/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, 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 <cmath>

 namespace lemon {

   /// \ingroup auxdat

   ///

   ///\brief 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

   ///\ref BinHeap "binary heap".

   ///

   ///\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 _Prio, 

 	    typename _ItemIntMap, 

 	    typename _Compare>

 #else

   template <typename _Prio, 

 	    typename _ItemIntMap, 

 	    typename _Compare = std::less<_Prio> >

 #endif

   class FibHeap {

   public:

     typedef _ItemIntMap ItemIntMap;

     typedef _Prio Prio;

     typedef typename ItemIntMap::Key Item;

     typedef std::pair<Item,Prio> Pair;

     typedef _Compare Compare;

   private:

     class store;

     std::vector<store> container;

     int minimum;

     ItemIntMap &iimap;

     Compare comp;

     int num_items;

   public:

     ///Status of the nodes

     enum State {

       ///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

     };

     /// \brief The constructor

     ///

     /// \c _iimap should be given to the constructor, since it is

     ///   used internally to handle the cross references.

     explicit FibHeap(ItemIntMap &_iimap) 

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

     /// \brief The constructor

     ///

     /// \c _iimap should be given to the constructor, since it is used

     /// internally to handle the cross references. \c _comp is an

     /// object for ordering of the priorities. 

     FibHeap(ItemIntMap &_iimap, const Compare &_comp) 

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

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

     ///

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

     int size() const { return num_items; }

     /// \brief 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; }

     /// \brief Make empty this heap.

     /// 

     /// Make empty this heap. It does not change the cross reference

     /// map.  If you want to reuse a heap what is not surely empty you

     /// should first clear the heap and after that you should set the

     /// cross reference map for each item to \c PRE_HEAP.

     void clear() {

       container.clear(); minimum = 0; num_items = 0;

     }

     /// \brief \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 (const Item& item, const Prio& 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);

     }

     /// \brief 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 (const Item& item, const Prio& 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;

     }

     /// \brief 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; }

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

     ///

     /// It returns the minimum priority relative to \c Compare.

     /// \pre The heap must be nonempty.

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

     /// \brief Returns the priority of \c item.

     ///

     /// It returns the priority of \c item.

     /// \pre \c item must be in the heap.

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

       return container[iimap[item]].prio; 

     }

     /// \brief 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() {

       /*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;   

     }

     /// \brief 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) {

       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();

       }

     }

     /// \brief 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, const Prio& 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; 

     }

     /// \brief 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, const Prio& value) {

       erase(item);

       push(item, value);

     }

     /// \brief 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 state(const Item &item) const {

       int i=iimap[item];

       if( i>=0 ) {

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

 	else i=-2; 

       }

       return State(i);

     }    

     /// \brief Sets the state of the \c item in the heap.

     ///

     /// Sets the state of the \c item in the heap. It can be used to

     /// manually clear the heap when it is important to achive the

     /// better time complexity.

     /// \param i The item.

     /// \param st The state. It should not be \c IN_HEAP. 

     void state(const Item& i, State st) {

       switch (st) {

       case POST_HEAP:

       case PRE_HEAP:

         if (state(i) == IN_HEAP) {

           erase(i);

         }

         iimap[i] = st;

         break;

       case IN_HEAP:

         break;

       }

     }

   private:

     void balance() {

       int maxdeg=int( std::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;

       Prio prio;

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

     };

   };    

 } //namespace lemon

 #endif //LEMON_FIB_HEAP_H