jacint@373: 	    typename Prio, 
jacint@373: 	    typename ItemIntMap, 
jacint@373: 	    typename Compare>
jacint@373: #else
jacint@373:   template <typename Item, 
jacint@373: 	    typename Prio, 
jacint@373: 	    typename ItemIntMap, 
alpar@255: 	    typename Compare = std::less<Prio> >
jacint@373: #endif
alpar@255:   class FibHeap {
jacint@387:   public:     
alpar@255:     typedef Prio PrioType;
alpar@255:     
jacint@373:   private:
alpar@255:     class store;
alpar@255:     
alpar@255:     std::vector<store> container;
alpar@255:     int minimum;
alpar@255:     ItemIntMap &iimap;
alpar@255:     Compare comp;
alpar@255:     int num_items;
jacint@373:     
alpar@255:   public:
alpar@255:     enum state_enum {
alpar@255:       IN_HEAP = 0,
alpar@255:       PRE_HEAP = -1,
alpar@255:       POST_HEAP = -2
alpar@255:     };
alpar@255:     
jacint@373:     FibHeap(ItemIntMap &_iimap) : minimum(0), iimap(_iimap), num_items() {} 
jacint@373:     FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), 
alpar@255:       iimap(_iimap), comp(_comp), num_items() {}
alpar@255:     
jacint@373:     ///The number of items stored in the heap.
jacint@373: 
jacint@373:     /**
jacint@387:        Returns the number of items stored in the heap.
jacint@373:     */
jacint@373:     int size() const { return num_items; }
jacint@373: 
jacint@373:     ///Checks if the heap stores no items.
alpar@255:     
jacint@373:     /**
jacint@387:        Returns \c true iff the heap stores no items.
jacint@373:     */
jacint@373:     bool empty() const { return num_items==0; }
jacint@373: 
jacint@387:     ///\c item gets to the heap with priority \c value independently if \c item was already there.
jacint@373: 
jacint@373:     /**
jacint@387:        This method calls \ref push(\c item, \c value) if \c item is not
jacint@387:        stored in the heap and it calls \ref decrease(\c item, \c value) or
jacint@387:        \ref increase(\c item, \c value) otherwise.
jacint@373:     */
jacint@387:     void set (Item const item, PrioType const value); 
jacint@373:     
jacint@373:     ///Adds \c item to the heap with priority \c value. 
jacint@373:     
jacint@373:     /**
jacint@373:        Adds \c item to the heap with priority \c value. 
jacint@373:        \pre \c item must not be stored in the heap. 
jacint@373:     */
jacint@387:     void push (Item const item, PrioType const value);
jacint@373:     
jacint@373:     
jacint@373:     ///Returns the item having the minimum priority w.r.t.  Compare.
jacint@373:     
jacint@373:     /**
jacint@373:        This method returns the item having the minimum priority w.r.t.  Compare. 
jacint@373:        \pre The heap must be nonempty.
jacint@373:     */
jacint@373:     Item top() const { return container[minimum].name; }
jacint@373:     
jacint@373: 
jacint@373:     ///Returns the minimum priority w.r.t.  Compare.
jacint@373: 
jacint@373:     /**
jacint@373:        It returns the minimum priority w.r.t.  Compare.
jacint@373:        \pre The heap must be nonempty.
jacint@373:     */
jacint@373:     PrioType prio() const { return container[minimum].prio; }
jacint@373:     
jacint@373: 
jacint@373:     ///Returns the priority of \c item.
jacint@373: 
jacint@373:     /**
jacint@373:        It returns the priority of \c item.
jacint@373:        \pre \c item must be in the heap.
jacint@373:     */
jacint@387:     PrioType& operator[](const Item& item) { 
jacint@387:       return container[iimap[item]].prio; 
jacint@387:     }
jacint@373:     
jacint@373:     ///Returns the priority of \c item.
jacint@373:     
jacint@373:     /**
jacint@373:        It returns the priority of \c item.
jacint@373:        \pre \c item must be in the heap.
jacint@373:     */
jacint@387:     const PrioType& operator[](const Item& item) const { 
jacint@387:       return container[iimap[item]].prio; 
alpar@255:     }
alpar@255: 
alpar@255: 
jacint@373:     ///Deletes the item with minimum priority w.r.t.  Compare.
alpar@255: 
jacint@373:     /**
jacint@373:     This method deletes the item with minimum priority w.r.t. 
jacint@373:     Compare from the heap.
jacint@373:     \pre The heap must be non-empty.
jacint@373:     */
jacint@373:     void pop();
jacint@373: 
jacint@373:     ///Deletes \c item from the heap.
jacint@373: 
jacint@373:     /**
jacint@373:        This method deletes \c item from the heap, if \c item was already
jacint@373:        stored in the heap. It is quite inefficient in Fibonacci heaps.
jacint@373:     */
jacint@387:     void erase (const Item& item); 
jacint@373: 
jacint@373:     ///Decreases the priority of \c item to \c value.
jacint@373: 
jacint@373:     /**
jacint@373:        This method decreases the priority of \c item to \c value.
jacint@373:        \pre \c item must be stored in the heap with priority at least \c
jacint@373:        value w.r.t.  Compare.
jacint@373:     */
jacint@387:     void decrease (Item item, PrioType const value); 
jacint@373: 
jacint@373: 
jacint@373:     ///Increases the priority of \c item to \c value.
jacint@373: 
jacint@373:     /**
jacint@373:        This method sets the priority of \c item to \c value. Though
jacint@373:        there is no precondition on the priority of \c item, this
jacint@387:        method should be used only if there is a need to really \e increase
jacint@373:        (w.r.t.  Compare) the priority of \c item, because this
jacint@373:        method is inefficient.
jacint@373:     */
jacint@387:     void increase (Item item, PrioType const value) {
jacint@387:       erase(item);
jacint@387:       push(item, value);
jacint@373:     }
jacint@373: 
jacint@373: 
jacint@387:     ///Tells if \c item is in, was already in, or has never been in the heap.
jacint@373: 
jacint@373:     /**
jacint@373:        This method returns PRE_HEAP if \c item has never been in the
jacint@373:        heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
jacint@373:        otherwise. In the latter case it is possible that \c item will
jacint@373:        get back to the heap again.
jacint@373:     */
jacint@387:     state_enum state(const Item &item) const {
jacint@387:       int i=iimap[item];
jacint@387:       if( i>=0 ) {
jacint@387: 	if ( container[i].in ) i=0;
jacint@387: 	else i=-2; 
jacint@387:       }
jacint@387:       return state_enum(i);
jacint@387:     }    
jacint@387:     
jacint@387:   private:
jacint@387:     
jacint@387:     void balance();
jacint@387:     void makeroot(int c);
jacint@387:     void cut(int a, int b);
jacint@387:     void cascade(int a);
jacint@387:     void fuse(int a, int b);
jacint@387:     void unlace(int a);
jacint@373: 
jacint@373: 
jacint@387:     class store {
jacint@387:       friend class FibHeap;
jacint@387:       
jacint@387:       Item name;
jacint@387:       int parent;
jacint@387:       int left_neighbor;
jacint@387:       int right_neighbor;
jacint@387:       int child;
jacint@387:       int degree;  
jacint@387:       bool marked;
jacint@387:       bool in;
jacint@387:       PrioType prio;
jacint@387:       
jacint@387:       store() : parent(-1), child(-1), degree(), marked(false), in(true) {} 
jacint@387:     };
jacint@387:   };    
jacint@387:  
jacint@387: 
jacint@373: 
jacint@373:     // **********************************************************************
jacint@373:     //  IMPLEMENTATIONS
jacint@373:     // **********************************************************************
jacint@373:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::set 
jacint@387:   (Item const item, PrioType const value) 
jacint@387:   {
jacint@387:     int i=iimap[item];
jacint@387:     if ( i >= 0 && container[i].in ) {
jacint@387:       if ( comp(value, container[i].prio) ) decrease(item, value); 
jacint@387:       if ( comp(container[i].prio, value) ) increase(item, value); 
jacint@387:     } else push(item, value);
jacint@387:   }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::push 
jacint@387:   (Item const item, PrioType const value) {
jacint@387:       int i=iimap[item];      
alpar@255:       if ( i < 0 ) {
alpar@255: 	int s=container.size();
jacint@387: 	iimap.set( item, s );	
alpar@255: 	store st;
jacint@387: 	st.name=item;
alpar@255: 	container.push_back(st);
alpar@255: 	i=s;
alpar@255:       } else {
alpar@255: 	container[i].parent=container[i].child=-1;
alpar@255: 	container[i].degree=0;
alpar@255: 	container[i].in=true;
alpar@255: 	container[i].marked=false;
alpar@255:       }
alpar@255: 
alpar@255:       if ( num_items ) {
alpar@255: 	container[container[minimum].right_neighbor].left_neighbor=i;
alpar@255: 	container[i].right_neighbor=container[minimum].right_neighbor;
alpar@255: 	container[minimum].right_neighbor=i;
alpar@255: 	container[i].left_neighbor=minimum;
alpar@255: 	if ( comp( value, container[minimum].prio) ) minimum=i; 
alpar@255:       } else {
alpar@255: 	container[i].right_neighbor=container[i].left_neighbor=i;
alpar@255: 	minimum=i;	
alpar@255:       }
alpar@255:       container[i].prio=value;
alpar@255:       ++num_items;
alpar@255:     }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() {
alpar@255:       /*The first case is that there are only one root.*/
alpar@255:       if ( container[minimum].left_neighbor==minimum ) {
alpar@255: 	container[minimum].in=false;
alpar@255: 	if ( container[minimum].degree!=0 ) { 
alpar@255: 	  makeroot(container[minimum].child);
alpar@255: 	  minimum=container[minimum].child;
alpar@255: 	  balance();
alpar@255: 	}
alpar@255:       } else {
alpar@255: 	int right=container[minimum].right_neighbor;
alpar@255: 	unlace(minimum);
alpar@255: 	container[minimum].in=false;
alpar@255: 	if ( container[minimum].degree > 0 ) {
alpar@255: 	  int left=container[minimum].left_neighbor;
alpar@255: 	  int child=container[minimum].child;
alpar@255: 	  int last_child=container[child].left_neighbor;
alpar@255: 	
alpar@255: 	  makeroot(child);
alpar@255: 	  
alpar@255: 	  container[left].right_neighbor=child;
alpar@255: 	  container[child].left_neighbor=left;
alpar@255: 	  container[right].left_neighbor=last_child;
alpar@255: 	  container[last_child].right_neighbor=right;
alpar@255: 	}
alpar@255: 	minimum=right;
alpar@255: 	balance();
alpar@255:       } // the case where there are more roots
alpar@255:       --num_items;   
alpar@255:     }
alpar@255: 
jacint@387: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::erase 
jacint@387:   (const Item& item) {
jacint@387:       int i=iimap[item];
alpar@255:       
alpar@255:       if ( i >= 0 && container[i].in ) { 	
alpar@255: 	if ( container[i].parent!=-1 ) {
alpar@255: 	  int p=container[i].parent;
alpar@255: 	  cut(i,p);	    
alpar@255: 	  cascade(p);
alpar@255: 	}
alpar@255: 	minimum=i;     //As if its prio would be -infinity
alpar@255: 	pop();
alpar@255:       }
jacint@387:   }
alpar@255:     
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease 
jacint@387:   (Item item, PrioType const value) {
jacint@387:       int i=iimap[item];
alpar@255:       container[i].prio=value;
alpar@255:       int p=container[i].parent;
alpar@255:       
alpar@255:       if ( p!=-1 && comp(value, container[p].prio) ) {
alpar@255: 	cut(i,p);	    
alpar@255: 	cascade(p);
alpar@255:       }      
alpar@255:       if ( comp(value, container[minimum].prio) ) minimum=i; 
jacint@387:   }
jacint@387:  
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() {      
alpar@255: 
alpar@255:     int maxdeg=int( floor( 2.08*log(double(container.size()))))+1;
alpar@255:   
alpar@255:     std::vector<int> A(maxdeg,-1); 
alpar@255:     
alpar@255:     /*
alpar@255:      *Recall that now minimum does not point to the minimum prio element.
alpar@255:      *We set minimum to this during balance().
alpar@255:      */
alpar@255:     int anchor=container[minimum].left_neighbor; 
alpar@255:     int next=minimum; 
alpar@255:     bool end=false; 
alpar@255:     	
alpar@255:        do {
alpar@255: 	int active=next;
alpar@255: 	if ( anchor==active ) end=true;
alpar@255: 	int d=container[active].degree;
alpar@255: 	next=container[active].right_neighbor;
alpar@255: 
alpar@255: 	while (A[d]!=-1) {	  
alpar@255: 	  if( comp(container[active].prio, container[A[d]].prio) ) {
alpar@255: 	    fuse(active,A[d]); 
alpar@255: 	  } else { 
alpar@255: 	    fuse(A[d],active);
alpar@255: 	    active=A[d];
alpar@255: 	  } 
alpar@255: 	  A[d]=-1;
alpar@255: 	  ++d;
alpar@255: 	}	
alpar@255: 	A[d]=active;
alpar@255:        } while ( !end );
alpar@255: 
alpar@255: 
alpar@255:        while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
alpar@255:        int s=minimum;
alpar@255:        int m=minimum;
alpar@255:        do {  
alpar@255: 	 if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
alpar@255: 	 s=container[s].right_neighbor;
alpar@255:        } while ( s != m );
alpar@255:     }
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot 
jacint@387:   (int c) {
alpar@255:       int s=c;
alpar@255:       do {  
alpar@255: 	container[s].parent=-1;
alpar@255: 	s=container[s].right_neighbor;
alpar@255:       } while ( s != c );
alpar@255:     }
jacint@387:   
jacint@387:   
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::cut 
jacint@387:   (int a, int b) {    
jacint@387:     /*
jacint@387:      *Replacing a from the children of b.
jacint@387:      */
jacint@387:     --container[b].degree;
alpar@255:     
jacint@387:     if ( container[b].degree !=0 ) {
jacint@387:       int child=container[b].child;
jacint@387:       if ( child==a ) 
jacint@387: 	container[b].child=container[child].right_neighbor;
jacint@387:       unlace(a);
jacint@387:     }
jacint@387:     
jacint@387:     
jacint@387:     /*Lacing a to the roots.*/
jacint@387:     int right=container[minimum].right_neighbor;
jacint@387:     container[minimum].right_neighbor=a;
jacint@387:     container[a].left_neighbor=minimum;
jacint@387:     container[a].right_neighbor=right;
jacint@387:     container[right].left_neighbor=a;
jacint@387:     
jacint@387:     container[a].parent=-1;
jacint@387:     container[a].marked=false;
jacint@387:   }
jacint@387:   
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade 
jacint@387:   (int a) 
alpar@255:     {
alpar@255:       if ( container[a].parent!=-1 ) {
alpar@255: 	int p=container[a].parent;
alpar@255: 	
alpar@255: 	if ( container[a].marked==false ) container[a].marked=true;
alpar@255: 	else {
alpar@255: 	  cut(a,p);
alpar@255: 	  cascade(p);
alpar@255: 	}
alpar@255:       }
alpar@255:     }
alpar@255: 
alpar@255: 
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse 
jacint@387:   (int a, int b) {
alpar@255:       unlace(b);
alpar@255:       
alpar@255:       /*Lacing b under a.*/
alpar@255:       container[b].parent=a;
alpar@255: 
alpar@255:       if (container[a].degree==0) {
alpar@255: 	container[b].left_neighbor=b;
alpar@255: 	container[b].right_neighbor=b;
alpar@255: 	container[a].child=b;	
alpar@255:       } else {
alpar@255: 	int child=container[a].child;
alpar@255: 	int last_child=container[child].left_neighbor;
alpar@255: 	container[child].left_neighbor=b;
alpar@255: 	container[b].right_neighbor=child;
alpar@255: 	container[last_child].right_neighbor=b;
alpar@255: 	container[b].left_neighbor=last_child;
alpar@255:       }
alpar@255: 
alpar@255:       ++container[a].degree;
alpar@255:       
alpar@255:       container[b].marked=false;
alpar@255:     }
alpar@255: 
jacint@387:   
jacint@387:   /*
jacint@387:    *It is invoked only if a has siblings.
jacint@387:    */
jacint@387:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@387:     typename Compare>
jacint@387:   void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace 
jacint@387:   (int a) {      
alpar@255:       int leftn=container[a].left_neighbor;
alpar@255:       int rightn=container[a].right_neighbor;
alpar@255:       container[leftn].right_neighbor=rightn;
alpar@255:       container[rightn].left_neighbor=leftn;
jacint@387:   }
alpar@255:   
alpar@430:   ///@}
alpar@430: 
alpar@255: } //namespace hugo
alpar@477: 
alpar@477: #endif //HUGO_FIB_HEAP_H
alpar@477: