diff -r e9c203fb003d -r 994c7df296c9 lemon/radix_heap.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/radix_heap.h	Thu Dec 10 17:05:35 2009 +0100
@@ -0,0 +1,433 @@
+/* -*- 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 auxdat
+///\file
+///\brief Radix Heap implementation.
+
+#include <vector>
+#include <lemon/error.h>
+
+namespace lemon {
+
+
+  /// \ingroup auxdata
+  ///
+  /// \brief A Radix Heap implementation.
+  ///
+  /// This class implements the \e radix \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. This heap type can store only items with \e int priority.
+  /// In a heap one can change the priority of an item, add or erase an
+  /// item, but the priority cannot be decreased under the last removed
+  /// item's priority.
+  ///
+  /// \param IM A read and writable Item int map, used internally
+  /// to handle the cross references.
+  ///
+  /// \see BinHeap
+  /// \see Dijkstra
+  template <typename IM>
+  class RadixHeap {
+
+  public:
+    typedef typename IM::Key Item;
+    typedef int Prio;
+    typedef IM ItemIntMap;
+
+    /// \brief Exception thrown by RadixHeap.
+    ///
+    /// This Exception is thrown when a smaller priority
+    /// is inserted into the \e RadixHeap then the last time erased.
+    /// \see RadixHeap
+
+    class UnderFlowPriorityError : public Exception {
+    public:
+      virtual const char* what() const throw() {
+        return "lemon::RadixHeap::UnderFlowPriorityError";
+      }
+    };
+
+    /// \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 ItemIntMap \e should be initialized in such way that it maps
+    /// PRE_HEAP (-1) to any element to be put in the heap...
+    enum State {
+      IN_HEAP = 0,
+      PRE_HEAP = -1,
+      POST_HEAP = -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 The constructor.
+    ///
+    /// The constructor.
+    ///
+    /// \param map It should be given to the constructor, since it is used
+    /// internally to handle the cross references. The value of the map
+    /// should be PRE_HEAP (-1) for each element.
+    ///
+    /// \param minimal The initial minimal value of the heap.
+    /// \param capacity It determines the initial capacity of the heap.
+    RadixHeap(ItemIntMap &map, int minimal = 0, int capacity = 0)
+      : _iim(map) {
+      boxes.push_back(RadixBox(minimal, 1));
+      boxes.push_back(RadixBox(minimal + 1, 1));
+      while (lower(boxes.size() - 1, capacity + minimal - 1)) {
+        extend();
+      }
+    }
+
+    /// The number of items stored in the heap.
+    ///
+    /// \brief Returns the number of items stored in the heap.
+    int size() const { return data.size(); }
+    /// \brief Checks if the heap stores no items.
+    ///
+    /// Returns \c true if and only if the heap stores no items.
+    bool empty() const { return data.empty(); }
+
+    /// \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(int minimal = 0, int capacity = 0) {
+      data.clear(); boxes.clear();
+      boxes.push_back(RadixBox(minimal, 1));
+      boxes.push_back(RadixBox(minimal + 1, 1));
+      while (lower(boxes.size() - 1, capacity + minimal - 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;
+    }
+
+    /// \brief 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;
+      }
+    }
+
+    /// \brief 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;
+    }
+
+    /// \brief 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));
+    }
+
+    /// \brief Move an item up into the proper box.
+    void bubble_up(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);
+    }
+
+    /// \brief Find up the proper box for the item with the given prio.
+    int findUp(int start, int pr) {
+      while (lower(start, pr)) {
+        if (++start == int(boxes.size())) {
+          extend();
+        }
+      }
+      return start;
+    }
+
+    /// \brief Move an item down into the proper box.
+    void bubble_down(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);
+    }
+
+    /// \brief Find up the proper box for the item with the given prio.
+    int findDown(int start, int pr) {
+      while (upper(start, pr)) {
+        if (--start < 0) throw UnderFlowPriorityError();
+      }
+      return start;
+    }
+
+    /// \brief Find the first not empty box.
+    int findFirst() {
+      int first = 0;
+      while (boxes[first].first == -1) ++first;
+      return first;
+    }
+
+    /// \brief Gives back the minimal prio of the 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;
+    }
+
+    /// \brief Rearrange the items of the heap and makes the
+    /// first box not 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;
+        bubble_down(curr);
+        curr = next;
+      }
+    }
+
+    void relocate_last(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.
+    ///
+    /// Adds \c i to the heap with priority \c p.
+    /// \param i The item to insert.
+    /// \param p The priority of the item.
+    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 Returns the item with minimum priority.
+    ///
+    /// This method returns the item with minimum priority.
+    /// \pre The heap must be nonempty.
+    Item top() const {
+      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
+      return data[boxes[0].first].item;
+    }
+
+    /// \brief Returns the minimum priority.
+    ///
+    /// It returns the minimum priority.
+    /// \pre The heap must be nonempty.
+    Prio prio() const {
+      const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
+      return data[boxes[0].first].prio;
+     }
+
+    /// \brief Deletes the item with minimum priority.
+    ///
+    /// This method deletes the item with 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);
+      relocate_last(index);
+    }
+
+    /// \brief Deletes \c i from the heap.
+    ///
+    /// This method deletes item \c i from the heap, if \c i was
+    /// already stored in the heap.
+    /// \param i The item to erase.
+    void erase(const Item &i) {
+      int index = _iim[i];
+      _iim[i] = POST_HEAP;
+      remove(index);
+      relocate_last(index);
+   }
+
+    /// \brief Returns the priority of \c i.
+    ///
+    /// This function returns the priority of item \c i.
+    /// \pre \c i must be in the heap.
+    /// \param i The item.
+    Prio operator[](const Item &i) const {
+      int idx = _iim[i];
+      return data[idx].prio;
+    }
+
+    /// \brief \c i gets to the heap with priority \c p independently
+    /// if \c i was already there.
+    ///
+    /// This method calls \ref push(\c i, \c p) if \c i is not stored
+    /// in the heap and sets the priority of \c i to \c p otherwise.
+    /// It may throw an \e UnderFlowPriorityException.
+    /// \param i The item.
+    /// \param p The priority.
+    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;
+        bubble_up(idx);
+      } else {
+        data[idx].prio = p;
+        bubble_down(idx);
+      }
+    }
+
+
+    /// \brief Decreases the priority of \c i to \c p.
+    ///
+    /// This method decreases the priority of item \c i to \c p.
+    /// \pre \c i must be stored in the heap with priority at least \c p, and
+    /// \c should be greater or equal to the last removed item's priority.
+    /// \param i The item.
+    /// \param p The priority.
+    void decrease(const Item &i, const Prio &p) {
+      int idx = _iim[i];
+      data[idx].prio = p;
+      bubble_down(idx);
+    }
+
+    /// \brief Increases the priority of \c i to \c p.
+    ///
+    /// This method sets the priority of item \c i to \c p.
+    /// \pre \c i must be stored in the heap with priority at most \c p
+    /// \param i The item.
+    /// \param p The priority.
+    void increase(const Item &i, const Prio &p) {
+      int idx = _iim[i];
+      data[idx].prio = p;
+      bubble_up(idx);
+    }
+
+    /// \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.
+    /// \param i The item.
+    State state(const Item &i) const {
+      int s = _iim[i];
+      if( s >= 0 ) s = 0;
+      return State(s);
+    }
+
+    /// \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;
+      }
+    }
+
+  }; // class RadixHeap
+
+} // namespace lemon
+
+#endif // LEMON_RADIX_HEAP_H