diff -r 98a30824fe36 -r ece80147fb08 lemon/pairing_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/pairing_heap.h	Fri Sep 25 09:06:32 2009 +0200
@@ -0,0 +1,474 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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_PAIRING_HEAP_H
+#define LEMON_PAIRING_HEAP_H
+
+///\file
+///\ingroup heaps
+///\brief Pairing heap implementation.
+
+#include <vector>
+#include <utility>
+#include <functional>
+#include <lemon/math.h>
+
+namespace lemon {
+
+  /// \ingroup heaps
+  ///
+  ///\brief Pairing Heap.
+  ///
+  /// This class implements the \e pairing \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 pairing 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 PairingHeap {
+  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;
+    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 PairingHeap(ItemIntMap &map)
+      : _min(0), _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.
+    PairingHeap(ItemIntMap &map, const Compare &comp)
+      : _min(0), _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;
+    }
+
+    /// \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;
+        _data.push_back(st);
+        i=s;
+      } else {
+        _data[i].parent=_data[i].child=-1;
+        _data[i].left_child=false;
+        _data[i].degree=0;
+        _data[i].in=true;
+      }
+
+      _data[i].prio=value;
+
+      if ( _num_items!=0 ) {
+        if ( _comp( value, _data[_min].prio) ) {
+          fuse(i,_min);
+          _min=i;
+        }
+        else fuse(_min,i);
+      }
+      else _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.
+    const 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() {
+      std::vector<int> trees;
+      int i=0, child_right = 0;
+      _data[_min].in=false;
+
+      if( -1!=_data[_min].child ) {
+        i=_data[_min].child;
+        trees.push_back(i);
+        _data[i].parent = -1;
+        _data[_min].child = -1;
+
+        int ch=-1;
+        while( _data[i].child!=-1 ) {
+          ch=_data[i].child;
+          if( _data[ch].left_child && i==_data[ch].parent ) {
+            break;
+          } else {
+            if( _data[ch].left_child ) {
+              child_right=_data[ch].parent;
+              _data[ch].parent = i;
+              --_data[i].degree;
+            }
+            else {
+              child_right=ch;
+              _data[i].child=-1;
+              _data[i].degree=0;
+            }
+            _data[child_right].parent = -1;
+            trees.push_back(child_right);
+            i = child_right;
+          }
+        }
+
+        int num_child = trees.size();
+        int other;
+        for( i=0; i<num_child-1; i+=2 ) {
+          if ( !_comp(_data[trees[i]].prio, _data[trees[i+1]].prio) ) {
+            other=trees[i];
+            trees[i]=trees[i+1];
+            trees[i+1]=other;
+          }
+          fuse( trees[i], trees[i+1] );
+        }
+
+        i = (0==(num_child % 2)) ? num_child-2 : num_child-1;
+        while(i>=2) {
+          if ( _comp(_data[trees[i]].prio, _data[trees[i-2]].prio) ) {
+            other=trees[i];
+            trees[i]=trees[i-2];
+            trees[i-2]=other;
+          }
+          fuse( trees[i-2], trees[i] );
+          i-=2;
+        }
+        _min = trees[0];
+      }
+      else {
+        _min = _data[_min].child;
+      }
+
+      if (_min >= 0) _data[_min].left_child = false;
+      --_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];
+      _data[i].prio=value;
+      int p=_data[i].parent;
+
+      if( _data[i].left_child && i!=_data[p].child ) {
+        p=_data[p].parent;
+      }
+
+      if ( p!=-1 && _comp(value,_data[p].prio) ) {
+        cut(i,p);
+        if ( _comp(_data[_min].prio,value) ) {
+          fuse(_min,i);
+        } else {
+          fuse(i,_min);
+          _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:
+
+    void cut(int a, int b) {
+      int child_a;
+      switch (_data[a].degree) {
+        case 2:
+          child_a = _data[_data[a].child].parent;
+          if( _data[a].left_child ) {
+            _data[child_a].left_child=true;
+            _data[b].child=child_a;
+            _data[child_a].parent=_data[a].parent;
+          }
+          else {
+            _data[child_a].left_child=false;
+            _data[child_a].parent=b;
+            if( a!=_data[b].child )
+              _data[_data[b].child].parent=child_a;
+            else
+              _data[b].child=child_a;
+          }
+          --_data[a].degree;
+          _data[_data[a].child].parent=a;
+          break;
+
+        case 1:
+          child_a = _data[a].child;
+          if( !_data[child_a].left_child ) {
+            --_data[a].degree;
+            if( _data[a].left_child ) {
+              _data[child_a].left_child=true;
+              _data[child_a].parent=_data[a].parent;
+              _data[b].child=child_a;
+            }
+            else {
+              _data[child_a].left_child=false;
+              _data[child_a].parent=b;
+              if( a!=_data[b].child )
+                _data[_data[b].child].parent=child_a;
+              else
+                _data[b].child=child_a;
+            }
+            _data[a].child=-1;
+          }
+          else {
+            --_data[b].degree;
+            if( _data[a].left_child ) {
+              _data[b].child =
+                (1==_data[b].degree) ? _data[a].parent : -1;
+            } else {
+              if (1==_data[b].degree)
+                _data[_data[b].child].parent=b;
+              else
+                _data[b].child=-1;
+            }
+          }
+          break;
+
+        case 0:
+          --_data[b].degree;
+          if( _data[a].left_child ) {
+            _data[b].child =
+              (0!=_data[b].degree) ? _data[a].parent : -1;
+          } else {
+            if( 0!=_data[b].degree )
+              _data[_data[b].child].parent=b;
+            else
+              _data[b].child=-1;
+          }
+          break;
+      }
+      _data[a].parent=-1;
+      _data[a].left_child=false;
+    }
+
+    void fuse(int a, int b) {
+      int child_a = _data[a].child;
+      int child_b = _data[b].child;
+      _data[a].child=b;
+      _data[b].parent=a;
+      _data[b].left_child=true;
+
+      if( -1!=child_a ) {
+        _data[b].child=child_a;
+        _data[child_a].parent=b;
+        _data[child_a].left_child=false;
+        ++_data[b].degree;
+
+        if( -1!=child_b ) {
+           _data[b].child=child_b;
+           _data[child_b].parent=child_a;
+        }
+      }
+      else { ++_data[a].degree; }
+    }
+
+    class store {
+      friend class PairingHeap;
+
+      Item name;
+      int parent;
+      int child;
+      bool left_child;
+      int degree;
+      bool in;
+      Prio prio;
+
+      store() : parent(-1), child(-1), left_child(false), degree(0), in(true) {}
+    };
+  };
+
+} //namespace lemon
+
+#endif //LEMON_PAIRING_HEAP_H
+