/* -*- 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 auxdat

///\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 auxdat

  ///

  /// \brief A Bucket Heap implementation.

  ///

  /// This class implements the \e bucket \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. The bucket heap is very simple implementation, it can store

  /// only integer priorities and it stores for each priority in the

  /// \f$ [0..C) \f$ range a list of items. So it should be used only when

  /// the priorities are small. It is not intended to use as dijkstra heap.

  ///

  /// \param IM A read and write Item int map, used internally

  /// to handle the cross references.

  /// \param MIN If the given parameter is false then instead of the

  /// minimum value the maximum can be retrivied with the top() and

  /// prio() member functions.

  template <typename IM, bool MIN = true>

  class BucketHeap {

  public:

    /// \e

    typedef typename IM::Key Item;

    /// \e

    typedef int Prio;

    /// \e

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

    /// \e

    typedef IM ItemIntMap;

  private:

    typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;

  public:

    /// \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 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 The constructor.

    ///

    /// The constructor.

    /// \param map 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 BucketHeap(ItemIntMap &map) : _iim(map), _minimum(0) {}

    /// 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() {

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

    }

  private:

    void relocate_last(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.

    ///

    /// Adds \c p.first to the heap with priority \c p.second.

    /// \param p The pair to insert.

    void push(const Pair& p) {

      push(p.first, p.second);

    }

    /// \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 idx = _data.size();

      _iim[i] = idx;

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

      lace(idx);

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

        _minimum = p;

      }

    }

    /// \brief Returns the item with minimum priority.

    ///

    /// This method returns the item with minimum priority.

    /// \pre The heap must be nonempty.

    Item top() const {

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

        Direction::increase(_minimum);

      }

      return _data[_first[_minimum]].item;

    }

    /// \brief Returns the minimum priority.

    ///

    /// It returns the minimum priority.

    /// \pre The heap must be nonempty.

    Prio prio() const {

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

        Direction::increase(_minimum);

      }

      return _minimum;

    }

    /// \brief Deletes the item with minimum priority.

    ///

    /// This method deletes the item with minimum priority from the heap.

    /// \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);

      relocate_last(idx);

    }

    /// \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 idx = _iim[i];

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

      unlace(idx);

      relocate_last(idx);

    }

    /// \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].value;

    }

    /// \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 (Direction::less(p, _data[idx].value)) {

        decrease(i, p);

      } else {

        increase(i, p);

      }

    }

    /// \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];

      unlace(idx);

      _data[idx].value = p;

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

        _minimum = p;

      }

      lace(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 relative to \c Compare.

    /// \param i The item.

    /// \param p The priority.

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

      int idx = _iim[i];

      unlace(idx);

      _data[idx].value = p;

      lace(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 idx = _iim[i];

      if (idx >= 0) idx = 0;

      return State(idx);

    }

    /// \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;

      }

    }

  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 auxdat

  ///

  /// \brief A Simplified Bucket Heap implementation.

  ///

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

  /// structure.  It does not provide some functionality but it faster

  /// and simplier data structure than the BucketHeap. The main

  /// difference is that the BucketHeap stores for every key a double

  /// linked list while this class stores just simple lists. In the

  /// other way it does not support erasing each elements just the

  /// minimal and it does not supports key increasing, decreasing.

  ///

  /// \param IM A read and write Item int map, used internally

  /// to handle the cross references.

  /// \param MIN If the given parameter is false then instead of the

  /// minimum value the maximum can be retrivied with the top() and

  /// prio() member functions.

  ///

  /// \sa BucketHeap

  template <typename IM, bool MIN = true >

  class SimpleBucketHeap {

  public:

    typedef typename IM::Key Item;

    typedef int Prio;

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

    typedef IM ItemIntMap;

  private:

    typedef _bucket_heap_bits::DirectionTraits<MIN> Direction;

  public:

    /// \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 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 The constructor.

    ///

    /// The constructor.

    /// \param map 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 SimpleBucketHeap(ItemIntMap &map)

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

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

    ///

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

    int size() const { return _num; }

    /// \brief Checks if the heap stores no items.

    ///

    /// Returns \c true if and only if the heap stores no items.

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

    /// \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() {

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

    }

    /// \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) {

      push(p.first, p.second);

    }

    /// \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 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 Returns the item with minimum priority.

    ///

    /// This method returns the item with minimum priority.

    /// \pre The heap must be nonempty.

    Item top() const {

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

        Direction::increase(_minimum);

      }

      return _data[_first[_minimum]].item;

    }

    /// \brief Returns the minimum priority.

    ///

    /// It returns the minimum priority.

    /// \pre The heap must be nonempty.

    Prio prio() const {

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

        Direction::increase(_minimum);

      }

      return _minimum;

    }

    /// \brief Deletes the item with minimum priority.

    ///

    /// This method deletes the item with minimum priority from the heap.

    /// \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 Returns the priority of \c i.

    ///

    /// This function returns the priority of item \c i.

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

    /// because it scans the whole data structure to find the proper

    /// value.

    /// \pre \c i must be in the heap.

    /// \param i The item.

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

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

        int idx = _first[k];

        while (idx != -1) {

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

            return k;

          }

          idx = _data[idx].next;

        }

      }

      return -1;

    }

    /// \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 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