/* -*- 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