// -*- 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=0;

	else i=-2; 

      }

      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