1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | #ifndef LEMON_DYNAMIC_TREE_H |
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19 | #define LEMON_DYNAMIC_TREE_H |
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20 | |
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21 | /// \ingroup auxdata |
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22 | /// \file |
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23 | /// \brief The dynamic tree data structure of Sleator and Tarjan. |
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24 | /// |
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25 | |
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26 | #include <vector> |
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27 | #include <limits> |
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28 | #include <lemon/tolerance.h> |
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29 | |
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30 | namespace lemon { |
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31 | |
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32 | /// \ingroup auxdata |
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33 | /// |
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34 | /// \brief The dynamic tree data structure of Sleator and Tarjan. |
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35 | /// |
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36 | /// This class provides an implementation of the dynamic tree data |
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37 | /// structure for maintaining a set of node-disjoint rooted |
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38 | /// trees. Each item has an associated value, and the item with |
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39 | /// minimum value can be find in \f$O(\log(n)\f$ on the path from a |
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40 | /// node to the its root, and the items on such path can be |
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41 | /// increased or decreased globally with a certain value in the same |
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42 | /// running time. We regard a tree edge as directed toward the root, |
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43 | /// that is from child to parent. Its structure can be modified by |
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44 | /// two basic operations: \e link(v,w) adds an edge between a root v |
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45 | /// and a node w in a different component; \e cut(v) removes the |
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46 | /// edge between v and its parent. |
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47 | /// |
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48 | /// \param _Value The value type of the items. |
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49 | /// \param _ItemIntMap Converts item type of node to integer. |
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50 | /// \param _Tolerance The tolerance class to handle computation |
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51 | /// problems. |
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52 | /// \param _enableSize If true then the data structre manatain the |
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53 | /// size of each tree. The feature is used in \ref GoldbergTarjan |
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54 | /// algorithm. The default value is true. |
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55 | /// |
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56 | /// \author Hamori Tamas |
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57 | #ifdef DOXYGEN |
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58 | template <typename _Value, typename _ItemIntMap, |
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59 | typename _Tolerance, bool _enableSize> |
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60 | #else |
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61 | template <typename _Value, typename _ItemIntMap, |
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62 | typename _Tolerance = lemon::Tolerance<_Value>, |
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63 | bool _enableSize = true> |
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64 | #endif |
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65 | class DynamicTree { |
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66 | public: |
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67 | /// \brief The integer map on the items. |
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68 | typedef _ItemIntMap ItemIntMap; |
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69 | /// \brief The item type of nodes. |
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70 | typedef typename ItemIntMap::Key Item; |
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71 | /// \brief The value type of the algorithms. |
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72 | typedef _Value Value; |
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73 | /// \brief The tolerance used by the algorithm. |
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74 | typedef _Tolerance Tolerance; |
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75 | |
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76 | private: |
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77 | |
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78 | class ItemData; |
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79 | |
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80 | std::vector<ItemData> _data; |
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81 | ItemIntMap &_iim; |
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82 | Value _max_value; |
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83 | Tolerance _tolerance; |
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84 | |
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85 | public: |
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86 | /// \brief The constructor of the class. |
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87 | /// |
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88 | /// \param iim The integer map on the items. |
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89 | /// \param tolerance Tolerance class. |
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90 | DynamicTree(ItemIntMap &iim, const Tolerance& tolerance = Tolerance()) |
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91 | : _iim(iim), _max_value(std::numeric_limits<Value>::max()), |
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92 | _tolerance(tolerance) {} |
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93 | |
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94 | ~DynamicTree() {} |
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95 | |
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96 | /// \brief Clears the data structure |
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97 | /// |
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98 | /// Clears the data structure |
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99 | void clear() { |
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100 | _data.clear(); |
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101 | } |
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102 | |
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103 | /// \brief Sets the tolerance used by algorithm. |
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104 | /// |
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105 | /// Sets the tolerance used by algorithm. |
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106 | void tolerance(const Tolerance& tolerance) const { |
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107 | _tolerance = tolerance; |
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108 | return *this; |
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109 | } |
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110 | |
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111 | /// \brief Returns the tolerance used by algorithm. |
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112 | /// |
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113 | /// Returns the tolerance used by algorithm. |
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114 | const Tolerance& tolerance() const { |
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115 | return tolerance; |
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116 | } |
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117 | |
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118 | /// \brief Create a new tree containing a single node with cost zero. |
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119 | void makeTree(const Item &item) { |
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120 | _data[makePath(item)].successor = -1; |
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121 | } |
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122 | |
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123 | /// \brief Return the root of the tree containing node with itemtype |
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124 | /// \e item. |
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125 | Item findRoot(const Item &item) { |
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126 | return _data[findTail(expose(_iim[item]))].id; |
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127 | } |
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128 | |
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129 | /// \brief Return the the value of nodes in the tree containing |
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130 | /// node with itemtype \e item. |
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131 | int findSize(const Item &item) { |
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132 | return _data[expose(_iim[item])].size; |
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133 | } |
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134 | |
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135 | /// \brief Return the minimum cost containing node. |
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136 | /// |
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137 | /// Return into \e d the minimum cost on the tree path from \e item |
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138 | /// to findRoot(item). Return the last item (closest to its root) |
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139 | /// on this path of the minimum cost. |
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140 | Item findCost(const Item &item, Value& d){ |
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141 | return _data[findPathCost(expose(_iim[item]),d)].id; |
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142 | } |
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143 | |
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144 | /// \brief Add \e x value to the cost of every node on the path from |
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145 | /// \e item to findRoot(item). |
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146 | void addCost(const Item &item, Value x) { |
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147 | addPathCost(expose(_iim[item]), x); |
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148 | } |
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149 | |
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150 | /// \brief Combine the trees containing nodes \e item1 and \e item2 |
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151 | /// by adding an edge from \e item1 \e item2. |
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152 | /// |
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153 | /// This operation assumes that \e item1 is root and \e item2 is in |
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154 | /// a different tree. |
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155 | void link(const Item &item1, const Item &item2){ |
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156 | int v = _iim[item1]; |
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157 | int w = _iim[item2]; |
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158 | int p = expose(w); |
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159 | join(-1, expose(v), p); |
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160 | _data[v].successor = -1; |
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161 | _data[v].size += _data[p].size; |
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162 | |
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163 | } |
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164 | |
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165 | /// \brief Divide the tree containing node \e item into two trees by |
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166 | /// deleting the edge out of \e item. |
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167 | /// |
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168 | /// This operation assumes that \e item is not a tree root. |
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169 | void cut(const Item &item) { |
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170 | int v = _iim[item]; |
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171 | int p, q; |
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172 | expose(v); |
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173 | split(p, v, q); |
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174 | if (p != -1) { |
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175 | _data[p].successor = v; |
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176 | } |
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177 | _data[v].size -= _data[q].size; |
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178 | if (q != -1) { |
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179 | _data[q].successor = _data[v].successor; |
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180 | } |
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181 | _data[v].successor = -1; |
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182 | } |
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183 | |
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184 | ///\brief |
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185 | Item parent(const Item &item){ |
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186 | return _data[_iim[item].p].id; |
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187 | } |
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188 | |
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189 | ///\brief Return the upper bound of the costs. |
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190 | Value maxValue() const { |
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191 | return _max_value; |
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192 | } |
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193 | |
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194 | private: |
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195 | |
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196 | int makePath(const Item &item) { |
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197 | _iim.set(item, _data.size()); |
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198 | ItemData v(item); |
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199 | _data.push_back(v); |
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200 | return _iim[item]; |
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201 | } |
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202 | |
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203 | int findPath(int v) { |
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204 | splay(v); |
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205 | return v; |
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206 | } |
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207 | |
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208 | int findPathCost(int p, Value &d) { |
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209 | while ((_data[p].right != -1 && |
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210 | !_tolerance.less(0, _data[_data[p].right].dmin)) || |
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211 | (_data[p].left != -1 && _tolerance.less(0, _data[p].dcost))) { |
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212 | if (_data[p].right != -1 && |
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213 | !_tolerance.less(0, _data[_data[p].right].dmin)) { |
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214 | p = _data[p].right; |
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215 | } else if (_data[p].left != -1 && |
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216 | !_tolerance.less(0, _data[_data[p].left].dmin)) { |
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217 | p = _data[p].left; |
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218 | } |
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219 | } |
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220 | splay(p); |
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221 | d = _data[p].dmin; |
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222 | return p; |
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223 | } |
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224 | |
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225 | int findTail(int p){ |
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226 | while (_data[p].right != -1) { |
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227 | p = _data[p].right; |
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228 | } |
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229 | splay(p); |
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230 | return p; |
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231 | } |
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232 | |
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233 | void addPathCost(int p, Value x) { |
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234 | if (!_tolerance.less(x, _max_value)) { |
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235 | _data[p].dmin = x; |
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236 | _data[p].dcost = x; |
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237 | } else if (!_tolerance.less(-x, _max_value)) { |
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238 | _data[p].dmin = 0; |
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239 | _data[p].dcost = 0; |
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240 | } else { |
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241 | _data[p].dmin += x; |
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242 | } |
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243 | } |
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244 | |
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245 | void join(int p, int v, int q) { |
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246 | Value min = _max_value; |
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247 | Value pmin = _max_value; |
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248 | Value vmin = _data[v].dmin; |
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249 | Value qmin = _max_value; |
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250 | if (p != -1){ |
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251 | pmin = _data[p].dmin; |
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252 | } |
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253 | if (q != -1){ |
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254 | qmin = _data[q].dmin; |
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255 | } |
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256 | |
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257 | if (_tolerance.less(vmin, qmin)) { |
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258 | if (_tolerance.less(vmin,pmin)) { |
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259 | min = vmin; |
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260 | } else { |
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261 | min = pmin; |
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262 | } |
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263 | } else if (_tolerance.less(qmin,pmin)) { |
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264 | min = qmin; |
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265 | } else { |
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266 | min = pmin; |
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267 | } |
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268 | |
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269 | if (p != -1){ |
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270 | _data[p].parent = v; |
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271 | _data[p].dmin -= min; |
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272 | } |
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273 | if (q!=-1){ |
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274 | _data[q].parent = v; |
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275 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
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276 | _data[q].dmin -= min; |
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277 | } |
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278 | } |
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279 | _data[v].left = p; |
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280 | _data[v].right = q; |
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281 | if (_tolerance.less(min,_max_value)) { |
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282 | _data[v].dcost = _data[v].dmin - min; |
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283 | } |
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284 | _data[v].dmin = min; |
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285 | } |
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286 | |
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287 | void split(int &p, int v, int &q){ |
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288 | splay(v); |
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289 | p = -1; |
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290 | if (_data[v].left != -1){ |
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291 | p = _data[v].left; |
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292 | _data[p].dmin += _data[v].dmin; |
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293 | _data[p].parent = -1; |
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294 | _data[v].left = -1; |
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295 | } |
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296 | q = -1; |
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297 | if (_data[v].right != -1) { |
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298 | q=_data[v].right; |
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299 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
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300 | _data[q].dmin += _data[v].dmin; |
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301 | } |
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302 | _data[q].parent = -1; |
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303 | _data[v].right = -1; |
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304 | } |
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305 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
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306 | _data[v].dmin += _data[v].dcost; |
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307 | _data[v].dcost = 0; |
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308 | } else { |
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309 | _data[v].dmin = _data[v].dcost; |
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310 | } |
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311 | } |
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312 | |
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313 | int expose(int v) { |
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314 | int p, q, r, w; |
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315 | p = -1; |
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316 | while (v != -1) { |
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317 | w = _data[findPath(v)].successor; |
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318 | split(q, v, r); |
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319 | if (q != -1) { |
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320 | _data[q].successor = v; |
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321 | } |
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322 | join(p, v, r); |
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323 | p = v; |
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324 | v = w; |
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325 | } |
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326 | _data[p].successor = -1; |
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327 | return p; |
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328 | } |
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329 | |
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330 | void splay(int v) { |
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331 | while (_data[v].parent != -1) { |
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332 | if (v == _data[_data[v].parent].left) { |
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333 | if (_data[_data[v].parent].parent == -1) { |
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334 | zig(v); |
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335 | } else { |
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336 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
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337 | zig(_data[v].parent); |
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338 | zig(v); |
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339 | } else { |
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340 | zig(v); |
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341 | zag(v); |
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342 | } |
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343 | } |
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344 | } else { |
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345 | if (_data[_data[v].parent].parent == -1) { |
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346 | zag(v); |
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347 | } else { |
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348 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
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349 | zag(v); |
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350 | zig(v); |
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351 | } else { |
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352 | zag(_data[v].parent); |
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353 | zag(v); |
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354 | } |
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355 | } |
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356 | } |
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357 | } |
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358 | } |
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359 | |
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360 | |
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361 | void zig(int v) { |
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362 | Value min = _data[_data[v].parent].dmin; |
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363 | int a = _data[v].parent; |
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364 | |
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365 | Value aa = _data[a].dcost; |
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366 | if (_tolerance.less(aa, _max_value)) { |
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367 | aa += min; |
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368 | } |
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369 | |
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370 | |
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371 | int b = v; |
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372 | Value ab = min + _data[b].dmin; |
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373 | Value bb = _data[b].dcost; |
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374 | if (_tolerance.less(bb, _max_value)) { |
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375 | bb += ab; |
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376 | } |
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377 | |
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378 | int c = -1; |
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379 | Value cc = _max_value; |
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380 | if (_data[a].right != -1) { |
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381 | c = _data[a].right; |
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382 | cc = _data[c].dmin; |
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383 | if (_tolerance.less(cc, _max_value)) { |
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384 | cc += min; |
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385 | } |
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386 | } |
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387 | |
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388 | int d = -1; |
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389 | Value dd = _max_value; |
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390 | if (_data[v].left != -1){ |
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391 | d = _data[v].left; |
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392 | dd = ab + _data[d].dmin; |
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393 | } |
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394 | |
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395 | int e = -1; |
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396 | Value ee = _max_value; |
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397 | if (_data[v].right != -1) { |
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398 | e = _data[v].right; |
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399 | ee = ab + _data[e].dmin; |
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400 | } |
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401 | |
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402 | Value min2; |
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403 | if (_tolerance.less(0, _data[b].dmin) || |
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404 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
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405 | min2 = min; |
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406 | } else { |
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407 | if (_tolerance.less(aa, cc)) { |
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408 | if (_tolerance.less(aa, ee)) { |
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409 | min2 = aa; |
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410 | } else { |
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411 | min2 = ee; |
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412 | } |
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413 | } else if (_tolerance.less(cc, ee)) { |
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414 | min2 = cc; |
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415 | } else { |
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416 | min2 = ee; |
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417 | } |
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418 | } |
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419 | |
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420 | _data[a].dcost = aa; |
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421 | if (_tolerance.less(aa, _max_value)) { |
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422 | _data[a].dcost -= min2; |
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423 | } |
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424 | _data[a].dmin = min2; |
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425 | if (_tolerance.less(min2,_max_value)) { |
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426 | _data[a].dmin -= min; |
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427 | } |
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428 | _data[a].size -= _data[b].size; |
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429 | _data[b].dcost = bb; |
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430 | if (_tolerance.less(bb, _max_value)) { |
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431 | _data[b].dcost -= min; |
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432 | } |
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433 | _data[b].dmin = min; |
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434 | _data[b].size += _data[a].size; |
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435 | if (c != -1) { |
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436 | _data[c].dmin = cc; |
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437 | if (_tolerance.less(cc, _max_value)) { |
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438 | _data[c].dmin -= min2; |
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439 | } |
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440 | } |
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441 | if (d != -1) { |
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442 | _data[d].dmin = dd - min; |
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443 | _data[a].size += _data[d].size; |
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444 | _data[b].size -= _data[d].size; |
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445 | } |
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446 | if (e != -1) { |
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447 | _data[e].dmin = ee - min2; |
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448 | } |
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449 | |
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450 | int w = _data[v].parent; |
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451 | _data[v].successor = _data[w].successor; |
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452 | _data[w].successor = -1; |
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453 | _data[v].parent = _data[w].parent; |
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454 | _data[w].parent = v; |
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455 | _data[w].left = _data[v].right; |
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456 | _data[v].right = w; |
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457 | if (_data[v].parent != -1){ |
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458 | if (_data[_data[v].parent].right == w) { |
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459 | _data[_data[v].parent].right = v; |
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460 | } else { |
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461 | _data[_data[v].parent].left = v; |
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462 | } |
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463 | } |
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464 | if (_data[w].left != -1){ |
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465 | _data[_data[w].left].parent = w; |
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466 | } |
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467 | } |
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468 | |
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469 | |
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470 | void zag(int v) { |
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471 | |
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472 | Value min = _data[_data[v].parent].dmin; |
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473 | |
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474 | int a = _data[v].parent; |
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475 | Value aa = _data[a].dcost; |
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476 | if (_tolerance.less(aa, _max_value)) { |
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477 | aa += min; |
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478 | } |
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479 | |
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480 | int b = v; |
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481 | Value ab = min + _data[b].dmin; |
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482 | Value bb = _data[b].dcost; |
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483 | if (_tolerance.less(bb, _max_value)) { |
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484 | bb += ab; |
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485 | } |
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486 | |
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487 | int c = -1; |
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488 | Value cc = _max_value; |
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489 | if (_data[a].left != -1){ |
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490 | c = _data[a].left; |
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491 | cc = min + _data[c].dmin; |
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492 | } |
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493 | |
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494 | int d = -1; |
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495 | Value dd = _max_value; |
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496 | if (_data[v].right!=-1) { |
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497 | d = _data[v].right; |
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498 | dd = _data[d].dmin; |
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499 | if (_tolerance.less(dd, _max_value)) { |
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500 | dd += ab; |
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501 | } |
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502 | } |
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503 | |
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504 | int e = -1; |
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505 | Value ee = _max_value; |
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506 | if (_data[v].left != -1){ |
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507 | e = _data[v].left; |
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508 | ee = ab + _data[e].dmin; |
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509 | } |
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510 | |
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511 | Value min2; |
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512 | if (_tolerance.less(0, _data[b].dmin) || |
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513 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
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514 | min2 = min; |
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515 | } else { |
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516 | if (_tolerance.less(aa, cc)) { |
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517 | if (_tolerance.less(aa, ee)) { |
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518 | min2 = aa; |
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519 | } else { |
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520 | min2 = ee; |
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521 | } |
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522 | } else if (_tolerance.less(cc, ee)) { |
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523 | min2 = cc; |
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524 | } else { |
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525 | min2 = ee; |
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526 | } |
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527 | } |
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528 | _data[a].dcost = aa; |
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529 | if (_tolerance.less(aa, _max_value)) { |
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530 | _data[a].dcost -= min2; |
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531 | } |
---|
532 | _data[a].dmin = min2; |
---|
533 | if (_tolerance.less(min2, _max_value)) { |
---|
534 | _data[a].dmin -= min; |
---|
535 | } |
---|
536 | _data[a].size -= _data[b].size; |
---|
537 | _data[b].dcost = bb; |
---|
538 | if (_tolerance.less(bb, _max_value)) { |
---|
539 | _data[b].dcost -= min; |
---|
540 | } |
---|
541 | _data[b].dmin = min; |
---|
542 | _data[b].size += _data[a].size; |
---|
543 | if (c != -1) { |
---|
544 | _data[c].dmin = cc - min2; |
---|
545 | } |
---|
546 | if (d != -1) { |
---|
547 | _data[d].dmin = dd; |
---|
548 | _data[a].size += _data[d].size; |
---|
549 | _data[b].size -= _data[d].size; |
---|
550 | if (_tolerance.less(dd, _max_value)) { |
---|
551 | _data[d].dmin -= min; |
---|
552 | } |
---|
553 | } |
---|
554 | if (e != -1) { |
---|
555 | _data[e].dmin = ee - min2; |
---|
556 | } |
---|
557 | |
---|
558 | int w = _data[v].parent; |
---|
559 | _data[v].successor = _data[w].successor; |
---|
560 | _data[w].successor = -1; |
---|
561 | _data[v].parent = _data[w].parent; |
---|
562 | _data[w].parent = v; |
---|
563 | _data[w].right = _data[v].left; |
---|
564 | _data[v].left = w; |
---|
565 | if (_data[v].parent != -1){ |
---|
566 | if (_data[_data[v].parent].left == w) { |
---|
567 | _data[_data[v].parent].left = v; |
---|
568 | } else { |
---|
569 | _data[_data[v].parent].right = v; |
---|
570 | } |
---|
571 | } |
---|
572 | if (_data[w].right != -1){ |
---|
573 | _data[_data[w].right].parent = w; |
---|
574 | } |
---|
575 | } |
---|
576 | |
---|
577 | private: |
---|
578 | |
---|
579 | class ItemData { |
---|
580 | public: |
---|
581 | Item id; |
---|
582 | int size; |
---|
583 | int successor; |
---|
584 | int parent; |
---|
585 | int left; |
---|
586 | int right; |
---|
587 | Value dmin; |
---|
588 | Value dcost; |
---|
589 | |
---|
590 | public: |
---|
591 | ItemData(const Item &item) |
---|
592 | : id(item), size(1), successor(), parent(-1), |
---|
593 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
594 | }; |
---|
595 | |
---|
596 | }; |
---|
597 | |
---|
598 | template <typename _Value, typename _ItemIntMap, typename _Tolerance> |
---|
599 | class DynamicTree<_Value, _ItemIntMap, _Tolerance, false> { |
---|
600 | public: |
---|
601 | typedef _ItemIntMap ItemIntMap; |
---|
602 | typedef typename ItemIntMap::Key Item; |
---|
603 | typedef _Value Value; |
---|
604 | typedef _Tolerance Tolerance; |
---|
605 | |
---|
606 | private: |
---|
607 | |
---|
608 | class ItemData; |
---|
609 | |
---|
610 | std::vector<ItemData> _data; |
---|
611 | ItemIntMap &_iim; |
---|
612 | Value _max_value; |
---|
613 | Tolerance _tolerance; |
---|
614 | |
---|
615 | public: |
---|
616 | DynamicTree(ItemIntMap &iim, const Tolerance& tolerance = Tolerance()) |
---|
617 | : _iim(iim), _max_value(std::numeric_limits<Value>::max()), |
---|
618 | _tolerance(tolerance) {} |
---|
619 | |
---|
620 | ~DynamicTree() {} |
---|
621 | |
---|
622 | void clear() { |
---|
623 | _data.clear(); |
---|
624 | } |
---|
625 | |
---|
626 | void tolerance(const Tolerance& tolerance) const { |
---|
627 | _tolerance = tolerance; |
---|
628 | return *this; |
---|
629 | } |
---|
630 | |
---|
631 | const Tolerance& tolerance() const { |
---|
632 | return tolerance; |
---|
633 | } |
---|
634 | |
---|
635 | void makeTree(const Item &item) { |
---|
636 | _data[makePath(item)].successor = -1; |
---|
637 | } |
---|
638 | |
---|
639 | Item findRoot(const Item &item) { |
---|
640 | return _data[findTail(expose(_iim[item]))].id; |
---|
641 | } |
---|
642 | |
---|
643 | Item findCost(const Item &item, Value& d){ |
---|
644 | return _data[findPathCost(expose(_iim[item]),d)].id; |
---|
645 | } |
---|
646 | |
---|
647 | void addCost(const Item &item, Value x){ |
---|
648 | addPathCost(expose(_iim[item]), x); |
---|
649 | } |
---|
650 | |
---|
651 | void link(const Item &item1, const Item &item2){ |
---|
652 | int v = _iim[item1]; |
---|
653 | int w = _iim[item2]; |
---|
654 | int p = expose(w); |
---|
655 | join(-1, expose(v), p); |
---|
656 | _data[v].successor = -1; |
---|
657 | } |
---|
658 | |
---|
659 | void cut(const Item &item) { |
---|
660 | int v = _iim[item]; |
---|
661 | int p, q; |
---|
662 | expose(v); |
---|
663 | split(p, v, q); |
---|
664 | if (p != -1) { |
---|
665 | _data[p].successor = v; |
---|
666 | } |
---|
667 | if (q != -1) { |
---|
668 | _data[q].successor = _data[v].successor; |
---|
669 | } |
---|
670 | _data[v].successor = -1; |
---|
671 | } |
---|
672 | |
---|
673 | Item parent(const Item &item){ |
---|
674 | return _data[_iim[item].p].id; |
---|
675 | } |
---|
676 | |
---|
677 | Value maxValue() const { |
---|
678 | return _max_value; |
---|
679 | } |
---|
680 | |
---|
681 | private: |
---|
682 | |
---|
683 | int makePath(const Item &item) { |
---|
684 | _iim.set(item, _data.size()); |
---|
685 | ItemData v(item); |
---|
686 | _data.push_back(v); |
---|
687 | return _iim[item]; |
---|
688 | } |
---|
689 | |
---|
690 | int findPath(int v) { |
---|
691 | splay(v); |
---|
692 | return v; |
---|
693 | } |
---|
694 | |
---|
695 | int findPathCost(int p, Value &d) { |
---|
696 | while ((_data[p].right != -1 && |
---|
697 | !_tolerance.less(0, _data[_data[p].right].dmin)) || |
---|
698 | (_data[p].left != -1 && _tolerance.less(0, _data[p].dcost))) { |
---|
699 | if (_data[p].right != -1 && |
---|
700 | !_tolerance.less(0, _data[_data[p].right].dmin)) { |
---|
701 | p = _data[p].right; |
---|
702 | } else if (_data[p].left != -1 && |
---|
703 | !_tolerance.less(0, _data[_data[p].left].dmin)){ |
---|
704 | p = _data[p].left; |
---|
705 | } |
---|
706 | } |
---|
707 | splay(p); |
---|
708 | d = _data[p].dmin; |
---|
709 | return p; |
---|
710 | } |
---|
711 | |
---|
712 | int findTail(int p) { |
---|
713 | while (_data[p].right != -1) { |
---|
714 | p = _data[p].right; |
---|
715 | } |
---|
716 | splay(p); |
---|
717 | return p; |
---|
718 | } |
---|
719 | |
---|
720 | void addPathCost(int p, Value x) { |
---|
721 | if (!_tolerance.less(x, _max_value)) { |
---|
722 | _data[p].dmin = x;_data[p].dcost = x; |
---|
723 | } else if (!_tolerance.less(-x, _max_value)) { |
---|
724 | _data[p].dmin = 0; |
---|
725 | _data[p].dcost = 0; |
---|
726 | } else { |
---|
727 | _data[p].dmin += x; |
---|
728 | } |
---|
729 | } |
---|
730 | |
---|
731 | void join(int p, int v, int q) { |
---|
732 | Value min = _max_value; |
---|
733 | Value pmin = _max_value; |
---|
734 | Value vmin = _data[v].dmin; |
---|
735 | Value qmin = _max_value; |
---|
736 | if (p != -1){ |
---|
737 | pmin = _data[p].dmin; |
---|
738 | } |
---|
739 | if (q != -1){ |
---|
740 | qmin = _data[q].dmin; |
---|
741 | } |
---|
742 | |
---|
743 | if (_tolerance.less(vmin, qmin)) { |
---|
744 | if (_tolerance.less(vmin,pmin)) { |
---|
745 | min = vmin; |
---|
746 | } else { |
---|
747 | min = pmin; |
---|
748 | } |
---|
749 | } else if (_tolerance.less(qmin,pmin)) { |
---|
750 | min = qmin; |
---|
751 | } else { |
---|
752 | min = pmin; |
---|
753 | } |
---|
754 | |
---|
755 | if (p != -1){ |
---|
756 | _data[p].parent = v; |
---|
757 | _data[p].dmin -= min; |
---|
758 | } |
---|
759 | if (q != -1){ |
---|
760 | _data[q].parent = v; |
---|
761 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
---|
762 | _data[q].dmin -= min; |
---|
763 | } |
---|
764 | } |
---|
765 | _data[v].left = p; |
---|
766 | _data[v].right = q; |
---|
767 | if (_tolerance.less(min, _max_value)) { |
---|
768 | _data[v].dcost = _data[v].dmin - min; |
---|
769 | } |
---|
770 | _data[v].dmin = min; |
---|
771 | } |
---|
772 | |
---|
773 | void split(int &p, int v, int &q){ |
---|
774 | splay(v); |
---|
775 | p = -1; |
---|
776 | if (_data[v].left != -1){ |
---|
777 | p = _data[v].left; |
---|
778 | _data[p].dmin += _data[v].dmin; |
---|
779 | _data[p].parent = -1; |
---|
780 | _data[v].left = -1; |
---|
781 | } |
---|
782 | q = -1; |
---|
783 | if (_data[v].right != -1) { |
---|
784 | q=_data[v].right; |
---|
785 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
---|
786 | _data[q].dmin += _data[v].dmin; |
---|
787 | } |
---|
788 | _data[q].parent = -1; |
---|
789 | _data[v].right = -1; |
---|
790 | } |
---|
791 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
---|
792 | _data[v].dmin += _data[v].dcost; |
---|
793 | _data[v].dcost = 0; |
---|
794 | } else { |
---|
795 | _data[v].dmin = _data[v].dcost; |
---|
796 | } |
---|
797 | } |
---|
798 | |
---|
799 | int expose(int v) { |
---|
800 | int p, q, r, w; |
---|
801 | p = -1; |
---|
802 | while (v != -1) { |
---|
803 | w = _data[findPath(v)].successor; |
---|
804 | split(q, v, r); |
---|
805 | if (q != -1) { |
---|
806 | _data[q].successor = v; |
---|
807 | } |
---|
808 | join(p, v, r); |
---|
809 | p = v; |
---|
810 | v = w; |
---|
811 | } |
---|
812 | _data[p].successor = -1; |
---|
813 | return p; |
---|
814 | } |
---|
815 | |
---|
816 | void splay(int v) { |
---|
817 | while (_data[v].parent != -1) { |
---|
818 | if (v == _data[_data[v].parent].left) { |
---|
819 | if (_data[_data[v].parent].parent == -1) { |
---|
820 | zig(v); |
---|
821 | } else { |
---|
822 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
823 | zig(_data[v].parent); |
---|
824 | zig(v); |
---|
825 | } else { |
---|
826 | zig(v); |
---|
827 | zag(v); |
---|
828 | } |
---|
829 | } |
---|
830 | } else { |
---|
831 | if (_data[_data[v].parent].parent == -1) { |
---|
832 | zag(v); |
---|
833 | } else { |
---|
834 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
835 | zag(v); |
---|
836 | zig(v); |
---|
837 | } else { |
---|
838 | zag(_data[v].parent); |
---|
839 | zag(v); |
---|
840 | } |
---|
841 | } |
---|
842 | } |
---|
843 | } |
---|
844 | } |
---|
845 | |
---|
846 | |
---|
847 | void zig(int v) { |
---|
848 | Value min = _data[_data[v].parent].dmin; |
---|
849 | int a = _data[v].parent; |
---|
850 | |
---|
851 | Value aa = _data[a].dcost; |
---|
852 | if (_tolerance.less(aa, _max_value)) { |
---|
853 | aa+= min; |
---|
854 | } |
---|
855 | |
---|
856 | |
---|
857 | int b = v; |
---|
858 | Value ab = min + _data[b].dmin; |
---|
859 | Value bb = _data[b].dcost; |
---|
860 | if (_tolerance.less(bb, _max_value)) { |
---|
861 | bb+= ab; |
---|
862 | } |
---|
863 | |
---|
864 | int c = -1; |
---|
865 | Value cc = _max_value; |
---|
866 | if (_data[a].right != -1) { |
---|
867 | c = _data[a].right; |
---|
868 | cc = _data[c].dmin; |
---|
869 | if (_tolerance.less(cc, _max_value)) { |
---|
870 | cc+=min; |
---|
871 | } |
---|
872 | } |
---|
873 | |
---|
874 | int d = -1; |
---|
875 | Value dd = _max_value; |
---|
876 | if (_data[v].left != -1){ |
---|
877 | d = _data[v].left; |
---|
878 | dd = ab + _data[d].dmin; |
---|
879 | } |
---|
880 | |
---|
881 | int e = -1; |
---|
882 | Value ee = _max_value; |
---|
883 | if (_data[v].right != -1) { |
---|
884 | e = _data[v].right; |
---|
885 | ee = ab + _data[e].dmin; |
---|
886 | } |
---|
887 | |
---|
888 | Value min2; |
---|
889 | if (_tolerance.less(0, _data[b].dmin) || |
---|
890 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
891 | min2 = min; |
---|
892 | } else { |
---|
893 | if (_tolerance.less(aa, cc)) { |
---|
894 | if (_tolerance.less(aa, ee)) { |
---|
895 | min2 = aa; |
---|
896 | } else { |
---|
897 | min2 = ee; |
---|
898 | } |
---|
899 | } else if (_tolerance.less(cc, ee)) { |
---|
900 | min2 = cc; |
---|
901 | } else { |
---|
902 | min2 = ee; |
---|
903 | } |
---|
904 | } |
---|
905 | |
---|
906 | _data[a].dcost = aa; |
---|
907 | if (_tolerance.less(aa, _max_value)) { |
---|
908 | _data[a].dcost -= min2; |
---|
909 | } |
---|
910 | _data[a].dmin = min2; |
---|
911 | if (_tolerance.less(min2,_max_value)) { |
---|
912 | _data[a].dmin -= min; |
---|
913 | } |
---|
914 | _data[b].dcost = bb; |
---|
915 | if (_tolerance.less(bb, _max_value)) { |
---|
916 | _data[b].dcost -= min; |
---|
917 | } |
---|
918 | _data[b].dmin = min; |
---|
919 | if (c != -1) { |
---|
920 | _data[c].dmin = cc; |
---|
921 | if (_tolerance.less(cc, _max_value)) { |
---|
922 | _data[c].dmin -= min2; |
---|
923 | } |
---|
924 | } |
---|
925 | if (d != -1) { |
---|
926 | _data[d].dmin = dd - min; |
---|
927 | } |
---|
928 | if (e != -1) { |
---|
929 | _data[e].dmin = ee - min2; |
---|
930 | } |
---|
931 | |
---|
932 | int w = _data[v].parent; |
---|
933 | _data[v].successor = _data[w].successor; |
---|
934 | _data[w].successor = -1; |
---|
935 | _data[v].parent = _data[w].parent; |
---|
936 | _data[w].parent = v; |
---|
937 | _data[w].left = _data[v].right; |
---|
938 | _data[v].right = w; |
---|
939 | if (_data[v].parent != -1){ |
---|
940 | if (_data[_data[v].parent].right == w) { |
---|
941 | _data[_data[v].parent].right = v; |
---|
942 | } else { |
---|
943 | _data[_data[v].parent].left = v; |
---|
944 | } |
---|
945 | } |
---|
946 | if (_data[w].left != -1){ |
---|
947 | _data[_data[w].left].parent = w; |
---|
948 | } |
---|
949 | } |
---|
950 | |
---|
951 | |
---|
952 | void zag(int v) { |
---|
953 | |
---|
954 | Value min = _data[_data[v].parent].dmin; |
---|
955 | |
---|
956 | int a = _data[v].parent; |
---|
957 | Value aa = _data[a].dcost; |
---|
958 | if (_tolerance.less(aa, _max_value)) { |
---|
959 | aa += min; |
---|
960 | } |
---|
961 | |
---|
962 | int b = v; |
---|
963 | Value ab = min + _data[b].dmin; |
---|
964 | Value bb = _data[b].dcost; |
---|
965 | if (_tolerance.less(bb, _max_value)) { |
---|
966 | bb += ab; |
---|
967 | } |
---|
968 | |
---|
969 | int c = -1; |
---|
970 | Value cc = _max_value; |
---|
971 | if (_data[a].left != -1){ |
---|
972 | c = _data[a].left; |
---|
973 | cc = min + _data[c].dmin; |
---|
974 | } |
---|
975 | |
---|
976 | int d = -1; |
---|
977 | Value dd = _max_value; |
---|
978 | if (_data[v].right!=-1) { |
---|
979 | d = _data[v].right; |
---|
980 | dd = _data[d].dmin; |
---|
981 | if (_tolerance.less(dd, _max_value)) { |
---|
982 | dd += ab; |
---|
983 | } |
---|
984 | } |
---|
985 | |
---|
986 | int e = -1; |
---|
987 | Value ee = _max_value; |
---|
988 | if (_data[v].left != -1){ |
---|
989 | e = _data[v].left; |
---|
990 | ee = ab + _data[e].dmin; |
---|
991 | } |
---|
992 | |
---|
993 | Value min2; |
---|
994 | if (_tolerance.less(0, _data[b].dmin) || |
---|
995 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
996 | min2 = min; |
---|
997 | } else { |
---|
998 | if (_tolerance.less(aa, cc)) { |
---|
999 | if (_tolerance.less(aa, ee)) { |
---|
1000 | min2 = aa; |
---|
1001 | } else { |
---|
1002 | min2 = ee; |
---|
1003 | } |
---|
1004 | } else if (_tolerance.less(cc, ee)) { |
---|
1005 | min2 = cc; |
---|
1006 | } else { |
---|
1007 | min2 = ee; |
---|
1008 | } |
---|
1009 | } |
---|
1010 | _data[a].dcost = aa; |
---|
1011 | if (_tolerance.less(aa, _max_value)) { |
---|
1012 | _data[a].dcost -= min2; |
---|
1013 | } |
---|
1014 | _data[a].dmin = min2; |
---|
1015 | if (_tolerance.less(min2, _max_value)) { |
---|
1016 | _data[a].dmin -= min; |
---|
1017 | } |
---|
1018 | _data[b].dcost = bb; |
---|
1019 | if (_tolerance.less(bb, _max_value)) { |
---|
1020 | _data[b].dcost -= min; |
---|
1021 | } |
---|
1022 | _data[b].dmin = min; |
---|
1023 | if (c != -1) { |
---|
1024 | _data[c].dmin = cc - min2; |
---|
1025 | } |
---|
1026 | if (d != -1) { |
---|
1027 | _data[d].dmin = dd; |
---|
1028 | if (_tolerance.less(dd, _max_value)) { |
---|
1029 | _data[d].dmin -= min; |
---|
1030 | } |
---|
1031 | } |
---|
1032 | if (e != -1) { |
---|
1033 | _data[e].dmin = ee - min2; |
---|
1034 | } |
---|
1035 | |
---|
1036 | int w = _data[v].parent; |
---|
1037 | _data[v].successor = _data[w].successor; |
---|
1038 | _data[w].successor = -1; |
---|
1039 | _data[v].parent = _data[w].parent; |
---|
1040 | _data[w].parent = v; |
---|
1041 | _data[w].right = _data[v].left; |
---|
1042 | _data[v].left = w; |
---|
1043 | if (_data[v].parent != -1){ |
---|
1044 | if (_data[_data[v].parent].left == w) { |
---|
1045 | _data[_data[v].parent].left = v; |
---|
1046 | } else { |
---|
1047 | _data[_data[v].parent].right = v; |
---|
1048 | } |
---|
1049 | } |
---|
1050 | if (_data[w].right != -1){ |
---|
1051 | _data[_data[w].right].parent = w; |
---|
1052 | } |
---|
1053 | } |
---|
1054 | |
---|
1055 | private: |
---|
1056 | |
---|
1057 | class ItemData { |
---|
1058 | public: |
---|
1059 | Item id; |
---|
1060 | int successor; |
---|
1061 | int parent; |
---|
1062 | int left; |
---|
1063 | int right; |
---|
1064 | Value dmin; |
---|
1065 | Value dcost; |
---|
1066 | |
---|
1067 | public: |
---|
1068 | ItemData(const Item &item) |
---|
1069 | : id(item), successor(), parent(-1), |
---|
1070 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
1071 | }; |
---|
1072 | |
---|
1073 | }; |
---|
1074 | |
---|
1075 | } |
---|
1076 | |
---|
1077 | #endif |
---|