// -*- 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