/* -*- 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_BUCKET_HEAP_H

 #define LEMON_BUCKET_HEAP_H

 ///\ingroup heaps

 ///\file

 ///\brief Bucket heap implementation.

 #include <vector>

 #include <utility>

 #include <functional>

 namespace lemon {

   namespace _bucket_heap_bits {

     template <bool MIN>

     struct DirectionTraits {

       static bool less(int left, int right) {

         return left < right;

       }

       static void increase(int& value) {

         ++value;

       }

     };

     template <>

     struct DirectionTraits<false> {

       static bool less(int left, int right) {

         return left > right;

       }

       static void increase(int& value) {

         --value;

       }

     };

   }

   /// \ingroup heaps

   ///

   /// \brief Bucket heap data structure.

   ///

   /// This class implements the \e bucket \e heap data structure.

   /// It practically conforms to the \ref concepts::Heap "heap concept",

   /// but it has some limitations.

   ///

   /// The bucket heap is a very simple structure. It can store only

   /// \c int priorities and it maintains a list of items for each priority

   /// in the range <tt>[0..C)</tt>. So it should only be used when the

   /// priorities are small. It is not intended to use as a Dijkstra heap.

   ///

   /// \tparam IM A read-writable item map with \c int values, used

   /// internally to handle the cross references.

   /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.

   /// The default is \e min-heap. If this parameter is set to \c false,

   /// then the comparison is reversed, so the top(), prio() and pop()

   /// functions deal with the item having maximum priority instead of the

   /// minimum.

   ///

   /// \sa SimpleBucketHeap

   template <typename IM, bool MIN = true>

   class BucketHeap {

   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;

     /// Type of the item-priority pairs.

     typedef std::pair<Item,Prio> Pair;

   private:

     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;

   public:

     /// \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.

     };

   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.

     explicit BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {}

     /// \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.

     void clear() {

       _data.clear(); _first.clear(); _minimum = 0;

     }

   private:

     void relocateLast(int idx) {

       if (idx + 1 < int(_data.size())) {

         _data[idx] = _data.back();

         if (_data[idx].prev != -1) {

           _data[_data[idx].prev].next = idx;

         } else {

           _first[_data[idx].value] = idx;

         }

         if (_data[idx].next != -1) {

           _data[_data[idx].next].prev = idx;

         }

         _iim[_data[idx].item] = idx;

       }

       _data.pop_back();

     }

     void unlace(int idx) {

       if (_data[idx].prev != -1) {

         _data[_data[idx].prev].next = _data[idx].next;

       } else {

         _first[_data[idx].value] = _data[idx].next;

       }

       if (_data[idx].next != -1) {

         _data[_data[idx].next].prev = _data[idx].prev;

       }

     }

     void lace(int idx) {

       if (int(_first.size()) <= _data[idx].value) {

         _first.resize(_data[idx].value + 1, -1);

       }

       _data[idx].next = _first[_data[idx].value];

       if (_data[idx].next != -1) {

         _data[_data[idx].next].prev = idx;

       }

       _first[_data[idx].value] = idx;

       _data[idx].prev = -1;

     }

   public:

     /// \brief Insert a pair of item and priority into the heap.

     ///

     /// This function inserts \c p.first to the heap with priority

     /// \c p.second.

     /// \param p The pair to insert.

     /// \pre \c p.first must not be stored in the heap.

     void push(const Pair& p) {

       push(p.first, p.second);

     }

     /// \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.

     void push(const Item &i, const Prio &p) {

       int idx = _data.size();

       _iim[i] = idx;

       _data.push_back(BucketItem(i, p));

       lace(idx);

       if (Direction::less(p, _minimum)) {

         _minimum = p;

       }

     }

     /// \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 {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       return _data[_first[_minimum]].item;

     }

     /// \brief The minimum priority.

     ///

     /// This function returns the minimum priority.

     /// \pre The heap must be non-empty.

     Prio prio() const {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       return _minimum;

     }

     /// \brief Remove the item having minimum priority.

     ///

     /// This function removes the item having minimum priority.

     /// \pre The heap must be non-empty.

     void pop() {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       int idx = _first[_minimum];

       _iim[_data[idx].item] = -2;

       unlace(idx);

       relocateLast(idx);

     }

     /// \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 idx = _iim[i];

       _iim[_data[idx].item] = -2;

       unlace(idx);

       relocateLast(idx);

     }

     /// \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].value;

     }

     /// \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.

     void set(const Item &i, const Prio &p) {

       int idx = _iim[i];

       if (idx < 0) {

         push(i, p);

       } else if (Direction::less(p, _data[idx].value)) {

         decrease(i, p);

       } else {

         increase(i, p);

       }

     }

     /// \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.

     void decrease(const Item &i, const Prio &p) {

       int idx = _iim[i];

       unlace(idx);

       _data[idx].value = p;

       if (Direction::less(p, _minimum)) {

         _minimum = p;

       }

       lace(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];

       unlace(idx);

       _data[idx].value = p;

       lace(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 idx = _iim[i];

       if (idx >= 0) idx = 0;

       return State(idx);

     }

     /// \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;

       }

     }

   private:

     struct BucketItem {

       BucketItem(const Item& _item, int _value)

         : item(_item), value(_value) {}

       Item item;

       int value;

       int prev, next;

     };

     ItemIntMap& _iim;

     std::vector<int> _first;

     std::vector<BucketItem> _data;

     mutable int _minimum;

   }; // class BucketHeap

   /// \ingroup heaps

   ///

   /// \brief Simplified bucket heap data structure.

   ///

   /// This class implements a simplified \e bucket \e heap data

   /// structure. It does not provide some functionality, but it is

   /// faster and simpler than BucketHeap. The main difference is

   /// that BucketHeap stores a doubly-linked list for each key while

   /// this class stores only simply-linked lists. It supports erasing

   /// only for the item having minimum priority and it does not support

   /// key increasing and decreasing.

   ///

   /// Note that this implementation does not conform to the

   /// \ref concepts::Heap "heap concept" due to the lack of some 

   /// functionality.

   ///

   /// \tparam IM A read-writable item map with \c int values, used

   /// internally to handle the cross references.

   /// \tparam MIN Indicate if the heap is a \e min-heap or a \e max-heap.

   /// The default is \e min-heap. If this parameter is set to \c false,

   /// then the comparison is reversed, so the top(), prio() and pop()

   /// functions deal with the item having maximum priority instead of the

   /// minimum.

   ///

   /// \sa BucketHeap

   template <typename IM, bool MIN = true >

   class SimpleBucketHeap {

   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;

     /// Type of the item-priority pairs.

     typedef std::pair<Item,Prio> Pair;

   private:

     typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;

   public:

     /// \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.

     };

   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.

     explicit SimpleBucketHeap(ItemIntMap &map)

       : _iim(map), _free(-1), _num(0), _minimum(0) {}

     /// \brief The number of items stored in the heap.

     ///

     /// This function returns the number of items stored in the heap.

     int size() const { return _num; }

     /// \brief Check if the heap is empty.

     ///

     /// This function returns \c true if the heap is empty.

     bool empty() const { return _num == 0; }

     /// \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.

     void clear() {

       _data.clear(); _first.clear(); _free = -1; _num = 0; _minimum = 0;

     }

     /// \brief Insert a pair of item and priority into the heap.

     ///

     /// This function inserts \c p.first to the heap with priority

     /// \c p.second.

     /// \param p The pair to insert.

     /// \pre \c p.first must not be stored in the heap.

     void push(const Pair& p) {

       push(p.first, p.second);

     }

     /// \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.

     void push(const Item &i, const Prio &p) {

       int idx;

       if (_free == -1) {

         idx = _data.size();

         _data.push_back(BucketItem(i));

       } else {

         idx = _free;

         _free = _data[idx].next;

         _data[idx].item = i;

       }

       _iim[i] = idx;

       if (p >= int(_first.size())) _first.resize(p + 1, -1);

       _data[idx].next = _first[p];

       _first[p] = idx;

       if (Direction::less(p, _minimum)) {

         _minimum = p;

       }

       ++_num;

     }

     /// \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 {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       return _data[_first[_minimum]].item;

     }

     /// \brief The minimum priority.

     ///

     /// This function returns the minimum priority.

     /// \pre The heap must be non-empty.

     Prio prio() const {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       return _minimum;

     }

     /// \brief Remove the item having minimum priority.

     ///

     /// This function removes the item having minimum priority.

     /// \pre The heap must be non-empty.

     void pop() {

       while (_first[_minimum] == -1) {

         Direction::increase(_minimum);

       }

       int idx = _first[_minimum];

       _iim[_data[idx].item] = -2;

       _first[_minimum] = _data[idx].next;

       _data[idx].next = _free;

       _free = idx;

       --_num;

     }

     /// \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.

     /// \warning This operator is not a constant time function because

     /// it scans the whole data structure to find the proper value.

     Prio operator[](const Item &i) const {

       for (int k = 0; k < int(_first.size()); ++k) {

         int idx = _first[k];

         while (idx != -1) {

           if (_data[idx].item == i) {

             return k;

           }

           idx = _data[idx].next;

         }

       }

       return -1;

     }

     /// \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 idx = _iim[i];

       if (idx >= 0) idx = 0;

       return State(idx);

     }

   private:

     struct BucketItem {

       BucketItem(const Item& _item)

         : item(_item) {}

       Item item;

       int next;

     };

     ItemIntMap& _iim;

     std::vector<int> _first;

     std::vector<BucketItem> _data;

     int _free, _num;

     mutable int _minimum;

   }; // class SimpleBucketHeap

 }

 #endif