88     /// The constructor.  | 
    88     /// The constructor.  | 
    89     /// \param _iim should be given to the constructor, since it is used  | 
    89     /// \param _iim should be given to the constructor, since it is used  | 
    90     /// internally to handle the cross references. The value of the map  | 
    90     /// internally to handle the cross references. The value of the map  | 
    91     /// should be PRE_HEAP (-1) for each element.  | 
    91     /// should be PRE_HEAP (-1) for each element.  | 
    92     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {} | 
    92     explicit BinHeap(ItemIntMap &_iim) : iim(_iim) {} | 
    93       | 
    93   | 
    94     /// \brief The constructor.  | 
    94     /// \brief The constructor.  | 
    95     ///  | 
    95     ///  | 
    96     /// The constructor.  | 
    96     /// The constructor.  | 
    97     /// \param _iim should be given to the constructor, since it is used  | 
    97     /// \param _iim should be given to the constructor, since it is used  | 
    98     /// internally to handle the cross references. The value of the map  | 
    98     /// internally to handle the cross references. The value of the map  | 
    99     /// should be PRE_HEAP (-1) for each element.  | 
    99     /// should be PRE_HEAP (-1) for each element.  | 
   100     ///  | 
   100     ///  | 
   101     /// \param _comp The comparator function object.  | 
   101     /// \param _comp The comparator function object.  | 
   102     BinHeap(ItemIntMap &_iim, const Compare &_comp)   | 
   102     BinHeap(ItemIntMap &_iim, const Compare &_comp)  | 
   103       : iim(_iim), comp(_comp) {} | 
   103       : iim(_iim), comp(_comp) {} | 
   104   | 
   104   | 
   105   | 
   105   | 
   106     /// The number of items stored in the heap.  | 
   106     /// The number of items stored in the heap.  | 
   107     ///  | 
   107     ///  | 
   108     /// \brief Returns the number of items stored in the heap.  | 
   108     /// \brief Returns the number of items stored in the heap.  | 
   109     int size() const { return data.size(); } | 
   109     int size() const { return data.size(); } | 
   110       | 
   110   | 
   111     /// \brief Checks if the heap stores no items.  | 
   111     /// \brief Checks if the heap stores no items.  | 
   112     ///  | 
   112     ///  | 
   113     /// Returns \c true if and only if the heap stores no items.  | 
   113     /// Returns \c true if and only if the heap stores no items.  | 
   114     bool empty() const { return data.empty(); } | 
   114     bool empty() const { return data.empty(); } | 
   115   | 
   115   | 
   116     /// \brief Make empty this heap.  | 
   116     /// \brief Make empty this heap.  | 
   117     ///   | 
   117     ///  | 
   118     /// Make empty this heap. It does not change the cross reference map.  | 
   118     /// Make empty this heap. It does not change the cross reference map.  | 
   119     /// If you want to reuse what is not surely empty you should first clear  | 
   119     /// If you want to reuse what is not surely empty you should first clear  | 
   120     /// the heap and after that you should set the cross reference map for  | 
   120     /// the heap and after that you should set the cross reference map for  | 
   121     /// each item to \c PRE_HEAP.  | 
   121     /// each item to \c PRE_HEAP.  | 
   122     void clear() {  | 
   122     void clear() { | 
   123       data.clear();   | 
   123       data.clear();  | 
   124     }  | 
   124     }  | 
   125   | 
   125   | 
   126   private:  | 
   126   private:  | 
   127     static int parent(int i) { return (i-1)/2; } | 
   127     static int parent(int i) { return (i-1)/2; } | 
   128   | 
   128   | 
   132     }  | 
   132     }  | 
   133   | 
   133   | 
   134     int bubble_up(int hole, Pair p) { | 
   134     int bubble_up(int hole, Pair p) { | 
   135       int par = parent(hole);  | 
   135       int par = parent(hole);  | 
   136       while( hole>0 && less(p,data[par]) ) { | 
   136       while( hole>0 && less(p,data[par]) ) { | 
   137 	move(data[par],hole);  | 
   137         move(data[par],hole);  | 
   138 	hole = par;  | 
   138         hole = par;  | 
   139 	par = parent(hole);  | 
   139         par = parent(hole);  | 
   140       }  | 
   140       }  | 
   141       move(p, hole);  | 
   141       move(p, hole);  | 
   142       return hole;  | 
   142       return hole;  | 
   143     }  | 
   143     }  | 
   144   | 
   144   | 
   145     int bubble_down(int hole, Pair p, int length) { | 
   145     int bubble_down(int hole, Pair p, int length) { | 
   146       int child = second_child(hole);  | 
   146       int child = second_child(hole);  | 
   147       while(child < length) { | 
   147       while(child < length) { | 
   148 	if( less(data[child-1], data[child]) ) { | 
   148         if( less(data[child-1], data[child]) ) { | 
   149 	  --child;  | 
   149           --child;  | 
   150 	}  | 
   150         }  | 
   151 	if( !less(data[child], p) )  | 
   151         if( !less(data[child], p) )  | 
   152 	  goto ok;  | 
   152           goto ok;  | 
   153 	move(data[child], hole);  | 
   153         move(data[child], hole);  | 
   154 	hole = child;  | 
   154         hole = child;  | 
   155 	child = second_child(hole);  | 
   155         child = second_child(hole);  | 
   156       }  | 
   156       }  | 
   157       child--;  | 
   157       child--;  | 
   158       if( child<length && less(data[child], p) ) { | 
   158       if( child<length && less(data[child], p) ) { | 
   159 	move(data[child], hole);  | 
   159         move(data[child], hole);  | 
   160 	hole=child;  | 
   160         hole=child;  | 
   161       }  | 
   161       }  | 
   162     ok:  | 
   162     ok:  | 
   163       move(p, hole);  | 
   163       move(p, hole);  | 
   164       return hole;  | 
   164       return hole;  | 
   165     }  | 
   165     }  | 
   179       data.resize(n+1);  | 
   179       data.resize(n+1);  | 
   180       bubble_up(n, p);  | 
   180       bubble_up(n, p);  | 
   181     }  | 
   181     }  | 
   182   | 
   182   | 
   183     /// \brief Insert an item into the heap with the given heap.  | 
   183     /// \brief Insert an item into the heap with the given heap.  | 
   184     ///      | 
   184     ///  | 
   185     /// Adds \c i to the heap with priority \c p.   | 
   185     /// Adds \c i to the heap with priority \c p.  | 
   186     /// \param i The item to insert.  | 
   186     /// \param i The item to insert.  | 
   187     /// \param p The priority of the item.  | 
   187     /// \param p The priority of the item.  | 
   188     void push(const Item &i, const Prio &p) { push(Pair(i,p)); } | 
   188     void push(const Item &i, const Prio &p) { push(Pair(i,p)); } | 
   189   | 
   189   | 
   190     /// \brief Returns the item with minimum priority relative to \c Compare.  | 
   190     /// \brief Returns the item with minimum priority relative to \c Compare.  | 
   191     ///  | 
   191     ///  | 
   192     /// This method returns the item with minimum priority relative to \c  | 
   192     /// This method returns the item with minimum priority relative to \c  | 
   193     /// Compare.    | 
   193     /// Compare.  | 
   194     /// \pre The heap must be nonempty.    | 
   194     /// \pre The heap must be nonempty.  | 
   195     Item top() const { | 
   195     Item top() const { | 
   196       return data[0].first;  | 
   196       return data[0].first;  | 
   197     }  | 
   197     }  | 
   198   | 
   198   | 
   199     /// \brief Returns the minimum priority relative to \c Compare.  | 
   199     /// \brief Returns the minimum priority relative to \c Compare.  | 
   205     }  | 
   205     }  | 
   206   | 
   206   | 
   207     /// \brief Deletes the item with minimum priority relative to \c Compare.  | 
   207     /// \brief Deletes the item with minimum priority relative to \c Compare.  | 
   208     ///  | 
   208     ///  | 
   209     /// This method deletes the item with minimum priority relative to \c  | 
   209     /// This method deletes the item with minimum priority relative to \c  | 
   210     /// Compare from the heap.    | 
   210     /// Compare from the heap.  | 
   211     /// \pre The heap must be non-empty.    | 
   211     /// \pre The heap must be non-empty.  | 
   212     void pop() { | 
   212     void pop() { | 
   213       int n = data.size()-1;  | 
   213       int n = data.size()-1;  | 
   214       iim.set(data[0].first, POST_HEAP);  | 
   214       iim.set(data[0].first, POST_HEAP);  | 
   215       if (n > 0) { | 
   215       if (n > 0) { | 
   216 	bubble_down(0, data[n], n);  | 
   216         bubble_down(0, data[n], n);  | 
   217       }  | 
   217       }  | 
   218       data.pop_back();  | 
   218       data.pop_back();  | 
   219     }  | 
   219     }  | 
   220   | 
   220   | 
   221     /// \brief Deletes \c i from the heap.  | 
   221     /// \brief Deletes \c i from the heap.  | 
   226     void erase(const Item &i) { | 
   226     void erase(const Item &i) { | 
   227       int h = iim[i];  | 
   227       int h = iim[i];  | 
   228       int n = data.size()-1;  | 
   228       int n = data.size()-1;  | 
   229       iim.set(data[h].first, POST_HEAP);  | 
   229       iim.set(data[h].first, POST_HEAP);  | 
   230       if( h < n ) { | 
   230       if( h < n ) { | 
   231 	if ( bubble_up(h, data[n]) == h) { | 
   231         if ( bubble_up(h, data[n]) == h) { | 
   232 	  bubble_down(h, data[n], n);  | 
   232           bubble_down(h, data[n], n);  | 
   233 	}  | 
   233         }  | 
   234       }  | 
   234       }  | 
   235       data.pop_back();  | 
   235       data.pop_back();  | 
   236     }  | 
   236     }  | 
   237   | 
   237   | 
   238       | 
   238   | 
   239     /// \brief Returns the priority of \c i.  | 
   239     /// \brief Returns the priority of \c i.  | 
   240     ///  | 
   240     ///  | 
   241     /// This function returns the priority of item \c i.    | 
   241     /// This function returns the priority of item \c i.  | 
   242     /// \pre \c i must be in the heap.  | 
   242     /// \pre \c i must be in the heap.  | 
   243     /// \param i The item.  | 
   243     /// \param i The item.  | 
   244     Prio operator[](const Item &i) const { | 
   244     Prio operator[](const Item &i) const { | 
   245       int idx = iim[i];  | 
   245       int idx = iim[i];  | 
   246       return data[idx].second;  | 
   246       return data[idx].second;  | 
   247     }  | 
   247     }  | 
   248   | 
   248   | 
   249     /// \brief \c i gets to the heap with priority \c p independently   | 
   249     /// \brief \c i gets to the heap with priority \c p independently  | 
   250     /// if \c i was already there.  | 
   250     /// if \c i was already there.  | 
   251     ///  | 
   251     ///  | 
   252     /// This method calls \ref push(\c i, \c p) if \c i is not stored  | 
   252     /// This method calls \ref push(\c i, \c p) if \c i is not stored  | 
   253     /// in the heap and sets the priority of \c i to \c p otherwise.  | 
   253     /// in the heap and sets the priority of \c i to \c p otherwise.  | 
   254     /// \param i The item.  | 
   254     /// \param i The item.  | 
   255     /// \param p The priority.  | 
   255     /// \param p The priority.  | 
   256     void set(const Item &i, const Prio &p) { | 
   256     void set(const Item &i, const Prio &p) { | 
   257       int idx = iim[i];  | 
   257       int idx = iim[i];  | 
   258       if( idx < 0 ) { | 
   258       if( idx < 0 ) { | 
   259 	push(i,p);  | 
   259         push(i,p);  | 
   260       }  | 
   260       }  | 
   261       else if( comp(p, data[idx].second) ) { | 
   261       else if( comp(p, data[idx].second) ) { | 
   262 	bubble_up(idx, Pair(i,p));  | 
   262         bubble_up(idx, Pair(i,p));  | 
   263       }  | 
   263       }  | 
   264       else { | 
   264       else { | 
   265 	bubble_down(idx, Pair(i,p), data.size());  | 
   265         bubble_down(idx, Pair(i,p), data.size());  | 
   266       }  | 
   266       }  | 
   267     }  | 
   267     }  | 
   268   | 
   268   | 
   269     /// \brief Decreases the priority of \c i to \c p.  | 
   269     /// \brief Decreases the priority of \c i to \c p.  | 
   270     ///  | 
   270     ///  | 
   275     /// \param p The priority.  | 
   275     /// \param p The priority.  | 
   276     void decrease(const Item &i, const Prio &p) { | 
   276     void decrease(const Item &i, const Prio &p) { | 
   277       int idx = iim[i];  | 
   277       int idx = iim[i];  | 
   278       bubble_up(idx, Pair(i,p));  | 
   278       bubble_up(idx, Pair(i,p));  | 
   279     }  | 
   279     }  | 
   280       | 
   280   | 
   281     /// \brief Increases the priority of \c i to \c p.  | 
   281     /// \brief Increases the priority of \c i to \c p.  | 
   282     ///  | 
   282     ///  | 
   283     /// This method sets the priority of item \c i to \c p.   | 
   283     /// This method sets the priority of item \c i to \c p.  | 
   284     /// \pre \c i must be stored in the heap with priority at most \c  | 
   284     /// \pre \c i must be stored in the heap with priority at most \c  | 
   285     /// p relative to \c Compare.  | 
   285     /// p relative to \c Compare.  | 
   286     /// \param i The item.  | 
   286     /// \param i The item.  | 
   287     /// \param p The priority.  | 
   287     /// \param p The priority.  | 
   288     void increase(const Item &i, const Prio &p) { | 
   288     void increase(const Item &i, const Prio &p) { | 
   289       int idx = iim[i];  | 
   289       int idx = iim[i];  | 
   290       bubble_down(idx, Pair(i,p), data.size());  | 
   290       bubble_down(idx, Pair(i,p), data.size());  | 
   291     }  | 
   291     }  | 
   292   | 
   292   | 
   293     /// \brief Returns if \c item is in, has already been in, or has   | 
   293     /// \brief Returns if \c item is in, has already been in, or has  | 
   294     /// never been in the heap.  | 
   294     /// never been in the heap.  | 
   295     ///  | 
   295     ///  | 
   296     /// This method returns PRE_HEAP if \c item has never been in the  | 
   296     /// This method returns PRE_HEAP if \c item has never been in the  | 
   297     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP  | 
   297     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP  | 
   298     /// otherwise. In the latter case it is possible that \c item will  | 
   298     /// otherwise. In the latter case it is possible that \c item will  | 
   299     /// get back to the heap again.  | 
   299     /// get back to the heap again.  | 
   300     /// \param i The item.  | 
   300     /// \param i The item.  | 
   301     State state(const Item &i) const { | 
   301     State state(const Item &i) const { | 
   302       int s = iim[i];  | 
   302       int s = iim[i];  | 
   303       if( s>=0 )  | 
   303       if( s>=0 )  | 
   304 	s=0;  | 
   304         s=0;  | 
   305       return State(s);  | 
   305       return State(s);  | 
   306     }  | 
   306     }  | 
   307   | 
   307   | 
   308     /// \brief Sets the state of the \c item in the heap.  | 
   308     /// \brief Sets the state of the \c item in the heap.  | 
   309     ///  | 
   309     ///  | 
   310     /// Sets the state of the \c item in the heap. It can be used to  | 
   310     /// Sets the state of the \c item in the heap. It can be used to  | 
   311     /// manually clear the heap when it is important to achive the  | 
   311     /// manually clear the heap when it is important to achive the  | 
   312     /// better time complexity.  | 
   312     /// better time complexity.  | 
   313     /// \param i The item.  | 
   313     /// \param i The item.  | 
   314     /// \param st The state. It should not be \c IN_HEAP.   | 
   314     /// \param st The state. It should not be \c IN_HEAP.  | 
   315     void state(const Item& i, State st) { | 
   315     void state(const Item& i, State st) { | 
   316       switch (st) { | 
   316       switch (st) { | 
   317       case POST_HEAP:  | 
   317       case POST_HEAP:  | 
   318       case PRE_HEAP:  | 
   318       case PRE_HEAP:  | 
   319         if (state(i) == IN_HEAP) { | 
   319         if (state(i) == IN_HEAP) { |