/* -*- C++ -*-

  * src/lemon/fib_heap.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Combinatorial Optimization Research Group, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_FIB_HEAP_H

 #define LEMON_FIB_HEAP_H

 ///\file

 ///\ingroup auxdat

 ///\brief Fibonacci Heap implementation.

 #include <vector>

 #include <functional>

 #include <math.h>

 namespace lemon {

   /// \addtogroup auxdat

   /// @{

   /// Fibonacci Heap.

   ///This class implements the \e Fibonacci \e heap data structure. A \e heap

   ///is a data structure for storing items with specified values called \e

   ///priorities in such a way that finding the item with minimum priority is

   ///efficient. \c Compare specifies the ordering of the priorities. In a heap

   ///one can change the priority of an item, add or erase an item, etc.

   ///

   ///The methods \ref increase and \ref erase are not efficient in a Fibonacci

   ///heap. In case of many calls to these operations, it is better to use a

   ///\e binary \e heap.

   ///

   ///\param Item Type of the items to be stored.  

   ///\param Prio Type of the priority of the items.

   ///\param ItemIntMap A read and writable Item int map, used internally

   ///to handle the cross references.

   ///\param Compare A class for the ordering of the priorities. The

   ///default is \c std::less<Prio>.

   ///

   ///\sa BinHeap

   ///\sa Dijkstra

   ///\author Jacint Szabo 

 #ifdef DOXYGEN

   template <typename Item, 

 	    typename Prio, 

 	    typename ItemIntMap, 

 	    typename Compare>

 #else

   template <typename Item, 

 	    typename Prio, 

 	    typename ItemIntMap, 

 	    typename Compare = std::less<Prio> >

 #endif

   class FibHeap {

   public:     

     typedef Prio PrioType;

   private:

     class store;

     std::vector<store> container;

     int minimum;

     ItemIntMap &iimap;

     Compare comp;

     int num_items;

   public:

     ///Status of the nodes

     enum state_enum {

       ///The node is in the heap

       IN_HEAP = 0,

       ///The node has never been in the heap

       PRE_HEAP = -1,

       ///The node was in the heap but it got out of it

       POST_HEAP = -2

     };

     explicit FibHeap(ItemIntMap &_iimap) 

       : minimum(0), iimap(_iimap), num_items() {} 

     FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), 

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

     ///The number of items stored in the heap.

     /**

        Returns the number of items stored in the heap.

     */

     int size() const { return num_items; }

     ///Checks if the heap stores no items.

     /**

        Returns \c true if and only if the heap stores no items.

     */

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

     ///\c item gets to the heap with priority \c value independently if \c item was already there.

     /**

        This method calls \ref push(\c item, \c value) if \c item is not

        stored in the heap and it calls \ref decrease(\c item, \c value) or

        \ref increase(\c item, \c value) otherwise.

     */

     void set (Item const item, PrioType const value); 

     ///Adds \c item to the heap with priority \c value. 

     /**

        Adds \c item to the heap with priority \c value. 

        \pre \c item must not be stored in the heap. 

     */

     void push (Item const item, PrioType const value);

     ///Returns the item with minimum priority relative to \c Compare.

     /**

        This method returns the item with minimum priority relative to \c

        Compare.  

        \pre The heap must be nonempty.  

     */

     Item top() const { return container[minimum].name; }

     ///Returns the minimum priority relative to \c Compare.

     /**

        It returns the minimum priority relative to \c Compare.

        \pre The heap must be nonempty.

     */

     PrioType prio() const { return container[minimum].prio; }

     ///Returns the priority of \c item.

     /**

        This function returns the priority of \c item.

        \pre \c item must be in the heap.

     */

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

       return container[iimap[item]].prio; 

     }

     ///Returns the priority of \c item.

     /**

        It returns the priority of \c item.

        \pre \c item must be in the heap.

     */

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

       return container[iimap[item]].prio; 

     }

     ///Deletes the item with minimum priority relative to \c Compare.

     /**

     This method deletes the item with minimum priority relative to \c

     Compare from the heap.  

     \pre The heap must be non-empty.  

     */

     void pop();

     ///Deletes \c item from the heap.

     /**

        This method deletes \c item from the heap, if \c item was already

        stored in the heap. It is quite inefficient in Fibonacci heaps.

     */

     void erase (const Item& item); 

     ///Decreases the priority of \c item to \c value.

     /**

        This method decreases the priority of \c item to \c value.

        \pre \c item must be stored in the heap with priority at least \c

        value relative to \c Compare.

     */

     void decrease (Item item, PrioType const value); 

     ///Increases the priority of \c item to \c value.

     /**

        This method sets the priority of \c item to \c value. Though

        there is no precondition on the priority of \c item, this

        method should be used only if it is indeed necessary to increase

        (relative to \c Compare) the priority of \c item, because this

        method is inefficient.

     */

     void increase (Item item, PrioType const value) {

       erase(item);

       push(item, value);

     }

     ///Returns if \c item is in, has already been in, or has never been in the heap.

     /**

        This method returns PRE_HEAP if \c item has never been in the

        heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP

        otherwise. In the latter case it is possible that \c item will

        get back to the heap again.

     */

     state_enum state(const Item &item) const {

       int i=iimap[item];

       if( i>=0 ) {

 	if ( container[i].in ) i=0;

 	else i=-2; 

       }

       return state_enum(i);

     }    

   private:

     void balance();

     void makeroot(int c);

     void cut(int a, int b);

     void cascade(int a);

     void fuse(int a, int b);

     void unlace(int a);

     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) {} 

     };

   };    

     // **********************************************************************

     //  IMPLEMENTATIONS

     // **********************************************************************

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::set 

   (Item const item, PrioType const value) 

   {

     int i=iimap[item];

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

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

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

     } else push(item, value);

   }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::push 

   (Item const item, PrioType const value) {

       int i=iimap[item];      

       if ( i < 0 ) {

 	int s=container.size();

 	iimap.set( item, s );	

 	store st;

 	st.name=item;

 	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;

     }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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;   

     }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::erase 

   (const Item& item) {

       int i=iimap[item];

       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();

       }

   }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease 

   (Item item, PrioType const value) {

       int i=iimap[item];

       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; 

   }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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 );

     }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot 

   (int c) {

       int s=c;

       do {  

 	container[s].parent=-1;

 	s=container[s].right_neighbor;

       } while ( s != c );

     }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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;

   }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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);

 	}

       }

     }

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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.

    */

   template <typename Item, typename Prio, typename ItemIntMap, 

     typename Compare>

   void FibHeap<Item, Prio, ItemIntMap, Compare>::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;

   }

   ///@}

 } //namespace lemon

 #endif //LEMON_FIB_HEAP_H