/* -*- 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_BINOM_HEAP_H

 #define LEMON_BINOM_HEAP_H

 ///\file

 ///\ingroup auxdat

 ///\brief Binomial Heap implementation.

 #include <vector>

 #include <functional>

 #include <lemon/math.h>

 #include <lemon/counter.h>

 namespace lemon {

   /// \ingroup auxdat

   ///

   ///\brief Binomial Heap.

   ///

   ///This class implements the \e Binomial \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 Binomial

   ///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 Dorian Batha

 #ifdef DOXYGEN

   template <typename _Prio,

             typename _ItemIntMap,

             typename _Compare>

 #else

   template <typename _Prio,

             typename _ItemIntMap,

             typename _Compare = std::less<_Prio> >

 #endif

   class BinomHeap {

   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, head;

     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 BinomHeap(ItemIntMap &_iimap)

       : minimum(0), head(-1), 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.

     BinomHeap(ItemIntMap &_iimap, const Compare &_comp)

       : minimum(0), head(-1), 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; head=-1;

     }

     /// \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].right_neighbor=container[i].child=-1;

         container[i].degree=0;

         container[i].in=true;

       }

       container[i].prio=value;

       if( 0==num_items ) { head=i; minimum=i; }

       else { merge(i); }

       minimum = find_min();

       ++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() {

       container[minimum].in=false;

       int head_child=-1;

       if ( container[minimum].child!=-1 ) {

         int child=container[minimum].child;

         int neighb;

         int prev=-1;

         while( child!=-1 ) {

           neighb=container[child].right_neighbor;

           container[child].parent=-1;

           container[child].right_neighbor=prev;

           head_child=child;

           prev=child;

           child=neighb;

         }

       }

       // The first case is that there are only one root.

       if ( -1==container[head].right_neighbor ) {

         head=head_child;

       }

       // The case where there are more roots.

       else {

         if( head!=minimum )  { unlace(minimum); }

         else { head=container[head].right_neighbor; }

         merge(head_child);

       }

       minimum=find_min();

       --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 Binomial heaps.

     void erase (const Item& item) {

       int i=iimap[item];

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

         decrease( item, container[minimum].prio-1 );

         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];

       if( comp( value,container[i].prio ) ) {

         container[i].prio=value;

         int p_loc=container[i].parent, loc=i;

         int parent, child, neighb;

         while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) {

           // parent set for other loc_child

           child=container[loc].child;

           while( -1!=child ) {

             container[child].parent=p_loc;

             child=container[child].right_neighbor;

           }

           // parent set for other p_loc_child

           child=container[p_loc].child;

           while( -1!=child ) {

             container[child].parent=loc;

             child=container[child].right_neighbor;

           }

           child=container[p_loc].child;

           container[p_loc].child=container[loc].child;

           if( child==loc )

             child=p_loc;

           container[loc].child=child;

           // left_neighb set for p_loc

           if( container[loc].child!=p_loc ) {

             while( container[child].right_neighbor!=loc )

               child=container[child].right_neighbor;

             container[child].right_neighbor=p_loc;

           }

           // left_neighb set for loc

           parent=container[p_loc].parent;

           if( -1!=parent ) child=container[parent].child;

           else child=head;

           if( child!=p_loc ) {

             while( container[child].right_neighbor!=p_loc )

               child=container[child].right_neighbor;

             container[child].right_neighbor=loc;

           }

           neighb=container[p_loc].right_neighbor;

           container[p_loc].right_neighbor=container[loc].right_neighbor;

           container[loc].right_neighbor=neighb;

           container[p_loc].parent=loc;

           container[loc].parent=parent;

           if( -1!=parent && container[parent].child==p_loc )

             container[parent].child=loc;

           /*if new parent will be the first root*/

           if( head==p_loc )

             head=loc;

           p_loc=container[loc].parent;

         }

       }

       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:

     int find_min() {

       int min_loc=-1, min_val;

       int x=head;

       if( x!=-1 ) {

         min_val=container[x].prio;

         min_loc=x;

         x=container[x].right_neighbor;

         while( x!=-1 ) {

           if( comp( container[x].prio,min_val ) ) {

             min_val=container[x].prio;

             min_loc=x;

           }

           x=container[x].right_neighbor;

         }

       }

       return min_loc;

     }

     void merge(int a) {

       interleave(a);

       int x=head;

       if( -1!=x ) {

         int x_prev=-1, x_next=container[x].right_neighbor;

         while( -1!=x_next ) {

           if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) {

             x_prev=x;

             x=x_next;

           }

           else {

             if( comp(container[x].prio,container[x_next].prio) ) {

               container[x].right_neighbor=container[x_next].right_neighbor;

               fuse(x_next,x);

             }

             else {

               if( -1==x_prev ) { head=x_next; }

               else {

                 container[x_prev].right_neighbor=x_next;

               }

               fuse(x,x_next);

               x=x_next;

             }

           }

           x_next=container[x].right_neighbor;

         }

       }

     }

     void interleave(int a) {

       int other=-1, head_other=-1;

       while( -1!=a || -1!=head ) {

         if( -1==a ) {

           if( -1==head_other ) {

             head_other=head;

           }

           else {

             container[other].right_neighbor=head;

           }

           head=-1;

         }

         else if( -1==head ) {

           if( -1==head_other ) {

             head_other=a;

           }

           else {

             container[other].right_neighbor=a;

           }

           a=-1;

         }

         else {

           if( container[a].degree<container[head].degree ) {

             if( -1==head_other ) {

               head_other=a;

             }

             else {

               container[other].right_neighbor=a;

             }

             other=a;

             a=container[a].right_neighbor;

           }

           else {

             if( -1==head_other ) {

               head_other=head;

             }

             else {

               container[other].right_neighbor=head;

             }

             other=head;

             head=container[head].right_neighbor;

           }

         }

       }

       head=head_other;

     }

     // Lacing a under b

     void fuse(int a, int b) {

       container[a].parent=b;

       container[a].right_neighbor=container[b].child;

       container[b].child=a;

       ++container[b].degree;

     }

     // It is invoked only if a has siblings.

     void unlace(int a) {

       int neighb=container[a].right_neighbor;

       int other=head;

       while( container[other].right_neighbor!=a )

         other=container[other].right_neighbor;

       container[other].right_neighbor=neighb;

     }

   private:

     class store {

       friend class BinomHeap;

       Item name;

       int parent;

       int right_neighbor;

       int child;

       int degree;

       bool in;

       Prio prio;

       store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {}

     };

   };

 } //namespace lemon

 #endif //LEMON_BINOM_HEAP_H