diff -r 70b199792735 -r ad40f7d32846 lemon/binomial_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/binomial_heap.h	Sun Aug 11 15:28:12 2013 +0200
@@ -0,0 +1,445 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2010
+ * 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_BINOMIAL_HEAP_H
+#define LEMON_BINOMIAL_HEAP_H
+
+///\file
+///\ingroup heaps
+///\brief Binomial Heap implementation.
+
+#include <vector>
+#include <utility>
+#include <functional>
+#include <lemon/math.h>
+#include <lemon/counter.h>
+
+namespace lemon {
+
+  /// \ingroup heaps
+  ///
+  ///\brief Binomial heap data structure.
+  ///
+  /// This class implements the \e binomial \e heap data structure.
+  /// It fully conforms to the \ref concepts::Heap "heap concept".
+  ///
+  /// The methods \ref increase() and \ref erase() are not efficient
+  /// in a binomial heap. In case of many calls of these operations,
+  /// it is better to use other heap structure, e.g. \ref BinHeap
+  /// "binary heap".
+  ///
+  /// \tparam PR Type of the priorities of the items.
+  /// \tparam IM A read-writable item map with \c int values, used
+  /// internally to handle the cross references.
+  /// \tparam CMP A functor class for comparing the priorities.
+  /// The default is \c std::less<PR>.
+#ifdef DOXYGEN
+  template <typename PR, typename IM, typename CMP>
+#else
+  template <typename PR, typename IM, typename CMP = std::less<PR> >
+#endif
+  class BinomialHeap {
+  public:
+    /// Type of the item-int map.
+    typedef IM ItemIntMap;
+    /// Type of the priorities.
+    typedef PR Prio;
+    /// Type of the items stored in the heap.
+    typedef typename ItemIntMap::Key Item;
+    /// Functor type for comparing the priorities.
+    typedef CMP Compare;
+
+    /// \brief Type to represent the states of the items.
+    ///
+    /// Each item has a state associated to it. It can be "in heap",
+    /// "pre-heap" or "post-heap". The latter two are indifferent from the
+    /// heap's point of view, but may be useful to the user.
+    ///
+    /// The item-int map must be initialized in such way that it assigns
+    /// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
+    enum State {
+      IN_HEAP = 0,    ///< = 0.
+      PRE_HEAP = -1,  ///< = -1.
+      POST_HEAP = -2  ///< = -2.
+    };
+
+  private:
+    class Store;
+
+    std::vector<Store> _data;
+    int _min, _head;
+    ItemIntMap &_iim;
+    Compare _comp;
+    int _num_items;
+
+  public:
+    /// \brief Constructor.
+    ///
+    /// Constructor.
+    /// \param map A map that assigns \c int values to the items.
+    /// It is used internally to handle the cross references.
+    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
+    explicit BinomialHeap(ItemIntMap &map)
+      : _min(0), _head(-1), _iim(map), _num_items(0) {}
+
+    /// \brief Constructor.
+    ///
+    /// Constructor.
+    /// \param map A map that assigns \c int values to the items.
+    /// It is used internally to handle the cross references.
+    /// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
+    /// \param comp The function object used for comparing the priorities.
+    BinomialHeap(ItemIntMap &map, const Compare &comp)
+      : _min(0), _head(-1), _iim(map), _comp(comp), _num_items(0) {}
+
+    /// \brief The number of items stored in the heap.
+    ///
+    /// This function returns the number of items stored in the heap.
+    int size() const { return _num_items; }
+
+    /// \brief Check if the heap is empty.
+    ///
+    /// This function returns \c true if the heap is empty.
+    bool empty() const { return _num_items==0; }
+
+    /// \brief Make the heap empty.
+    ///
+    /// This functon makes the heap empty.
+    /// It does not change the cross reference map. If you want to reuse
+    /// a heap that is not surely empty, you should first clear it and
+    /// then you should set the cross reference map to \c PRE_HEAP
+    /// for each item.
+    void clear() {
+      _data.clear(); _min=0; _num_items=0; _head=-1;
+    }
+
+    /// \brief Set the priority of an item or insert it, if it is
+    /// not stored in the heap.
+    ///
+    /// This method sets the priority of the given item if it is
+    /// already stored in the heap. Otherwise it inserts the given
+    /// item into the heap with the given priority.
+    /// \param item The item.
+    /// \param value The priority.
+    void set (const Item& item, const Prio& value) {
+      int i=_iim[item];
+      if ( i >= 0 && _data[i].in ) {
+        if ( _comp(value, _data[i].prio) ) decrease(item, value);
+        if ( _comp(_data[i].prio, value) ) increase(item, value);
+      } else push(item, value);
+    }
+
+    /// \brief Insert an item into the heap with the given priority.
+    ///
+    /// This function inserts the given item into the heap with the
+    /// given priority.
+    /// \param item The item to insert.
+    /// \param value The priority of the item.
+    /// \pre \e item must not be stored in the heap.
+    void push (const Item& item, const Prio& value) {
+      int i=_iim[item];
+      if ( i<0 ) {
+        int s=_data.size();
+        _iim.set( item,s );
+        Store st;
+        st.name=item;
+        st.prio=value;
+        _data.push_back(st);
+        i=s;
+      }
+      else {
+        _data[i].parent=_data[i].right_neighbor=_data[i].child=-1;
+        _data[i].degree=0;
+        _data[i].in=true;
+        _data[i].prio=value;
+      }
+
+      if( 0==_num_items ) {
+        _head=i;
+        _min=i;
+      } else {
+        merge(i);
+        if( _comp(_data[i].prio, _data[_min].prio) ) _min=i;
+      }
+      ++_num_items;
+    }
+
+    /// \brief Return the item having minimum priority.
+    ///
+    /// This function returns the item having minimum priority.
+    /// \pre The heap must be non-empty.
+    Item top() const { return _data[_min].name; }
+
+    /// \brief The minimum priority.
+    ///
+    /// This function returns the minimum priority.
+    /// \pre The heap must be non-empty.
+    Prio prio() const { return _data[_min].prio; }
+
+    /// \brief The priority of the given item.
+    ///
+    /// This function returns the priority of the given item.
+    /// \param item The item.
+    /// \pre \e item must be in the heap.
+    const Prio& operator[](const Item& item) const {
+      return _data[_iim[item]].prio;
+    }
+
+    /// \brief Remove the item having minimum priority.
+    ///
+    /// This function removes the item having minimum priority.
+    /// \pre The heap must be non-empty.
+    void pop() {
+      _data[_min].in=false;
+
+      int head_child=-1;
+      if ( _data[_min].child!=-1 ) {
+        int child=_data[_min].child;
+        int neighb;
+        while( child!=-1 ) {
+          neighb=_data[child].right_neighbor;
+          _data[child].parent=-1;
+          _data[child].right_neighbor=head_child;
+          head_child=child;
+          child=neighb;
+        }
+      }
+
+      if ( _data[_head].right_neighbor==-1 ) {
+        // there was only one root
+        _head=head_child;
+      }
+      else {
+        // there were more roots
+        if( _head!=_min )  { unlace(_min); }
+        else { _head=_data[_head].right_neighbor; }
+        merge(head_child);
+      }
+      _min=findMin();
+      --_num_items;
+    }
+
+    /// \brief Remove the given item from the heap.
+    ///
+    /// This function removes the given item from the heap if it is
+    /// already stored.
+    /// \param item The item to delete.
+    /// \pre \e item must be in the heap.
+    void erase (const Item& item) {
+      int i=_iim[item];
+      if ( i >= 0 && _data[i].in ) {
+        decrease( item, _data[_min].prio-1 );
+        pop();
+      }
+    }
+
+    /// \brief Decrease the priority of an item to the given value.
+    ///
+    /// This function decreases the priority of an item to the given value.
+    /// \param item The item.
+    /// \param value The priority.
+    /// \pre \e item must be stored in the heap with priority at least \e value.
+    void decrease (Item item, const Prio& value) {
+      int i=_iim[item];
+      int p=_data[i].parent;
+      _data[i].prio=value;
+
+      while( p!=-1 && _comp(value, _data[p].prio) ) {
+        _data[i].name=_data[p].name;
+        _data[i].prio=_data[p].prio;
+        _data[p].name=item;
+        _data[p].prio=value;
+        _iim[_data[i].name]=i;
+        i=p;
+        p=_data[p].parent;
+      }
+      _iim[item]=i;
+      if ( _comp(value, _data[_min].prio) ) _min=i;
+    }
+
+    /// \brief Increase the priority of an item to the given value.
+    ///
+    /// This function increases the priority of an item to the given value.
+    /// \param item The item.
+    /// \param value The priority.
+    /// \pre \e item must be stored in the heap with priority at most \e value.
+    void increase (Item item, const Prio& value) {
+      erase(item);
+      push(item, value);
+    }
+
+    /// \brief Return the state of an item.
+    ///
+    /// This method returns \c PRE_HEAP if the given item has never
+    /// been in the heap, \c IN_HEAP if it is in the heap at the moment,
+    /// and \c POST_HEAP otherwise.
+    /// In the latter case it is possible that the item will get back
+    /// to the heap again.
+    /// \param item The item.
+    State state(const Item &item) const {
+      int i=_iim[item];
+      if( i>=0 ) {
+        if ( _data[i].in ) i=0;
+        else i=-2;
+      }
+      return State(i);
+    }
+
+    /// \brief Set the state of an item in the heap.
+    ///
+    /// This function sets the state of the given item in the heap.
+    /// It can be used to manually clear the heap when it is important
+    /// to achive 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);
+        }
+        _iim[i] = st;
+        break;
+      case IN_HEAP:
+        break;
+      }
+    }
+
+  private:
+
+    // Find the minimum of the roots
+    int findMin() {
+      if( _head!=-1 ) {
+        int min_loc=_head, min_val=_data[_head].prio;
+        for( int x=_data[_head].right_neighbor; x!=-1;
+             x=_data[x].right_neighbor ) {
+          if( _comp( _data[x].prio,min_val ) ) {
+            min_val=_data[x].prio;
+            min_loc=x;
+          }
+        }
+        return min_loc;
+      }
+      else return -1;
+    }
+
+    // Merge the heap with another heap starting at the given position
+    void merge(int a) {
+      if( _head==-1 || a==-1 ) return;
+      if( _data[a].right_neighbor==-1 &&
+          _data[a].degree<=_data[_head].degree ) {
+        _data[a].right_neighbor=_head;
+        _head=a;
+      } else {
+        interleave(a);
+      }
+      if( _data[_head].right_neighbor==-1 ) return;
+
+      int x=_head;
+      int x_prev=-1, x_next=_data[x].right_neighbor;
+      while( x_next!=-1 ) {
+        if( _data[x].degree!=_data[x_next].degree ||
+            ( _data[x_next].right_neighbor!=-1 &&
+              _data[_data[x_next].right_neighbor].degree==_data[x].degree ) ) {
+          x_prev=x;
+          x=x_next;
+        }
+        else {
+          if( _comp(_data[x_next].prio,_data[x].prio) ) {
+            if( x_prev==-1 ) {
+              _head=x_next;
+            } else {
+              _data[x_prev].right_neighbor=x_next;
+            }
+            fuse(x,x_next);
+            x=x_next;
+          }
+          else {
+            _data[x].right_neighbor=_data[x_next].right_neighbor;
+            fuse(x_next,x);
+          }
+        }
+        x_next=_data[x].right_neighbor;
+      }
+    }
+
+    // Interleave the elements of the given list into the list of the roots
+    void interleave(int a) {
+      int p=_head, q=a;
+      int curr=_data.size();
+      _data.push_back(Store());
+
+      while( p!=-1 || q!=-1 ) {
+        if( q==-1 || ( p!=-1 && _data[p].degree<_data[q].degree ) ) {
+          _data[curr].right_neighbor=p;
+          curr=p;
+          p=_data[p].right_neighbor;
+        }
+        else {
+          _data[curr].right_neighbor=q;
+          curr=q;
+          q=_data[q].right_neighbor;
+        }
+      }
+
+      _head=_data.back().right_neighbor;
+      _data.pop_back();
+    }
+
+    // Lace node a under node b
+    void fuse(int a, int b) {
+      _data[a].parent=b;
+      _data[a].right_neighbor=_data[b].child;
+      _data[b].child=a;
+
+      ++_data[b].degree;
+    }
+
+    // Unlace node a (if it has siblings)
+    void unlace(int a) {
+      int neighb=_data[a].right_neighbor;
+      int other=_head;
+
+      while( _data[other].right_neighbor!=a )
+        other=_data[other].right_neighbor;
+      _data[other].right_neighbor=neighb;
+    }
+
+  private:
+
+    class Store {
+      friend class BinomialHeap;
+
+      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_BINOMIAL_HEAP_H
+