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 set(Item, Prio) : calls push(Item, Prio) if Item is not |
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19 | * in the heap, and calls decrease/increase(Item, Prio) otherwise |
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20 | * |
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21 | *void push(Item, Prio) : pushes Item to the heap with priority Prio. Item |
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22 | * mustn't be in the heap. |
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23 | * |
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24 | *Item top() : returns the Item with least Prio |
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25 | * |
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26 | *Prio prio() : returns the least Prio |
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27 | * |
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28 | *Prio get(Item) : returns Prio of Item |
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29 | * |
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30 | *void pop() : deletes the Item with least Prio |
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31 | * |
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32 | *void erase(Item) : deletes Item from the heap if it was already there |
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33 | * |
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34 | *void decrease(Item, P) : decreases prio of Item to P. |
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35 | * Item must be in the heap with prio at least P. |
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36 | * |
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37 | *void increase(Item, P) : sets prio of Item to P. |
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38 | * |
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39 | *state_enum state(Item) : returns PRE_HEAP if Item has not been in the |
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40 | * heap until now, IN_HEAP if it is in the heap at the moment, and |
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41 | * POST_HEAP otherwise. In the latter case it is possible that Item |
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42 | * will get back to the heap again. |
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43 | * |
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44 | *In Fibonacci heaps, increase and erase are not efficient, in case of |
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45 | *many calls to these operations, it is better to use bin_heap. |
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46 | */ |
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47 | |
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48 | #ifndef FIB_HEAP_H |
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49 | #define FIB_HEAP_H |
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50 | |
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51 | #include <vector> |
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52 | #include <functional> |
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53 | #include <math.h> |
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54 | |
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55 | namespace hugo { |
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56 | |
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57 | template <typename Item, typename Prio, typename ItemIntMap, |
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58 | typename Compare = std::less<Prio> > |
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59 | |
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60 | class FibHeap { |
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61 | |
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62 | typedef Prio PrioType; |
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63 | |
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64 | class store; |
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65 | |
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66 | std::vector<store> container; |
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67 | int minimum; |
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68 | bool blank; |
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69 | ItemIntMap &iimap; |
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70 | Compare comp; |
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71 | |
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72 | enum state_enum { |
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73 | IN_HEAP = 0, |
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74 | PRE_HEAP = -1, |
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75 | POST_HEAP = -2 |
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76 | }; |
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77 | |
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78 | public : |
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79 | |
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80 | FibHeap(ItemIntMap &_iimap) : minimum(), blank(true), iimap(_iimap) {} |
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81 | FibHeap(ItemIntMap &_iimap, const Compare &_comp) : minimum(), |
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82 | blank(true), iimap(_iimap), comp(_comp) {} |
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83 | |
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84 | |
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85 | int size() const { |
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86 | int s=0; |
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87 | for ( unsigned int i=0; i!=container.size(); ++i ) |
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88 | if ( container[i].in ) ++s; |
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89 | return s; |
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90 | } |
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91 | |
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92 | |
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93 | bool empty() const { return blank; } |
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94 | |
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95 | |
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96 | void set (Item const it, PrioType const value) { |
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97 | int i=iimap.get(it); |
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98 | if ( i >= 0 && container[i].in ) { |
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99 | if ( !comp(container[i].prio, value) ) decrease(it, value); |
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100 | if ( comp(container[i].prio, value) ) increase(it, value); |
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101 | } else push(it, value); |
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102 | } |
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103 | |
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104 | |
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105 | void push (Item const it, PrioType const value) { |
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106 | int i=iimap.get(it); |
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107 | if ( i < 0 ) { |
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108 | int s=container.size(); |
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109 | iimap.set( it, s ); |
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110 | store st; |
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111 | st.name=it; |
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112 | container.push_back(st); |
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113 | i=s; |
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114 | } else { |
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115 | container[i].parent=container[i].child=-1; |
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116 | container[i].degree=0; |
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117 | container[i].in=true; |
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118 | container[i].marked=false; |
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119 | } |
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120 | |
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121 | if ( !blank ) { |
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122 | container[container[minimum].right_neighbor].left_neighbor=i; |
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123 | container[i].right_neighbor=container[minimum].right_neighbor; |
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124 | container[minimum].right_neighbor=i; |
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125 | container[i].left_neighbor=minimum; |
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126 | if ( !comp( container[minimum].prio, value) ) minimum=i; |
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127 | } else { |
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128 | container[i].right_neighbor=container[i].left_neighbor=i; |
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129 | minimum=i; |
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130 | blank=false; |
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131 | } |
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132 | container[i].prio=value; |
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133 | } |
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134 | |
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135 | |
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136 | Item top() const { |
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137 | if ( !blank ) { |
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138 | return container[minimum].name; |
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139 | } else { |
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140 | return Item(); |
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141 | } |
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142 | } |
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143 | |
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144 | |
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145 | PrioType prio() const { |
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146 | if ( !blank ) { |
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147 | return container[minimum].prio; |
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148 | } else { |
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149 | return PrioType(); |
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150 | } |
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151 | } |
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152 | |
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153 | |
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154 | const PrioType get(const Item& it) const { |
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155 | int i=iimap.get(it); |
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156 | |
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157 | if ( i >= 0 && container[i].in ) { |
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158 | return container[i].prio; |
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159 | } else { |
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160 | return PrioType(); |
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161 | } |
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162 | } |
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163 | |
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164 | |
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165 | |
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166 | |
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167 | void pop() { |
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168 | /*The first case is that there are only one root.*/ |
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169 | if ( container[minimum].left_neighbor==minimum ) { |
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170 | container[minimum].in=false; |
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171 | if ( container[minimum].degree==0 ) blank=true; |
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172 | else { |
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173 | makeroot(container[minimum].child); |
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174 | minimum=container[minimum].child; |
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175 | balance(); |
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176 | } |
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177 | } else { |
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178 | int right=container[minimum].right_neighbor; |
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179 | unlace(minimum); |
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180 | container[minimum].in=false; |
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181 | if ( container[minimum].degree > 0 ) { |
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182 | int left=container[minimum].left_neighbor; |
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183 | int child=container[minimum].child; |
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184 | int last_child=container[child].left_neighbor; |
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185 | |
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186 | makeroot(child); |
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187 | |
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188 | container[left].right_neighbor=child; |
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189 | container[child].left_neighbor=left; |
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190 | container[right].left_neighbor=last_child; |
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191 | container[last_child].right_neighbor=right; |
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192 | } |
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193 | minimum=right; |
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194 | balance(); |
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195 | } // the case where there are more roots |
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196 | } |
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197 | |
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198 | |
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199 | void erase (const Item& it) { |
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200 | int i=iimap.get(it); |
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201 | |
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202 | if ( i >= 0 && container[i].in ) { |
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203 | |
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204 | if ( container[i].parent!=-1 ) { |
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205 | int p=container[i].parent; |
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206 | cut(i,p); |
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207 | cascade(p); |
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208 | minimum=i; //As if its prio would be -infinity |
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209 | } |
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210 | pop(); |
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211 | } |
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212 | } |
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213 | |
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214 | |
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215 | void decrease (Item it, PrioType const value) { |
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216 | int i=iimap.get(it); |
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217 | container[i].prio=value; |
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218 | int p=container[i].parent; |
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219 | |
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220 | if ( p!=-1 && comp(value, container[p].prio) ) { |
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221 | cut(i,p); |
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222 | cascade(p); |
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223 | if ( comp(value, container[minimum].prio) ) minimum=i; |
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224 | } |
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225 | } |
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226 | |
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227 | |
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228 | void increase (Item it, PrioType const value) { |
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229 | erase(it); |
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230 | push(it, value); |
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231 | } |
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232 | |
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233 | |
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234 | state_enum state(const Item &it) const { |
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235 | int i=iimap.get(it); |
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236 | if( i>=0 ) { |
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237 | if ( container[i].in ) i=0; |
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238 | else i=-2; |
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239 | } |
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240 | return state_enum(i); |
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241 | } |
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242 | |
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243 | |
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244 | private: |
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245 | |
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246 | void balance() { |
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247 | |
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248 | int maxdeg=int( floor( 2.08*log(double(container.size()))))+1; |
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249 | |
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250 | std::vector<int> A(maxdeg,-1); |
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251 | |
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252 | /* |
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253 | *Recall that now minimum does not point to the minimum prio element. |
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254 | *We set minimum to this during balance(). |
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255 | */ |
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256 | int anchor=container[minimum].left_neighbor; |
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257 | int next=minimum; |
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258 | bool end=false; |
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259 | |
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260 | do { |
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261 | int active=next; |
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262 | if ( anchor==active ) end=true; |
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263 | int d=container[active].degree; |
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264 | next=container[active].right_neighbor; |
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265 | |
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266 | while (A[d]!=-1) { |
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267 | if( comp(container[active].prio, container[A[d]].prio) ) { |
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268 | fuse(active,A[d]); |
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269 | } else { |
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270 | fuse(A[d],active); |
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271 | active=A[d]; |
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272 | } |
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273 | A[d]=-1; |
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274 | ++d; |
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275 | } |
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276 | A[d]=active; |
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277 | } while ( !end ); |
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278 | |
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279 | |
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280 | while ( container[minimum].parent >=0 ) minimum=container[minimum].parent; |
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281 | int s=minimum; |
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282 | int m=minimum; |
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283 | do { |
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284 | if ( comp(container[s].prio, container[minimum].prio) ) minimum=s; |
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285 | s=container[s].right_neighbor; |
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286 | } while ( s != m ); |
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287 | } |
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288 | |
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289 | |
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290 | void makeroot (int c) { |
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291 | int s=c; |
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292 | do { |
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293 | container[s].parent=-1; |
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294 | s=container[s].right_neighbor; |
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295 | } while ( s != c ); |
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296 | } |
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297 | |
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298 | |
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299 | void cut (int a, int b) { |
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300 | /* |
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301 | *Replacing a from the children of b. |
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302 | */ |
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303 | --container[b].degree; |
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304 | |
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305 | if ( container[b].degree !=0 ) { |
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306 | int child=container[b].child; |
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307 | if ( child==a ) |
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308 | container[b].child=container[child].right_neighbor; |
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309 | unlace(a); |
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310 | } |
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311 | |
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312 | |
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313 | /*Lacing i to the roots.*/ |
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314 | int right=container[minimum].right_neighbor; |
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315 | container[minimum].right_neighbor=a; |
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316 | container[a].left_neighbor=minimum; |
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317 | container[a].right_neighbor=right; |
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318 | container[right].left_neighbor=a; |
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319 | |
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320 | container[a].parent=-1; |
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321 | container[a].marked=false; |
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322 | } |
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323 | |
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324 | |
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325 | void cascade (int a) |
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326 | { |
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327 | if ( container[a].parent!=-1 ) { |
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328 | int p=container[a].parent; |
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329 | |
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330 | if ( container[a].marked==false ) container[a].marked=true; |
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331 | else { |
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332 | cut(a,p); |
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333 | cascade(p); |
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334 | } |
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335 | } |
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336 | } |
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337 | |
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338 | |
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339 | void fuse (int a, int b) { |
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340 | unlace(b); |
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341 | |
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342 | /*Lacing b under a.*/ |
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343 | container[b].parent=a; |
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344 | |
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345 | if (container[a].degree==0) { |
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346 | container[b].left_neighbor=b; |
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347 | container[b].right_neighbor=b; |
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348 | container[a].child=b; |
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349 | } else { |
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350 | int child=container[a].child; |
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351 | int last_child=container[child].left_neighbor; |
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352 | container[child].left_neighbor=b; |
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353 | container[b].right_neighbor=child; |
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354 | container[last_child].right_neighbor=b; |
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355 | container[b].left_neighbor=last_child; |
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356 | } |
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357 | |
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358 | ++container[a].degree; |
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359 | |
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360 | container[b].marked=false; |
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361 | } |
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362 | |
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363 | |
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364 | /* |
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365 | *It is invoked only if a has siblings. |
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366 | */ |
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367 | void unlace (int a) { |
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368 | int leftn=container[a].left_neighbor; |
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369 | int rightn=container[a].right_neighbor; |
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370 | container[leftn].right_neighbor=rightn; |
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371 | container[rightn].left_neighbor=leftn; |
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372 | } |
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373 | |
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374 | |
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375 | class store { |
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376 | friend class FibHeap; |
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377 | |
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378 | Item name; |
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379 | int parent; |
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380 | int left_neighbor; |
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381 | int right_neighbor; |
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382 | int child; |
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383 | int degree; |
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384 | bool marked; |
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385 | bool in; |
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386 | PrioType prio; |
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387 | |
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388 | store() : parent(-1), child(-1), degree(), marked(false), in(true) {} |
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389 | }; |
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390 | |
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391 | }; |
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392 | |
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393 | } //namespace hugo |
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394 | #endif |
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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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400 | |
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