[255] | 1 | // -*- C++ -*- |
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| 2 | |
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[373] | 3 | #ifndef HUGO_FIB_HEAP_H |
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| 4 | #define HUGO_FIB_HEAP_H |
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[255] | 5 | |
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[857] | 6 | ///\file |
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[491] | 7 | ///\ingroup auxdat |
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[255] | 8 | ///\brief Fibonacci Heap implementation. |
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| 9 | |
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| 10 | #include <vector> |
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| 11 | #include <functional> |
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| 12 | #include <math.h> |
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| 13 | |
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| 14 | namespace hugo { |
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| 15 | |
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[430] | 16 | /// \addtogroup auxdat |
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| 17 | /// @{ |
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| 18 | |
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[857] | 19 | /// Fibonacci Heap. |
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[373] | 20 | |
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[857] | 21 | ///This class implements the \e Fibonacci \e heap data structure. A \e heap |
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| 22 | ///is a data structure for storing items with specified values called \e |
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| 23 | ///priorities in such a way that finding the item with minimum priority is |
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| 24 | ///efficient. \ref Compare specifies the ordering of the priorities. In a heap |
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| 25 | ///one can change the priority of an item, add or erase an item, etc. |
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| 26 | /// |
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| 27 | ///The methods \ref increase and \ref erase are not efficient in a Fibonacci |
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| 28 | ///heap. In case of many calls to these operations, it is better to use a |
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| 29 | ///\e binary \e heap. |
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| 30 | /// |
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| 31 | ///\param Item Type of the items to be stored. |
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| 32 | ///\param Prio Type of the priority of the items. |
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| 33 | ///\param ItemIntMap A read and writable Item int map, for the usage of |
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| 34 | ///the heap. |
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| 35 | ///\param Compare A class for the ordering of the priorities. The |
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| 36 | ///default is \c std::less<Prio>. |
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| 37 | /// |
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| 38 | ///\author Jacint Szabo |
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| 39 | |
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[373] | 40 | #ifdef DOXYGEN |
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| 41 | template <typename Item, |
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| 42 | typename Prio, |
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| 43 | typename ItemIntMap, |
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| 44 | typename Compare> |
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| 45 | #else |
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| 46 | template <typename Item, |
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| 47 | typename Prio, |
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| 48 | typename ItemIntMap, |
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[255] | 49 | typename Compare = std::less<Prio> > |
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[373] | 50 | #endif |
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[255] | 51 | class FibHeap { |
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[387] | 52 | public: |
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[255] | 53 | typedef Prio PrioType; |
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| 54 | |
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[373] | 55 | private: |
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[255] | 56 | class store; |
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| 57 | |
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| 58 | std::vector<store> container; |
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| 59 | int minimum; |
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| 60 | ItemIntMap &iimap; |
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| 61 | Compare comp; |
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| 62 | int num_items; |
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[373] | 63 | |
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[255] | 64 | public: |
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| 65 | enum state_enum { |
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| 66 | IN_HEAP = 0, |
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| 67 | PRE_HEAP = -1, |
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| 68 | POST_HEAP = -2 |
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| 69 | }; |
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| 70 | |
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[373] | 71 | FibHeap(ItemIntMap &_iimap) : minimum(0), iimap(_iimap), num_items() {} |
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| 72 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(0), |
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[255] | 73 | iimap(_iimap), comp(_comp), num_items() {} |
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| 74 | |
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[373] | 75 | ///The number of items stored in the heap. |
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| 76 | |
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| 77 | /** |
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[387] | 78 | Returns the number of items stored in the heap. |
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[373] | 79 | */ |
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| 80 | int size() const { return num_items; } |
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| 81 | |
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| 82 | ///Checks if the heap stores no items. |
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[255] | 83 | |
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[373] | 84 | /** |
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[857] | 85 | Returns \c true if and only if the heap stores no items. |
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[373] | 86 | */ |
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| 87 | bool empty() const { return num_items==0; } |
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| 88 | |
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[387] | 89 | ///\c item gets to the heap with priority \c value independently if \c item was already there. |
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[373] | 90 | |
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| 91 | /** |
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[387] | 92 | This method calls \ref push(\c item, \c value) if \c item is not |
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| 93 | stored in the heap and it calls \ref decrease(\c item, \c value) or |
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| 94 | \ref increase(\c item, \c value) otherwise. |
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[373] | 95 | */ |
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[387] | 96 | void set (Item const item, PrioType const value); |
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[373] | 97 | |
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| 98 | ///Adds \c item to the heap with priority \c value. |
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| 99 | |
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| 100 | /** |
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| 101 | Adds \c item to the heap with priority \c value. |
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| 102 | \pre \c item must not be stored in the heap. |
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| 103 | */ |
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[387] | 104 | void push (Item const item, PrioType const value); |
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[373] | 105 | |
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[857] | 106 | ///Returns the item with minimum priority relative to \ref Compare. |
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[373] | 107 | |
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| 108 | /** |
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[857] | 109 | This method returns the item with minimum priority relative to \ref |
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| 110 | Compare. |
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| 111 | \pre The heap must be nonempty. |
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[373] | 112 | */ |
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| 113 | Item top() const { return container[minimum].name; } |
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| 114 | |
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[857] | 115 | ///Returns the minimum priority relative to \ref Compare. |
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[373] | 116 | |
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| 117 | /** |
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[857] | 118 | It returns the minimum priority relative to \ref Compare. |
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[373] | 119 | \pre The heap must be nonempty. |
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| 120 | */ |
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| 121 | PrioType prio() const { return container[minimum].prio; } |
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| 122 | |
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| 123 | ///Returns the priority of \c item. |
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| 124 | |
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| 125 | /** |
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[857] | 126 | This function returns the priority of \c item. |
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[373] | 127 | \pre \c item must be in the heap. |
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| 128 | */ |
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[387] | 129 | PrioType& operator[](const Item& item) { |
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| 130 | return container[iimap[item]].prio; |
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| 131 | } |
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[373] | 132 | |
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| 133 | ///Returns the priority of \c item. |
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| 134 | |
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| 135 | /** |
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| 136 | It returns the priority of \c item. |
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| 137 | \pre \c item must be in the heap. |
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| 138 | */ |
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[387] | 139 | const PrioType& operator[](const Item& item) const { |
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| 140 | return container[iimap[item]].prio; |
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[255] | 141 | } |
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| 142 | |
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| 143 | |
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[857] | 144 | ///Deletes the item with minimum priority relative to \ref Compare. |
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[255] | 145 | |
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[373] | 146 | /** |
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[857] | 147 | This method deletes the item with minimum priority relative to \ref |
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| 148 | Compare from the heap. |
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| 149 | \pre The heap must be non-empty. |
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[373] | 150 | */ |
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| 151 | void pop(); |
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| 152 | |
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| 153 | ///Deletes \c item from the heap. |
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| 154 | |
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| 155 | /** |
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| 156 | This method deletes \c item from the heap, if \c item was already |
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| 157 | stored in the heap. It is quite inefficient in Fibonacci heaps. |
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| 158 | */ |
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[387] | 159 | void erase (const Item& item); |
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[373] | 160 | |
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| 161 | ///Decreases the priority of \c item to \c value. |
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| 162 | |
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| 163 | /** |
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| 164 | This method decreases the priority of \c item to \c value. |
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| 165 | \pre \c item must be stored in the heap with priority at least \c |
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[857] | 166 | value relative to \ref Compare. |
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[373] | 167 | */ |
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[387] | 168 | void decrease (Item item, PrioType const value); |
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[373] | 169 | |
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| 170 | ///Increases the priority of \c item to \c value. |
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| 171 | |
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| 172 | /** |
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| 173 | This method sets the priority of \c item to \c value. Though |
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| 174 | there is no precondition on the priority of \c item, this |
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[857] | 175 | method should be used only if it is indeed necessary to increase |
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| 176 | (relative to \ref Compare) the priority of \c item, because this |
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[373] | 177 | method is inefficient. |
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| 178 | */ |
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[387] | 179 | void increase (Item item, PrioType const value) { |
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| 180 | erase(item); |
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| 181 | push(item, value); |
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[373] | 182 | } |
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| 183 | |
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| 184 | |
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[857] | 185 | ///Returns if \c item is in, has already been in, or has never been in the heap. |
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[373] | 186 | |
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| 187 | /** |
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| 188 | This method returns PRE_HEAP if \c item has never been in the |
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| 189 | heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP |
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| 190 | otherwise. In the latter case it is possible that \c item will |
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| 191 | get back to the heap again. |
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| 192 | */ |
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[387] | 193 | state_enum state(const Item &item) const { |
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| 194 | int i=iimap[item]; |
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| 195 | if( i>=0 ) { |
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| 196 | if ( container[i].in ) i=0; |
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| 197 | else i=-2; |
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| 198 | } |
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| 199 | return state_enum(i); |
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| 200 | } |
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| 201 | |
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| 202 | private: |
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| 203 | |
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| 204 | void balance(); |
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| 205 | void makeroot(int c); |
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| 206 | void cut(int a, int b); |
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| 207 | void cascade(int a); |
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| 208 | void fuse(int a, int b); |
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| 209 | void unlace(int a); |
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[373] | 210 | |
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| 211 | |
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[387] | 212 | class store { |
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| 213 | friend class FibHeap; |
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| 214 | |
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| 215 | Item name; |
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| 216 | int parent; |
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| 217 | int left_neighbor; |
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| 218 | int right_neighbor; |
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| 219 | int child; |
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| 220 | int degree; |
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| 221 | bool marked; |
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| 222 | bool in; |
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| 223 | PrioType prio; |
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| 224 | |
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| 225 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 226 | }; |
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| 227 | }; |
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| 228 | |
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| 229 | |
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[373] | 230 | |
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| 231 | // ********************************************************************** |
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| 232 | // IMPLEMENTATIONS |
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| 233 | // ********************************************************************** |
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| 234 | |
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[387] | 235 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 236 | typename Compare> |
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| 237 | void FibHeap<Item, Prio, ItemIntMap, Compare>::set |
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| 238 | (Item const item, PrioType const value) |
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| 239 | { |
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| 240 | int i=iimap[item]; |
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| 241 | if ( i >= 0 && container[i].in ) { |
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| 242 | if ( comp(value, container[i].prio) ) decrease(item, value); |
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| 243 | if ( comp(container[i].prio, value) ) increase(item, value); |
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| 244 | } else push(item, value); |
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| 245 | } |
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[255] | 246 | |
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[387] | 247 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 248 | typename Compare> |
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| 249 | void FibHeap<Item, Prio, ItemIntMap, Compare>::push |
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| 250 | (Item const item, PrioType const value) { |
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| 251 | int i=iimap[item]; |
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[255] | 252 | if ( i < 0 ) { |
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| 253 | int s=container.size(); |
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[387] | 254 | iimap.set( item, s ); |
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[255] | 255 | store st; |
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[387] | 256 | st.name=item; |
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[255] | 257 | container.push_back(st); |
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| 258 | i=s; |
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| 259 | } else { |
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| 260 | container[i].parent=container[i].child=-1; |
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| 261 | container[i].degree=0; |
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| 262 | container[i].in=true; |
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| 263 | container[i].marked=false; |
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| 264 | } |
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| 265 | |
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| 266 | if ( num_items ) { |
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| 267 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 268 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 269 | container[minimum].right_neighbor=i; |
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| 270 | container[i].left_neighbor=minimum; |
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| 271 | if ( comp( value, container[minimum].prio) ) minimum=i; |
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| 272 | } else { |
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| 273 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 274 | minimum=i; |
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| 275 | } |
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| 276 | container[i].prio=value; |
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| 277 | ++num_items; |
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| 278 | } |
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| 279 | |
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[387] | 280 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 281 | typename Compare> |
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| 282 | void FibHeap<Item, Prio, ItemIntMap, Compare>::pop() { |
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[255] | 283 | /*The first case is that there are only one root.*/ |
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| 284 | if ( container[minimum].left_neighbor==minimum ) { |
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| 285 | container[minimum].in=false; |
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| 286 | if ( container[minimum].degree!=0 ) { |
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| 287 | makeroot(container[minimum].child); |
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| 288 | minimum=container[minimum].child; |
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| 289 | balance(); |
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| 290 | } |
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| 291 | } else { |
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| 292 | int right=container[minimum].right_neighbor; |
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| 293 | unlace(minimum); |
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| 294 | container[minimum].in=false; |
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| 295 | if ( container[minimum].degree > 0 ) { |
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| 296 | int left=container[minimum].left_neighbor; |
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| 297 | int child=container[minimum].child; |
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| 298 | int last_child=container[child].left_neighbor; |
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| 299 | |
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| 300 | makeroot(child); |
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| 301 | |
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| 302 | container[left].right_neighbor=child; |
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| 303 | container[child].left_neighbor=left; |
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| 304 | container[right].left_neighbor=last_child; |
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| 305 | container[last_child].right_neighbor=right; |
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| 306 | } |
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| 307 | minimum=right; |
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| 308 | balance(); |
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| 309 | } // the case where there are more roots |
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| 310 | --num_items; |
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| 311 | } |
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| 312 | |
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[387] | 313 | |
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| 314 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 315 | typename Compare> |
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| 316 | void FibHeap<Item, Prio, ItemIntMap, Compare>::erase |
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| 317 | (const Item& item) { |
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| 318 | int i=iimap[item]; |
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[255] | 319 | |
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| 320 | if ( i >= 0 && container[i].in ) { |
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| 321 | if ( container[i].parent!=-1 ) { |
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| 322 | int p=container[i].parent; |
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| 323 | cut(i,p); |
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| 324 | cascade(p); |
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| 325 | } |
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| 326 | minimum=i; //As if its prio would be -infinity |
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| 327 | pop(); |
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| 328 | } |
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[387] | 329 | } |
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[255] | 330 | |
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[387] | 331 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 332 | typename Compare> |
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| 333 | void FibHeap<Item, Prio, ItemIntMap, Compare>::decrease |
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| 334 | (Item item, PrioType const value) { |
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| 335 | int i=iimap[item]; |
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[255] | 336 | container[i].prio=value; |
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| 337 | int p=container[i].parent; |
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| 338 | |
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| 339 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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| 340 | cut(i,p); |
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| 341 | cascade(p); |
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| 342 | } |
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| 343 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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[387] | 344 | } |
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| 345 | |
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[255] | 346 | |
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[387] | 347 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 348 | typename Compare> |
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| 349 | void FibHeap<Item, Prio, ItemIntMap, Compare>::balance() { |
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[255] | 350 | |
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| 351 | int maxdeg=int( floor( 2.08*log(double(container.size()))))+1; |
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| 352 | |
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| 353 | std::vector<int> A(maxdeg,-1); |
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| 354 | |
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| 355 | /* |
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| 356 | *Recall that now minimum does not point to the minimum prio element. |
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| 357 | *We set minimum to this during balance(). |
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| 358 | */ |
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| 359 | int anchor=container[minimum].left_neighbor; |
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| 360 | int next=minimum; |
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| 361 | bool end=false; |
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| 362 | |
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| 363 | do { |
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| 364 | int active=next; |
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| 365 | if ( anchor==active ) end=true; |
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| 366 | int d=container[active].degree; |
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| 367 | next=container[active].right_neighbor; |
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| 368 | |
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| 369 | while (A[d]!=-1) { |
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| 370 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 371 | fuse(active,A[d]); |
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| 372 | } else { |
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| 373 | fuse(A[d],active); |
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| 374 | active=A[d]; |
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| 375 | } |
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| 376 | A[d]=-1; |
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| 377 | ++d; |
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| 378 | } |
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| 379 | A[d]=active; |
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| 380 | } while ( !end ); |
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| 381 | |
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| 382 | |
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| 383 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
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| 384 | int s=minimum; |
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| 385 | int m=minimum; |
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| 386 | do { |
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| 387 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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| 388 | s=container[s].right_neighbor; |
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| 389 | } while ( s != m ); |
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| 390 | } |
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| 391 | |
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[387] | 392 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 393 | typename Compare> |
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| 394 | void FibHeap<Item, Prio, ItemIntMap, Compare>::makeroot |
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| 395 | (int c) { |
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[255] | 396 | int s=c; |
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| 397 | do { |
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| 398 | container[s].parent=-1; |
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| 399 | s=container[s].right_neighbor; |
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| 400 | } while ( s != c ); |
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| 401 | } |
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[387] | 402 | |
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| 403 | |
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| 404 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 405 | typename Compare> |
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| 406 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cut |
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| 407 | (int a, int b) { |
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| 408 | /* |
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| 409 | *Replacing a from the children of b. |
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| 410 | */ |
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| 411 | --container[b].degree; |
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[255] | 412 | |
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[387] | 413 | if ( container[b].degree !=0 ) { |
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| 414 | int child=container[b].child; |
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| 415 | if ( child==a ) |
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| 416 | container[b].child=container[child].right_neighbor; |
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| 417 | unlace(a); |
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| 418 | } |
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| 419 | |
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| 420 | |
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| 421 | /*Lacing a to the roots.*/ |
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| 422 | int right=container[minimum].right_neighbor; |
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| 423 | container[minimum].right_neighbor=a; |
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| 424 | container[a].left_neighbor=minimum; |
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| 425 | container[a].right_neighbor=right; |
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| 426 | container[right].left_neighbor=a; |
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| 427 | |
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| 428 | container[a].parent=-1; |
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| 429 | container[a].marked=false; |
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| 430 | } |
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| 431 | |
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[255] | 432 | |
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[387] | 433 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 434 | typename Compare> |
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| 435 | void FibHeap<Item, Prio, ItemIntMap, Compare>::cascade |
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| 436 | (int a) |
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[255] | 437 | { |
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| 438 | if ( container[a].parent!=-1 ) { |
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| 439 | int p=container[a].parent; |
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| 440 | |
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| 441 | if ( container[a].marked==false ) container[a].marked=true; |
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| 442 | else { |
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| 443 | cut(a,p); |
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| 444 | cascade(p); |
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| 445 | } |
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| 446 | } |
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| 447 | } |
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| 448 | |
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| 449 | |
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[387] | 450 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 451 | typename Compare> |
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| 452 | void FibHeap<Item, Prio, ItemIntMap, Compare>::fuse |
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| 453 | (int a, int b) { |
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[255] | 454 | unlace(b); |
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| 455 | |
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| 456 | /*Lacing b under a.*/ |
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| 457 | container[b].parent=a; |
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| 458 | |
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| 459 | if (container[a].degree==0) { |
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| 460 | container[b].left_neighbor=b; |
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| 461 | container[b].right_neighbor=b; |
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| 462 | container[a].child=b; |
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| 463 | } else { |
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| 464 | int child=container[a].child; |
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| 465 | int last_child=container[child].left_neighbor; |
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| 466 | container[child].left_neighbor=b; |
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| 467 | container[b].right_neighbor=child; |
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| 468 | container[last_child].right_neighbor=b; |
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| 469 | container[b].left_neighbor=last_child; |
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| 470 | } |
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| 471 | |
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| 472 | ++container[a].degree; |
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| 473 | |
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| 474 | container[b].marked=false; |
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| 475 | } |
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| 476 | |
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[387] | 477 | |
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| 478 | /* |
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| 479 | *It is invoked only if a has siblings. |
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| 480 | */ |
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| 481 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 482 | typename Compare> |
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| 483 | void FibHeap<Item, Prio, ItemIntMap, Compare>::unlace |
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| 484 | (int a) { |
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[255] | 485 | int leftn=container[a].left_neighbor; |
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| 486 | int rightn=container[a].right_neighbor; |
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| 487 | container[leftn].right_neighbor=rightn; |
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| 488 | container[rightn].left_neighbor=leftn; |
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[387] | 489 | } |
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[255] | 490 | |
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[430] | 491 | ///@} |
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| 492 | |
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[255] | 493 | } //namespace hugo |
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[477] | 494 | |
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| 495 | #endif //HUGO_FIB_HEAP_H |
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| 496 | |
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