diff --git a/lemon/pairing_heap.h b/lemon/pairing_heap.h
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+/* -*- 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_PAIRING_HEAP_H
+#define LEMON_PAIRING_HEAP_H
+
+///\file
+///\ingroup auxdat
+///\brief Pairing Heap implementation.
+
+#include <vector>
+#include <functional>
+#include <lemon/math.h>
+
+namespace lemon {
+
+  /// \ingroup auxdat
+  ///
+  ///\brief Pairing Heap.
+  ///
+  ///This class implements the \e Pairing \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 Pairing
+  ///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 PairingHeap {
+  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;
+    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 PairingHeap(ItemIntMap &_iimap)
+      : minimum(0), iimap(_iimap), num_items(0) {}
+
+    /// \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.
+    PairingHeap(ItemIntMap &_iimap, const Compare &_comp)
+      : minimum(0), iimap(_iimap), comp(_comp), num_items(0) {}
+
+    /// \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;
+    }
+
+    /// \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].child=-1;
+        container[i].left_child=false;
+        container[i].degree=0;
+        container[i].in=true;
+      }
+
+      container[i].prio=value;
+
+      if ( num_items!=0 ) {
+        if ( comp( value, container[minimum].prio) ) {
+          fuse(i,minimum);
+          minimum=i;
+        }
+        else fuse(minimum,i);
+      }
+      else minimum=i;
+
+      ++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() {
+      int TreeArray[num_items];
+      int i=0, num_child=0, child_right = 0;
+      container[minimum].in=false;
+
+      if( -1!=container[minimum].child ) {
+        i=container[minimum].child;
+        TreeArray[num_child] = i;
+        container[i].parent = -1;
+        container[minimum].child = -1;
+
+        ++num_child;
+        int ch=-1;
+        while( container[i].child!=-1 ) {
+          ch=container[i].child;
+          if( container[ch].left_child && i==container[ch].parent ) {
+            i=ch;
+            //break;
+          } else {
+            if( container[ch].left_child ) {
+              child_right=container[ch].parent;
+              container[ch].parent = i;
+              --container[i].degree;
+            }
+            else {
+              child_right=ch;
+              container[i].child=-1;
+              container[i].degree=0;
+            }
+            container[child_right].parent = -1;
+            TreeArray[num_child] = child_right;
+            i = child_right;
+            ++num_child;
+          }
+        }
+
+        int other;
+        for( i=0; i<num_child-1; i+=2 ) {
+          if ( !comp(container[TreeArray[i]].prio,
+                     container[TreeArray[i+1]].prio) ) {
+            other=TreeArray[i];
+            TreeArray[i]=TreeArray[i+1];
+            TreeArray[i+1]=other;
+          }
+          fuse( TreeArray[i], TreeArray[i+1] );
+        }
+
+        i = (0==(num_child % 2)) ? num_child-2 : num_child-1;
+        while(i>=2) {
+          if ( comp(container[TreeArray[i]].prio,
+                    container[TreeArray[i-2]].prio) ) {
+            other=TreeArray[i];
+            TreeArray[i]=TreeArray[i-2];
+            TreeArray[i-2]=other;
+          }
+          fuse( TreeArray[i-2], TreeArray[i] );
+          i-=2;
+        }
+        minimum = TreeArray[0];
+      }
+
+      if ( 0==num_child ) {
+        minimum = container[minimum].child;
+      }
+
+      --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 Pairing 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];
+      container[i].prio=value;
+      int p=container[i].parent;
+
+      if( container[i].left_child && i!=container[p].child ) {
+        p=container[p].parent;
+      }
+
+      if ( p!=-1 && comp(value,container[p].prio) ) {
+        cut(i,p);
+        if ( comp(container[minimum].prio,value) ) {
+          fuse(minimum,i);
+        } else {
+          fuse(i,minimum);
+          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:
+
+    void cut(int a, int b) {
+      int child_a;
+      switch (container[a].degree) {
+        case 2:
+          child_a = container[container[a].child].parent;
+          if( container[a].left_child ) {
+            container[child_a].left_child=true;
+            container[b].child=child_a;
+            container[child_a].parent=container[a].parent;
+          }
+          else {
+            container[child_a].left_child=false;
+            container[child_a].parent=b;
+            if( a!=container[b].child )
+              container[container[b].child].parent=child_a;
+            else
+              container[b].child=child_a;
+          }
+          --container[a].degree;
+          container[container[a].child].parent=a;
+          break;
+
+        case 1:
+          child_a = container[a].child;
+          if( !container[child_a].left_child ) {
+            --container[a].degree;
+            if( container[a].left_child ) {
+              container[child_a].left_child=true;
+              container[child_a].parent=container[a].parent;
+              container[b].child=child_a;
+            }
+            else {
+              container[child_a].left_child=false;
+              container[child_a].parent=b;
+              if( a!=container[b].child )
+                container[container[b].child].parent=child_a;
+              else
+                container[b].child=child_a;
+            }
+            container[a].child=-1;
+          }
+          else {
+            --container[b].degree;
+            if( container[a].left_child ) {
+              container[b].child =
+                (1==container[b].degree) ? container[a].parent : -1;
+            } else {
+              if (1==container[b].degree)
+                container[container[b].child].parent=b;
+              else
+                container[b].child=-1;
+            }
+          }
+          break;
+
+        case 0:
+          --container[b].degree;
+          if( container[a].left_child ) {
+            container[b].child =
+              (0!=container[b].degree) ? container[a].parent : -1;
+          } else {
+            if( 0!=container[b].degree )
+              container[container[b].child].parent=b;
+            else
+              container[b].child=-1;
+          }
+          break;
+      }
+      container[a].parent=-1;
+      container[a].left_child=false;
+    }
+
+    void fuse(int a, int b) {
+      int child_a = container[a].child;
+      int child_b = container[b].child;
+      container[a].child=b;
+      container[b].parent=a;
+      container[b].left_child=true;
+
+      if( -1!=child_a ) {
+        container[b].child=child_a;
+        container[child_a].parent=b;
+        container[child_a].left_child=false;
+        ++container[b].degree;
+
+        if( -1!=child_b ) {
+           container[b].child=child_b;
+           container[child_b].parent=child_a;
+        }
+      }
+      else { ++container[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
+