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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_KARY_HEAP_H
+#define LEMON_KARY_HEAP_H
+
+///\ingroup auxdat
+///\file
+///\brief Kary Heap implementation.
+
+#include <iostream>
+#include <vector>
+#include <utility>
+#include <functional>
+
+namespace lemon {
+
+  ///\ingroup auxdat
+  ///
+  ///\brief A Kary Heap implementation.
+  ///
+  ///This class implements the \e Kary \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.
+  ///
+  ///\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 FibHeap
+  ///\sa Dijkstra
+  ///\author Dorian Batha
+
+  template <typename _Prio, typename _ItemIntMap,
+            typename _Compare = std::less<_Prio> >
+
+  class KaryHeap {
+
+  public:
+    ///\e
+    typedef _ItemIntMap ItemIntMap;
+    ///\e
+    typedef _Prio Prio;
+    ///\e
+    typedef typename ItemIntMap::Key Item;
+    ///\e
+    typedef std::pair<Item,Prio> Pair;
+    ///\e
+    typedef _Compare Compare;
+    ///\e
+
+    /// \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:
+    std::vector<Pair> data;
+    Compare comp;
+    ItemIntMap &iim;
+    int K;
+
+  public:
+    /// \brief The constructor.
+    ///
+    /// The constructor.
+    /// \param _iim 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.
+    explicit KaryHeap(ItemIntMap &_iim, const int &_K=32) : iim(_iim), K(_K) {}
+
+    /// \brief The constructor.
+    ///
+    /// The constructor.
+    /// \param _iim 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 _comp The comparator function object.
+    KaryHeap(ItemIntMap &_iim, const Compare &_comp, const int &_K=32)
+      : iim(_iim), comp(_comp), K(_K) {}
+
+
+    /// 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 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(); }
+
+  private:
+    int parent(int i) { return (i-1)/K; }
+    int first_child(int i) { return K*i+1; }
+
+    bool less(const Pair &p1, const Pair &p2) const {
+      return comp(p1.second, p2.second);
+    }
+
+    int find_min(const int child, const int length) {
+      int min=child, i=1;
+      while( i<K && child+i<length ) {
+        if( less(data[child+i], data[min]) )
+          min=child+i;
+        ++i;
+      }
+      return min;
+    }
+
+    void bubble_up(int hole, Pair p) {
+      int par = parent(hole);
+      while( hole>0 && less(p,data[par]) ) {
+        move(data[par],hole);
+        hole = par;
+        par = parent(hole);
+      }
+      move(p, hole);
+    }
+
+    void bubble_down(int hole, Pair p, int length) {
+      if( length>1 ) {
+        int child = first_child(hole);
+        while( child<length ) {
+          child = find_min(child, length);
+          if( !less(data[child], p) )
+            goto ok;
+          move(data[child], hole);
+          hole = child;
+          child = first_child(hole);
+        }
+      }
+    ok:
+      move(p, hole);
+    }
+
+    void move(const Pair &p, int i) {
+      data[i] = p;
+      iim.set(p.first, i);
+    }
+
+  public:
+    /// \brief Insert a pair of item and priority into the heap.
+    ///
+    /// Adds \c p.first to the heap with priority \c p.second.
+    /// \param p The pair to insert.
+    void push(const Pair &p) {
+      int n = data.size();
+      data.resize(n+1);
+      bubble_up(n, p);
+    }
+
+    /// \brief Insert an item into the heap with the given heap.
+    ///
+    /// 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) { push(Pair(i,p)); }
+
+    /// \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[0].first; }
+
+    /// \brief Returns the minimum priority relative to \c Compare.
+    ///
+    /// It returns the minimum priority relative to \c Compare.
+    /// \pre The heap must be nonempty.
+    Prio prio() const { return data[0].second; }
+
+    /// \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 n = data.size()-1;
+      iim.set(data[0].first, POST_HEAP);
+      if (n>0) bubble_down(0, data[n], n);
+      data.pop_back();
+    }
+
+    /// \brief Deletes \c i from the heap.
+    ///
+    /// This method deletes item \c i from the heap.
+    /// \param i The item to erase.
+    /// \pre The item should be in the heap.
+    void erase(const Item &i) {
+      int h = iim[i];
+      int n = data.size()-1;
+      iim.set(data[h].first, POST_HEAP);
+      if( h<n ) {
+        if( less(data[parent(h)], data[n]) )
+          bubble_down(h, data[n], n);
+        else
+          bubble_up(h, data[n]);
+      }
+      data.pop_back();
+    }
+
+
+    /// \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].second;
+    }
+
+    /// \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.
+    /// \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( comp(p, data[idx].second) )
+        bubble_up(idx, Pair(i,p));
+      else
+        bubble_down(idx, Pair(i,p), data.size());
+    }
+
+    /// \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 relative to \c Compare.
+    /// \param i The item.
+    /// \param p The priority.
+    void decrease(const Item &i, const Prio &p) {
+      int idx = iim[i];
+      bubble_up(idx, Pair(i,p));
+    }
+
+    /// \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 relative to \c Compare.
+    /// \param i The item.
+    /// \param p The priority.
+    void increase(const Item &i, const Prio &p) {
+      int idx = iim[i];
+      bubble_down(idx, Pair(i,p), data.size());
+    }
+
+    /// \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;
+      }
+    }
+
+    /// \brief Replaces an item in the heap.
+    ///
+    /// The \c i item is replaced with \c j item. The \c i item should
+    /// be in the heap, while the \c j should be out of the heap. The
+    /// \c i item will out of the heap and \c j will be in the heap
+    /// with the same prioriority as prevoiusly the \c i item.
+    void replace(const Item& i, const Item& j) {
+      int idx=iim[i];
+      iim.set(i, iim[j]);
+      iim.set(j, idx);
+      data[idx].first=j;
+    }
+
+  }; // class KaryHeap
+
+} // namespace lemon
+
+#endif // LEMON_KARY_HEAP_H