/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2007

  * 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 {

   /// \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 _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 _ItemIntMap, bool minimize = true >

   class BucketHeap {

   public:

     typedef typename _ItemIntMap::Key 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 BucketHeap(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. 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(); 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(BucketItem(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 BucketItem {

       BucketItem(const Item& _item, int _value) 

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

       Item item;

       int value;

       int prev, next;

     };

     ItemIntMap& index;

     std::vector<int> first;

     std::vector<BucketItem> data;

     mutable int minimal;

   }; // class BucketHeap

   template <typename _ItemIntMap>

   class BucketHeap<_ItemIntMap, false> {

   public:

     typedef typename _ItemIntMap::Key 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 BucketHeap(ItemIntMap &_index) : index(_index), maximal(-1) {}

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

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

     void clear() { 

       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(BucketItem(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 BucketItem {

       BucketItem(const Item& _item, int _value) 

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

       Item item;

       int value;

       int prev, next;

     };

     ItemIntMap& index;

     std::vector<int> first;

     std::vector<BucketItem> data;

     mutable int maximal;

   }; // 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 supports erasing each elements just the

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

   ///

   /// \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.

   ///

   /// \sa BucketHeap 

   template <typename _ItemIntMap, bool minimize = true >

   class SimpleBucketHeap {

   public:

     typedef typename _ItemIntMap::Key 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 SimpleBucketHeap(ItemIntMap &_index) 

       : index(_index), free(-1), num(0), minimal(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; minimal = 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;

       }

       index[i] = idx;

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

       data[idx].next = first[p];

       first[p] = idx;

       if (p < minimal) {

 	minimal = 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[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;

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

       int idx = index[i];

       if (idx >= 0) idx = 0;

       return state_enum(idx);

     }

   private:

     struct BucketItem {

       BucketItem(const Item& _item) 

 	: item(_item) {}

       Item item;

       int next;

     };

     ItemIntMap& index;

     std::vector<int> first;

     std::vector<BucketItem> data;

     int free, num;

     mutable int minimal;

   }; // class SimpleBucketHeap

   template <typename _ItemIntMap>

   class SimpleBucketHeap<_ItemIntMap, false> {

   public:

     typedef typename _ItemIntMap::Key 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 SimpleBucketHeap(ItemIntMap &_index) 

       : index(_index), free(-1), num(0), maximal(0) {}

     int size() const { return num; }

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

     void clear() { 

       data.clear(); first.clear(); free = -1; num = 0; maximal = 0;

     }

     void push(const Pair& p) {

       push(p.first, p.second);

     }

     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;

       }

       index[i] = idx;

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

       data[idx].next = first[p];

       first[p] = idx;

       if (p > maximal) {

 	maximal = p;

       }

       ++num;

     }

     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;

       first[maximal] = data[idx].next;

       data[idx].next = free;

       free = idx;

       --num;

     }

     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;

     }

     state_enum state(const Item &i) const {

       int idx = index[i];

       if (idx >= 0) idx = 0;

       return state_enum(idx);

     }

   private:

     struct BucketItem {

       BucketItem(const Item& _item) : item(_item) {}

       Item item;

       int next;

     };

     ItemIntMap& index;

     std::vector<int> first;

     std::vector<BucketItem> data;

     int free, num;

     mutable int maximal;

   };

 }

 #endif