kpeter@701: /* -*- C++ -*-
kpeter@701:  *
kpeter@701:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@701:  *
kpeter@701:  * Copyright (C) 2003-2008
kpeter@701:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@701:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@701:  *
kpeter@701:  * Permission to use, modify and distribute this software is granted
kpeter@701:  * provided that this copyright notice appears in all copies. For
kpeter@701:  * precise terms see the accompanying LICENSE file.
kpeter@701:  *
kpeter@701:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@701:  * express or implied, and with no claim as to its suitability for any
kpeter@701:  * purpose.
kpeter@701:  *
kpeter@701:  */
kpeter@701: 
kpeter@701: #ifndef LEMON_BINOM_HEAP_H
kpeter@701: #define LEMON_BINOM_HEAP_H
kpeter@701: 
kpeter@701: ///\file
kpeter@701: ///\ingroup auxdat
kpeter@701: ///\brief Binomial Heap implementation.
kpeter@701: 
kpeter@701: #include <vector>
kpeter@701: #include <functional>
kpeter@701: #include <lemon/math.h>
kpeter@701: #include <lemon/counter.h>
kpeter@701: 
kpeter@701: namespace lemon {
kpeter@701: 
kpeter@701:   /// \ingroup auxdat
kpeter@701:   ///
kpeter@701:   ///\brief Binomial Heap.
kpeter@701:   ///
kpeter@701:   ///This class implements the \e Binomial \e heap data structure. A \e heap
kpeter@701:   ///is a data structure for storing items with specified values called \e
kpeter@701:   ///priorities in such a way that finding the item with minimum priority is
kpeter@701:   ///efficient. \c Compare specifies the ordering of the priorities. In a heap
kpeter@701:   ///one can change the priority of an item, add or erase an item, etc.
kpeter@701:   ///
kpeter@701:   ///The methods \ref increase and \ref erase are not efficient in a Binomial
kpeter@701:   ///heap. In case of many calls to these operations, it is better to use a
kpeter@701:   ///\ref BinHeap "binary heap".
kpeter@701:   ///
kpeter@701:   ///\param _Prio Type of the priority of the items.
kpeter@701:   ///\param _ItemIntMap A read and writable Item int map, used internally
kpeter@701:   ///to handle the cross references.
kpeter@701:   ///\param _Compare A class for the ordering of the priorities. The
kpeter@701:   ///default is \c std::less<_Prio>.
kpeter@701:   ///
kpeter@701:   ///\sa BinHeap
kpeter@701:   ///\sa Dijkstra
kpeter@701:   ///\author Dorian Batha
kpeter@701: 
kpeter@701: #ifdef DOXYGEN
kpeter@701:   template <typename _Prio,
kpeter@701:             typename _ItemIntMap,
kpeter@701:             typename _Compare>
kpeter@701: #else
kpeter@701:   template <typename _Prio,
kpeter@701:             typename _ItemIntMap,
kpeter@701:             typename _Compare = std::less<_Prio> >
kpeter@701: #endif
kpeter@701:   class BinomHeap {
kpeter@701:   public:
kpeter@701:     typedef _ItemIntMap ItemIntMap;
kpeter@701:     typedef _Prio Prio;
kpeter@701:     typedef typename ItemIntMap::Key Item;
kpeter@701:     typedef std::pair<Item,Prio> Pair;
kpeter@701:     typedef _Compare Compare;
kpeter@701: 
kpeter@701:   private:
kpeter@701:     class store;
kpeter@701: 
kpeter@701:     std::vector<store> container;
kpeter@701:     int minimum, head;
kpeter@701:     ItemIntMap &iimap;
kpeter@701:     Compare comp;
kpeter@701:     int num_items;
kpeter@701: 
kpeter@701:   public:
kpeter@701:     ///Status of the nodes
kpeter@701:     enum State {
kpeter@701:       ///The node is in the heap
kpeter@701:       IN_HEAP = 0,
kpeter@701:       ///The node has never been in the heap
kpeter@701:       PRE_HEAP = -1,
kpeter@701:       ///The node was in the heap but it got out of it
kpeter@701:       POST_HEAP = -2
kpeter@701:     };
kpeter@701: 
kpeter@701:     /// \brief The constructor
kpeter@701:     ///
kpeter@701:     /// \c _iimap should be given to the constructor, since it is
kpeter@701:     ///   used internally to handle the cross references.
kpeter@701:     explicit BinomHeap(ItemIntMap &_iimap)
kpeter@701:       : minimum(0), head(-1), iimap(_iimap), num_items() {}
kpeter@701: 
kpeter@701:     /// \brief The constructor
kpeter@701:     ///
kpeter@701:     /// \c _iimap should be given to the constructor, since it is used
kpeter@701:     /// internally to handle the cross references. \c _comp is an
kpeter@701:     /// object for ordering of the priorities.
kpeter@701:     BinomHeap(ItemIntMap &_iimap, const Compare &_comp)
kpeter@701:       : minimum(0), head(-1), iimap(_iimap), comp(_comp), num_items() {}
kpeter@701: 
kpeter@701:     /// \brief The number of items stored in the heap.
kpeter@701:     ///
kpeter@701:     /// Returns the number of items stored in the heap.
kpeter@701:     int size() const { return num_items; }
kpeter@701: 
kpeter@701:     /// \brief Checks if the heap stores no items.
kpeter@701:     ///
kpeter@701:     ///   Returns \c true if and only if the heap stores no items.
kpeter@701:     bool empty() const { return num_items==0; }
kpeter@701: 
kpeter@701:     /// \brief Make empty this heap.
kpeter@701:     ///
kpeter@701:     /// Make empty this heap. It does not change the cross reference
kpeter@701:     /// map.  If you want to reuse a heap what is not surely empty you
kpeter@701:     /// should first clear the heap and after that you should set the
kpeter@701:     /// cross reference map for each item to \c PRE_HEAP.
kpeter@701:     void clear() {
kpeter@701:       container.clear(); minimum=0; num_items=0; head=-1;
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief \c item gets to the heap with priority \c value independently
kpeter@701:     /// if \c item was already there.
kpeter@701:     ///
kpeter@701:     /// This method calls \ref push(\c item, \c value) if \c item is not
kpeter@701:     /// stored in the heap and it calls \ref decrease(\c item, \c value) or
kpeter@701:     /// \ref increase(\c item, \c value) otherwise.
kpeter@701:     void set (const Item& item, const Prio& value) {
kpeter@701:       int i=iimap[item];
kpeter@701:       if ( i >= 0 && container[i].in ) {
kpeter@701:         if ( comp(value, container[i].prio) ) decrease(item, value);
kpeter@701:         if ( comp(container[i].prio, value) ) increase(item, value);
kpeter@701:       } else push(item, value);
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Adds \c item to the heap with priority \c value.
kpeter@701:     ///
kpeter@701:     /// Adds \c item to the heap with priority \c value.
kpeter@701:     /// \pre \c item must not be stored in the heap.
kpeter@701:     void push (const Item& item, const Prio& value) {
kpeter@701:       int i=iimap[item];
kpeter@701:       if ( i<0 ) {
kpeter@701:         int s=container.size();
kpeter@701:         iimap.set( item,s );
kpeter@701:         store st;
kpeter@701:         st.name=item;
kpeter@701:         container.push_back(st);
kpeter@701:         i=s;
kpeter@701:       }
kpeter@701:       else {
kpeter@701:         container[i].parent=container[i].right_neighbor=container[i].child=-1;
kpeter@701:         container[i].degree=0;
kpeter@701:         container[i].in=true;
kpeter@701:       }
kpeter@701:       container[i].prio=value;
kpeter@701: 
kpeter@701:       if( 0==num_items ) { head=i; minimum=i; }
kpeter@701:       else { merge(i); }
kpeter@701: 
kpeter@701:       minimum = find_min();
kpeter@701: 
kpeter@701:       ++num_items;
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Returns the item with minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// This method returns the item with minimum priority relative to \c
kpeter@701:     /// Compare.
kpeter@701:     /// \pre The heap must be nonempty.
kpeter@701:     Item top() const { return container[minimum].name; }
kpeter@701: 
kpeter@701:     /// \brief Returns the minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// It returns the minimum priority relative to \c Compare.
kpeter@701:     /// \pre The heap must be nonempty.
kpeter@701:     const Prio& prio() const { return container[minimum].prio; }
kpeter@701: 
kpeter@701:     /// \brief Returns the priority of \c item.
kpeter@701:     ///
kpeter@701:     /// It returns the priority of \c item.
kpeter@701:     /// \pre \c item must be in the heap.
kpeter@701:     const Prio& operator[](const Item& item) const {
kpeter@701:       return container[iimap[item]].prio;
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Deletes the item with minimum priority relative to \c Compare.
kpeter@701:     ///
kpeter@701:     /// This method deletes the item with minimum priority relative to \c
kpeter@701:     /// Compare from the heap.
kpeter@701:     /// \pre The heap must be non-empty.
kpeter@701:     void pop() {
kpeter@701:       container[minimum].in=false;
kpeter@701: 
kpeter@701:       int head_child=-1;
kpeter@701:       if ( container[minimum].child!=-1 ) {
kpeter@701:         int child=container[minimum].child;
kpeter@701:         int neighb;
kpeter@701:         int prev=-1;
kpeter@701:         while( child!=-1 ) {
kpeter@701:           neighb=container[child].right_neighbor;
kpeter@701:           container[child].parent=-1;
kpeter@701:           container[child].right_neighbor=prev;
kpeter@701:           head_child=child;
kpeter@701:           prev=child;
kpeter@701:           child=neighb;
kpeter@701:         }
kpeter@701:       }
kpeter@701: 
kpeter@701:       // The first case is that there are only one root.
kpeter@701:       if ( -1==container[head].right_neighbor ) {
kpeter@701:         head=head_child;
kpeter@701:       }
kpeter@701:       // The case where there are more roots.
kpeter@701:       else {
kpeter@701:         if( head!=minimum )  { unlace(minimum); }
kpeter@701:         else { head=container[head].right_neighbor; }
kpeter@701: 
kpeter@701:         merge(head_child);
kpeter@701:       }
kpeter@701:       minimum=find_min();
kpeter@701:       --num_items;
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Deletes \c item from the heap.
kpeter@701:     ///
kpeter@701:     /// This method deletes \c item from the heap, if \c item was already
kpeter@701:     /// stored in the heap. It is quite inefficient in Binomial heaps.
kpeter@701:     void erase (const Item& item) {
kpeter@701:       int i=iimap[item];
kpeter@701:       if ( i >= 0 && container[i].in ) {
kpeter@701:         decrease( item, container[minimum].prio-1 );
kpeter@701:         pop();
kpeter@701:       }
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Decreases the priority of \c item to \c value.
kpeter@701:     ///
kpeter@701:     /// This method decreases the priority of \c item to \c value.
kpeter@701:     /// \pre \c item must be stored in the heap with priority at least \c
kpeter@701:     ///   value relative to \c Compare.
kpeter@701:     void decrease (Item item, const Prio& value) {
kpeter@701:       int i=iimap[item];
kpeter@701: 
kpeter@701:       if( comp( value,container[i].prio ) ) {
kpeter@701:         container[i].prio=value;
kpeter@701: 
kpeter@701:         int p_loc=container[i].parent, loc=i;
kpeter@701:         int parent, child, neighb;
kpeter@701: 
kpeter@701:         while( -1!=p_loc && comp(container[loc].prio,container[p_loc].prio) ) {
kpeter@701: 
kpeter@701:           // parent set for other loc_child
kpeter@701:           child=container[loc].child;
kpeter@701:           while( -1!=child ) {
kpeter@701:             container[child].parent=p_loc;
kpeter@701:             child=container[child].right_neighbor;
kpeter@701:           }
kpeter@701: 
kpeter@701:           // parent set for other p_loc_child
kpeter@701:           child=container[p_loc].child;
kpeter@701:           while( -1!=child ) {
kpeter@701:             container[child].parent=loc;
kpeter@701:             child=container[child].right_neighbor;
kpeter@701:           }
kpeter@701: 
kpeter@701:           child=container[p_loc].child;
kpeter@701:           container[p_loc].child=container[loc].child;
kpeter@701:           if( child==loc )
kpeter@701:             child=p_loc;
kpeter@701:           container[loc].child=child;
kpeter@701: 
kpeter@701:           // left_neighb set for p_loc
kpeter@701:           if( container[loc].child!=p_loc ) {
kpeter@701:             while( container[child].right_neighbor!=loc )
kpeter@701:               child=container[child].right_neighbor;
kpeter@701:             container[child].right_neighbor=p_loc;
kpeter@701:           }
kpeter@701: 
kpeter@701:           // left_neighb set for loc
kpeter@701:           parent=container[p_loc].parent;
kpeter@701:           if( -1!=parent ) child=container[parent].child;
kpeter@701:           else child=head;
kpeter@701: 
kpeter@701:           if( child!=p_loc ) {
kpeter@701:             while( container[child].right_neighbor!=p_loc )
kpeter@701:               child=container[child].right_neighbor;
kpeter@701:             container[child].right_neighbor=loc;
kpeter@701:           }
kpeter@701: 
kpeter@701:           neighb=container[p_loc].right_neighbor;
kpeter@701:           container[p_loc].right_neighbor=container[loc].right_neighbor;
kpeter@701:           container[loc].right_neighbor=neighb;
kpeter@701: 
kpeter@701:           container[p_loc].parent=loc;
kpeter@701:           container[loc].parent=parent;
kpeter@701: 
kpeter@701:           if( -1!=parent && container[parent].child==p_loc )
kpeter@701:             container[parent].child=loc;
kpeter@701: 
kpeter@701:           /*if new parent will be the first root*/
kpeter@701:           if( head==p_loc )
kpeter@701:             head=loc;
kpeter@701: 
kpeter@701:           p_loc=container[loc].parent;
kpeter@701:         }
kpeter@701:       }
kpeter@701:       if( comp(value,container[minimum].prio) ) {
kpeter@701:         minimum=i;
kpeter@701:       }
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Increases the priority of \c item to \c value.
kpeter@701:     ///
kpeter@701:     /// This method sets the priority of \c item to \c value. Though
kpeter@701:     /// there is no precondition on the priority of \c item, this
kpeter@701:     /// method should be used only if it is indeed necessary to increase
kpeter@701:     /// (relative to \c Compare) the priority of \c item, because this
kpeter@701:     /// method is inefficient.
kpeter@701:     void increase (Item item, const Prio& value) {
kpeter@701:       erase(item);
kpeter@701:       push(item, value);
kpeter@701:     }
kpeter@701: 
kpeter@701: 
kpeter@701:     /// \brief Returns if \c item is in, has already been in, or has never
kpeter@701:     /// been in the heap.
kpeter@701:     ///
kpeter@701:     /// This method returns PRE_HEAP if \c item has never been in the
kpeter@701:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
kpeter@701:     /// otherwise. In the latter case it is possible that \c item will
kpeter@701:     /// get back to the heap again.
kpeter@701:     State state(const Item &item) const {
kpeter@701:       int i=iimap[item];
kpeter@701:       if( i>=0 ) {
kpeter@701:         if ( container[i].in ) i=0;
kpeter@701:         else i=-2;
kpeter@701:       }
kpeter@701:       return State(i);
kpeter@701:     }
kpeter@701: 
kpeter@701:     /// \brief Sets the state of the \c item in the heap.
kpeter@701:     ///
kpeter@701:     /// Sets the state of the \c item in the heap. It can be used to
kpeter@701:     /// manually clear the heap when it is important to achive the
kpeter@701:     /// better time complexity.
kpeter@701:     /// \param i The item.
kpeter@701:     /// \param st The state. It should not be \c IN_HEAP.
kpeter@701:     void state(const Item& i, State st) {
kpeter@701:       switch (st) {
kpeter@701:       case POST_HEAP:
kpeter@701:       case PRE_HEAP:
kpeter@701:         if (state(i) == IN_HEAP) {
kpeter@701:           erase(i);
kpeter@701:         }
kpeter@701:         iimap[i] = st;
kpeter@701:         break;
kpeter@701:       case IN_HEAP:
kpeter@701:         break;
kpeter@701:       }
kpeter@701:     }
kpeter@701: 
kpeter@701:   private:
kpeter@701:     int find_min() {
kpeter@701:       int min_loc=-1, min_val;
kpeter@701:       int x=head;
kpeter@701:       if( x!=-1 ) {
kpeter@701:         min_val=container[x].prio;
kpeter@701:         min_loc=x;
kpeter@701:         x=container[x].right_neighbor;
kpeter@701: 
kpeter@701:         while( x!=-1 ) {
kpeter@701:           if( comp( container[x].prio,min_val ) ) {
kpeter@701:             min_val=container[x].prio;
kpeter@701:             min_loc=x;
kpeter@701:           }
kpeter@701:           x=container[x].right_neighbor;
kpeter@701:         }
kpeter@701:       }
kpeter@701:       return min_loc;
kpeter@701:     }
kpeter@701: 
kpeter@701:     void merge(int a) {
kpeter@701:       interleave(a);
kpeter@701: 
kpeter@701:       int x=head;
kpeter@701:       if( -1!=x ) {
kpeter@701:         int x_prev=-1, x_next=container[x].right_neighbor;
kpeter@701:         while( -1!=x_next ) {
kpeter@701:           if( container[x].degree!=container[x_next].degree || ( -1!=container[x_next].right_neighbor && container[container[x_next].right_neighbor].degree==container[x].degree ) ) {
kpeter@701:             x_prev=x;
kpeter@701:             x=x_next;
kpeter@701:           }
kpeter@701:           else {
kpeter@701:             if( comp(container[x].prio,container[x_next].prio) ) {
kpeter@701:               container[x].right_neighbor=container[x_next].right_neighbor;
kpeter@701:               fuse(x_next,x);
kpeter@701:             }
kpeter@701:             else {
kpeter@701:               if( -1==x_prev ) { head=x_next; }
kpeter@701:               else {
kpeter@701:                 container[x_prev].right_neighbor=x_next;
kpeter@701:               }
kpeter@701:               fuse(x,x_next);
kpeter@701:               x=x_next;
kpeter@701:             }
kpeter@701:           }
kpeter@701:           x_next=container[x].right_neighbor;
kpeter@701:         }
kpeter@701:       }
kpeter@701:     }
kpeter@701: 
kpeter@701:     void interleave(int a) {
kpeter@701:       int other=-1, head_other=-1;
kpeter@701: 
kpeter@701:       while( -1!=a || -1!=head ) {
kpeter@701:         if( -1==a ) {
kpeter@701:           if( -1==head_other ) {
kpeter@701:             head_other=head;
kpeter@701:           }
kpeter@701:           else {
kpeter@701:             container[other].right_neighbor=head;
kpeter@701:           }
kpeter@701:           head=-1;
kpeter@701:         }
kpeter@701:         else if( -1==head ) {
kpeter@701:           if( -1==head_other ) {
kpeter@701:             head_other=a;
kpeter@701:           }
kpeter@701:           else {
kpeter@701:             container[other].right_neighbor=a;
kpeter@701:           }
kpeter@701:           a=-1;
kpeter@701:         }
kpeter@701:         else {
kpeter@701:           if( container[a].degree<container[head].degree ) {
kpeter@701:             if( -1==head_other ) {
kpeter@701:               head_other=a;
kpeter@701:             }
kpeter@701:             else {
kpeter@701:               container[other].right_neighbor=a;
kpeter@701:             }
kpeter@701:             other=a;
kpeter@701:             a=container[a].right_neighbor;
kpeter@701:           }
kpeter@701:           else {
kpeter@701:             if( -1==head_other ) {
kpeter@701:               head_other=head;
kpeter@701:             }
kpeter@701:             else {
kpeter@701:               container[other].right_neighbor=head;
kpeter@701:             }
kpeter@701:             other=head;
kpeter@701:             head=container[head].right_neighbor;
kpeter@701:           }
kpeter@701:         }
kpeter@701:       }
kpeter@701:       head=head_other;
kpeter@701:     }
kpeter@701: 
kpeter@701:     // Lacing a under b
kpeter@701:     void fuse(int a, int b) {
kpeter@701:       container[a].parent=b;
kpeter@701:       container[a].right_neighbor=container[b].child;
kpeter@701:       container[b].child=a;
kpeter@701: 
kpeter@701:       ++container[b].degree;
kpeter@701:     }
kpeter@701: 
kpeter@701:     // It is invoked only if a has siblings.
kpeter@701:     void unlace(int a) {
kpeter@701:       int neighb=container[a].right_neighbor;
kpeter@701:       int other=head;
kpeter@701: 
kpeter@701:       while( container[other].right_neighbor!=a )
kpeter@701:         other=container[other].right_neighbor;
kpeter@701:       container[other].right_neighbor=neighb;
kpeter@701:     }
kpeter@701: 
kpeter@701:   private:
kpeter@701: 
kpeter@701:     class store {
kpeter@701:       friend class BinomHeap;
kpeter@701: 
kpeter@701:       Item name;
kpeter@701:       int parent;
kpeter@701:       int right_neighbor;
kpeter@701:       int child;
kpeter@701:       int degree;
kpeter@701:       bool in;
kpeter@701:       Prio prio;
kpeter@701: 
kpeter@701:       store() : parent(-1), right_neighbor(-1), child(-1), degree(0), in(true) {}
kpeter@701:     };
kpeter@701:   };
kpeter@701: 
kpeter@701: } //namespace lemon
kpeter@701: 
kpeter@701: #endif //LEMON_BINOM_HEAP_H
kpeter@701: