/* -*- C++ -*-

 * lemon/linear_heap.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2006 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_LINEAR_HEAP_H

#define LEMON_LINEAR_HEAP_H

///\ingroup auxdat

///\file

///\brief Binary Heap implementation.

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  /// \ingroup auxdat

  /// \brief A Linear Heap implementation.

  ///

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

  /// only integer priorities and it stores for each priority in the [0..C]

  /// 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 _Item Type of the items to be stored.  

  /// \param _ItemIntMap A read and writable Item int map, used internally

  /// to handle the cross references.

  /// \param minimize If the given parameter is true then the heap gives back

  /// the lowest priority. 

  template <typename _Item, typename _ItemIntMap, bool minimize = true >

  class LinearHeap {

  public:

    typedef _Item Item;

    typedef int Prio;

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

    typedef _ItemIntMap ItemIntMap;

    /// \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_enum {

      IN_HEAP = 0,

      PRE_HEAP = -1,

      POST_HEAP = -2

    };

  public:

    /// \brief The constructor.

    ///

    /// The constructor.

    /// \param _index 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 LinearHeap(ItemIntMap &_index) : index(_index), minimal(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.

    void clear() { 

      for (int i = 0; i < (int)data.size(); ++i) {

	index[data[i].item] = -2;

      }

      data.clear(); first.clear(); minimal = 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;

	}

	index[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();

      index[i] = idx;

      data.push_back(LinearItem(i, p));

      lace(idx);

      if (p < minimal) {

	minimal = 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[minimal] == -1) {

	++minimal;

      }

      return data[first[minimal]].item;

    }

    /// \brief Returns the minimum priority.

    ///

    /// It returns the minimum priority.

    /// \pre The heap must be nonempty.

    Prio prio() const {

      while (first[minimal] == -1) {

	++minimal;

      }

      return minimal;

    }

    /// \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[minimal] == -1) {

	++minimal;

      }

      int idx = first[minimal];

      index[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 = index[i];

      index[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 = index[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 = index[i];

      if (idx < 0) {

	push(i,p);

      } else if (p > data[idx].value) {

	increase(i, p);

      } else {

	decrease(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 = index[i];

      unlace(idx);

      data[idx].value = p;

      if (p < minimal) {

	minimal = 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 = index[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_enum state(const Item &i) const {

      int idx = index[i];

      if (idx >= 0) idx = 0;

      return state_enum(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_enum st) {

      switch (st) {

      case POST_HEAP:

      case PRE_HEAP:

        if (state(i) == IN_HEAP) {

          erase(i);

        }

        index[i] = st;

        break;

      case IN_HEAP:

        break;

      }

    }

  private:

    struct LinearItem {

      LinearItem(const Item& _item, int _value) 

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

      Item item;

      int value;

      int prev, next;

    };

    ItemIntMap& index;

    std::vector<int> first;

    std::vector<LinearItem> data;

    mutable int minimal;

  }; // class LinearHeap

  template <typename _Item, typename _ItemIntMap>

  class LinearHeap<_Item, _ItemIntMap, false> {

  public:

    typedef _Item Item;

    typedef int Prio;

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

    typedef _ItemIntMap ItemIntMap;

    enum state_enum {

      IN_HEAP = 0,

      PRE_HEAP = -1,

      POST_HEAP = -2

    };

  public:

    explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {}

    int size() const { return data.size(); }

    bool empty() const { return data.empty(); }

    void clear() { 

      for (int i = 0; i < (int)data.size(); ++i) {

	index[data[i].item] = -2;

      }

      data.clear(); first.clear(); maximal = -1; 

    }

  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;

	}

	index[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:

    void push(const Pair& p) {

      push(p.first, p.second);

    }

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

      int idx = data.size();

      index[i] = idx;

      data.push_back(LinearItem(i, p));

      lace(idx);

      if (data[idx].value > maximal) {

	maximal = data[idx].value;

      }

    }

    Item top() const {

      while (first[maximal] == -1) {

	--maximal;

      }

      return data[first[maximal]].item;

    }

    Prio prio() const {

      while (first[maximal] == -1) {

	--maximal;

      }

      return maximal;

    }

    void pop() {

      while (first[maximal] == -1) {

	--maximal;

      }

      int idx = first[maximal];

      index[data[idx].item] = -2;

      unlace(idx);

      relocate_last(idx);

    }

    void erase(const Item &i) {

      int idx = index[i];

      index[data[idx].item] = -2;

      unlace(idx);

      relocate_last(idx);

    }

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

      int idx = index[i];

      return data[idx].value;

    }

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

      int idx = index[i];

      if (idx < 0) {

	push(i,p);

      } else if (p > data[idx].value) {

	decrease(i, p);

      } else {

	increase(i, p);

      }

    }

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

      int idx = index[i];

      unlace(idx);

      data[idx].value = p;

      if (p > maximal) {

	maximal = p;

      }

      lace(idx);

    }

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

      int idx = index[i];

      unlace(idx);

      data[idx].value = p;

      lace(idx);

    }

    state_enum state(const Item &i) const {

      int idx = index[i];

      if (idx >= 0) idx = 0;

      return state_enum(idx);

    }

    void state(const Item& i, state_enum st) {

      switch (st) {

      case POST_HEAP:

      case PRE_HEAP:

        if (state(i) == IN_HEAP) {

          erase(i);

        }

        index[i] = st;

        break;

      case IN_HEAP:

        break;

      }

    }

  private:

    struct LinearItem {

      LinearItem(const Item& _item, int _value) 

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

      Item item;

      int value;

      int prev, next;

    };

    ItemIntMap& index;

    std::vector<int> first;

    std::vector<LinearItem> data;

    mutable int maximal;

  }; // class LinearHeap

}

#endif