/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * 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