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/* -*- mode: C++; indent-tabs-mode: nil; -*- |
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* |
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* This file is a part of LEMON, a generic C++ optimization library. |
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* |
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* Copyright (C) 2003-2009 |
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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* (Egervary Research Group on Combinatorial Optimization, EGRES). |
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* |
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* Permission to use, modify and distribute this software is granted |
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* provided that this copyright notice appears in all copies. For |
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* precise terms see the accompanying LICENSE file. |
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* |
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* This software is provided "AS IS" with no warranty of any kind, |
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* express or implied, and with no claim as to its suitability for any |
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* purpose. |
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* |
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*/ |
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#ifndef LEMON_BUCKET_HEAP_H |
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#define LEMON_BUCKET_HEAP_H |
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|
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///\ingroup auxdat |
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///\file |
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///\brief Bucket Heap implementation. |
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|
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#include <vector> |
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#include <utility> |
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#include <functional> |
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|
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namespace lemon { |
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|
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/// \ingroup auxdat |
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/// |
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/// \brief A Bucket Heap implementation. |
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/// |
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/// This class implements the \e bucket \e heap data structure. A \e heap |
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/// is a data structure for storing items with specified values called \e |
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/// priorities in such a way that finding the item with minimum priority is |
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/// efficient. The bucket heap is very simple implementation, it can store |
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/// only integer priorities and it stores for each priority in the |
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/// \f$ [0..C) \f$ range a list of items. So it should be used only when |
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/// the priorities are small. It is not intended to use as dijkstra heap. |
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/// |
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/// \param _ItemIntMap A read and writable Item int map, used internally |
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/// to handle the cross references. |
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/// \param minimize If the given parameter is true then the heap gives back |
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/// the lowest priority. |
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template <typename _ItemIntMap, bool minimize = true > |
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class BucketHeap { |
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|
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public: |
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/// \e |
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typedef typename _ItemIntMap::Key Item; |
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/// \e |
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typedef int Prio; |
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/// \e |
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typedef std::pair<Item, Prio> Pair; |
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/// \e |
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typedef _ItemIntMap ItemIntMap; |
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|
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/// \brief Type to represent the items states. |
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/// |
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/// Each Item element have a state associated to it. It may be "in heap", |
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/// "pre heap" or "post heap". The latter two are indifferent from the |
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/// heap's point of view, but may be useful to the user. |
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/// |
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/// The ItemIntMap \e should be initialized in such way that it maps |
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/// PRE_HEAP (-1) to any element to be put in the heap... |
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enum State { |
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IN_HEAP = 0, |
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PRE_HEAP = -1, |
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POST_HEAP = -2 |
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}; |
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|
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public: |
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/// \brief The constructor. |
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/// |
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/// The constructor. |
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/// \param _index should be given to the constructor, since it is used |
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/// internally to handle the cross references. The value of the map |
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/// should be PRE_HEAP (-1) for each element. |
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explicit BucketHeap(ItemIntMap &_index) : index(_index), minimal(0) {} |
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|
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/// The number of items stored in the heap. |
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/// |
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/// \brief Returns the number of items stored in the heap. |
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int size() const { return data.size(); } |
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|
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/// \brief Checks if the heap stores no items. |
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/// |
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/// Returns \c true if and only if the heap stores no items. |
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bool empty() const { return data.empty(); } |
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|
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/// \brief Make empty this heap. |
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/// |
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/// Make empty this heap. It does not change the cross reference |
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/// map. If you want to reuse a heap what is not surely empty you |
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/// should first clear the heap and after that you should set the |
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/// cross reference map for each item to \c PRE_HEAP. |
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void clear() { |
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data.clear(); first.clear(); minimal = 0; |
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} |
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private: |
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|
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void relocate_last(int idx) { |
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if (idx + 1 < int(data.size())) { |
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data[idx] = data.back(); |
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if (data[idx].prev != -1) { |
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data[data[idx].prev].next = idx; |
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} else { |
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first[data[idx].value] = idx; |
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} |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = idx; |
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} |
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index[data[idx].item] = idx; |
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} |
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data.pop_back(); |
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} |
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|
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void unlace(int idx) { |
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if (data[idx].prev != -1) { |
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data[data[idx].prev].next = data[idx].next; |
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} else { |
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first[data[idx].value] = data[idx].next; |
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} |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = data[idx].prev; |
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} |
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} |
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|
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void lace(int idx) { |
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if (int(first.size()) <= data[idx].value) { |
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first.resize(data[idx].value + 1, -1); |
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} |
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data[idx].next = first[data[idx].value]; |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = idx; |
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} |
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first[data[idx].value] = idx; |
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data[idx].prev = -1; |
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} |
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public: |
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/// \brief Insert a pair of item and priority into the heap. |
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/// |
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/// Adds \c p.first to the heap with priority \c p.second. |
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/// \param p The pair to insert. |
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void push(const Pair& p) { |
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push(p.first, p.second); |
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} |
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/// \brief Insert an item into the heap with the given priority. |
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/// |
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/// Adds \c i to the heap with priority \c p. |
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/// \param i The item to insert. |
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/// \param p The priority of the item. |
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void push(const Item &i, const Prio &p) { |
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int idx = data.size(); |
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index[i] = idx; |
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data.push_back(BucketItem(i, p)); |
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lace(idx); |
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if (p < minimal) { |
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minimal = p; |
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} |
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} |
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/// \brief Returns the item with minimum priority. |
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/// |
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/// This method returns the item with minimum priority. |
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/// \pre The heap must be nonempty. |
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Item top() const { |
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while (first[minimal] == -1) { |
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++minimal; |
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} |
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return data[first[minimal]].item; |
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} |
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|
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/// \brief Returns the minimum priority. |
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/// |
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/// It returns the minimum priority. |
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/// \pre The heap must be nonempty. |
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Prio prio() const { |
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while (first[minimal] == -1) { |
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++minimal; |
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} |
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return minimal; |
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} |
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|
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/// \brief Deletes the item with minimum priority. |
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/// |
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/// This method deletes the item with minimum priority from the heap. |
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/// \pre The heap must be non-empty. |
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void pop() { |
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while (first[minimal] == -1) { |
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++minimal; |
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} |
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int idx = first[minimal]; |
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index[data[idx].item] = -2; |
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unlace(idx); |
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relocate_last(idx); |
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} |
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/// \brief Deletes \c i from the heap. |
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/// |
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/// This method deletes item \c i from the heap, if \c i was |
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/// already stored in the heap. |
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/// \param i The item to erase. |
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void erase(const Item &i) { |
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int idx = index[i]; |
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index[data[idx].item] = -2; |
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unlace(idx); |
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relocate_last(idx); |
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} |
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/// \brief Returns the priority of \c i. |
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/// |
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/// This function returns the priority of item \c i. |
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/// \pre \c i must be in the heap. |
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/// \param i The item. |
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Prio operator[](const Item &i) const { |
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int idx = index[i]; |
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return data[idx].value; |
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} |
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/// \brief \c i gets to the heap with priority \c p independently |
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/// if \c i was already there. |
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/// |
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/// This method calls \ref push(\c i, \c p) if \c i is not stored |
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/// in the heap and sets the priority of \c i to \c p otherwise. |
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/// \param i The item. |
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/// \param p The priority. |
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void set(const Item &i, const Prio &p) { |
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int idx = index[i]; |
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if (idx < 0) { |
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push(i,p); |
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} else if (p > data[idx].value) { |
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increase(i, p); |
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} else { |
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decrease(i, p); |
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} |
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} |
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|
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/// \brief Decreases the priority of \c i to \c p. |
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/// |
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/// This method decreases the priority of item \c i to \c p. |
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/// \pre \c i must be stored in the heap with priority at least \c |
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/// p relative to \c Compare. |
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/// \param i The item. |
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/// \param p The priority. |
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void decrease(const Item &i, const Prio &p) { |
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int idx = index[i]; |
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unlace(idx); |
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data[idx].value = p; |
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if (p < minimal) { |
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minimal = p; |
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} |
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lace(idx); |
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} |
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|
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/// \brief Increases the priority of \c i to \c p. |
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/// |
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/// This method sets the priority of item \c i to \c p. |
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/// \pre \c i must be stored in the heap with priority at most \c |
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/// p relative to \c Compare. |
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/// \param i The item. |
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/// \param p The priority. |
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void increase(const Item &i, const Prio &p) { |
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int idx = index[i]; |
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unlace(idx); |
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data[idx].value = p; |
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lace(idx); |
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} |
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|
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/// \brief Returns if \c item is in, has already been in, or has |
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/// never been in the heap. |
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/// |
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/// This method returns PRE_HEAP if \c item has never been in the |
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/// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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/// otherwise. In the latter case it is possible that \c item will |
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/// get back to the heap again. |
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/// \param i The item. |
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State state(const Item &i) const { |
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int idx = index[i]; |
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if (idx >= 0) idx = 0; |
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return State(idx); |
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} |
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|
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/// \brief Sets the state of the \c item in the heap. |
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/// |
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/// Sets the state of the \c item in the heap. It can be used to |
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/// manually clear the heap when it is important to achive the |
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/// better time complexity. |
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/// \param i The item. |
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/// \param st The state. It should not be \c IN_HEAP. |
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void state(const Item& i, State st) { |
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switch (st) { |
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case POST_HEAP: |
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case PRE_HEAP: |
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if (state(i) == IN_HEAP) { |
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erase(i); |
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} |
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index[i] = st; |
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break; |
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case IN_HEAP: |
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break; |
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} |
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} |
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private: |
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|
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struct BucketItem { |
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BucketItem(const Item& _item, int _value) |
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: item(_item), value(_value) {} |
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|
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Item item; |
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int value; |
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|
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int prev, next; |
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}; |
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|
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ItemIntMap& index; |
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std::vector<int> first; |
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std::vector<BucketItem> data; |
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mutable int minimal; |
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|
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}; // class BucketHeap |
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|
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|
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template <typename _ItemIntMap> |
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class BucketHeap<_ItemIntMap, false> { |
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|
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public: |
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typedef typename _ItemIntMap::Key Item; |
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typedef int Prio; |
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typedef std::pair<Item, Prio> Pair; |
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typedef _ItemIntMap ItemIntMap; |
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|
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enum State { |
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IN_HEAP = 0, |
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PRE_HEAP = -1, |
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POST_HEAP = -2 |
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}; |
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|
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public: |
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|
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explicit BucketHeap(ItemIntMap &_index) : index(_index), maximal(-1) {} |
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|
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int size() const { return data.size(); } |
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bool empty() const { return data.empty(); } |
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|
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void clear() { |
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data.clear(); first.clear(); maximal = -1; |
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} |
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|
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private: |
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|
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void relocate_last(int idx) { |
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if (idx + 1 != int(data.size())) { |
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data[idx] = data.back(); |
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if (data[idx].prev != -1) { |
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data[data[idx].prev].next = idx; |
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} else { |
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first[data[idx].value] = idx; |
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} |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = idx; |
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} |
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index[data[idx].item] = idx; |
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} |
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data.pop_back(); |
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} |
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|
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void unlace(int idx) { |
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if (data[idx].prev != -1) { |
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data[data[idx].prev].next = data[idx].next; |
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} else { |
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first[data[idx].value] = data[idx].next; |
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} |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = data[idx].prev; |
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} |
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} |
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386 |
|
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void lace(int idx) { |
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if (int(first.size()) <= data[idx].value) { |
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first.resize(data[idx].value + 1, -1); |
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} |
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data[idx].next = first[data[idx].value]; |
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if (data[idx].next != -1) { |
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data[data[idx].next].prev = idx; |
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} |
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first[data[idx].value] = idx; |
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data[idx].prev = -1; |
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} |
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398 |
|
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public: |
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400 |
|
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401 |
void push(const Pair& p) { |
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push(p.first, p.second); |
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} |
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404 |
|
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void push(const Item &i, const Prio &p) { |
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int idx = data.size(); |
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index[i] = idx; |
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data.push_back(BucketItem(i, p)); |
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lace(idx); |
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410 |
if (data[idx].value > maximal) { |
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maximal = data[idx].value; |
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} |
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413 |
} |
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414 |
|
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Item top() const { |
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416 |
while (first[maximal] == -1) { |
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417 |
--maximal; |
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} |
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419 |
return data[first[maximal]].item; |
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420 |
} |
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421 |
|
|
422 |
Prio prio() const { |
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423 |
while (first[maximal] == -1) { |
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--maximal; |
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} |
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426 |
return maximal; |
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427 |
} |
|
428 |
|
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429 |
void pop() { |
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430 |
while (first[maximal] == -1) { |
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431 |
--maximal; |
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} |
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433 |
int idx = first[maximal]; |
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434 |
index[data[idx].item] = -2; |
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435 |
unlace(idx); |
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436 |
relocate_last(idx); |
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437 |
} |
|
438 |
|
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439 |
void erase(const Item &i) { |
|
440 |
int idx = index[i]; |
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441 |
index[data[idx].item] = -2; |
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unlace(idx); |
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relocate_last(idx); |
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} |
|
445 |
|
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Prio operator[](const Item &i) const { |
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447 |
int idx = index[i]; |
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return data[idx].value; |
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} |
|
450 |
|
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void set(const Item &i, const Prio &p) { |
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452 |
int idx = index[i]; |
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453 |
if (idx < 0) { |
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push(i,p); |
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455 |
} else if (p > data[idx].value) { |
|
456 |
decrease(i, p); |
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457 |
} else { |
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458 |
increase(i, p); |
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459 |
} |
|
460 |
} |
|
461 |
|
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462 |
void decrease(const Item &i, const Prio &p) { |
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463 |
int idx = index[i]; |
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464 |
unlace(idx); |
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465 |
data[idx].value = p; |
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466 |
if (p > maximal) { |
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467 |
maximal = p; |
|
468 |
} |
|
469 |
lace(idx); |
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470 |
} |
|
471 |
|
|
472 |
void increase(const Item &i, const Prio &p) { |
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473 |
int idx = index[i]; |
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474 |
unlace(idx); |
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475 |
data[idx].value = p; |
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476 |
lace(idx); |
|
477 |
} |
|
478 |
|
|
479 |
State state(const Item &i) const { |
|
480 |
int idx = index[i]; |
|
481 |
if (idx >= 0) idx = 0; |
|
482 |
return State(idx); |
|
483 |
} |
|
484 |
|
|
485 |
void state(const Item& i, State st) { |
|
486 |
switch (st) { |
|
487 |
case POST_HEAP: |
|
488 |
case PRE_HEAP: |
|
489 |
if (state(i) == IN_HEAP) { |
|
490 |
erase(i); |
|
491 |
} |
|
492 |
index[i] = st; |
|
493 |
break; |
|
494 |
case IN_HEAP: |
|
495 |
break; |
|
496 |
} |
|
497 |
} |
|
498 |
|
|
499 |
private: |
|
500 |
|
|
501 |
struct BucketItem { |
|
502 |
BucketItem(const Item& _item, int _value) |
|
503 |
: item(_item), value(_value) {} |
|
504 |
|
|
505 |
Item item; |
|
506 |
int value; |
|
507 |
|
|
508 |
int prev, next; |
|
509 |
}; |
|
510 |
|
|
511 |
ItemIntMap& index; |
|
512 |
std::vector<int> first; |
|
513 |
std::vector<BucketItem> data; |
|
514 |
mutable int maximal; |
|
515 |
|
|
516 |
}; // class BucketHeap |
|
517 |
|
|
518 |
/// \ingroup auxdat |
|
519 |
/// |
|
520 |
/// \brief A Simplified Bucket Heap implementation. |
|
521 |
/// |
|
522 |
/// This class implements a simplified \e bucket \e heap data |
|
523 |
/// structure. It does not provide some functionality but it faster |
|
524 |
/// and simplier data structure than the BucketHeap. The main |
|
525 |
/// difference is that the BucketHeap stores for every key a double |
|
526 |
/// linked list while this class stores just simple lists. In the |
|
527 |
/// other way it does not supports erasing each elements just the |
|
528 |
/// minimal and it does not supports key increasing, decreasing. |
|
529 |
/// |
|
530 |
/// \param _ItemIntMap A read and writable Item int map, used internally |
|
531 |
/// to handle the cross references. |
|
532 |
/// \param minimize If the given parameter is true then the heap gives back |
|
533 |
/// the lowest priority. |
|
534 |
/// |
|
535 |
/// \sa BucketHeap |
|
536 |
template <typename _ItemIntMap, bool minimize = true > |
|
537 |
class SimpleBucketHeap { |
|
538 |
|
|
539 |
public: |
|
540 |
typedef typename _ItemIntMap::Key Item; |
|
541 |
typedef int Prio; |
|
542 |
typedef std::pair<Item, Prio> Pair; |
|
543 |
typedef _ItemIntMap ItemIntMap; |
|
544 |
|
|
545 |
/// \brief Type to represent the items states. |
|
546 |
/// |
|
547 |
/// Each Item element have a state associated to it. It may be "in heap", |
|
548 |
/// "pre heap" or "post heap". The latter two are indifferent from the |
|
549 |
/// heap's point of view, but may be useful to the user. |
|
550 |
/// |
|
551 |
/// The ItemIntMap \e should be initialized in such way that it maps |
|
552 |
/// PRE_HEAP (-1) to any element to be put in the heap... |
|
553 |
enum State { |
|
554 |
IN_HEAP = 0, |
|
555 |
PRE_HEAP = -1, |
|
556 |
POST_HEAP = -2 |
|
557 |
}; |
|
558 |
|
|
559 |
public: |
|
560 |
|
|
561 |
/// \brief The constructor. |
|
562 |
/// |
|
563 |
/// The constructor. |
|
564 |
/// \param _index should be given to the constructor, since it is used |
|
565 |
/// internally to handle the cross references. The value of the map |
|
566 |
/// should be PRE_HEAP (-1) for each element. |
|
567 |
explicit SimpleBucketHeap(ItemIntMap &_index) |
|
568 |
: index(_index), free(-1), num(0), minimal(0) {} |
|
569 |
|
|
570 |
/// \brief Returns the number of items stored in the heap. |
|
571 |
/// |
|
572 |
/// The number of items stored in the heap. |
|
573 |
int size() const { return num; } |
|
574 |
|
|
575 |
/// \brief Checks if the heap stores no items. |
|
576 |
/// |
|
577 |
/// Returns \c true if and only if the heap stores no items. |
|
578 |
bool empty() const { return num == 0; } |
|
579 |
|
|
580 |
/// \brief Make empty this heap. |
|
581 |
/// |
|
582 |
/// Make empty this heap. It does not change the cross reference |
|
583 |
/// map. If you want to reuse a heap what is not surely empty you |
|
584 |
/// should first clear the heap and after that you should set the |
|
585 |
/// cross reference map for each item to \c PRE_HEAP. |
|
586 |
void clear() { |
|
587 |
data.clear(); first.clear(); free = -1; num = 0; minimal = 0; |
|
588 |
} |
|
589 |
|
|
590 |
/// \brief Insert a pair of item and priority into the heap. |
|
591 |
/// |
|
592 |
/// Adds \c p.first to the heap with priority \c p.second. |
|
593 |
/// \param p The pair to insert. |
|
594 |
void push(const Pair& p) { |
|
595 |
push(p.first, p.second); |
|
596 |
} |
|
597 |
|
|
598 |
/// \brief Insert an item into the heap with the given priority. |
|
599 |
/// |
|
600 |
/// Adds \c i to the heap with priority \c p. |
|
601 |
/// \param i The item to insert. |
|
602 |
/// \param p The priority of the item. |
|
603 |
void push(const Item &i, const Prio &p) { |
|
604 |
int idx; |
|
605 |
if (free == -1) { |
|
606 |
idx = data.size(); |
|
607 |
data.push_back(BucketItem(i)); |
|
608 |
} else { |
|
609 |
idx = free; |
|
610 |
free = data[idx].next; |
|
611 |
data[idx].item = i; |
|
612 |
} |
|
613 |
index[i] = idx; |
|
614 |
if (p >= int(first.size())) first.resize(p + 1, -1); |
|
615 |
data[idx].next = first[p]; |
|
616 |
first[p] = idx; |
|
617 |
if (p < minimal) { |
|
618 |
minimal = p; |
|
619 |
} |
|
620 |
++num; |
|
621 |
} |
|
622 |
|
|
623 |
/// \brief Returns the item with minimum priority. |
|
624 |
/// |
|
625 |
/// This method returns the item with minimum priority. |
|
626 |
/// \pre The heap must be nonempty. |
|
627 |
Item top() const { |
|
628 |
while (first[minimal] == -1) { |
|
629 |
++minimal; |
|
630 |
} |
|
631 |
return data[first[minimal]].item; |
|
632 |
} |
|
633 |
|
|
634 |
/// \brief Returns the minimum priority. |
|
635 |
/// |
|
636 |
/// It returns the minimum priority. |
|
637 |
/// \pre The heap must be nonempty. |
|
638 |
Prio prio() const { |
|
639 |
while (first[minimal] == -1) { |
|
640 |
++minimal; |
|
641 |
} |
|
642 |
return minimal; |
|
643 |
} |
|
644 |
|
|
645 |
/// \brief Deletes the item with minimum priority. |
|
646 |
/// |
|
647 |
/// This method deletes the item with minimum priority from the heap. |
|
648 |
/// \pre The heap must be non-empty. |
|
649 |
void pop() { |
|
650 |
while (first[minimal] == -1) { |
|
651 |
++minimal; |
|
652 |
} |
|
653 |
int idx = first[minimal]; |
|
654 |
index[data[idx].item] = -2; |
|
655 |
first[minimal] = data[idx].next; |
|
656 |
data[idx].next = free; |
|
657 |
free = idx; |
|
658 |
--num; |
|
659 |
} |
|
660 |
|
|
661 |
/// \brief Returns the priority of \c i. |
|
662 |
/// |
|
663 |
/// This function returns the priority of item \c i. |
|
664 |
/// \warning This operator is not a constant time function |
|
665 |
/// because it scans the whole data structure to find the proper |
|
666 |
/// value. |
|
667 |
/// \pre \c i must be in the heap. |
|
668 |
/// \param i The item. |
|
669 |
Prio operator[](const Item &i) const { |
|
670 |
for (int k = 0; k < first.size(); ++k) { |
|
671 |
int idx = first[k]; |
|
672 |
while (idx != -1) { |
|
673 |
if (data[idx].item == i) { |
|
674 |
return k; |
|
675 |
} |
|
676 |
idx = data[idx].next; |
|
677 |
} |
|
678 |
} |
|
679 |
return -1; |
|
680 |
} |
|
681 |
|
|
682 |
/// \brief Returns if \c item is in, has already been in, or has |
|
683 |
/// never been in the heap. |
|
684 |
/// |
|
685 |
/// This method returns PRE_HEAP if \c item has never been in the |
|
686 |
/// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
|
687 |
/// otherwise. In the latter case it is possible that \c item will |
|
688 |
/// get back to the heap again. |
|
689 |
/// \param i The item. |
|
690 |
State state(const Item &i) const { |
|
691 |
int idx = index[i]; |
|
692 |
if (idx >= 0) idx = 0; |
|
693 |
return State(idx); |
|
694 |
} |
|
695 |
|
|
696 |
private: |
|
697 |
|
|
698 |
struct BucketItem { |
|
699 |
BucketItem(const Item& _item) |
|
700 |
: item(_item) {} |
|
701 |
|
|
702 |
Item item; |
|
703 |
int next; |
|
704 |
}; |
|
705 |
|
|
706 |
ItemIntMap& index; |
|
707 |
std::vector<int> first; |
|
708 |
std::vector<BucketItem> data; |
|
709 |
int free, num; |
|
710 |
mutable int minimal; |
|
711 |
|
|
712 |
}; // class SimpleBucketHeap |
|
713 |
|
|
714 |
template <typename _ItemIntMap> |
|
715 |
class SimpleBucketHeap<_ItemIntMap, false> { |
|
716 |
|
|
717 |
public: |
|
718 |
typedef typename _ItemIntMap::Key Item; |
|
719 |
typedef int Prio; |
|
720 |
typedef std::pair<Item, Prio> Pair; |
|
721 |
typedef _ItemIntMap ItemIntMap; |
|
722 |
|
|
723 |
enum State { |
|
724 |
IN_HEAP = 0, |
|
725 |
PRE_HEAP = -1, |
|
726 |
POST_HEAP = -2 |
|
727 |
}; |
|
728 |
|
|
729 |
public: |
|
730 |
|
|
731 |
explicit SimpleBucketHeap(ItemIntMap &_index) |
|
732 |
: index(_index), free(-1), num(0), maximal(0) {} |
|
733 |
|
|
734 |
int size() const { return num; } |
|
735 |
|
|
736 |
bool empty() const { return num == 0; } |
|
737 |
|
|
738 |
void clear() { |
|
739 |
data.clear(); first.clear(); free = -1; num = 0; maximal = 0; |
|
740 |
} |
|
741 |
|
|
742 |
void push(const Pair& p) { |
|
743 |
push(p.first, p.second); |
|
744 |
} |
|
745 |
|
|
746 |
void push(const Item &i, const Prio &p) { |
|
747 |
int idx; |
|
748 |
if (free == -1) { |
|
749 |
idx = data.size(); |
|
750 |
data.push_back(BucketItem(i)); |
|
751 |
} else { |
|
752 |
idx = free; |
|
753 |
free = data[idx].next; |
|
754 |
data[idx].item = i; |
|
755 |
} |
|
756 |
index[i] = idx; |
|
757 |
if (p >= int(first.size())) first.resize(p + 1, -1); |
|
758 |
data[idx].next = first[p]; |
|
759 |
first[p] = idx; |
|
760 |
if (p > maximal) { |
|
761 |
maximal = p; |
|
762 |
} |
|
763 |
++num; |
|
764 |
} |
|
765 |
|
|
766 |
Item top() const { |
|
767 |
while (first[maximal] == -1) { |
|
768 |
--maximal; |
|
769 |
} |
|
770 |
return data[first[maximal]].item; |
|
771 |
} |
|
772 |
|
|
773 |
Prio prio() const { |
|
774 |
while (first[maximal] == -1) { |
|
775 |
--maximal; |
|
776 |
} |
|
777 |
return maximal; |
|
778 |
} |
|
779 |
|
|
780 |
void pop() { |
|
781 |
while (first[maximal] == -1) { |
|
782 |
--maximal; |
|
783 |
} |
|
784 |
int idx = first[maximal]; |
|
785 |
index[data[idx].item] = -2; |
|
786 |
first[maximal] = data[idx].next; |
|
787 |
data[idx].next = free; |
|
788 |
free = idx; |
|
789 |
--num; |
|
790 |
} |
|
791 |
|
|
792 |
Prio operator[](const Item &i) const { |
|
793 |
for (int k = 0; k < first.size(); ++k) { |
|
794 |
int idx = first[k]; |
|
795 |
while (idx != -1) { |
|
796 |
if (data[idx].item == i) { |
|
797 |
return k; |
|
798 |
} |
|
799 |
idx = data[idx].next; |
|
800 |
} |
|
801 |
} |
|
802 |
return -1; |
|
803 |
} |
|
804 |
|
|
805 |
State state(const Item &i) const { |
|
806 |
int idx = index[i]; |
|
807 |
if (idx >= 0) idx = 0; |
|
808 |
return State(idx); |
|
809 |
} |
|
810 |
|
|
811 |
private: |
|
812 |
|
|
813 |
struct BucketItem { |
|
814 |
BucketItem(const Item& _item) : item(_item) {} |
|
815 |
|
|
816 |
Item item; |
|
817 |
|
|
818 |
int next; |
|
819 |
}; |
|
820 |
|
|
821 |
ItemIntMap& index; |
|
822 |
std::vector<int> first; |
|
823 |
std::vector<BucketItem> data; |
|
824 |
int free, num; |
|
825 |
mutable int maximal; |
|
826 |
|
|
827 |
}; |
|
828 |
|
|
829 |
} |
|
830 |
|
|
831 |
#endif |
1 |
/* -*- mode: C++; indent-tabs-mode: nil; -*- |
|
2 |
* |
|
3 |
* This file is a part of LEMON, a generic C++ optimization library. |
|
4 |
* |
|
5 |
* Copyright (C) 2003-2009 |
|
6 |
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
|
7 |
* (Egervary Research Group on Combinatorial Optimization, EGRES). |
|
8 |
* |
|
9 |
* Permission to use, modify and distribute this software is granted |
|
10 |
* provided that this copyright notice appears in all copies. For |
|
11 |
* precise terms see the accompanying LICENSE file. |
|
12 |
* |
|
13 |
* This software is provided "AS IS" with no warranty of any kind, |
|
14 |
* express or implied, and with no claim as to its suitability for any |
|
15 |
* purpose. |
|
16 |
* |
|
17 |
*/ |
|
18 |
|
|
19 |
#ifndef LEMON_FIB_HEAP_H |
|
20 |
#define LEMON_FIB_HEAP_H |
|
21 |
|
|
22 |
///\file |
|
23 |
///\ingroup auxdat |
|
24 |
///\brief Fibonacci Heap implementation. |
|
25 |
|
|
26 |
#include <vector> |
|
27 |
#include <functional> |
|
28 |
#include <lemon/math.h> |
|
29 |
|
|
30 |
namespace lemon { |
|
31 |
|
|
32 |
/// \ingroup auxdat |
|
33 |
/// |
|
34 |
///\brief Fibonacci Heap. |
|
35 |
/// |
|
36 |
///This class implements the \e Fibonacci \e heap data structure. A \e heap |
|
37 |
///is a data structure for storing items with specified values called \e |
|
38 |
///priorities in such a way that finding the item with minimum priority is |
|
39 |
///efficient. \c Compare specifies the ordering of the priorities. In a heap |
|
40 |
///one can change the priority of an item, add or erase an item, etc. |
|
41 |
/// |
|
42 |
///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
|
43 |
///heap. In case of many calls to these operations, it is better to use a |
|
44 |
///\ref BinHeap "binary heap". |
|
45 |
/// |
|
46 |
///\param _Prio Type of the priority of the items. |
|
47 |
///\param _ItemIntMap A read and writable Item int map, used internally |
|
48 |
///to handle the cross references. |
|
49 |
///\param _Compare A class for the ordering of the priorities. The |
|
50 |
///default is \c std::less<_Prio>. |
|
51 |
/// |
|
52 |
///\sa BinHeap |
|
53 |
///\sa Dijkstra |
|
54 |
#ifdef DOXYGEN |
|
55 |
template <typename _Prio, |
|
56 |
typename _ItemIntMap, |
|
57 |
typename _Compare> |
|
58 |
#else |
|
59 |
template <typename _Prio, |
|
60 |
typename _ItemIntMap, |
|
61 |
typename _Compare = std::less<_Prio> > |
|
62 |
#endif |
|
63 |
class FibHeap { |
|
64 |
public: |
|
65 |
///\e |
|
66 |
typedef _ItemIntMap ItemIntMap; |
|
67 |
///\e |
|
68 |
typedef _Prio Prio; |
|
69 |
///\e |
|
70 |
typedef typename ItemIntMap::Key Item; |
|
71 |
///\e |
|
72 |
typedef std::pair<Item,Prio> Pair; |
|
73 |
///\e |
|
74 |
typedef _Compare Compare; |
|
75 |
|
|
76 |
private: |
|
77 |
class store; |
|
78 |
|
|
79 |
std::vector<store> container; |
|
80 |
int minimum; |
|
81 |
ItemIntMap &iimap; |
|
82 |
Compare comp; |
|
83 |
int num_items; |
|
84 |
|
|
85 |
public: |
|
86 |
///Status of the nodes |
|
87 |
enum State { |
|
88 |
///The node is in the heap |
|
89 |
IN_HEAP = 0, |
|
90 |
///The node has never been in the heap |
|
91 |
PRE_HEAP = -1, |
|
92 |
///The node was in the heap but it got out of it |
|
93 |
POST_HEAP = -2 |
|
94 |
}; |
|
95 |
|
|
96 |
/// \brief The constructor |
|
97 |
/// |
|
98 |
/// \c _iimap should be given to the constructor, since it is |
|
99 |
/// used internally to handle the cross references. |
|
100 |
explicit FibHeap(ItemIntMap &_iimap) |
|
101 |
: minimum(0), iimap(_iimap), num_items() {} |
|
102 |
|
|
103 |
/// \brief The constructor |
|
104 |
/// |
|
105 |
/// \c _iimap should be given to the constructor, since it is used |
|
106 |
/// internally to handle the cross references. \c _comp is an |
|
107 |
/// object for ordering of the priorities. |
|
108 |
FibHeap(ItemIntMap &_iimap, const Compare &_comp) |
|
109 |
: minimum(0), iimap(_iimap), comp(_comp), num_items() {} |
|
110 |
|
|
111 |
/// \brief The number of items stored in the heap. |
|
112 |
/// |
|
113 |
/// Returns the number of items stored in the heap. |
|
114 |
int size() const { return num_items; } |
|
115 |
|
|
116 |
/// \brief Checks if the heap stores no items. |
|
117 |
/// |
|
118 |
/// Returns \c true if and only if the heap stores no items. |
|
119 |
bool empty() const { return num_items==0; } |
|
120 |
|
|
121 |
/// \brief Make empty this heap. |
|
122 |
/// |
|
123 |
/// Make empty this heap. It does not change the cross reference |
|
124 |
/// map. If you want to reuse a heap what is not surely empty you |
|
125 |
/// should first clear the heap and after that you should set the |
|
126 |
/// cross reference map for each item to \c PRE_HEAP. |
|
127 |
void clear() { |
|
128 |
container.clear(); minimum = 0; num_items = 0; |
|
129 |
} |
|
130 |
|
|
131 |
/// \brief \c item gets to the heap with priority \c value independently |
|
132 |
/// if \c item was already there. |
|
133 |
/// |
|
134 |
/// This method calls \ref push(\c item, \c value) if \c item is not |
|
135 |
/// stored in the heap and it calls \ref decrease(\c item, \c value) or |
|
136 |
/// \ref increase(\c item, \c value) otherwise. |
|
137 |
void set (const Item& item, const Prio& value) { |
|
138 |
int i=iimap[item]; |
|
139 |
if ( i >= 0 && container[i].in ) { |
|
140 |
if ( comp(value, container[i].prio) ) decrease(item, value); |
|
141 |
if ( comp(container[i].prio, value) ) increase(item, value); |
|
142 |
} else push(item, value); |
|
143 |
} |
|
144 |
|
|
145 |
/// \brief Adds \c item to the heap with priority \c value. |
|
146 |
/// |
|
147 |
/// Adds \c item to the heap with priority \c value. |
|
148 |
/// \pre \c item must not be stored in the heap. |
|
149 |
void push (const Item& item, const Prio& value) { |
|
150 |
int i=iimap[item]; |
|
151 |
if ( i < 0 ) { |
|
152 |
int s=container.size(); |
|
153 |
iimap.set( item, s ); |
|
154 |
store st; |
|
155 |
st.name=item; |
|
156 |
container.push_back(st); |
|
157 |
i=s; |
|
158 |
} else { |
|
159 |
container[i].parent=container[i].child=-1; |
|
160 |
container[i].degree=0; |
|
161 |
container[i].in=true; |
|
162 |
container[i].marked=false; |
|
163 |
} |
|
164 |
|
|
165 |
if ( num_items ) { |
|
166 |
container[container[minimum].right_neighbor].left_neighbor=i; |
|
167 |
container[i].right_neighbor=container[minimum].right_neighbor; |
|
168 |
container[minimum].right_neighbor=i; |
|
169 |
container[i].left_neighbor=minimum; |
|
170 |
if ( comp( value, container[minimum].prio) ) minimum=i; |
|
171 |
} else { |
|
172 |
container[i].right_neighbor=container[i].left_neighbor=i; |
|
173 |
minimum=i; |
|
174 |
} |
|
175 |
container[i].prio=value; |
|
176 |
++num_items; |
|
177 |
} |
|
178 |
|
|
179 |
/// \brief Returns the item with minimum priority relative to \c Compare. |
|
180 |
/// |
|
181 |
/// This method returns the item with minimum priority relative to \c |
|
182 |
/// Compare. |
|
183 |
/// \pre The heap must be nonempty. |
|
184 |
Item top() const { return container[minimum].name; } |
|
185 |
|
|
186 |
/// \brief Returns the minimum priority relative to \c Compare. |
|
187 |
/// |
|
188 |
/// It returns the minimum priority relative to \c Compare. |
|
189 |
/// \pre The heap must be nonempty. |
|
190 |
const Prio& prio() const { return container[minimum].prio; } |
|
191 |
|
|
192 |
/// \brief Returns the priority of \c item. |
|
193 |
/// |
|
194 |
/// It returns the priority of \c item. |
|
195 |
/// \pre \c item must be in the heap. |
|
196 |
const Prio& operator[](const Item& item) const { |
|
197 |
return container[iimap[item]].prio; |
|
198 |
} |
|
199 |
|
|
200 |
/// \brief Deletes the item with minimum priority relative to \c Compare. |
|
201 |
/// |
|
202 |
/// This method deletes the item with minimum priority relative to \c |
|
203 |
/// Compare from the heap. |
|
204 |
/// \pre The heap must be non-empty. |
|
205 |
void pop() { |
|
206 |
/*The first case is that there are only one root.*/ |
|
207 |
if ( container[minimum].left_neighbor==minimum ) { |
|
208 |
container[minimum].in=false; |
|
209 |
if ( container[minimum].degree!=0 ) { |
|
210 |
makeroot(container[minimum].child); |
|
211 |
minimum=container[minimum].child; |
|
212 |
balance(); |
|
213 |
} |
|
214 |
} else { |
|
215 |
int right=container[minimum].right_neighbor; |
|
216 |
unlace(minimum); |
|
217 |
container[minimum].in=false; |
|
218 |
if ( container[minimum].degree > 0 ) { |
|
219 |
int left=container[minimum].left_neighbor; |
|
220 |
int child=container[minimum].child; |
|
221 |
int last_child=container[child].left_neighbor; |
|
222 |
|
|
223 |
makeroot(child); |
|
224 |
|
|
225 |
container[left].right_neighbor=child; |
|
226 |
container[child].left_neighbor=left; |
|
227 |
container[right].left_neighbor=last_child; |
|
228 |
container[last_child].right_neighbor=right; |
|
229 |
} |
|
230 |
minimum=right; |
|
231 |
balance(); |
|
232 |
} // the case where there are more roots |
|
233 |
--num_items; |
|
234 |
} |
|
235 |
|
|
236 |
/// \brief Deletes \c item from the heap. |
|
237 |
/// |
|
238 |
/// This method deletes \c item from the heap, if \c item was already |
|
239 |
/// stored in the heap. It is quite inefficient in Fibonacci heaps. |
|
240 |
void erase (const Item& item) { |
|
241 |
int i=iimap[item]; |
|
242 |
|
|
243 |
if ( i >= 0 && container[i].in ) { |
|
244 |
if ( container[i].parent!=-1 ) { |
|
245 |
int p=container[i].parent; |
|
246 |
cut(i,p); |
|
247 |
cascade(p); |
|
248 |
} |
|
249 |
minimum=i; //As if its prio would be -infinity |
|
250 |
pop(); |
|
251 |
} |
|
252 |
} |
|
253 |
|
|
254 |
/// \brief Decreases the priority of \c item to \c value. |
|
255 |
/// |
|
256 |
/// This method decreases the priority of \c item to \c value. |
|
257 |
/// \pre \c item must be stored in the heap with priority at least \c |
|
258 |
/// value relative to \c Compare. |
|
259 |
void decrease (Item item, const Prio& value) { |
|
260 |
int i=iimap[item]; |
|
261 |
container[i].prio=value; |
|
262 |
int p=container[i].parent; |
|
263 |
|
|
264 |
if ( p!=-1 && comp(value, container[p].prio) ) { |
|
265 |
cut(i,p); |
|
266 |
cascade(p); |
|
267 |
} |
|
268 |
if ( comp(value, container[minimum].prio) ) minimum=i; |
|
269 |
} |
|
270 |
|
|
271 |
/// \brief Increases the priority of \c item to \c value. |
|
272 |
/// |
|
273 |
/// This method sets the priority of \c item to \c value. Though |
|
274 |
/// there is no precondition on the priority of \c item, this |
|
275 |
/// method should be used only if it is indeed necessary to increase |
|
276 |
/// (relative to \c Compare) the priority of \c item, because this |
|
277 |
/// method is inefficient. |
|
278 |
void increase (Item item, const Prio& value) { |
|
279 |
erase(item); |
|
280 |
push(item, value); |
|
281 |
} |
|
282 |
|
|
283 |
|
|
284 |
/// \brief Returns if \c item is in, has already been in, or has never |
|
285 |
/// been in the heap. |
|
286 |
/// |
|
287 |
/// This method returns PRE_HEAP if \c item has never been in the |
|
288 |
/// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
|
289 |
/// otherwise. In the latter case it is possible that \c item will |
|
290 |
/// get back to the heap again. |
|
291 |
State state(const Item &item) const { |
|
292 |
int i=iimap[item]; |
|
293 |
if( i>=0 ) { |
|
294 |
if ( container[i].in ) i=0; |
|
295 |
else i=-2; |
|
296 |
} |
|
297 |
return State(i); |
|
298 |
} |
|
299 |
|
|
300 |
/// \brief Sets the state of the \c item in the heap. |
|
301 |
/// |
|
302 |
/// Sets the state of the \c item in the heap. It can be used to |
|
303 |
/// manually clear the heap when it is important to achive the |
|
304 |
/// better time complexity. |
|
305 |
/// \param i The item. |
|
306 |
/// \param st The state. It should not be \c IN_HEAP. |
|
307 |
void state(const Item& i, State st) { |
|
308 |
switch (st) { |
|
309 |
case POST_HEAP: |
|
310 |
case PRE_HEAP: |
|
311 |
if (state(i) == IN_HEAP) { |
|
312 |
erase(i); |
|
313 |
} |
|
314 |
iimap[i] = st; |
|
315 |
break; |
|
316 |
case IN_HEAP: |
|
317 |
break; |
|
318 |
} |
|
319 |
} |
|
320 |
|
|
321 |
private: |
|
322 |
|
|
323 |
void balance() { |
|
324 |
|
|
325 |
int maxdeg=int( std::floor( 2.08*log(double(container.size()))))+1; |
|
326 |
|
|
327 |
std::vector<int> A(maxdeg,-1); |
|
328 |
|
|
329 |
/* |
|
330 |
*Recall that now minimum does not point to the minimum prio element. |
|
331 |
*We set minimum to this during balance(). |
|
332 |
*/ |
|
333 |
int anchor=container[minimum].left_neighbor; |
|
334 |
int next=minimum; |
|
335 |
bool end=false; |
|
336 |
|
|
337 |
do { |
|
338 |
int active=next; |
|
339 |
if ( anchor==active ) end=true; |
|
340 |
int d=container[active].degree; |
|
341 |
next=container[active].right_neighbor; |
|
342 |
|
|
343 |
while (A[d]!=-1) { |
|
344 |
if( comp(container[active].prio, container[A[d]].prio) ) { |
|
345 |
fuse(active,A[d]); |
|
346 |
} else { |
|
347 |
fuse(A[d],active); |
|
348 |
active=A[d]; |
|
349 |
} |
|
350 |
A[d]=-1; |
|
351 |
++d; |
|
352 |
} |
|
353 |
A[d]=active; |
|
354 |
} while ( !end ); |
|
355 |
|
|
356 |
|
|
357 |
while ( container[minimum].parent >=0 ) |
|
358 |
minimum=container[minimum].parent; |
|
359 |
int s=minimum; |
|
360 |
int m=minimum; |
|
361 |
do { |
|
362 |
if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
|
363 |
s=container[s].right_neighbor; |
|
364 |
} while ( s != m ); |
|
365 |
} |
|
366 |
|
|
367 |
void makeroot(int c) { |
|
368 |
int s=c; |
|
369 |
do { |
|
370 |
container[s].parent=-1; |
|
371 |
s=container[s].right_neighbor; |
|
372 |
} while ( s != c ); |
|
373 |
} |
|
374 |
|
|
375 |
void cut(int a, int b) { |
|
376 |
/* |
|
377 |
*Replacing a from the children of b. |
|
378 |
*/ |
|
379 |
--container[b].degree; |
|
380 |
|
|
381 |
if ( container[b].degree !=0 ) { |
|
382 |
int child=container[b].child; |
|
383 |
if ( child==a ) |
|
384 |
container[b].child=container[child].right_neighbor; |
|
385 |
unlace(a); |
|
386 |
} |
|
387 |
|
|
388 |
|
|
389 |
/*Lacing a to the roots.*/ |
|
390 |
int right=container[minimum].right_neighbor; |
|
391 |
container[minimum].right_neighbor=a; |
|
392 |
container[a].left_neighbor=minimum; |
|
393 |
container[a].right_neighbor=right; |
|
394 |
container[right].left_neighbor=a; |
|
395 |
|
|
396 |
container[a].parent=-1; |
|
397 |
container[a].marked=false; |
|
398 |
} |
|
399 |
|
|
400 |
void cascade(int a) { |
|
401 |
if ( container[a].parent!=-1 ) { |
|
402 |
int p=container[a].parent; |
|
403 |
|
|
404 |
if ( container[a].marked==false ) container[a].marked=true; |
|
405 |
else { |
|
406 |
cut(a,p); |
|
407 |
cascade(p); |
|
408 |
} |
|
409 |
} |
|
410 |
} |
|
411 |
|
|
412 |
void fuse(int a, int b) { |
|
413 |
unlace(b); |
|
414 |
|
|
415 |
/*Lacing b under a.*/ |
|
416 |
container[b].parent=a; |
|
417 |
|
|
418 |
if (container[a].degree==0) { |
|
419 |
container[b].left_neighbor=b; |
|
420 |
container[b].right_neighbor=b; |
|
421 |
container[a].child=b; |
|
422 |
} else { |
|
423 |
int child=container[a].child; |
|
424 |
int last_child=container[child].left_neighbor; |
|
425 |
container[child].left_neighbor=b; |
|
426 |
container[b].right_neighbor=child; |
|
427 |
container[last_child].right_neighbor=b; |
|
428 |
container[b].left_neighbor=last_child; |
|
429 |
} |
|
430 |
|
|
431 |
++container[a].degree; |
|
432 |
|
|
433 |
container[b].marked=false; |
|
434 |
} |
|
435 |
|
|
436 |
/* |
|
437 |
*It is invoked only if a has siblings. |
|
438 |
*/ |
|
439 |
void unlace(int a) { |
|
440 |
int leftn=container[a].left_neighbor; |
|
441 |
int rightn=container[a].right_neighbor; |
|
442 |
container[leftn].right_neighbor=rightn; |
|
443 |
container[rightn].left_neighbor=leftn; |
|
444 |
} |
|
445 |
|
|
446 |
|
|
447 |
class store { |
|
448 |
friend class FibHeap; |
|
449 |
|
|
450 |
Item name; |
|
451 |
int parent; |
|
452 |
int left_neighbor; |
|
453 |
int right_neighbor; |
|
454 |
int child; |
|
455 |
int degree; |
|
456 |
bool marked; |
|
457 |
bool in; |
|
458 |
Prio prio; |
|
459 |
|
|
460 |
store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
|
461 |
}; |
|
462 |
}; |
|
463 |
|
|
464 |
} //namespace lemon |
|
465 |
|
|
466 |
#endif //LEMON_FIB_HEAP_H |
|
467 |
1 |
/* -*- mode: C++; indent-tabs-mode: nil; -*- |
|
2 |
* |
|
3 |
* This file is a part of LEMON, a generic C++ optimization library. |
|
4 |
* |
|
5 |
* Copyright (C) 2003-2009 |
|
6 |
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
|
7 |
* (Egervary Research Group on Combinatorial Optimization, EGRES). |
|
8 |
* |
|
9 |
* Permission to use, modify and distribute this software is granted |
|
10 |
* provided that this copyright notice appears in all copies. For |
|
11 |
* precise terms see the accompanying LICENSE file. |
|
12 |
* |
|
13 |
* This software is provided "AS IS" with no warranty of any kind, |
|
14 |
* express or implied, and with no claim as to its suitability for any |
|
15 |
* purpose. |
|
16 |
* |
|
17 |
*/ |
|
18 |
|
|
19 |
#ifndef LEMON_RADIX_HEAP_H |
|
20 |
#define LEMON_RADIX_HEAP_H |
|
21 |
|
|
22 |
///\ingroup auxdat |
|
23 |
///\file |
|
24 |
///\brief Radix Heap implementation. |
|
25 |
|
|
26 |
#include <vector> |
|
27 |
#include <lemon/error.h> |
|
28 |
|
|
29 |
namespace lemon { |
|
30 |
|
|
31 |
|
|
32 |
/// \ingroup auxdata |
|
33 |
/// |
|
34 |
/// \brief A Radix Heap implementation. |
|
35 |
/// |
|
36 |
/// This class implements the \e radix \e heap data structure. A \e heap |
|
37 |
/// is a data structure for storing items with specified values called \e |
|
38 |
/// priorities in such a way that finding the item with minimum priority is |
|
39 |
/// efficient. This heap type can store only items with \e int priority. |
|
40 |
/// In a heap one can change the priority of an item, add or erase an |
|
41 |
/// item, but the priority cannot be decreased under the last removed |
|
42 |
/// item's priority. |
|
43 |
/// |
|
44 |
/// \param _ItemIntMap A read and writable Item int map, used internally |
|
45 |
/// to handle the cross references. |
|
46 |
/// |
|
47 |
/// \see BinHeap |
|
48 |
/// \see Dijkstra |
|
49 |
template <typename _ItemIntMap> |
|
50 |
class RadixHeap { |
|
51 |
|
|
52 |
public: |
|
53 |
typedef typename _ItemIntMap::Key Item; |
|
54 |
typedef int Prio; |
|
55 |
typedef _ItemIntMap ItemIntMap; |
|
56 |
|
|
57 |
/// \brief Exception thrown by RadixHeap. |
|
58 |
/// |
|
59 |
/// This Exception is thrown when a smaller priority |
|
60 |
/// is inserted into the \e RadixHeap then the last time erased. |
|
61 |
/// \see RadixHeap |
|
62 |
|
|
63 |
class UnderFlowPriorityError : public Exception { |
|
64 |
public: |
|
65 |
virtual const char* what() const throw() { |
|
66 |
return "lemon::RadixHeap::UnderFlowPriorityError"; |
|
67 |
} |
|
68 |
}; |
|
69 |
|
|
70 |
/// \brief Type to represent the items states. |
|
71 |
/// |
|
72 |
/// Each Item element have a state associated to it. It may be "in heap", |
|
73 |
/// "pre heap" or "post heap". The latter two are indifferent from the |
|
74 |
/// heap's point of view, but may be useful to the user. |
|
75 |
/// |
|
76 |
/// The ItemIntMap \e should be initialized in such way that it maps |
|
77 |
/// PRE_HEAP (-1) to any element to be put in the heap... |
|
78 |
enum State { |
|
79 |
IN_HEAP = 0, |
|
80 |
PRE_HEAP = -1, |
|
81 |
POST_HEAP = -2 |
|
82 |
}; |
|
83 |
|
|
84 |
private: |
|
85 |
|
|
86 |
struct RadixItem { |
|
87 |
int prev, next, box; |
|
88 |
Item item; |
|
89 |
int prio; |
|
90 |
RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {} |
|
91 |
}; |
|
92 |
|
|
93 |
struct RadixBox { |
|
94 |
int first; |
|
95 |
int min, size; |
|
96 |
RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {} |
|
97 |
}; |
|
98 |
|
|
99 |
std::vector<RadixItem> data; |
|
100 |
std::vector<RadixBox> boxes; |
|
101 |
|
|
102 |
ItemIntMap &iim; |
|
103 |
|
|
104 |
|
|
105 |
public: |
|
106 |
/// \brief The constructor. |
|
107 |
/// |
|
108 |
/// The constructor. |
|
109 |
/// |
|
110 |
/// \param _iim It should be given to the constructor, since it is used |
|
111 |
/// internally to handle the cross references. The value of the map |
|
112 |
/// should be PRE_HEAP (-1) for each element. |
|
113 |
/// |
|
114 |
/// \param minimal The initial minimal value of the heap. |
|
115 |
/// \param capacity It determines the initial capacity of the heap. |
|
116 |
RadixHeap(ItemIntMap &_iim, int minimal = 0, int capacity = 0) |
|
117 |
: iim(_iim) { |
|
118 |
boxes.push_back(RadixBox(minimal, 1)); |
|
119 |
boxes.push_back(RadixBox(minimal + 1, 1)); |
|
120 |
while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
|
121 |
extend(); |
|
122 |
} |
|
123 |
} |
|
124 |
|
|
125 |
/// The number of items stored in the heap. |
|
126 |
/// |
|
127 |
/// \brief Returns the number of items stored in the heap. |
|
128 |
int size() const { return data.size(); } |
|
129 |
/// \brief Checks if the heap stores no items. |
|
130 |
/// |
|
131 |
/// Returns \c true if and only if the heap stores no items. |
|
132 |
bool empty() const { return data.empty(); } |
|
133 |
|
|
134 |
/// \brief Make empty this heap. |
|
135 |
/// |
|
136 |
/// Make empty this heap. It does not change the cross reference |
|
137 |
/// map. If you want to reuse a heap what is not surely empty you |
|
138 |
/// should first clear the heap and after that you should set the |
|
139 |
/// cross reference map for each item to \c PRE_HEAP. |
|
140 |
void clear(int minimal = 0, int capacity = 0) { |
|
141 |
data.clear(); boxes.clear(); |
|
142 |
boxes.push_back(RadixBox(minimal, 1)); |
|
143 |
boxes.push_back(RadixBox(minimal + 1, 1)); |
|
144 |
while (lower(boxes.size() - 1, capacity + minimal - 1)) { |
|
145 |
extend(); |
|
146 |
} |
|
147 |
} |
|
148 |
|
|
149 |
private: |
|
150 |
|
|
151 |
bool upper(int box, Prio pr) { |
|
152 |
return pr < boxes[box].min; |
|
153 |
} |
|
154 |
|
|
155 |
bool lower(int box, Prio pr) { |
|
156 |
return pr >= boxes[box].min + boxes[box].size; |
|
157 |
} |
|
158 |
|
|
159 |
/// \brief Remove item from the box list. |
|
160 |
void remove(int index) { |
|
161 |
if (data[index].prev >= 0) { |
|
162 |
data[data[index].prev].next = data[index].next; |
|
163 |
} else { |
|
164 |
boxes[data[index].box].first = data[index].next; |
|
165 |
} |
|
166 |
if (data[index].next >= 0) { |
|
167 |
data[data[index].next].prev = data[index].prev; |
|
168 |
} |
|
169 |
} |
|
170 |
|
|
171 |
/// \brief Insert item into the box list. |
|
172 |
void insert(int box, int index) { |
|
173 |
if (boxes[box].first == -1) { |
|
174 |
boxes[box].first = index; |
|
175 |
data[index].next = data[index].prev = -1; |
|
176 |
} else { |
|
177 |
data[index].next = boxes[box].first; |
|
178 |
data[boxes[box].first].prev = index; |
|
179 |
data[index].prev = -1; |
|
180 |
boxes[box].first = index; |
|
181 |
} |
|
182 |
data[index].box = box; |
|
183 |
} |
|
184 |
|
|
185 |
/// \brief Add a new box to the box list. |
|
186 |
void extend() { |
|
187 |
int min = boxes.back().min + boxes.back().size; |
|
188 |
int bs = 2 * boxes.back().size; |
|
189 |
boxes.push_back(RadixBox(min, bs)); |
|
190 |
} |
|
191 |
|
|
192 |
/// \brief Move an item up into the proper box. |
|
193 |
void bubble_up(int index) { |
|
194 |
if (!lower(data[index].box, data[index].prio)) return; |
|
195 |
remove(index); |
|
196 |
int box = findUp(data[index].box, data[index].prio); |
|
197 |
insert(box, index); |
|
198 |
} |
|
199 |
|
|
200 |
/// \brief Find up the proper box for the item with the given prio. |
|
201 |
int findUp(int start, int pr) { |
|
202 |
while (lower(start, pr)) { |
|
203 |
if (++start == int(boxes.size())) { |
|
204 |
extend(); |
|
205 |
} |
|
206 |
} |
|
207 |
return start; |
|
208 |
} |
|
209 |
|
|
210 |
/// \brief Move an item down into the proper box. |
|
211 |
void bubble_down(int index) { |
|
212 |
if (!upper(data[index].box, data[index].prio)) return; |
|
213 |
remove(index); |
|
214 |
int box = findDown(data[index].box, data[index].prio); |
|
215 |
insert(box, index); |
|
216 |
} |
|
217 |
|
|
218 |
/// \brief Find up the proper box for the item with the given prio. |
|
219 |
int findDown(int start, int pr) { |
|
220 |
while (upper(start, pr)) { |
|
221 |
if (--start < 0) throw UnderFlowPriorityError(); |
|
222 |
} |
|
223 |
return start; |
|
224 |
} |
|
225 |
|
|
226 |
/// \brief Find the first not empty box. |
|
227 |
int findFirst() { |
|
228 |
int first = 0; |
|
229 |
while (boxes[first].first == -1) ++first; |
|
230 |
return first; |
|
231 |
} |
|
232 |
|
|
233 |
/// \brief Gives back the minimal prio of the box. |
|
234 |
int minValue(int box) { |
|
235 |
int min = data[boxes[box].first].prio; |
|
236 |
for (int k = boxes[box].first; k != -1; k = data[k].next) { |
|
237 |
if (data[k].prio < min) min = data[k].prio; |
|
238 |
} |
|
239 |
return min; |
|
240 |
} |
|
241 |
|
|
242 |
/// \brief Rearrange the items of the heap and makes the |
|
243 |
/// first box not empty. |
|
244 |
void moveDown() { |
|
245 |
int box = findFirst(); |
|
246 |
if (box == 0) return; |
|
247 |
int min = minValue(box); |
|
248 |
for (int i = 0; i <= box; ++i) { |
|
249 |
boxes[i].min = min; |
|
250 |
min += boxes[i].size; |
|
251 |
} |
|
252 |
int curr = boxes[box].first, next; |
|
253 |
while (curr != -1) { |
|
254 |
next = data[curr].next; |
|
255 |
bubble_down(curr); |
|
256 |
curr = next; |
|
257 |
} |
|
258 |
} |
|
259 |
|
|
260 |
void relocate_last(int index) { |
|
261 |
if (index != int(data.size()) - 1) { |
|
262 |
data[index] = data.back(); |
|
263 |
if (data[index].prev != -1) { |
|
264 |
data[data[index].prev].next = index; |
|
265 |
} else { |
|
266 |
boxes[data[index].box].first = index; |
|
267 |
} |
|
268 |
if (data[index].next != -1) { |
|
269 |
data[data[index].next].prev = index; |
|
270 |
} |
|
271 |
iim[data[index].item] = index; |
|
272 |
} |
|
273 |
data.pop_back(); |
|
274 |
} |
|
275 |
|
|
276 |
public: |
|
277 |
|
|
278 |
/// \brief Insert an item into the heap with the given priority. |
|
279 |
/// |
|
280 |
/// Adds \c i to the heap with priority \c p. |
|
281 |
/// \param i The item to insert. |
|
282 |
/// \param p The priority of the item. |
|
283 |
void push(const Item &i, const Prio &p) { |
|
284 |
int n = data.size(); |
|
285 |
iim.set(i, n); |
|
286 |
data.push_back(RadixItem(i, p)); |
|
287 |
while (lower(boxes.size() - 1, p)) { |
|
288 |
extend(); |
|
289 |
} |
|
290 |
int box = findDown(boxes.size() - 1, p); |
|
291 |
insert(box, n); |
|
292 |
} |
|
293 |
|
|
294 |
/// \brief Returns the item with minimum priority. |
|
295 |
/// |
|
296 |
/// This method returns the item with minimum priority. |
|
297 |
/// \pre The heap must be nonempty. |
|
298 |
Item top() const { |
|
299 |
const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
|
300 |
return data[boxes[0].first].item; |
|
301 |
} |
|
302 |
|
|
303 |
/// \brief Returns the minimum priority. |
|
304 |
/// |
|
305 |
/// It returns the minimum priority. |
|
306 |
/// \pre The heap must be nonempty. |
|
307 |
Prio prio() const { |
|
308 |
const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown(); |
|
309 |
return data[boxes[0].first].prio; |
|
310 |
} |
|
311 |
|
|
312 |
/// \brief Deletes the item with minimum priority. |
|
313 |
/// |
|
314 |
/// This method deletes the item with minimum priority. |
|
315 |
/// \pre The heap must be non-empty. |
|
316 |
void pop() { |
|
317 |
moveDown(); |
|
318 |
int index = boxes[0].first; |
|
319 |
iim[data[index].item] = POST_HEAP; |
|
320 |
remove(index); |
|
321 |
relocate_last(index); |
|
322 |
} |
|
323 |
|
|
324 |
/// \brief Deletes \c i from the heap. |
|
325 |
/// |
|
326 |
/// This method deletes item \c i from the heap, if \c i was |
|
327 |
/// already stored in the heap. |
|
328 |
/// \param i The item to erase. |
|
329 |
void erase(const Item &i) { |
|
330 |
int index = iim[i]; |
|
331 |
iim[i] = POST_HEAP; |
|
332 |
remove(index); |
|
333 |
relocate_last(index); |
|
334 |
} |
|
335 |
|
|
336 |
/// \brief Returns the priority of \c i. |
|
337 |
/// |
|
338 |
/// This function returns the priority of item \c i. |
|
339 |
/// \pre \c i must be in the heap. |
|
340 |
/// \param i The item. |
|
341 |
Prio operator[](const Item &i) const { |
|
342 |
int idx = iim[i]; |
|
343 |
return data[idx].prio; |
|
344 |
} |
|
345 |
|
|
346 |
/// \brief \c i gets to the heap with priority \c p independently |
|
347 |
/// if \c i was already there. |
|
348 |
/// |
|
349 |
/// This method calls \ref push(\c i, \c p) if \c i is not stored |
|
350 |
/// in the heap and sets the priority of \c i to \c p otherwise. |
|
351 |
/// It may throw an \e UnderFlowPriorityException. |
|
352 |
/// \param i The item. |
|
353 |
/// \param p The priority. |
|
354 |
void set(const Item &i, const Prio &p) { |
|
355 |
int idx = iim[i]; |
|
356 |
if( idx < 0 ) { |
|
357 |
push(i, p); |
|
358 |
} |
|
359 |
else if( p >= data[idx].prio ) { |
|
360 |
data[idx].prio = p; |
|
361 |
bubble_up(idx); |
|
362 |
} else { |
|
363 |
data[idx].prio = p; |
|
364 |
bubble_down(idx); |
|
365 |
} |
|
366 |
} |
|
367 |
|
|
368 |
|
|
369 |
/// \brief Decreases the priority of \c i to \c p. |
|
370 |
/// |
|
371 |
/// This method decreases the priority of item \c i to \c p. |
|
372 |
/// \pre \c i must be stored in the heap with priority at least \c p, and |
|
373 |
/// \c should be greater or equal to the last removed item's priority. |
|
374 |
/// \param i The item. |
|
375 |
/// \param p The priority. |
|
376 |
void decrease(const Item &i, const Prio &p) { |
|
377 |
int idx = iim[i]; |
|
378 |
data[idx].prio = p; |
|
379 |
bubble_down(idx); |
|
380 |
} |
|
381 |
|
|
382 |
/// \brief Increases the priority of \c i to \c p. |
|
383 |
/// |
|
384 |
/// This method sets the priority of item \c i to \c p. |
|
385 |
/// \pre \c i must be stored in the heap with priority at most \c p |
|
386 |
/// \param i The item. |
|
387 |
/// \param p The priority. |
|
388 |
void increase(const Item &i, const Prio &p) { |
|
389 |
int idx = iim[i]; |
|
390 |
data[idx].prio = p; |
|
391 |
bubble_up(idx); |
|
392 |
} |
|
393 |
|
|
394 |
/// \brief Returns if \c item is in, has already been in, or has |
|
395 |
/// never been in the heap. |
|
396 |
/// |
|
397 |
/// This method returns PRE_HEAP if \c item has never been in the |
|
398 |
/// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
|
399 |
/// otherwise. In the latter case it is possible that \c item will |
|
400 |
/// get back to the heap again. |
|
401 |
/// \param i The item. |
|
402 |
State state(const Item &i) const { |
|
403 |
int s = iim[i]; |
|
404 |
if( s >= 0 ) s = 0; |
|
405 |
return State(s); |
|
406 |
} |
|
407 |
|
|
408 |
/// \brief Sets the state of the \c item in the heap. |
|
409 |
/// |
|
410 |
/// Sets the state of the \c item in the heap. It can be used to |
|
411 |
/// manually clear the heap when it is important to achive the |
|
412 |
/// better time complexity. |
|
413 |
/// \param i The item. |
|
414 |
/// \param st The state. It should not be \c IN_HEAP. |
|
415 |
void state(const Item& i, State st) { |
|
416 |
switch (st) { |
|
417 |
case POST_HEAP: |
|
418 |
case PRE_HEAP: |
|
419 |
if (state(i) == IN_HEAP) { |
|
420 |
erase(i); |
|
421 |
} |
|
422 |
iim[i] = st; |
|
423 |
break; |
|
424 |
case IN_HEAP: |
|
425 |
break; |
|
426 |
} |
|
427 |
} |
|
428 |
|
|
429 |
}; // class RadixHeap |
|
430 |
|
|
431 |
} // namespace lemon |
|
432 |
|
|
433 |
#endif // LEMON_RADIX_HEAP_H |
... | ... |
@@ -59,6 +59,7 @@ |
59 | 59 |
lemon/assert.h \ |
60 | 60 |
lemon/bfs.h \ |
61 | 61 |
lemon/bin_heap.h \ |
62 |
lemon/bucket_heap.h \ |
|
62 | 63 |
lemon/cbc.h \ |
63 | 64 |
lemon/circulation.h \ |
64 | 65 |
lemon/clp.h \ |
... | ... |
@@ -76,6 +77,7 @@ |
76 | 77 |
lemon/elevator.h \ |
77 | 78 |
lemon/error.h \ |
78 | 79 |
lemon/euler.h \ |
80 |
lemon/fib_heap.h \ |
|
79 | 81 |
lemon/full_graph.h \ |
80 | 82 |
lemon/glpk.h \ |
81 | 83 |
lemon/gomory_hu.h \ |
... | ... |
@@ -99,6 +101,7 @@ |
99 | 101 |
lemon/network_simplex.h \ |
100 | 102 |
lemon/path.h \ |
101 | 103 |
lemon/preflow.h \ |
104 |
lemon/radix_heap.h \ |
|
102 | 105 |
lemon/radix_sort.h \ |
103 | 106 |
lemon/random.h \ |
104 | 107 |
lemon/smart_graph.h \ |
... | ... |
@@ -31,6 +31,9 @@ |
31 | 31 |
#include <lemon/maps.h> |
32 | 32 |
|
33 | 33 |
#include <lemon/bin_heap.h> |
34 |
#include <lemon/fib_heap.h> |
|
35 |
#include <lemon/radix_heap.h> |
|
36 |
#include <lemon/bucket_heap.h> |
|
34 | 37 |
|
35 | 38 |
#include "test_tools.h" |
36 | 39 |
|
... | ... |
@@ -183,5 +186,39 @@ |
183 | 186 |
dijkstraHeapTest<NodeHeap>(digraph, length, source); |
184 | 187 |
} |
185 | 188 |
|
189 |
{ |
|
190 |
typedef FibHeap<Prio, ItemIntMap> IntHeap; |
|
191 |
checkConcept<Heap<Prio, ItemIntMap>, IntHeap>(); |
|
192 |
heapSortTest<IntHeap>(); |
|
193 |
heapIncreaseTest<IntHeap>(); |
|
194 |
|
|
195 |
typedef FibHeap<Prio, IntNodeMap > NodeHeap; |
|
196 |
checkConcept<Heap<Prio, IntNodeMap >, NodeHeap>(); |
|
197 |
dijkstraHeapTest<NodeHeap>(digraph, length, source); |
|
198 |
} |
|
199 |
|
|
200 |
{ |
|
201 |
typedef RadixHeap<ItemIntMap> IntHeap; |
|
202 |
checkConcept<Heap<Prio, ItemIntMap>, IntHeap>(); |
|
203 |
heapSortTest<IntHeap>(); |
|
204 |
heapIncreaseTest<IntHeap>(); |
|
205 |
|
|
206 |
typedef RadixHeap<IntNodeMap > NodeHeap; |
|
207 |
checkConcept<Heap<Prio, IntNodeMap >, NodeHeap>(); |
|
208 |
dijkstraHeapTest<NodeHeap>(digraph, length, source); |
|
209 |
} |
|
210 |
|
|
211 |
{ |
|
212 |
typedef BucketHeap<ItemIntMap> IntHeap; |
|
213 |
checkConcept<Heap<Prio, ItemIntMap>, IntHeap>(); |
|
214 |
heapSortTest<IntHeap>(); |
|
215 |
heapIncreaseTest<IntHeap>(); |
|
216 |
|
|
217 |
typedef BucketHeap<IntNodeMap > NodeHeap; |
|
218 |
checkConcept<Heap<Prio, IntNodeMap >, NodeHeap>(); |
|
219 |
dijkstraHeapTest<NodeHeap>(digraph, length, source); |
|
220 |
} |
|
221 |
|
|
222 |
|
|
186 | 223 |
return 0; |
187 | 224 |
} |
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