diff -r e9c203fb003d -r 994c7df296c9 lemon/fib_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/fib_heap.h	Thu Dec 10 17:05:35 2009 +0100
@@ -0,0 +1,468 @@
+/* -*- 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_FIB_HEAP_H
+#define LEMON_FIB_HEAP_H
+
+///\file
+///\ingroup auxdat
+///\brief Fibonacci Heap implementation.
+
+#include <vector>
+#include <functional>
+#include <lemon/math.h>
+
+namespace lemon {
+
+  /// \ingroup auxdat
+  ///
+  ///\brief Fibonacci Heap.
+  ///
+  ///This class implements the \e Fibonacci \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 CMP 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 Fibonacci
+  ///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 IM A read and writable Item int map, used internally
+  ///to handle the cross references.
+  ///\param CMP A class for the ordering of the priorities. The
+  ///default is \c std::less<PRIO>.
+  ///
+  ///\sa BinHeap
+  ///\sa Dijkstra
+#ifdef DOXYGEN
+  template <typename PRIO, typename IM, typename CMP>
+#else
+  template <typename PRIO, typename IM, typename CMP = std::less<PRIO> >
+#endif
+  class FibHeap {
+  public:
+    ///\e
+    typedef IM ItemIntMap;
+    ///\e
+    typedef PRIO Prio;
+    ///\e
+    typedef typename ItemIntMap::Key Item;
+    ///\e
+    typedef std::pair<Item,Prio> Pair;
+    ///\e
+    typedef CMP Compare;
+
+  private:
+    class Store;
+
+    std::vector<Store> _data;
+    int _minimum;
+    ItemIntMap &_iim;
+    Compare _comp;
+    int _num;
+
+  public:
+
+    /// \brief Type to represent the items states.
+    ///
+    /// Each Item element have a state associated to it. It may 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.
+    };
+
+    /// \brief The constructor
+    ///
+    /// \c map should be given to the constructor, since it is
+    ///   used internally to handle the cross references.
+    explicit FibHeap(ItemIntMap &map)
+      : _minimum(0), _iim(map), _num() {}
+
+    /// \brief The constructor
+    ///
+    /// \c map 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.
+    FibHeap(ItemIntMap &map, const Compare &comp)
+      : _minimum(0), _iim(map), _comp(comp), _num() {}
+
+    /// \brief The number of items stored in the heap.
+    ///
+    /// Returns the number of items stored in the heap.
+    int size() const { return _num; }
+
+    /// \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==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() {
+      _data.clear(); _minimum = 0; _num = 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=_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 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=_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].degree=0;
+        _data[i].in=true;
+        _data[i].marked=false;
+      }
+
+      if ( _num ) {
+        _data[_data[_minimum].right_neighbor].left_neighbor=i;
+        _data[i].right_neighbor=_data[_minimum].right_neighbor;
+        _data[_minimum].right_neighbor=i;
+        _data[i].left_neighbor=_minimum;
+        if ( _comp( value, _data[_minimum].prio) ) _minimum=i;
+      } else {
+        _data[i].right_neighbor=_data[i].left_neighbor=i;
+        _minimum=i;
+      }
+      _data[i].prio=value;
+      ++_num;
+    }
+
+    /// \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 _data[_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 _data[_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 _data[_iim[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() {
+      /*The first case is that there are only one root.*/
+      if ( _data[_minimum].left_neighbor==_minimum ) {
+        _data[_minimum].in=false;
+        if ( _data[_minimum].degree!=0 ) {
+          makeroot(_data[_minimum].child);
+          _minimum=_data[_minimum].child;
+          balance();
+        }
+      } else {
+        int right=_data[_minimum].right_neighbor;
+        unlace(_minimum);
+        _data[_minimum].in=false;
+        if ( _data[_minimum].degree > 0 ) {
+          int left=_data[_minimum].left_neighbor;
+          int child=_data[_minimum].child;
+          int last_child=_data[child].left_neighbor;
+
+          makeroot(child);
+
+          _data[left].right_neighbor=child;
+          _data[child].left_neighbor=left;
+          _data[right].left_neighbor=last_child;
+          _data[last_child].right_neighbor=right;
+        }
+        _minimum=right;
+        balance();
+      } // the case where there are more roots
+      --_num;
+    }
+
+    /// \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 Fibonacci heaps.
+    void erase (const Item& item) {
+      int i=_iim[item];
+
+      if ( i >= 0 && _data[i].in ) {
+        if ( _data[i].parent!=-1 ) {
+          int p=_data[i].parent;
+          cut(i,p);
+          cascade(p);
+        }
+        _minimum=i;     //As if its prio would be -infinity
+        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=_iim[item];
+      _data[i].prio=value;
+      int p=_data[i].parent;
+
+      if ( p!=-1 && _comp(value, _data[p].prio) ) {
+        cut(i,p);
+        cascade(p);
+      }
+      if ( _comp(value, _data[_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=_iim[item];
+      if( i>=0 ) {
+        if ( _data[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);
+        }
+        _iim[i] = st;
+        break;
+      case IN_HEAP:
+        break;
+      }
+    }
+
+  private:
+
+    void balance() {
+
+      int maxdeg=int( std::floor( 2.08*log(double(_data.size()))))+1;
+
+      std::vector<int> A(maxdeg,-1);
+
+      /*
+       *Recall that now minimum does not point to the minimum prio element.
+       *We set minimum to this during balance().
+       */
+      int anchor=_data[_minimum].left_neighbor;
+      int next=_minimum;
+      bool end=false;
+
+      do {
+        int active=next;
+        if ( anchor==active ) end=true;
+        int d=_data[active].degree;
+        next=_data[active].right_neighbor;
+
+        while (A[d]!=-1) {
+          if( _comp(_data[active].prio, _data[A[d]].prio) ) {
+            fuse(active,A[d]);
+          } else {
+            fuse(A[d],active);
+            active=A[d];
+          }
+          A[d]=-1;
+          ++d;
+        }
+        A[d]=active;
+      } while ( !end );
+
+
+      while ( _data[_minimum].parent >=0 )
+        _minimum=_data[_minimum].parent;
+      int s=_minimum;
+      int m=_minimum;
+      do {
+        if ( _comp(_data[s].prio, _data[_minimum].prio) ) _minimum=s;
+        s=_data[s].right_neighbor;
+      } while ( s != m );
+    }
+
+    void makeroot(int c) {
+      int s=c;
+      do {
+        _data[s].parent=-1;
+        s=_data[s].right_neighbor;
+      } while ( s != c );
+    }
+
+    void cut(int a, int b) {
+      /*
+       *Replacing a from the children of b.
+       */
+      --_data[b].degree;
+
+      if ( _data[b].degree !=0 ) {
+        int child=_data[b].child;
+        if ( child==a )
+          _data[b].child=_data[child].right_neighbor;
+        unlace(a);
+      }
+
+
+      /*Lacing a to the roots.*/
+      int right=_data[_minimum].right_neighbor;
+      _data[_minimum].right_neighbor=a;
+      _data[a].left_neighbor=_minimum;
+      _data[a].right_neighbor=right;
+      _data[right].left_neighbor=a;
+
+      _data[a].parent=-1;
+      _data[a].marked=false;
+    }
+
+    void cascade(int a) {
+      if ( _data[a].parent!=-1 ) {
+        int p=_data[a].parent;
+
+        if ( _data[a].marked==false ) _data[a].marked=true;
+        else {
+          cut(a,p);
+          cascade(p);
+        }
+      }
+    }
+
+    void fuse(int a, int b) {
+      unlace(b);
+
+      /*Lacing b under a.*/
+      _data[b].parent=a;
+
+      if (_data[a].degree==0) {
+        _data[b].left_neighbor=b;
+        _data[b].right_neighbor=b;
+        _data[a].child=b;
+      } else {
+        int child=_data[a].child;
+        int last_child=_data[child].left_neighbor;
+        _data[child].left_neighbor=b;
+        _data[b].right_neighbor=child;
+        _data[last_child].right_neighbor=b;
+        _data[b].left_neighbor=last_child;
+      }
+
+      ++_data[a].degree;
+
+      _data[b].marked=false;
+    }
+
+    /*
+     *It is invoked only if a has siblings.
+     */
+    void unlace(int a) {
+      int leftn=_data[a].left_neighbor;
+      int rightn=_data[a].right_neighbor;
+      _data[leftn].right_neighbor=rightn;
+      _data[rightn].left_neighbor=leftn;
+    }
+
+
+    class Store {
+      friend class FibHeap;
+
+      Item name;
+      int parent;
+      int left_neighbor;
+      int right_neighbor;
+      int child;
+      int degree;
+      bool marked;
+      bool in;
+      Prio prio;
+
+      Store() : parent(-1), child(-1), degree(), marked(false), in(true) {}
+    };
+  };
+
+} //namespace lemon
+
+#endif //LEMON_FIB_HEAP_H
+