/* -*- C++ -*-

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

 *

 * Copyright (C) 2006 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

  /// 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

    };

    /// \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.

    void clear() {

      if (num_items != 0) {

	for (int i = 0; i < (int)container.size(); ++i) {

	  iimap[container[i].name] = -2;

	}

      }

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

    /// \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.

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

    /// \brief 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; 

    }

    /// \brief 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; 

    }

    /// \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();

    /// \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); 

    /// \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, PrioType const value); 

    /// \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, PrioType const 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_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);

    }    

    /// \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_enum 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();

    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( 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 );

    }

  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