[159] | 1 | // -*- C++ -*- |
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| 2 | /* |
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| 3 | *template <typename Item, |
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| 4 | * typename Prio, |
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| 5 | * typename ItemIntMap, |
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| 6 | * typename Compare = std::less<Prio> > |
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| 7 | * |
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| 8 | *constructors: |
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| 9 | * |
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| 10 | *FibHeap(ItemIntMap), FibHeap(ItemIntMap, Compare) |
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| 11 | * |
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| 12 | *Member functions: |
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| 13 | * |
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| 14 | *int size() : returns the number of elements in the heap |
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| 15 | * |
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| 16 | *bool empty() : true iff size()=0 |
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| 17 | * |
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| 18 | *void push(Item, Prio) : pushes Item to the heap with priority Prio. If |
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| 19 | * Item was already in the heap, it calls decrease(Item, Prio) |
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| 20 | * |
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| 21 | *Item top() : returns the Item with least Prio |
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| 22 | * |
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| 23 | *Prio prio() : returns the least Prio |
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| 24 | * |
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| 25 | *Prio get(Item) : returns Prio of Item |
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| 26 | * |
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| 27 | *void pop() : deletes the Item with least Prio |
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| 28 | * |
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| 29 | *void erase(Item) : deletes Item from the heap if it was already there |
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| 30 | * |
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| 31 | *void decrease(Item, P) : If Item was not in the heap, then it calls |
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| 32 | * push(Item, P). If item is in the heap with Prio more than P |
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| 33 | * then sets its Prio to P. |
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| 34 | * |
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| 35 | *void increase(Item, P) : If Item was not in the heap, then it calls |
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| 36 | * push(Item, P). If item is in the heap with Prio less than P |
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| 37 | * then sets its Prio to P. |
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| 38 | * |
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| 39 | * |
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| 40 | *In Fibonacci heaps, increase and erase are not efficient, in case of |
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| 41 | *many calls to these operations, it is better to use bin_heap. |
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| 42 | */ |
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| 43 | |
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| 44 | #ifndef FIB_HEAP_H |
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| 45 | #define FIB_HEAP_H |
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| 46 | |
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| 47 | #include <vector> |
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| 48 | #include <functional> |
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| 49 | #include <math.h> |
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| 50 | |
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| 51 | namespace hugo { |
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| 52 | |
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| 53 | template <typename Item, typename Prio, typename ItemIntMap, |
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| 54 | typename Compare = std::less<Prio> > |
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| 55 | |
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| 56 | class FibHeap { |
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| 57 | |
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| 58 | typedef Prio PrioType; |
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| 59 | |
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| 60 | class store; |
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| 61 | |
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| 62 | std::vector<store> container; |
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| 63 | int minimum; |
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| 64 | bool blank; |
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| 65 | ItemIntMap &iimap; |
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| 66 | Compare comp; |
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| 67 | |
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| 68 | public : |
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| 69 | |
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| 70 | FibHeap(ItemIntMap &_iimap) : minimum(), blank(true), iimap(_iimap) {} |
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| 71 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(), |
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| 72 | blank(true), iimap(_iimap), comp(_comp) {} |
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| 73 | |
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| 74 | |
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| 75 | int size() const { |
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| 76 | int s=0; |
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| 77 | for ( unsigned int i=0; i!=container.size(); ++i ) |
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| 78 | if ( container[i].in ) ++s; |
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| 79 | return s; |
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| 80 | } |
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| 81 | |
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| 82 | |
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| 83 | bool empty() const { return blank; } |
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| 84 | |
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| 85 | |
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| 86 | void push (Item const it, PrioType const value) |
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| 87 | { |
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| 88 | |
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| 89 | int i=iimap.get(it); |
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| 90 | |
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| 91 | if ( i >= 0 && container[i].in ) decrease(it, value); |
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| 92 | else { |
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| 93 | if ( i < 0 ) { |
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| 94 | int s=container.size(); |
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| 95 | iimap.set( it, s ); |
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| 96 | store st; |
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| 97 | st.name=it; |
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| 98 | container.push_back(st); |
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| 99 | i=s; |
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| 100 | } |
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| 101 | |
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| 102 | if ( !blank ) { |
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| 103 | container[container[minimum].right_neighbor].left_neighbor=i; |
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| 104 | container[i].right_neighbor=container[minimum].right_neighbor; |
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| 105 | container[minimum].right_neighbor=i; |
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| 106 | container[i].left_neighbor=minimum; |
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| 107 | if ( !comp( container[minimum].prio, value) ) minimum=i; |
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| 108 | |
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| 109 | |
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| 110 | |
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| 111 | } else { |
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| 112 | container[i].right_neighbor=container[i].left_neighbor=i; |
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| 113 | minimum=i; |
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| 114 | blank=false; |
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| 115 | } |
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| 116 | container[i].prio=value; |
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| 117 | } |
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| 118 | } |
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| 119 | |
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| 120 | |
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| 121 | Item top() const { |
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| 122 | if ( !blank ) { |
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| 123 | return container[minimum].name; |
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| 124 | } else { |
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| 125 | return Item(); |
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| 126 | } |
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| 127 | } |
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| 128 | |
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| 129 | |
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| 130 | PrioType prio() const { |
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| 131 | if ( !blank ) { |
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| 132 | return container[minimum].prio; |
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| 133 | } else { |
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| 134 | return PrioType(); |
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| 135 | } |
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| 136 | } |
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| 137 | |
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| 138 | |
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| 139 | const PrioType get(const Item& it) const |
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| 140 | { |
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| 141 | int i=iimap.get(it); |
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| 142 | |
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| 143 | if ( i >= 0 && container[i].in ) { |
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| 144 | return container[i].prio; |
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| 145 | } else { |
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| 146 | return PrioType(); |
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| 147 | } |
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| 148 | } |
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| 149 | |
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| 150 | |
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| 151 | void pop() { |
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| 152 | if ( !blank ) { |
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| 153 | |
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| 154 | /*The first case is that there are only one root.*/ |
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| 155 | if ( container[minimum].left_neighbor==minimum ) { |
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| 156 | container[minimum].in=false; |
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| 157 | if ( container[minimum].degree==0 ) blank=true; |
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| 158 | else { |
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| 159 | makeroot(container[minimum].child); |
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| 160 | minimum=container[minimum].child; |
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| 161 | balance(); |
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| 162 | } |
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| 163 | } else { |
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| 164 | int right=container[minimum].right_neighbor; |
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| 165 | unlace(minimum); |
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| 166 | container[minimum].in=false; |
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| 167 | if ( container[minimum].degree > 0 ) { |
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| 168 | int left=container[minimum].left_neighbor; |
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| 169 | int child=container[minimum].child; |
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| 170 | int last_child=container[child].left_neighbor; |
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| 171 | |
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| 172 | container[left].right_neighbor=child; |
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| 173 | container[child].left_neighbor=left; |
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| 174 | container[right].left_neighbor=last_child; |
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| 175 | container[last_child].right_neighbor=right; |
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| 176 | |
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| 177 | makeroot(child); |
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| 178 | } |
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| 179 | minimum=right; |
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| 180 | balance(); |
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| 181 | } // the case where there are more roots |
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| 182 | } |
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| 183 | } |
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| 184 | |
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| 185 | |
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| 186 | void erase (const Item& it) { |
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| 187 | int i=iimap.get(it); |
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| 188 | |
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| 189 | if ( i >= 0 && container[i].in ) { |
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| 190 | |
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| 191 | if ( container[i].parent!=-1 ) { |
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| 192 | int p=container[i].parent; |
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| 193 | cut(i,p); |
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| 194 | cascade(p); |
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| 195 | minimum=i; //As if its prio would be -infinity |
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| 196 | } |
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| 197 | pop(); |
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| 198 | } |
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| 199 | } |
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| 200 | |
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| 201 | |
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| 202 | void decrease (Item it, PrioType const value) { |
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| 203 | int i=iimap.get(it); |
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| 204 | if ( i >= 0 && container[i].in ) { |
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| 205 | |
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| 206 | if ( comp(value, container[i].prio) ) { |
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| 207 | container[i].prio=value; |
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| 208 | |
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| 209 | if ( container[i].parent!=-1 ) { |
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| 210 | int p=container[i].parent; |
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| 211 | |
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| 212 | if ( !comp(container[p].prio, value) ) { |
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| 213 | cut(i,p); |
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| 214 | cascade(p); |
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| 215 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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| 216 | } |
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| 217 | } |
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| 218 | } |
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| 219 | } else push(it, value); |
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| 220 | } |
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| 221 | |
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| 222 | |
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| 223 | void increase (Item it, PrioType const value) { |
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| 224 | int i=iimap.get(it); |
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| 225 | |
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| 226 | if ( i >= 0 && container[i].in ) { |
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| 227 | if ( comp(container[i].prio, value) ) { |
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| 228 | erase(it); |
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| 229 | push(it, value); |
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| 230 | } |
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| 231 | } else push(it, value); |
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| 232 | } |
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| 233 | |
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| 234 | |
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| 235 | private: |
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| 236 | |
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| 237 | void balance() { |
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| 238 | int maxdeg=int( floor( 2.08*log(double(container.size()))))+1; |
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| 239 | |
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| 240 | std::vector<int> A(maxdeg,-1); |
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| 241 | |
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| 242 | /* |
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| 243 | *Recall that now minimum does not point to the minimum prio element. |
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| 244 | *We set minimum to this during balance(). |
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| 245 | */ |
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| 246 | int anchor=container[minimum].left_neighbor; |
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| 247 | int next=minimum; |
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| 248 | bool end=false; |
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| 249 | |
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| 250 | do { |
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| 251 | int active=next; |
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| 252 | int d=container[active].degree; |
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| 253 | if ( anchor==active ) end=true; |
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| 254 | next = container[active].right_neighbor; |
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| 255 | if ( !comp(container[minimum].prio, container[active].prio) ) |
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| 256 | minimum=active; |
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| 257 | |
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| 258 | while (A[d]!=-1) { |
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| 259 | |
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| 260 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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| 261 | fuse(active,A[d]); |
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| 262 | } else { |
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| 263 | fuse(A[d],active); |
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| 264 | active=A[d]; |
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| 265 | } |
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| 266 | A[d]=-1; |
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| 267 | ++d; |
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| 268 | } |
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| 269 | |
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| 270 | A[d]=active; |
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| 271 | } while ( !end ); |
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| 272 | } |
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| 273 | |
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| 274 | |
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| 275 | |
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| 276 | |
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| 277 | /* |
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| 278 | *All the siblings of a are made roots. |
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| 279 | */ |
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| 280 | void makeroot (int c) |
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| 281 | { |
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| 282 | int s=c; |
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| 283 | do { |
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| 284 | container[s].parent=-1; |
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| 285 | s=container[s].right_neighbor; |
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| 286 | } while ( s != c ); |
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| 287 | } |
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| 288 | |
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| 289 | |
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| 290 | void cut (int a, int b) |
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| 291 | { |
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| 292 | |
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| 293 | /* |
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| 294 | *Replacing a from the children of b. |
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| 295 | */ |
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| 296 | --container[b].degree; |
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| 297 | |
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| 298 | if ( container[b].degree !=0 ) { |
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| 299 | int child=container[b].child; |
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| 300 | if ( child==a ) |
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| 301 | container[b].child=container[child].right_neighbor; |
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| 302 | |
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| 303 | unlace(a); |
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| 304 | |
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| 305 | } |
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| 306 | |
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| 307 | |
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| 308 | /*Lacing i to the roots.*/ |
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| 309 | int right=container[minimum].right_neighbor; |
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| 310 | container[minimum].right_neighbor=a; |
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| 311 | container[a].left_neighbor=minimum; |
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| 312 | container[a].right_neighbor=right; |
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| 313 | container[right].left_neighbor=a; |
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| 314 | |
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| 315 | container[a].parent=-1; |
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| 316 | container[a].marked=false; |
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| 317 | } |
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| 318 | |
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| 319 | |
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| 320 | void cascade (int a) |
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| 321 | { |
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| 322 | if ( container[a].parent!=-1 ) { |
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| 323 | int p=container[a].parent; |
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| 324 | |
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| 325 | if ( container[a].marked==false ) container[a].marked=true; |
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| 326 | else { |
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| 327 | cut(a,p); |
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| 328 | cascade(p); |
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| 329 | } |
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| 330 | } |
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| 331 | } |
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| 332 | |
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| 333 | |
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| 334 | void fuse (int a, int b) |
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| 335 | { |
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| 336 | |
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| 337 | unlace(b); |
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| 338 | |
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| 339 | |
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| 340 | /*Lacing b under a.*/ |
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| 341 | container[b].parent=a; |
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| 342 | |
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| 343 | if (container[a].degree==0) { |
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| 344 | container[b].left_neighbor=b; |
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| 345 | container[b].right_neighbor=b; |
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| 346 | container[a].child=b; |
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| 347 | } else { |
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| 348 | int child=container[a].child; |
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| 349 | int last_child=container[child].left_neighbor; |
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| 350 | container[child].left_neighbor=b; |
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| 351 | container[b].right_neighbor=child; |
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| 352 | container[last_child].right_neighbor=b; |
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| 353 | container[b].left_neighbor=last_child; |
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| 354 | } |
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| 355 | |
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| 356 | ++container[a].degree; |
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| 357 | |
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| 358 | container[b].marked=false; |
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| 359 | } |
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| 360 | |
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| 361 | |
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| 362 | /* |
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| 363 | *It is invoked only if a has siblings. |
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| 364 | */ |
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| 365 | |
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| 366 | void unlace (int a) { |
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| 367 | int leftn=container[a].left_neighbor; |
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| 368 | int rightn=container[a].right_neighbor; |
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| 369 | container[leftn].right_neighbor=rightn; |
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| 370 | container[rightn].left_neighbor=leftn; |
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| 371 | } |
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| 372 | |
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| 373 | |
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| 374 | class store { |
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| 375 | friend class FibHeap; |
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| 376 | |
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| 377 | Item name; |
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| 378 | int parent; |
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| 379 | int left_neighbor; |
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| 380 | int right_neighbor; |
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| 381 | int child; |
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| 382 | int degree; |
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| 383 | bool marked; |
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| 384 | bool in; |
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| 385 | PrioType prio; |
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| 386 | |
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| 387 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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| 388 | }; |
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| 389 | |
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| 390 | }; |
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| 391 | |
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| 392 | } //namespace hugo |
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| 393 | #endif |
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| 394 | |
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| 395 | |
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| 396 | |
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| 397 | |
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| 398 | |
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| 399 | |
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