// -*- C++ -*-

 /*

  *template <typename Item, 

  *          typename Prio, 

  *          typename ItemIntMap, 

  *          typename Compare = std::less<Prio> >

  * 

  *constructors:

  *

  *FibHeap(ItemIntMap),   FibHeap(ItemIntMap, Compare)

  *

  *Member functions:

  *

  *int size() : returns the number of elements in the heap

  *

  *bool empty() : true iff size()=0

  *

  *void set(Item, Prio) : calls push(Item, Prio) if Item is not

  *     in the heap, and calls decrease/increase(Item, Prio) otherwise

  *

  *void push(Item, Prio) : pushes Item to the heap with priority Prio. Item

  *     mustn't be in the heap.

  *

  *Item top() : returns the Item with least Prio. 

  *     Must be called only if heap is nonempty.

  *

  *Prio prio() : returns the least Prio

  *     Must be called only if heap is nonempty.

  *

  *Prio get(Item) : returns Prio of Item

  *     Must be called only if Item is in heap.

  *

  *void pop() : deletes the Item with least Prio

  *

  *void erase(Item) : deletes Item from the heap if it was already there

  *

  *void decrease(Item, P) : decreases prio of Item to P. 

  *     Item must be in the heap with prio at least P.

  *

  *void increase(Item, P) : sets prio of Item to P. 

  *

  *state_enum state(Item) : returns PRE_HEAP if Item has not been in the 

  *     heap until now, IN_HEAP if it is in the heap at the moment, and 

  *     POST_HEAP otherwise. In the latter case it is possible that Item

  *     will get back to the heap again. 

  *

  *In Fibonacci heaps, increase and erase are not efficient, in case of

  *many calls to these operations, it is better to use bin_heap.

  */

 #ifndef FIB_HEAP_H

 #define FIB_HEAP_H

 #include <vector>

 #include <functional>

 #include <math.h>

 namespace hugo {

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare = std::less<Prio> >

   class FibHeap {

     typedef Prio PrioType;

     class store;

     std::vector<store> container;

     int minimum;

     ItemIntMap &iimap;

     Compare comp;

     int num_items;

     enum state_enum {

       IN_HEAP = 0,

       PRE_HEAP = -1,

       POST_HEAP = -2

     };

   public :

     FibHeap(ItemIntMap &_iimap) : minimum(), iimap(_iimap), num_items() {} 

     FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(), 

       iimap(_iimap), comp(_comp), num_items() {}

     int size() const {

       return num_items; 

     }

     bool empty() const { return num_items==0; }

     void set (Item const it, PrioType const value) {

       int i=iimap[it];

       if ( i >= 0 && container[i].in ) {

 	if ( comp(value, container[i].prio) ) decrease(it, value); 

 	if ( comp(container[i].prio, value) ) increase(it, value); 

       } else push(it, value);

     }

     void push (Item const it, PrioType const value) {

       int i=iimap[it];      

       if ( i < 0 ) {

 	int s=container.size();

 	iimap.set( it, s );	

 	store st;

 	st.name=it;

 	container.push_back(st);

 	i=s;

       } else {

 	container[i].parent=container[i].child=-1;

 	container[i].degree=0;

 	container[i].in=true;

 	container[i].marked=false;

       }

       if ( num_items ) {

 	container[container[minimum].right_neighbor].left_neighbor=i;

 	container[i].right_neighbor=container[minimum].right_neighbor;

 	container[minimum].right_neighbor=i;

 	container[i].left_neighbor=minimum;

 	if ( comp( value, container[minimum].prio) ) minimum=i; 

       } else {

 	container[i].right_neighbor=container[i].left_neighbor=i;

 	minimum=i;	

       }

       container[i].prio=value;

       ++num_items;

     }

     Item top() const {

       return container[minimum].name;

     }

     PrioType prio() const {

       return container[minimum].prio;

     }

     PrioType& operator[](const Item& it) {

       return container[iimap[it]].prio;

     }

     const PrioType& operator[](const Item& it) const {

       return container[iimap[it]].prio;

     }

     const PrioType get(const Item& it) const {

       return container[iimap[it]].prio;

     }

     void pop() {

       /*The first case is that there are only one root.*/

       if ( container[minimum].left_neighbor==minimum ) {

 	container[minimum].in=false;

 	if ( container[minimum].degree!=0 ) { 

 	  makeroot(container[minimum].child);

 	  minimum=container[minimum].child;

 	  balance();

 	}

       } else {

 	int right=container[minimum].right_neighbor;

 	unlace(minimum);

 	container[minimum].in=false;

 	if ( container[minimum].degree > 0 ) {

 	  int left=container[minimum].left_neighbor;

 	  int child=container[minimum].child;

 	  int last_child=container[child].left_neighbor;

 	  makeroot(child);

 	  container[left].right_neighbor=child;

 	  container[child].left_neighbor=left;

 	  container[right].left_neighbor=last_child;

 	  container[last_child].right_neighbor=right;

 	}

 	minimum=right;

 	balance();

       } // the case where there are more roots

       --num_items;   

     }

     void erase (const Item& it) {

       int i=iimap[it];

       if ( i >= 0 && container[i].in ) { 	

 	if ( container[i].parent!=-1 ) {

 	  int p=container[i].parent;

 	  cut(i,p);	    

 	  cascade(p);

 	}

 	minimum=i;     //As if its prio would be -infinity

 	pop();

       }

     }

     void decrease (Item it, PrioType const value) {

       int i=iimap[it];

       container[i].prio=value;

       int p=container[i].parent;

       if ( p!=-1 && comp(value, container[p].prio) ) {

 	cut(i,p);	    

 	cascade(p);

       }      

       if ( comp(value, container[minimum].prio) ) minimum=i; 

     }

     void increase (Item it, PrioType const value) {

       erase(it);

       push(it, value);

     }

     state_enum state(const Item &it) const {

       int i=iimap[it];

       if( i>=0 ) {

 	if ( container[i].in ) i=IN_HEAP;

 	else i=POST_HEAP; 

       }

       return state_enum(i);

     }

   private:

     void balance() {      

     int maxdeg=int( floor( 2.08*log(double(container.size()))))+1;

     std::vector<int> A(maxdeg,-1); 

     /*

      *Recall that now minimum does not point to the minimum prio element.

      *We set minimum to this during balance().

      */

     int anchor=container[minimum].left_neighbor; 

     int next=minimum; 

     bool end=false; 

        do {

 	int active=next;

 	if ( anchor==active ) end=true;

 	int d=container[active].degree;

 	next=container[active].right_neighbor;

 	while (A[d]!=-1) {	  

 	  if( comp(container[active].prio, container[A[d]].prio) ) {

 	    fuse(active,A[d]); 

 	  } else { 

 	    fuse(A[d],active);

 	    active=A[d];

 	  } 

 	  A[d]=-1;

 	  ++d;

 	}	

 	A[d]=active;

        } while ( !end );

        while ( container[minimum].parent >=0 ) minimum=container[minimum].parent;

        int s=minimum;

        int m=minimum;

        do {  

 	 if ( comp(container[s].prio, container[minimum].prio) ) minimum=s;

 	 s=container[s].right_neighbor;

        } while ( s != m );

     }

     void makeroot (int c) {

       int s=c;

       do {  

 	container[s].parent=-1;

 	s=container[s].right_neighbor;

       } while ( s != c );

     }

     void cut (int a, int b) {    

       /*

        *Replacing a from the children of b.

        */

       --container[b].degree;

       if ( container[b].degree !=0 ) {

 	int child=container[b].child;

 	if ( child==a ) 

 	  container[b].child=container[child].right_neighbor;

 	unlace(a);

       }

       /*Lacing a to the roots.*/

       int right=container[minimum].right_neighbor;

       container[minimum].right_neighbor=a;

       container[a].left_neighbor=minimum;

       container[a].right_neighbor=right;

       container[right].left_neighbor=a;

       container[a].parent=-1;

       container[a].marked=false;

     }

     void cascade (int a) 

     {

       if ( container[a].parent!=-1 ) {

 	int p=container[a].parent;

 	if ( container[a].marked==false ) container[a].marked=true;

 	else {

 	  cut(a,p);

 	  cascade(p);

 	}

       }

     }

     void fuse (int a, int b) {

       unlace(b);

       /*Lacing b under a.*/

       container[b].parent=a;

       if (container[a].degree==0) {

 	container[b].left_neighbor=b;

 	container[b].right_neighbor=b;

 	container[a].child=b;	

       } else {

 	int child=container[a].child;

 	int last_child=container[child].left_neighbor;

 	container[child].left_neighbor=b;

 	container[b].right_neighbor=child;

 	container[last_child].right_neighbor=b;

 	container[b].left_neighbor=last_child;

       }

       ++container[a].degree;

       container[b].marked=false;

     }

     /*

      *It is invoked only if a has siblings.

      */

     void unlace (int a) {      

       int leftn=container[a].left_neighbor;

       int rightn=container[a].right_neighbor;

       container[leftn].right_neighbor=rightn;

       container[rightn].left_neighbor=leftn;

     }

     class store {

       friend class FibHeap;

       Item name;

       int parent;

       int left_neighbor;

       int right_neighbor;

       int child;

       int degree;  

       bool marked;

       bool in;

       PrioType prio;

       store() : parent(-1), child(-1), degree(), marked(false), in(true) {} 

     };

   };

 } //namespace hugo

 #endif