jacint@167: // -*- C++ -*-
jacint@167: /*
jacint@167:  *template <typename Item, 
jacint@167:  *          typename Prio, 
jacint@167:  *          typename ItemIntMap, 
jacint@167:  *          typename Compare = std::less<Prio> >
jacint@167:  * 
jacint@167:  *constructors:
jacint@167:  *
jacint@167:  *FibHeap(ItemIntMap),   FibHeap(ItemIntMap, Compare)
jacint@167:  *
jacint@167:  *Member functions:
jacint@167:  *
jacint@167:  *int size() : returns the number of elements in the heap
jacint@167:  *
jacint@167:  *bool empty() : true iff size()=0
jacint@167:  *
jacint@167:  *void set(Item, Prio) : calls push(Item, Prio) if Item is not
jacint@167:  *     in the heap, and calls decrease/increase(Item, Prio) otherwise
jacint@167:  *
jacint@167:  *void push(Item, Prio) : pushes Item to the heap with priority Prio. Item
jacint@167:  *     mustn't be in the heap.
jacint@167:  *
jacint@173:  *Item top() : returns the Item with least Prio. 
jacint@173:  *     Must be called only if heap is nonempty.
jacint@167:  *
jacint@167:  *Prio prio() : returns the least Prio
jacint@173:  *     Must be called only if heap is nonempty.
jacint@173:  *
jacint@167:  *Prio get(Item) : returns Prio of Item
jacint@173:  *     Must be called only if Item is in heap.
jacint@167:  *
jacint@167:  *void pop() : deletes the Item with least Prio
jacint@167:  *
jacint@167:  *void erase(Item) : deletes Item from the heap if it was already there
jacint@167:  *
jacint@167:  *void decrease(Item, P) : decreases prio of Item to P. 
jacint@167:  *     Item must be in the heap with prio at least P.
jacint@167:  *
jacint@167:  *void increase(Item, P) : sets prio of Item to P. 
jacint@167:  *
jacint@167:  *state_enum state(Item) : returns PRE_HEAP if Item has not been in the 
jacint@167:  *     heap until now, IN_HEAP if it is in the heap at the moment, and 
jacint@167:  *     POST_HEAP otherwise. In the latter case it is possible that Item
jacint@167:  *     will get back to the heap again. 
jacint@167:  *
jacint@167:  *In Fibonacci heaps, increase and erase are not efficient, in case of
jacint@167:  *many calls to these operations, it is better to use bin_heap.
jacint@167:  */
jacint@167: 
jacint@167: #ifndef FIB_HEAP_H
jacint@167: #define FIB_HEAP_H
jacint@167: 
jacint@167: #include <vector>
jacint@167: #include <functional>
jacint@167: #include <math.h>
jacint@167: 
jacint@167: namespace hugo {
jacint@167:   
jacint@167:   template <typename Item, typename Prio, typename ItemIntMap, 
jacint@167:     typename Compare = std::less<Prio> >
jacint@167:  
jacint@167:   class FibHeap {
jacint@167:   
jacint@167:     typedef Prio PrioType;
jacint@167:     
jacint@167:     class store;
jacint@167:     
jacint@167:     std::vector<store> container;
jacint@167:     int minimum;
jacint@167:     ItemIntMap &iimap;
jacint@167:     Compare comp;
jacint@173:     int num_items;
jacint@167: 
jacint@167:     enum state_enum {
jacint@167:       IN_HEAP = 0,
jacint@167:       PRE_HEAP = -1,
jacint@167:       POST_HEAP = -2
jacint@167:     };
jacint@167:     
jacint@167:   public :
jacint@167:     
jacint@173:     FibHeap(ItemIntMap &_iimap) : minimum(), iimap(_iimap), num_items() {} 
jacint@167:     FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(), 
jacint@173:       iimap(_iimap), comp(_comp), num_items() {}
jacint@167:     
jacint@167:     
jacint@167:     int size() const {
jacint@173:       return num_items; 
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@173:     bool empty() const { return num_items==0; }
jacint@167: 
jacint@167: 
jacint@167:     void set (Item const it, PrioType const value) {
alpar@217:       int i=iimap[it];
jacint@167:       if ( i >= 0 && container[i].in ) {
jacint@173: 	if ( comp(value, container[i].prio) ) decrease(it, value); 
jacint@167: 	if ( comp(container[i].prio, value) ) increase(it, value); 
jacint@167:       } else push(it, value);
jacint@167:     }
jacint@167:     
jacint@167: 
jacint@167:     void push (Item const it, PrioType const value) {
alpar@217:       int i=iimap[it];      
jacint@167:       if ( i < 0 ) {
jacint@167: 	int s=container.size();
jacint@167: 	iimap.set( it, s );	
jacint@167: 	store st;
jacint@167: 	st.name=it;
jacint@167: 	container.push_back(st);
jacint@167: 	i=s;
jacint@167:       } else {
jacint@167: 	container[i].parent=container[i].child=-1;
jacint@167: 	container[i].degree=0;
jacint@167: 	container[i].in=true;
jacint@167: 	container[i].marked=false;
jacint@167:       }
jacint@167: 
jacint@173:       if ( num_items ) {
jacint@167: 	container[container[minimum].right_neighbor].left_neighbor=i;
jacint@167: 	container[i].right_neighbor=container[minimum].right_neighbor;
jacint@167: 	container[minimum].right_neighbor=i;
jacint@167: 	container[i].left_neighbor=minimum;
jacint@173: 	if ( comp( value, container[minimum].prio) ) minimum=i; 
jacint@167:       } else {
jacint@167: 	container[i].right_neighbor=container[i].left_neighbor=i;
jacint@167: 	minimum=i;	
jacint@167:       }
jacint@167:       container[i].prio=value;
jacint@173:       ++num_items;
jacint@167:     }
jacint@167:     
jacint@167: 
jacint@167:     Item top() const {
jacint@173:       return container[minimum].name;
jacint@167:     }
jacint@167:     
jacint@167:     
jacint@167:     PrioType prio() const {
jacint@173:       return container[minimum].prio;
jacint@167:     }
jacint@167:     
jacint@167: 
alpar@217:     PrioType& operator[](const Item& it) {
alpar@217:       return container[iimap[it]].prio;
jacint@211:     }
jacint@220: 
jacint@211:     
jacint@211:     const PrioType& operator[](const Item& it) const {
alpar@217:       return container[iimap[it]].prio;
jacint@211:     }
jacint@211: 
jacint@211: 
jacint@220:     const PrioType get(const Item& it) const {
jacint@220:       return container[iimap[it]].prio;
jacint@220:     }
jacint@220:     
jacint@167:     void pop() {
jacint@167:       /*The first case is that there are only one root.*/
jacint@167:       if ( container[minimum].left_neighbor==minimum ) {
jacint@167: 	container[minimum].in=false;
jacint@173: 	if ( container[minimum].degree!=0 ) { 
jacint@167: 	  makeroot(container[minimum].child);
jacint@167: 	  minimum=container[minimum].child;
jacint@167: 	  balance();
jacint@173: 	}
jacint@167:       } else {
jacint@167: 	int right=container[minimum].right_neighbor;
jacint@167: 	unlace(minimum);
jacint@167: 	container[minimum].in=false;
jacint@167: 	if ( container[minimum].degree > 0 ) {
jacint@167: 	  int left=container[minimum].left_neighbor;
jacint@167: 	  int child=container[minimum].child;
jacint@167: 	  int last_child=container[child].left_neighbor;
jacint@167: 	
jacint@167: 	  makeroot(child);
jacint@167: 	  
jacint@167: 	  container[left].right_neighbor=child;
jacint@167: 	  container[child].left_neighbor=left;
jacint@167: 	  container[right].left_neighbor=last_child;
jacint@167: 	  container[last_child].right_neighbor=right;
jacint@167: 	}
jacint@167: 	minimum=right;
jacint@167: 	balance();
jacint@167:       } // the case where there are more roots
jacint@173:       --num_items;   
jacint@167:     }
jacint@167: 
jacint@167:     
jacint@167:     void erase (const Item& it) {
alpar@217:       int i=iimap[it];
jacint@167:       
jacint@173:       if ( i >= 0 && container[i].in ) { 	
jacint@173: 	if ( container[i].parent!=-1 ) {
jacint@173: 	  int p=container[i].parent;
jacint@173: 	  cut(i,p);	    
jacint@173: 	  cascade(p);
jacint@173: 	}
jacint@173: 	minimum=i;     //As if its prio would be -infinity
jacint@173: 	pop();
jacint@173:       }
jacint@173:     }
jacint@167:     
jacint@167: 
jacint@167:     void decrease (Item it, PrioType const value) {
alpar@217:       int i=iimap[it];
jacint@167:       container[i].prio=value;
jacint@167:       int p=container[i].parent;
jacint@167:       
jacint@167:       if ( p!=-1 && comp(value, container[p].prio) ) {
jacint@167: 	cut(i,p);	    
jacint@167: 	cascade(p);
jacint@173:       }      
jacint@173:       if ( comp(value, container[minimum].prio) ) minimum=i; 
jacint@167:     }
jacint@167:    
jacint@167: 
jacint@167:     void increase (Item it, PrioType const value) {
jacint@167:       erase(it);
jacint@167:       push(it, value);
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     state_enum state(const Item &it) const {
alpar@217:       int i=iimap[it];
jacint@167:       if( i>=0 ) {
jacint@241: 	if ( container[i].in ) i=IN_HEAP;
jacint@241: 	else i=POST_HEAP; 
jacint@167:       }
jacint@167:       return state_enum(i);
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:   private:
jacint@167:     
jacint@167:     void balance() {      
jacint@167: 
jacint@167:     int maxdeg=int( floor( 2.08*log(double(container.size()))))+1;
jacint@167:   
jacint@167:     std::vector<int> A(maxdeg,-1); 
jacint@167:     
jacint@167:     /*
jacint@167:      *Recall that now minimum does not point to the minimum prio element.
jacint@167:      *We set minimum to this during balance().
jacint@167:      */
jacint@167:     int anchor=container[minimum].left_neighbor; 
jacint@167:     int next=minimum; 
jacint@167:     bool end=false; 
jacint@167:     	
jacint@167:        do {
jacint@167: 	int active=next;
jacint@167: 	if ( anchor==active ) end=true;
jacint@167: 	int d=container[active].degree;
jacint@167: 	next=container[active].right_neighbor;
jacint@167: 
jacint@167: 	while (A[d]!=-1) {	  
jacint@167: 	  if( comp(container[active].prio, container[A[d]].prio) ) {
jacint@167: 	    fuse(active,A[d]); 
jacint@167: 	  } else { 
jacint@167: 	    fuse(A[d],active);
jacint@167: 	    active=A[d];
jacint@167: 	  } 
jacint@167: 	  A[d]=-1;
jacint@167: 	  ++d;
jacint@167: 	}	
jacint@167: 	A[d]=active;
jacint@167:        } while ( !end );
jacint@167: 
jacint@167: 
jacint@167:        while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;
jacint@167:        int s=minimum;
jacint@167:        int m=minimum;
jacint@167:        do {  
jacint@167: 	 if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;
jacint@167: 	 s=container[s].right_neighbor;
jacint@167:        } while ( s != m );
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     void makeroot (int c) {
jacint@167:       int s=c;
jacint@167:       do {  
jacint@167: 	container[s].parent=-1;
jacint@167: 	s=container[s].right_neighbor;
jacint@167:       } while ( s != c );
jacint@167:     }
jacint@167:     
jacint@167: 
jacint@167:     void cut (int a, int b) {    
jacint@167:       /*
jacint@167:        *Replacing a from the children of b.
jacint@167:        */
jacint@167:       --container[b].degree;
jacint@167:       
jacint@167:       if ( container[b].degree !=0 ) {
jacint@167: 	int child=container[b].child;
jacint@167: 	if ( child==a ) 
jacint@167: 	  container[b].child=container[child].right_neighbor;
jacint@167: 	unlace(a);
jacint@167:       }
jacint@167:       
jacint@167:       
jacint@173:       /*Lacing a to the roots.*/
jacint@167:       int right=container[minimum].right_neighbor;
jacint@167:       container[minimum].right_neighbor=a;
jacint@167:       container[a].left_neighbor=minimum;
jacint@167:       container[a].right_neighbor=right;
jacint@167:       container[right].left_neighbor=a;
jacint@167: 
jacint@167:       container[a].parent=-1;
jacint@167:       container[a].marked=false;
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     void cascade (int a) 
jacint@167:     {
jacint@167:       if ( container[a].parent!=-1 ) {
jacint@167: 	int p=container[a].parent;
jacint@167: 	
jacint@167: 	if ( container[a].marked==false ) container[a].marked=true;
jacint@167: 	else {
jacint@167: 	  cut(a,p);
jacint@167: 	  cascade(p);
jacint@167: 	}
jacint@167:       }
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     void fuse (int a, int b) {
jacint@167:       unlace(b);
jacint@167:       
jacint@167:       /*Lacing b under a.*/
jacint@167:       container[b].parent=a;
jacint@167: 
jacint@167:       if (container[a].degree==0) {
jacint@167: 	container[b].left_neighbor=b;
jacint@167: 	container[b].right_neighbor=b;
jacint@167: 	container[a].child=b;	
jacint@167:       } else {
jacint@167: 	int child=container[a].child;
jacint@167: 	int last_child=container[child].left_neighbor;
jacint@167: 	container[child].left_neighbor=b;
jacint@167: 	container[b].right_neighbor=child;
jacint@167: 	container[last_child].right_neighbor=b;
jacint@167: 	container[b].left_neighbor=last_child;
jacint@167:       }
jacint@167: 
jacint@167:       ++container[a].degree;
jacint@167:       
jacint@167:       container[b].marked=false;
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     /*
jacint@167:      *It is invoked only if a has siblings.
jacint@167:      */
jacint@167:     void unlace (int a) {      
jacint@167:       int leftn=container[a].left_neighbor;
jacint@167:       int rightn=container[a].right_neighbor;
jacint@167:       container[leftn].right_neighbor=rightn;
jacint@167:       container[rightn].left_neighbor=leftn;
jacint@167:     }
jacint@167: 
jacint@167: 
jacint@167:     class store {
jacint@167:       friend class FibHeap;
jacint@167:       
jacint@167:       Item name;
jacint@167:       int parent;
jacint@167:       int left_neighbor;
jacint@167:       int right_neighbor;
jacint@167:       int child;
jacint@167:       int degree;  
jacint@167:       bool marked;
jacint@167:       bool in;
jacint@167:       PrioType prio;
jacint@167: 
jacint@167:       store() : parent(-1), child(-1), degree(), marked(false), in(true) {} 
jacint@167:     };
jacint@167:     
jacint@167:   };
jacint@167:   
jacint@167: } //namespace hugo
jacint@167: #endif