deba@1724: /* -*- C++ -*-
deba@1724:  * lemon/linear_heap.h - Part of LEMON, a generic C++ optimization library
deba@1724:  *
deba@1724:  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1724:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1724:  *
deba@1724:  * Permission to use, modify and distribute this software is granted
deba@1724:  * provided that this copyright notice appears in all copies. For
deba@1724:  * precise terms see the accompanying LICENSE file.
deba@1724:  *
deba@1724:  * This software is provided "AS IS" with no warranty of any kind,
deba@1724:  * express or implied, and with no claim as to its suitability for any
deba@1724:  * purpose.
deba@1724:  *
deba@1724:  */
deba@1724: 
deba@1724: #ifndef LEMON_LINEAR_HEAP_H
deba@1724: #define LEMON_LINEAR_HEAP_H
deba@1724: 
deba@1724: ///\ingroup auxdat
deba@1724: ///\file
deba@1724: ///\brief Binary Heap implementation.
deba@1724: 
deba@1724: #include <vector>
deba@1724: #include <utility>
deba@1724: #include <functional>
deba@1724: 
deba@1724: namespace lemon {
deba@1724: 
deba@1724:   /// \addtogroup auxdat
deba@1724:   /// @{
deba@1724: 
deba@1724:   /// \brief A Linear Heap implementation.
deba@1724:   ///
deba@1724:   /// This class implements the \e linear \e heap data structure. A \e heap
deba@1724:   /// is a data structure for storing items with specified values called \e
deba@1724:   /// priorities in such a way that finding the item with minimum priority is
deba@1724:   /// efficient. The linear heap is very simple implementation, it can store
deba@1724:   /// only integer priorities and it stores for each priority in the [0..C]
deba@1724:   /// range a list of items. So it should be used only when the priorities
deba@1724:   /// are small. It is not intended to use as dijkstra heap.
deba@1724:   ///
deba@1724:   /// \param _Item Type of the items to be stored.  
deba@1724:   /// \param _ItemIntMap A read and writable Item int map, used internally
deba@1724:   /// to handle the cross references.
deba@1724:   /// \param minimize If the given parameter is true then the heap gives back
deba@1724:   /// the lowest priority. 
deba@1724:   template <typename _Item, typename _ItemIntMap, bool minimize = true >
deba@1724:   class LinearHeap {
deba@1724: 
deba@1724:   public:
deba@1724:     typedef _Item Item;
deba@1724:     typedef int Prio;
deba@1724:     typedef std::pair<Item, Prio> Pair;
deba@1724:     typedef _ItemIntMap ItemIntMap;
deba@1724: 
deba@1724:     /// \brief Type to represent the items states.
deba@1724:     ///
deba@1724:     /// Each Item element have a state associated to it. It may be "in heap",
deba@1724:     /// "pre heap" or "post heap". The latter two are indifferent from the
deba@1724:     /// heap's point of view, but may be useful to the user.
deba@1724:     ///
deba@1724:     /// The ItemIntMap \e should be initialized in such way that it maps
deba@1724:     /// PRE_HEAP (-1) to any element to be put in the heap...
deba@1724:     enum state_enum {
deba@1724:       IN_HEAP = 0,
deba@1724:       PRE_HEAP = -1,
deba@1724:       POST_HEAP = -2
deba@1724:     };
deba@1724: 
deba@1724:   public:
deba@1724:     /// \brief The constructor.
deba@1724:     ///
deba@1724:     /// The constructor.
deba@1724:     /// \param _index should be given to the constructor, since it is used
deba@1724:     /// internally to handle the cross references. The value of the map
deba@1724:     /// should be PRE_HEAP (-1) for each element.
deba@1724:     explicit LinearHeap(ItemIntMap &_index) : index(_index), minimal(0) {}
deba@1724:     
deba@1724:     /// The number of items stored in the heap.
deba@1724:     ///
deba@1724:     /// \brief Returns the number of items stored in the heap.
deba@1724:     int size() const { return data.size(); }
deba@1724:     
deba@1724:     /// \brief Checks if the heap stores no items.
deba@1724:     ///
deba@1724:     /// Returns \c true if and only if the heap stores no items.
deba@1724:     bool empty() const { return data.empty(); }
deba@1724: 
deba@1724:     /// \brief Make empty this heap.
deba@1724:     /// 
deba@1724:     /// Make empty this heap.
deba@1724:     void clear() { 
deba@1724:       for (int i = 0; i < (int)data.size(); ++i) {
deba@1724: 	index[data[i].item] = -2;
deba@1724:       }
deba@1724:       data.clear(); first.clear(); minimal = 0;
deba@1724:     }
deba@1724: 
deba@1724:   private:
deba@1724: 
deba@1724:     void relocate_last(int idx) {
deba@1724:       if (idx + 1 < (int)data.size()) {
deba@1724: 	data[idx] = data.back();
deba@1724: 	if (data[idx].prev != -1) {
deba@1724: 	  data[data[idx].prev].next = idx;
deba@1724: 	} else {
deba@1724: 	  first[data[idx].value] = idx;
deba@1724: 	}
deba@1724: 	if (data[idx].next != -1) {
deba@1724: 	  data[data[idx].next].prev = idx;
deba@1724: 	}
deba@1724: 	index[data[idx].item] = idx;
deba@1724:       }
deba@1724:       data.pop_back();
deba@1724:     }
deba@1724: 
deba@1724:     void unlace(int idx) {
deba@1724:       if (data[idx].prev != -1) {
deba@1724: 	data[data[idx].prev].next = data[idx].next;
deba@1724:       } else {
deba@1724: 	first[data[idx].value] = data[idx].next;
deba@1724:       }
deba@1724:       if (data[idx].next != -1) {
deba@1724: 	data[data[idx].next].prev = data[idx].prev;
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     void lace(int idx) {
deba@1724:       if ((int)first.size() <= data[idx].value) {
deba@1724: 	first.resize(data[idx].value + 1, -1);
deba@1724:       }
deba@1724:       data[idx].next = first[data[idx].value];
deba@1724:       if (data[idx].next != -1) {
deba@1724: 	data[data[idx].next].prev = idx;
deba@1724:       }
deba@1724:       first[data[idx].value] = idx;
deba@1724:       data[idx].prev = -1;
deba@1724:     }
deba@1724: 
deba@1724:   public:
deba@1724:     /// \brief Insert a pair of item and priority into the heap.
deba@1724:     ///
deba@1724:     /// Adds \c p.first to the heap with priority \c p.second.
deba@1724:     /// \param p The pair to insert.
deba@1724:     void push(const Pair& p) {
deba@1724:       push(p.first, p.second);
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Insert an item into the heap with the given priority.
deba@1724:     ///    
deba@1724:     /// Adds \c i to the heap with priority \c p. 
deba@1724:     /// \param i The item to insert.
deba@1724:     /// \param p The priority of the item.
deba@1724:     void push(const Item &i, const Prio &p) { 
deba@1724:       int idx = data.size();
deba@1724:       index[i] = idx;
deba@1724:       data.push_back(LinearItem(i, p));
deba@1724:       lace(idx);
deba@1724:       if (p < minimal) {
deba@1724: 	minimal = p;
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Returns the item with minimum priority relative to \c Compare.
deba@1724:     ///
deba@1724:     /// This method returns the item with minimum priority relative to \c
deba@1724:     /// Compare.  
deba@1724:     /// \pre The heap must be nonempty.  
deba@1724:     Item top() const {
deba@1724:       while (first[minimal] == -1) {
deba@1724: 	++minimal;
deba@1724:       }
deba@1724:       return data[first[minimal]].item;
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Returns the minimum priority relative to \c Compare.
deba@1724:     ///
deba@1724:     /// It returns the minimum priority relative to \c Compare.
deba@1724:     /// \pre The heap must be nonempty.
deba@1724:     Prio prio() const {
deba@1724:       while (first[minimal] == -1) {
deba@1724: 	++minimal;
deba@1724:       }
deba@1724:       return minimal;
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Deletes the item with minimum priority relative to \c Compare.
deba@1724:     ///
deba@1724:     /// This method deletes the item with minimum priority relative to \c
deba@1724:     /// Compare from the heap.  
deba@1724:     /// \pre The heap must be non-empty.  
deba@1724:     void pop() {
deba@1724:       while (first[minimal] == -1) {
deba@1724: 	++minimal;
deba@1724:       }
deba@1724:       int idx = first[minimal];
deba@1724:       index[data[idx].item] = -2;
deba@1724:       unlace(idx);
deba@1724:       relocate_last(idx);
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Deletes \c i from the heap.
deba@1724:     ///
deba@1724:     /// This method deletes item \c i from the heap, if \c i was
deba@1724:     /// already stored in the heap.
deba@1724:     /// \param i The item to erase. 
deba@1724:     void erase(const Item &i) {
deba@1724:       int idx = index[i];
deba@1724:       index[data[idx].item] = -2;
deba@1724:       unlace(idx);
deba@1724:       relocate_last(idx);
deba@1724:     }
deba@1724: 
deba@1724:     
deba@1724:     /// \brief Returns the priority of \c i.
deba@1724:     ///
deba@1724:     /// This function returns the priority of item \c i.  
deba@1724:     /// \pre \c i must be in the heap.
deba@1724:     /// \param i The item.
deba@1724:     Prio operator[](const Item &i) const {
deba@1724:       int idx = index[i];
deba@1724:       return data[idx].value;
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief \c i gets to the heap with priority \c p independently 
deba@1724:     /// if \c i was already there.
deba@1724:     ///
deba@1724:     /// This method calls \ref push(\c i, \c p) if \c i is not stored
deba@1724:     /// in the heap and sets the priority of \c i to \c p otherwise.
deba@1724:     /// \param i The item.
deba@1724:     /// \param p The priority.
deba@1724:     void set(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       if (idx < 0) {
deba@1724: 	push(i,p);
deba@1724:       } else if (p > data[idx].value) {
deba@1724: 	increase(i, p);
deba@1724:       } else {
deba@1724: 	decrease(i, p);
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Decreases the priority of \c i to \c p.
deba@1724: 
deba@1724:     /// This method decreases the priority of item \c i to \c p.
deba@1724:     /// \pre \c i must be stored in the heap with priority at least \c
deba@1724:     /// p relative to \c Compare.
deba@1724:     /// \param i The item.
deba@1724:     /// \param p The priority.
deba@1724:     void decrease(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       unlace(idx);
deba@1724:       data[idx].value = p;
deba@1724:       if (p < minimal) {
deba@1724: 	minimal = p;
deba@1724:       }
deba@1724:       lace(idx);
deba@1724:     }
deba@1724:     
deba@1724:     /// \brief Increases the priority of \c i to \c p.
deba@1724:     ///
deba@1724:     /// This method sets the priority of item \c i to \c p. 
deba@1724:     /// \pre \c i must be stored in the heap with priority at most \c
deba@1724:     /// p relative to \c Compare.
deba@1724:     /// \param i The item.
deba@1724:     /// \param p The priority.
deba@1724:     void increase(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       unlace(idx);
deba@1724:       data[idx].value = p;
deba@1724:       lace(idx);
deba@1724:     }
deba@1724: 
deba@1724:     /// \brief Returns if \c item is in, has already been in, or has 
deba@1724:     /// never been in the heap.
deba@1724:     ///
deba@1724:     /// This method returns PRE_HEAP if \c item has never been in the
deba@1724:     /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
deba@1724:     /// otherwise. In the latter case it is possible that \c item will
deba@1724:     /// get back to the heap again.
deba@1724:     /// \param i The item.
deba@1724:     state_enum state(const Item &i) const {
deba@1724:       int idx = index[i];
deba@1724:       if (idx >= 0) idx = 0;
deba@1724:       return state_enum(idx);
deba@1724:     }
deba@1724: 
deba@1724:   private:
deba@1724: 
deba@1724:     struct LinearItem {
deba@1724:       LinearItem(const Item& _item, int _value) 
deba@1724: 	: item(_item), value(_value) {}
deba@1724: 
deba@1724:       Item item;
deba@1724:       int value;
deba@1724: 
deba@1724:       int prev, next;
deba@1724:     };
deba@1724: 
deba@1724:     ItemIntMap& index;
deba@1724:     std::vector<int> first;
deba@1724:     std::vector<LinearItem> data;
deba@1724:     mutable int minimal;
deba@1724: 
deba@1724:   }; // class LinearHeap
deba@1724: 
deba@1724: 
deba@1724:   template <typename _Item, typename _ItemIntMap>
deba@1724:   class LinearHeap<_Item, _ItemIntMap, false> {
deba@1724: 
deba@1724:   public:
deba@1724:     typedef _Item Item;
deba@1724:     typedef int Prio;
deba@1724:     typedef std::pair<Item, Prio> Pair;
deba@1724:     typedef _ItemIntMap ItemIntMap;
deba@1724: 
deba@1724:     enum state_enum {
deba@1724:       IN_HEAP = 0,
deba@1724:       PRE_HEAP = -1,
deba@1724:       POST_HEAP = -2
deba@1724:     };
deba@1724: 
deba@1724:   public:
deba@1724: 
deba@1724:     explicit LinearHeap(ItemIntMap &_index) : index(_index), maximal(-1) {}
deba@1724: 
deba@1724:     int size() const { return data.size(); }
deba@1724:     bool empty() const { return data.empty(); }
deba@1724: 
deba@1724:     void clear() { 
deba@1724:       for (int i = 0; i < (int)data.size(); ++i) {
deba@1724: 	index[data[i].item] = -2;
deba@1724:       }
deba@1724:       data.clear(); first.clear(); maximal = -1; 
deba@1724:     }
deba@1724: 
deba@1724:   private:
deba@1724: 
deba@1724:     void relocate_last(int idx) {
deba@1724:       if (idx + 1 != (int)data.size()) {
deba@1724: 	data[idx] = data.back();
deba@1724: 	if (data[idx].prev != -1) {
deba@1724: 	  data[data[idx].prev].next = idx;
deba@1724: 	} else {
deba@1724: 	  first[data[idx].value] = idx;
deba@1724: 	}
deba@1724: 	if (data[idx].next != -1) {
deba@1724: 	  data[data[idx].next].prev = idx;
deba@1724: 	}
deba@1724: 	index[data[idx].item] = idx;
deba@1724:       }
deba@1724:       data.pop_back();
deba@1724:     }
deba@1724: 
deba@1724:     void unlace(int idx) {
deba@1724:       if (data[idx].prev != -1) {
deba@1724: 	data[data[idx].prev].next = data[idx].next;
deba@1724:       } else {
deba@1724: 	first[data[idx].value] = data[idx].next;
deba@1724:       }
deba@1724:       if (data[idx].next != -1) {
deba@1724: 	data[data[idx].next].prev = data[idx].prev;
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     void lace(int idx) {
deba@1724:       if ((int)first.size() <= data[idx].value) {
deba@1724: 	first.resize(data[idx].value + 1, -1);
deba@1724:       }
deba@1724:       data[idx].next = first[data[idx].value];
deba@1724:       if (data[idx].next != -1) {
deba@1724: 	data[data[idx].next].prev = idx;
deba@1724:       }
deba@1724:       first[data[idx].value] = idx;
deba@1724:       data[idx].prev = -1;
deba@1724:     }
deba@1724: 
deba@1724:   public:
deba@1724: 
deba@1724:     void push(const Pair& p) {
deba@1724:       push(p.first, p.second);
deba@1724:     }
deba@1724: 
deba@1724:     void push(const Item &i, const Prio &p) { 
deba@1724:       int idx = data.size();
deba@1724:       index[i] = idx;
deba@1724:       data.push_back(LinearItem(i, p));
deba@1724:       lace(idx);
deba@1724:       if (data[idx].value > maximal) {
deba@1724: 	maximal = data[idx].value;
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     Item top() const {
deba@1724:       while (first[maximal] == -1) {
deba@1724: 	--maximal;
deba@1724:       }
deba@1724:       return data[first[maximal]].item;
deba@1724:     }
deba@1724: 
deba@1724:     Prio prio() const {
deba@1724:       while (first[maximal] == -1) {
deba@1724: 	--maximal;
deba@1724:       }
deba@1724:       return maximal;
deba@1724:     }
deba@1724: 
deba@1724:     void pop() {
deba@1724:       while (first[maximal] == -1) {
deba@1724: 	--maximal;
deba@1724:       }
deba@1724:       int idx = first[maximal];
deba@1724:       index[data[idx].item] = -2;
deba@1724:       unlace(idx);
deba@1724:       relocate_last(idx);
deba@1724:     }
deba@1724: 
deba@1724:     void erase(const Item &i) {
deba@1724:       int idx = index[i];
deba@1724:       index[data[idx].item] = -2;
deba@1724:       unlace(idx);
deba@1724:       relocate_last(idx);
deba@1724:     }
deba@1724: 
deba@1724:     Prio operator[](const Item &i) const {
deba@1724:       int idx = index[i];
deba@1724:       return data[idx].value;
deba@1724:     }
deba@1724: 
deba@1724:     void set(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       if (idx < 0) {
deba@1724: 	push(i,p);
deba@1724:       } else if (p > data[idx].value) {
deba@1724: 	decrease(i, p);
deba@1724:       } else {
deba@1724: 	increase(i, p);
deba@1724:       }
deba@1724:     }
deba@1724: 
deba@1724:     void decrease(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       unlace(idx);
deba@1724:       data[idx].value = p;
deba@1724:       if (p > maximal) {
deba@1724: 	maximal = p;
deba@1724:       }
deba@1724:       lace(idx);
deba@1724:     }
deba@1724:     
deba@1724:     void increase(const Item &i, const Prio &p) {
deba@1724:       int idx = index[i];
deba@1724:       unlace(idx);
deba@1724:       data[idx].value = p;
deba@1724:       lace(idx);
deba@1724:     }
deba@1724: 
deba@1724:     state_enum state(const Item &i) const {
deba@1724:       int idx = index[i];
deba@1724:       if (idx >= 0) idx = 0;
deba@1724:       return state_enum(idx);
deba@1724:     }
deba@1724: 
deba@1724:   private:
deba@1724: 
deba@1724:     struct LinearItem {
deba@1724:       LinearItem(const Item& _item, int _value) 
deba@1724: 	: item(_item), value(_value) {}
deba@1724: 
deba@1724:       Item item;
deba@1724:       int value;
deba@1724: 
deba@1724:       int prev, next;
deba@1724:     };
deba@1724: 
deba@1724:     ItemIntMap& index;
deba@1724:     std::vector<int> first;
deba@1724:     std::vector<LinearItem> data;
deba@1724:     mutable int maximal;
deba@1724: 
deba@1724:   }; // class LinearHeap
deba@1724: 
deba@1724: }
deba@1724:   
deba@1724: #endif