diff -r f47b6c94577e -r 684964884a2e lemon/radix_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/radix_heap.h	Fri Sep 25 09:13:03 2009 +0200
@@ -0,0 +1,438 @@
+/* -*- 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_RADIX_HEAP_H
+#define LEMON_RADIX_HEAP_H
+
+///\ingroup heaps
+///\file
+///\brief Radix heap implementation.
+
+#include <vector>
+#include <lemon/error.h>
+
+namespace lemon {
+
+
+  /// \ingroup heaps
+  ///
+  /// \brief Radix heap data structure.
+  ///
+  /// This class implements the \e radix \e heap data structure.
+  /// It practically conforms to the \ref concepts::Heap "heap concept",
+  /// but it has some limitations due its special implementation.
+  /// The type of the priorities must be \c int and the priority of an
+  /// item cannot be decreased under the priority of the last removed item.
+  ///
+  /// \tparam IM A read-writable item map with \c int values, used
+  /// internally to handle the cross references.
+  template <typename IM>
+  class RadixHeap {
+
+  public:
+
+    /// Type of the item-int map.
+    typedef IM ItemIntMap;
+    /// Type of the priorities.
+    typedef int Prio;
+    /// Type of the items stored in the heap.
+    typedef typename ItemIntMap::Key Item;
+
+    /// \brief Exception thrown by RadixHeap.
+    ///
+    /// This exception is thrown when an item is inserted into a
+    /// RadixHeap with a priority smaller than the last erased one.
+    /// \see RadixHeap
+    class PriorityUnderflowError : public Exception {
+    public:
+      virtual const char* what() const throw() {
+        return "lemon::RadixHeap::PriorityUnderflowError";
+      }
+    };
+
+    /// \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:
+
+    struct RadixItem {
+      int prev, next, box;
+      Item item;
+      int prio;
+      RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
+    };
+
+    struct RadixBox {
+      int first;
+      int min, size;
+      RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
+    };
+
+    std::vector<RadixItem> _data;
+    std::vector<RadixBox> _boxes;
+
+    ItemIntMap &_iim;
+
+  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.
+    /// \param minimum The initial minimum value of the heap.
+    /// \param capacity The initial capacity of the heap.
+    RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)
+      : _iim(map)
+    {
+      _boxes.push_back(RadixBox(minimum, 1));
+      _boxes.push_back(RadixBox(minimum + 1, 1));
+      while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
+        extend();
+      }
+    }
+
+    /// \brief The number of items stored in the heap.
+    ///
+    /// This function returns the number of items stored in the heap.
+    int size() const { return _data.size(); }
+
+    /// \brief Check if the heap is empty.
+    ///
+    /// This function returns \c true if the heap is empty.
+    bool empty() const { return _data.empty(); }
+
+    /// \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.
+    /// \param minimum The minimum value of the heap.
+    /// \param capacity The capacity of the heap.
+    void clear(int minimum = 0, int capacity = 0) {
+      _data.clear(); _boxes.clear();
+      _boxes.push_back(RadixBox(minimum, 1));
+      _boxes.push_back(RadixBox(minimum + 1, 1));
+      while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
+        extend();
+      }
+    }
+
+  private:
+
+    bool upper(int box, Prio pr) {
+      return pr < _boxes[box].min;
+    }
+
+    bool lower(int box, Prio pr) {
+      return pr >= _boxes[box].min + _boxes[box].size;
+    }
+
+    // Remove item from the box list
+    void remove(int index) {
+      if (_data[index].prev >= 0) {
+        _data[_data[index].prev].next = _data[index].next;
+      } else {
+        _boxes[_data[index].box].first = _data[index].next;
+      }
+      if (_data[index].next >= 0) {
+        _data[_data[index].next].prev = _data[index].prev;
+      }
+    }
+
+    // Insert item into the box list
+    void insert(int box, int index) {
+      if (_boxes[box].first == -1) {
+        _boxes[box].first = index;
+        _data[index].next = _data[index].prev = -1;
+      } else {
+        _data[index].next = _boxes[box].first;
+        _data[_boxes[box].first].prev = index;
+        _data[index].prev = -1;
+        _boxes[box].first = index;
+      }
+      _data[index].box = box;
+    }
+
+    // Add a new box to the box list
+    void extend() {
+      int min = _boxes.back().min + _boxes.back().size;
+      int bs = 2 * _boxes.back().size;
+      _boxes.push_back(RadixBox(min, bs));
+    }
+
+    // Move an item up into the proper box.
+    void bubbleUp(int index) {
+      if (!lower(_data[index].box, _data[index].prio)) return;
+      remove(index);
+      int box = findUp(_data[index].box, _data[index].prio);
+      insert(box, index);
+    }
+
+    // Find up the proper box for the item with the given priority
+    int findUp(int start, int pr) {
+      while (lower(start, pr)) {
+        if (++start == int(_boxes.size())) {
+          extend();
+        }
+      }
+      return start;
+    }
+
+    // Move an item down into the proper box
+    void bubbleDown(int index) {
+      if (!upper(_data[index].box, _data[index].prio)) return;
+      remove(index);
+      int box = findDown(_data[index].box, _data[index].prio);
+      insert(box, index);
+    }
+
+    // Find down the proper box for the item with the given priority
+    int findDown(int start, int pr) {
+      while (upper(start, pr)) {
+        if (--start < 0) throw PriorityUnderflowError();
+      }
+      return start;
+    }
+
+    // Find the first non-empty box
+    int findFirst() {
+      int first = 0;
+      while (_boxes[first].first == -1) ++first;
+      return first;
+    }
+
+    // Gives back the minimum priority of the given box
+    int minValue(int box) {
+      int min = _data[_boxes[box].first].prio;
+      for (int k = _boxes[box].first; k != -1; k = _data[k].next) {
+        if (_data[k].prio < min) min = _data[k].prio;
+      }
+      return min;
+    }
+
+    // Rearrange the items of the heap and make the first box non-empty
+    void moveDown() {
+      int box = findFirst();
+      if (box == 0) return;
+      int min = minValue(box);
+      for (int i = 0; i <= box; ++i) {
+        _boxes[i].min = min;
+        min += _boxes[i].size;
+      }
+      int curr = _boxes[box].first, next;
+      while (curr != -1) {
+        next = _data[curr].next;
+        bubbleDown(curr);
+        curr = next;
+      }
+    }
+
+    void relocateLast(int index) {
+      if (index != int(_data.size()) - 1) {
+        _data[index] = _data.back();
+        if (_data[index].prev != -1) {
+          _data[_data[index].prev].next = index;
+        } else {
+          _boxes[_data[index].box].first = index;
+        }
+        if (_data[index].next != -1) {
+          _data[_data[index].next].prev = index;
+        }
+        _iim[_data[index].item] = index;
+      }
+      _data.pop_back();
+    }
+
+  public:
+
+    /// \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 i The item to insert.
+    /// \param p The priority of the item.
+    /// \pre \e i must not be stored in the heap.
+    /// \warning This method may throw an \c UnderFlowPriorityException.
+    void push(const Item &i, const Prio &p) {
+      int n = _data.size();
+      _iim.set(i, n);
+      _data.push_back(RadixItem(i, p));
+      while (lower(_boxes.size() - 1, p)) {
+        extend();
+      }
+      int box = findDown(_boxes.size() - 1, p);
+      insert(box, n);
+    }
+
+    /// \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 {
+      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
+      return _data[_boxes[0].first].item;
+    }
+
+    /// \brief The minimum priority.
+    ///
+    /// This function returns the minimum priority.
+    /// \pre The heap must be non-empty.
+    Prio prio() const {
+      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
+      return _data[_boxes[0].first].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() {
+      moveDown();
+      int index = _boxes[0].first;
+      _iim[_data[index].item] = POST_HEAP;
+      remove(index);
+      relocateLast(index);
+    }
+
+    /// \brief Remove the given item from the heap.
+    ///
+    /// This function removes the given item from the heap if it is
+    /// already stored.
+    /// \param i The item to delete.
+    /// \pre \e i must be in the heap.
+    void erase(const Item &i) {
+      int index = _iim[i];
+      _iim[i] = POST_HEAP;
+      remove(index);
+      relocateLast(index);
+   }
+
+    /// \brief The priority of the given item.
+    ///
+    /// This function returns the priority of the given item.
+    /// \param i The item.
+    /// \pre \e i must be in the heap.
+    Prio operator[](const Item &i) const {
+      int idx = _iim[i];
+      return _data[idx].prio;
+    }
+
+    /// \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 i The item.
+    /// \param p The priority.
+    /// \pre \e i must be in the heap.
+    /// \warning This method may throw an \c UnderFlowPriorityException.
+    void set(const Item &i, const Prio &p) {
+      int idx = _iim[i];
+      if( idx < 0 ) {
+        push(i, p);
+      }
+      else if( p >= _data[idx].prio ) {
+        _data[idx].prio = p;
+        bubbleUp(idx);
+      } else {
+        _data[idx].prio = p;
+        bubbleDown(idx);
+      }
+    }
+
+    /// \brief Decrease the priority of an item to the given value.
+    ///
+    /// This function decreases the priority of an item to the given value.
+    /// \param i The item.
+    /// \param p The priority.
+    /// \pre \e i must be stored in the heap with priority at least \e p.
+    /// \warning This method may throw an \c UnderFlowPriorityException.
+    void decrease(const Item &i, const Prio &p) {
+      int idx = _iim[i];
+      _data[idx].prio = p;
+      bubbleDown(idx);
+    }
+
+    /// \brief Increase the priority of an item to the given value.
+    ///
+    /// This function increases the priority of an item to the given value.
+    /// \param i The item.
+    /// \param p The priority.
+    /// \pre \e i must be stored in the heap with priority at most \e p.
+    void increase(const Item &i, const Prio &p) {
+      int idx = _iim[i];
+      _data[idx].prio = p;
+      bubbleUp(idx);
+    }
+
+    /// \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 i The item.
+    State state(const Item &i) const {
+      int s = _iim[i];
+      if( s >= 0 ) s = 0;
+      return State(s);
+    }
+
+    /// \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;
+      }
+    }
+
+  }; // class RadixHeap
+
+} // namespace lemon
+
+#endif // LEMON_RADIX_HEAP_H