[2514] | 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;_data[p].dcost = x; |
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| 236 | } else if (!_tolerance.less(-x, _max_value)) { |
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| 237 | _data[p].dmin = 0; |
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| 238 | _data[p].dcost = 0; |
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| 239 | } else { |
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| 240 | _data[p].dmin += x; |
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| 241 | } |
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| 242 | } |
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| 243 | |
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| 244 | void join(int p, int v, int q) { |
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| 245 | Value min = _max_value; |
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| 246 | Value pmin = _max_value; |
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| 247 | Value vmin = _data[v].dmin; |
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| 248 | Value qmin = _max_value; |
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| 249 | if (p != -1){ |
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| 250 | pmin = _data[p].dmin; |
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| 251 | } |
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| 252 | if (q != -1){ |
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| 253 | qmin = _data[q].dmin; |
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| 254 | } |
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| 255 | |
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| 256 | if (_tolerance.less(vmin, qmin)) { |
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| 257 | if (_tolerance.less(vmin,pmin)) { |
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| 258 | min = vmin; |
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| 259 | } else { |
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| 260 | min = pmin; |
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| 261 | } |
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| 262 | } else if (_tolerance.less(qmin,pmin)) { |
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| 263 | min = qmin; |
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| 264 | } else { |
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| 265 | min = pmin; |
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| 266 | } |
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| 267 | |
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| 268 | if (p != -1){ |
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| 269 | _data[p].parent = v; |
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| 270 | _data[p].dmin -= min; |
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| 271 | } |
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| 272 | if (q!=-1){ |
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| 273 | _data[q].parent = v; |
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| 274 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
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| 275 | _data[q].dmin -= min; |
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| 276 | } |
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| 277 | } |
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| 278 | _data[v].left = p; |
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| 279 | _data[v].right = q; |
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| 280 | if (_tolerance.less(min,_max_value)) { |
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| 281 | _data[v].dcost = _data[v].dmin - min; |
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| 282 | } |
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| 283 | _data[v].dmin = min; |
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| 284 | } |
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| 285 | |
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| 286 | void split(int &p, int v, int &q){ |
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| 287 | splay(v); |
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| 288 | p = -1; |
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| 289 | if (_data[v].left != -1){ |
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| 290 | p = _data[v].left; |
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| 291 | _data[p].dmin += _data[v].dmin; |
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| 292 | _data[p].parent = -1; |
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| 293 | _data[v].left = -1; |
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| 294 | } |
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| 295 | q = -1; |
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| 296 | if (_data[v].right != -1) { |
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| 297 | q=_data[v].right; |
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| 298 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
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| 299 | _data[q].dmin += _data[v].dmin; |
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| 300 | } |
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| 301 | _data[q].parent = -1; |
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| 302 | _data[v].right = -1; |
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| 303 | } |
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| 304 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
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| 305 | _data[v].dmin += _data[v].dcost; |
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| 306 | _data[v].dcost = 0; |
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| 307 | } else { |
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| 308 | _data[v].dmin = _data[v].dcost; |
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| 309 | } |
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| 310 | } |
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| 311 | |
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| 312 | int expose(int v) { |
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| 313 | int p, q, r, w; |
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| 314 | p = -1; |
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| 315 | while (v != -1) { |
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| 316 | w = _data[findPath(v)].successor; |
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| 317 | split(q, v, r); |
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| 318 | if (q != -1) { |
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| 319 | _data[q].successor = v; |
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| 320 | } |
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| 321 | join(p, v, r); |
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| 322 | p = v; |
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| 323 | v = w; |
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| 324 | } |
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| 325 | _data[p].successor = -1; |
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| 326 | return p; |
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| 327 | } |
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| 328 | |
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| 329 | void splay(int v) { |
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| 330 | while (_data[v].parent != -1) { |
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| 331 | if (v == _data[_data[v].parent].left) { |
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| 332 | if (_data[_data[v].parent].parent == -1) { |
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| 333 | zig(v); |
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| 334 | } else { |
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| 335 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
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| 336 | zig(_data[v].parent); |
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| 337 | zig(v); |
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| 338 | } else { |
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| 339 | zig(v); |
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| 340 | zag(v); |
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| 341 | } |
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| 342 | } |
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| 343 | } else { |
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| 344 | if (_data[_data[v].parent].parent == -1) { |
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| 345 | zag(v); |
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| 346 | } else { |
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| 347 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
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| 348 | zag(v); |
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| 349 | zig(v); |
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| 350 | } else { |
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| 351 | zag(_data[v].parent); |
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| 352 | zag(v); |
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| 353 | } |
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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 | void zig(int v) { |
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| 361 | Value min = _data[_data[v].parent].dmin; |
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| 362 | int a = _data[v].parent; |
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| 363 | |
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| 364 | Value aa = _data[a].dcost; |
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| 365 | if (_tolerance.less(aa, _max_value)) { |
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| 366 | aa+= min; |
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| 367 | } |
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| 368 | |
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| 369 | |
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| 370 | int b = v; |
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| 371 | Value ab = min + _data[b].dmin; |
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| 372 | Value bb = _data[b].dcost; |
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| 373 | if (_tolerance.less(bb, _max_value)) { |
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| 374 | bb+= ab; |
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| 375 | } |
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| 376 | |
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| 377 | int c = -1; |
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| 378 | Value cc = _max_value; |
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| 379 | if (_data[a].right != -1) { |
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| 380 | c = _data[a].right; |
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| 381 | cc = _data[c].dmin; |
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| 382 | if (_tolerance.less(cc, _max_value)) { |
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| 383 | cc+=min; |
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| 384 | } |
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| 385 | } |
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| 386 | |
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| 387 | int d = -1; |
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| 388 | Value dd = _max_value; |
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| 389 | if (_data[v].left != -1){ |
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| 390 | d = _data[v].left; |
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| 391 | dd = ab + _data[d].dmin; |
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| 392 | } |
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| 393 | |
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| 394 | int e = -1; |
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| 395 | Value ee = _max_value; |
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| 396 | if (_data[v].right != -1) { |
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| 397 | e = _data[v].right; |
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| 398 | ee = ab + _data[e].dmin; |
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| 399 | } |
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| 400 | |
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| 401 | Value min2; |
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| 402 | if (_tolerance.less(0, _data[b].dmin) || |
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| 403 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
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| 404 | min2 = min; |
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| 405 | } else { |
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| 406 | if (_tolerance.less(aa, cc)) { |
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| 407 | if (_tolerance.less(aa, ee)) { |
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| 408 | min2 = aa; |
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| 409 | } else { |
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| 410 | min2 = ee; |
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| 411 | } |
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| 412 | } else if (_tolerance.less(cc, ee)) { |
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| 413 | min2 = cc; |
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| 414 | } else { |
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| 415 | min2 = ee; |
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| 416 | } |
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| 417 | } |
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| 418 | |
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| 419 | _data[a].dcost = aa; |
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| 420 | if (_tolerance.less(aa, _max_value)) { |
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| 421 | _data[a].dcost -= min2; |
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| 422 | } |
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| 423 | _data[a].dmin = min2; |
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| 424 | if (_tolerance.less(min2,_max_value)) { |
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| 425 | _data[a].dmin -= min; |
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| 426 | } |
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| 427 | _data[a].size -= _data[b].size; |
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| 428 | _data[b].dcost = bb; |
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| 429 | if (_tolerance.less(bb, _max_value)) { |
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| 430 | _data[b].dcost -= min; |
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| 431 | } |
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| 432 | _data[b].dmin = min; |
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| 433 | _data[b].size += _data[a].size; |
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| 434 | if (c != -1) { |
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| 435 | _data[c].dmin = cc; |
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| 436 | if (_tolerance.less(cc, _max_value)) { |
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| 437 | _data[c].dmin -= min2; |
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| 438 | } |
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| 439 | } |
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| 440 | if (d != -1) { |
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| 441 | _data[d].dmin = dd - min; |
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| 442 | _data[a].size += _data[d].size; |
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| 443 | _data[b].size -= _data[d].size; |
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| 444 | } |
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| 445 | if (e != -1) { |
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| 446 | _data[e].dmin = ee - min2; |
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| 447 | } |
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| 448 | |
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| 449 | int w = _data[v].parent; |
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| 450 | _data[v].successor = _data[w].successor; |
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| 451 | _data[w].successor = -1; |
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| 452 | _data[v].parent = _data[w].parent; |
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| 453 | _data[w].parent = v; |
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| 454 | _data[w].left = _data[v].right; |
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| 455 | _data[v].right = w; |
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| 456 | if (_data[v].parent != -1){ |
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| 457 | if (_data[_data[v].parent].right == w) { |
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| 458 | _data[_data[v].parent].right = v; |
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| 459 | } else { |
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| 460 | _data[_data[v].parent].left = v; |
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| 461 | } |
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| 462 | } |
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| 463 | if (_data[w].left != -1){ |
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| 464 | _data[_data[w].left].parent = w; |
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| 465 | } |
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| 466 | } |
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| 467 | |
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| 468 | |
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| 469 | void zag(int v) { |
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| 470 | |
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| 471 | Value min = _data[_data[v].parent].dmin; |
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| 472 | |
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| 473 | int a = _data[v].parent; |
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| 474 | Value aa = _data[a].dcost; |
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| 475 | if (_tolerance.less(aa, _max_value)) { |
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| 476 | aa += min; |
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| 477 | } |
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| 478 | |
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| 479 | int b = v; |
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| 480 | Value ab = min + _data[b].dmin; |
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| 481 | Value bb = _data[b].dcost; |
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| 482 | if (_tolerance.less(bb, _max_value)) { |
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| 483 | bb += ab; |
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| 484 | } |
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| 485 | |
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| 486 | int c = -1; |
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| 487 | Value cc = _max_value; |
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| 488 | if (_data[a].left != -1){ |
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| 489 | c = _data[a].left; |
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| 490 | cc = min + _data[c].dmin; |
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| 491 | } |
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| 492 | |
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| 493 | int d = -1; |
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| 494 | Value dd = _max_value; |
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| 495 | if (_data[v].right!=-1) { |
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| 496 | d = _data[v].right; |
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| 497 | dd = _data[d].dmin; |
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| 498 | if (_tolerance.less(dd, _max_value)) { |
---|
| 499 | dd += ab; |
---|
| 500 | } |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | int e = -1; |
---|
| 504 | Value ee = _max_value; |
---|
| 505 | if (_data[v].left != -1){ |
---|
| 506 | e = _data[v].left; |
---|
| 507 | ee = ab + _data[e].dmin; |
---|
| 508 | } |
---|
| 509 | |
---|
| 510 | Value min2; |
---|
| 511 | if (_tolerance.less(0, _data[b].dmin) || |
---|
| 512 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
| 513 | min2 = min; |
---|
| 514 | } else { |
---|
| 515 | if (_tolerance.less(aa, cc)) { |
---|
| 516 | if (_tolerance.less(aa, ee)) { |
---|
| 517 | min2 = aa; |
---|
| 518 | } else { |
---|
| 519 | min2 = ee; |
---|
| 520 | } |
---|
| 521 | } else if (_tolerance.less(cc, ee)) { |
---|
| 522 | min2 = cc; |
---|
| 523 | } else { |
---|
| 524 | min2 = ee; |
---|
| 525 | } |
---|
| 526 | } |
---|
| 527 | _data[a].dcost = aa; |
---|
| 528 | if (_tolerance.less(aa, _max_value)) { |
---|
| 529 | _data[a].dcost -= min2; |
---|
| 530 | } |
---|
| 531 | _data[a].dmin = min2; |
---|
| 532 | if (_tolerance.less(min2, _max_value)) { |
---|
| 533 | _data[a].dmin -= min; |
---|
| 534 | } |
---|
| 535 | _data[a].size -= _data[b].size; |
---|
| 536 | _data[b].dcost = bb; |
---|
| 537 | if (_tolerance.less(bb, _max_value)) { |
---|
| 538 | _data[b].dcost -= min; |
---|
| 539 | } |
---|
| 540 | _data[b].dmin = min; |
---|
| 541 | _data[b].size += _data[a].size; |
---|
| 542 | if (c != -1) { |
---|
| 543 | _data[c].dmin = cc - min2; |
---|
| 544 | } |
---|
| 545 | if (d != -1) { |
---|
| 546 | _data[d].dmin = dd; |
---|
| 547 | _data[a].size += _data[d].size; |
---|
| 548 | _data[b].size -= _data[d].size; |
---|
| 549 | if (_tolerance.less(dd, _max_value)) { |
---|
| 550 | _data[d].dmin -= min; |
---|
| 551 | } |
---|
| 552 | } |
---|
| 553 | if (e != -1) { |
---|
| 554 | _data[e].dmin = ee - min2; |
---|
| 555 | } |
---|
| 556 | |
---|
| 557 | int w = _data[v].parent; |
---|
| 558 | _data[v].successor = _data[w].successor; |
---|
| 559 | _data[w].successor = -1; |
---|
| 560 | _data[v].parent = _data[w].parent; |
---|
| 561 | _data[w].parent = v; |
---|
| 562 | _data[w].right = _data[v].left; |
---|
| 563 | _data[v].left = w; |
---|
| 564 | if (_data[v].parent != -1){ |
---|
| 565 | if (_data[_data[v].parent].left == w) { |
---|
| 566 | _data[_data[v].parent].left = v; |
---|
| 567 | } else { |
---|
| 568 | _data[_data[v].parent].right = v; |
---|
| 569 | } |
---|
| 570 | } |
---|
| 571 | if (_data[w].right != -1){ |
---|
| 572 | _data[_data[w].right].parent = w; |
---|
| 573 | } |
---|
| 574 | } |
---|
| 575 | |
---|
| 576 | private: |
---|
| 577 | |
---|
| 578 | class ItemData { |
---|
| 579 | public: |
---|
| 580 | Item id; |
---|
| 581 | int size; |
---|
| 582 | int successor; |
---|
| 583 | int parent; |
---|
| 584 | int left; |
---|
| 585 | int right; |
---|
| 586 | Value dmin; |
---|
| 587 | Value dcost; |
---|
| 588 | |
---|
| 589 | public: |
---|
| 590 | ItemData(const Item &item) |
---|
| 591 | : id(item), size(1), successor(), parent(-1), |
---|
| 592 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
| 593 | }; |
---|
| 594 | |
---|
| 595 | }; |
---|
| 596 | |
---|
| 597 | template <typename _Value, typename _ItemIntMap, typename _Tolerance> |
---|
| 598 | class DynamicTree<_Value, _ItemIntMap, _Tolerance, false> { |
---|
| 599 | public: |
---|
| 600 | typedef _ItemIntMap ItemIntMap; |
---|
| 601 | typedef typename ItemIntMap::Key Item; |
---|
| 602 | typedef _Value Value; |
---|
| 603 | typedef _Tolerance Tolerance; |
---|
| 604 | |
---|
| 605 | private: |
---|
| 606 | |
---|
| 607 | class ItemData; |
---|
| 608 | |
---|
| 609 | std::vector<ItemData> _data; |
---|
| 610 | ItemIntMap &_iim; |
---|
| 611 | Value _max_value; |
---|
| 612 | Tolerance _tolerance; |
---|
| 613 | |
---|
| 614 | public: |
---|
| 615 | DynamicTree(ItemIntMap &iim, const Tolerance& tolerance = Tolerance()) |
---|
| 616 | : _iim(iim), _max_value(std::numeric_limits<Value>::max()), |
---|
| 617 | _tolerance(tolerance) {} |
---|
| 618 | |
---|
| 619 | ~DynamicTree() {} |
---|
| 620 | |
---|
| 621 | void clear() { |
---|
| 622 | _data.clear(); |
---|
| 623 | } |
---|
| 624 | |
---|
| 625 | void tolerance(const Tolerance& tolerance) const { |
---|
| 626 | _tolerance = tolerance; |
---|
| 627 | return *this; |
---|
| 628 | } |
---|
| 629 | |
---|
| 630 | const Tolerance& tolerance() const { |
---|
| 631 | return tolerance; |
---|
| 632 | } |
---|
| 633 | |
---|
| 634 | void makeTree(const Item &item) { |
---|
| 635 | _data[makePath(item)].successor = -1; |
---|
| 636 | } |
---|
| 637 | |
---|
| 638 | Item findRoot(const Item &item) { |
---|
| 639 | return _data[findTail(expose(_iim[item]))].id; |
---|
| 640 | } |
---|
| 641 | |
---|
| 642 | Item findCost(const Item &item, Value& d){ |
---|
| 643 | return _data[findPathCost(expose(_iim[item]),d)].id; |
---|
| 644 | } |
---|
| 645 | |
---|
| 646 | void addCost(const Item &item, Value x){ |
---|
| 647 | addPathCost(expose(_iim[item]), x); |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | void link(const Item &item1, const Item &item2){ |
---|
| 651 | int v = _iim[item1]; |
---|
| 652 | int w = _iim[item2]; |
---|
| 653 | int p = expose(w); |
---|
| 654 | join(-1, expose(v), p); |
---|
| 655 | _data[v].successor = -1; |
---|
| 656 | } |
---|
| 657 | |
---|
| 658 | void cut(const Item &item) { |
---|
| 659 | int v = _iim[item]; |
---|
| 660 | int p, q; |
---|
| 661 | expose(v); |
---|
| 662 | split(p, v, q); |
---|
| 663 | if (p != -1) { |
---|
| 664 | _data[p].successor = v; |
---|
| 665 | } |
---|
| 666 | if (q != -1) { |
---|
| 667 | _data[q].successor = _data[v].successor; |
---|
| 668 | } |
---|
| 669 | _data[v].successor = -1; |
---|
| 670 | } |
---|
| 671 | |
---|
| 672 | Item parent(const Item &item){ |
---|
| 673 | return _data[_iim[item].p].id; |
---|
| 674 | } |
---|
| 675 | |
---|
| 676 | Value maxValue() const { |
---|
| 677 | return _max_value; |
---|
| 678 | } |
---|
| 679 | |
---|
| 680 | private: |
---|
| 681 | |
---|
| 682 | int makePath(const Item &item) { |
---|
| 683 | _iim.set(item, _data.size()); |
---|
| 684 | ItemData v(item); |
---|
| 685 | _data.push_back(v); |
---|
| 686 | return _iim[item]; |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | int findPath(int v){ |
---|
| 690 | splay(v); |
---|
| 691 | return v; |
---|
| 692 | } |
---|
| 693 | |
---|
| 694 | int findPathCost(int p, Value &d){ |
---|
| 695 | while ((_data[p].right != -1 && |
---|
| 696 | !_tolerance.less(0, _data[_data[p].right].dmin)) || |
---|
| 697 | (_data[p].left != -1 && _tolerance.less(0, _data[p].dcost))) { |
---|
| 698 | if (_data[p].right != -1 && |
---|
| 699 | !_tolerance.less(0, _data[_data[p].right].dmin)) { |
---|
| 700 | p = _data[p].right; |
---|
| 701 | } else if (_data[p].left != -1 && |
---|
| 702 | !_tolerance.less(0, _data[_data[p].left].dmin)){ |
---|
| 703 | p = _data[p].left; |
---|
| 704 | } |
---|
| 705 | } |
---|
| 706 | splay(p); |
---|
| 707 | d = _data[p].dmin; |
---|
| 708 | return p; |
---|
| 709 | } |
---|
| 710 | |
---|
| 711 | int findTail(int p){ |
---|
| 712 | while (_data[p].right != -1) { |
---|
| 713 | p = _data[p].right; |
---|
| 714 | } |
---|
| 715 | splay(p); |
---|
| 716 | return p; |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | void addPathCost(int p, Value x){ |
---|
| 720 | if (!_tolerance.less(x, _max_value)) { |
---|
| 721 | _data[p].dmin = x;_data[p].dcost = x; |
---|
| 722 | } else if (!_tolerance.less(-x, _max_value)) { |
---|
| 723 | _data[p].dmin = 0; |
---|
| 724 | _data[p].dcost = 0; |
---|
| 725 | } else { |
---|
| 726 | _data[p].dmin += x; |
---|
| 727 | } |
---|
| 728 | } |
---|
| 729 | |
---|
| 730 | void join(int p, int v, int q) { |
---|
| 731 | Value min = _max_value; |
---|
| 732 | Value pmin = _max_value; |
---|
| 733 | Value vmin = _data[v].dmin; |
---|
| 734 | Value qmin = _max_value; |
---|
| 735 | if (p != -1){ |
---|
| 736 | pmin = _data[p].dmin; |
---|
| 737 | } |
---|
| 738 | if (q != -1){ |
---|
| 739 | qmin = _data[q].dmin; |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | if (_tolerance.less(vmin, qmin)) { |
---|
| 743 | if (_tolerance.less(vmin,pmin)) { |
---|
| 744 | min = vmin; |
---|
| 745 | } else { |
---|
| 746 | min = pmin; |
---|
| 747 | } |
---|
| 748 | } else if (_tolerance.less(qmin,pmin)) { |
---|
| 749 | min = qmin; |
---|
| 750 | } else { |
---|
| 751 | min = pmin; |
---|
| 752 | } |
---|
| 753 | |
---|
| 754 | if (p != -1){ |
---|
| 755 | _data[p].parent = v; |
---|
| 756 | _data[p].dmin -= min; |
---|
| 757 | } |
---|
| 758 | if (q!=-1){ |
---|
| 759 | _data[q].parent = v; |
---|
| 760 | if (_tolerance.less(_data[q].dmin,_max_value)) { |
---|
| 761 | _data[q].dmin -= min; |
---|
| 762 | } |
---|
| 763 | } |
---|
| 764 | _data[v].left = p; |
---|
| 765 | _data[v].right = q; |
---|
| 766 | if (_tolerance.less(min,_max_value)) { |
---|
| 767 | _data[v].dcost = _data[v].dmin - min; |
---|
| 768 | } |
---|
| 769 | _data[v].dmin = min; |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | void split(int &p, int v, int &q){ |
---|
| 773 | splay(v); |
---|
| 774 | p = -1; |
---|
| 775 | if (_data[v].left != -1){ |
---|
| 776 | p = _data[v].left; |
---|
| 777 | _data[p].dmin += _data[v].dmin; |
---|
| 778 | _data[p].parent = -1; |
---|
| 779 | _data[v].left = -1; |
---|
| 780 | } |
---|
| 781 | q = -1; |
---|
| 782 | if (_data[v].right != -1) { |
---|
| 783 | q=_data[v].right; |
---|
| 784 | if (_tolerance.less(_data[q].dmin, _max_value)) { |
---|
| 785 | _data[q].dmin += _data[v].dmin; |
---|
| 786 | } |
---|
| 787 | _data[q].parent = -1; |
---|
| 788 | _data[v].right = -1; |
---|
| 789 | } |
---|
| 790 | if (_tolerance.less(_data[v].dcost, _max_value)) { |
---|
| 791 | _data[v].dmin += _data[v].dcost; |
---|
| 792 | _data[v].dcost = 0; |
---|
| 793 | } else { |
---|
| 794 | _data[v].dmin = _data[v].dcost; |
---|
| 795 | } |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | int expose(int v) { |
---|
| 799 | int p, q, r, w; |
---|
| 800 | p = -1; |
---|
| 801 | while (v != -1) { |
---|
| 802 | w = _data[findPath(v)].successor; |
---|
| 803 | split(q, v, r); |
---|
| 804 | if (q != -1) { |
---|
| 805 | _data[q].successor = v; |
---|
| 806 | } |
---|
| 807 | join(p, v, r); |
---|
| 808 | p = v; |
---|
| 809 | v = w; |
---|
| 810 | } |
---|
| 811 | _data[p].successor = -1; |
---|
| 812 | return p; |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | void splay(int v) { |
---|
| 816 | while (_data[v].parent != -1) { |
---|
| 817 | if (v == _data[_data[v].parent].left) { |
---|
| 818 | if (_data[_data[v].parent].parent == -1) { |
---|
| 819 | zig(v); |
---|
| 820 | } else { |
---|
| 821 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
| 822 | zig(_data[v].parent); |
---|
| 823 | zig(v); |
---|
| 824 | } else { |
---|
| 825 | zig(v); |
---|
| 826 | zag(v); |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | } else { |
---|
| 830 | if (_data[_data[v].parent].parent == -1) { |
---|
| 831 | zag(v); |
---|
| 832 | } else { |
---|
| 833 | if (_data[v].parent == _data[_data[_data[v].parent].parent].left) { |
---|
| 834 | zag(v); |
---|
| 835 | zig(v); |
---|
| 836 | } else { |
---|
| 837 | zag(_data[v].parent); |
---|
| 838 | zag(v); |
---|
| 839 | } |
---|
| 840 | } |
---|
| 841 | } |
---|
| 842 | } |
---|
| 843 | } |
---|
| 844 | |
---|
| 845 | |
---|
| 846 | void zig(int v) { |
---|
| 847 | Value min = _data[_data[v].parent].dmin; |
---|
| 848 | int a = _data[v].parent; |
---|
| 849 | |
---|
| 850 | Value aa = _data[a].dcost; |
---|
| 851 | if (_tolerance.less(aa, _max_value)) { |
---|
| 852 | aa+= min; |
---|
| 853 | } |
---|
| 854 | |
---|
| 855 | |
---|
| 856 | int b = v; |
---|
| 857 | Value ab = min + _data[b].dmin; |
---|
| 858 | Value bb = _data[b].dcost; |
---|
| 859 | if (_tolerance.less(bb, _max_value)) { |
---|
| 860 | bb+= ab; |
---|
| 861 | } |
---|
| 862 | |
---|
| 863 | int c = -1; |
---|
| 864 | Value cc = _max_value; |
---|
| 865 | if (_data[a].right != -1) { |
---|
| 866 | c = _data[a].right; |
---|
| 867 | cc = _data[c].dmin; |
---|
| 868 | if (_tolerance.less(cc, _max_value)) { |
---|
| 869 | cc+=min; |
---|
| 870 | } |
---|
| 871 | } |
---|
| 872 | |
---|
| 873 | int d = -1; |
---|
| 874 | Value dd = _max_value; |
---|
| 875 | if (_data[v].left != -1){ |
---|
| 876 | d = _data[v].left; |
---|
| 877 | dd = ab + _data[d].dmin; |
---|
| 878 | } |
---|
| 879 | |
---|
| 880 | int e = -1; |
---|
| 881 | Value ee = _max_value; |
---|
| 882 | if (_data[v].right != -1) { |
---|
| 883 | e = _data[v].right; |
---|
| 884 | ee = ab + _data[e].dmin; |
---|
| 885 | } |
---|
| 886 | |
---|
| 887 | Value min2; |
---|
| 888 | if (_tolerance.less(0, _data[b].dmin) || |
---|
| 889 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
| 890 | min2 = min; |
---|
| 891 | } else { |
---|
| 892 | if (_tolerance.less(aa, cc)) { |
---|
| 893 | if (_tolerance.less(aa, ee)) { |
---|
| 894 | min2 = aa; |
---|
| 895 | } else { |
---|
| 896 | min2 = ee; |
---|
| 897 | } |
---|
| 898 | } else if (_tolerance.less(cc, ee)) { |
---|
| 899 | min2 = cc; |
---|
| 900 | } else { |
---|
| 901 | min2 = ee; |
---|
| 902 | } |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | _data[a].dcost = aa; |
---|
| 906 | if (_tolerance.less(aa, _max_value)) { |
---|
| 907 | _data[a].dcost -= min2; |
---|
| 908 | } |
---|
| 909 | _data[a].dmin = min2; |
---|
| 910 | if (_tolerance.less(min2,_max_value)) { |
---|
| 911 | _data[a].dmin -= min; |
---|
| 912 | } |
---|
| 913 | _data[b].dcost = bb; |
---|
| 914 | if (_tolerance.less(bb, _max_value)) { |
---|
| 915 | _data[b].dcost -= min; |
---|
| 916 | } |
---|
| 917 | _data[b].dmin = min; |
---|
| 918 | if (c != -1) { |
---|
| 919 | _data[c].dmin = cc; |
---|
| 920 | if (_tolerance.less(cc, _max_value)) { |
---|
| 921 | _data[c].dmin -= min2; |
---|
| 922 | } |
---|
| 923 | } |
---|
| 924 | if (d != -1) { |
---|
| 925 | _data[d].dmin = dd - min; |
---|
| 926 | } |
---|
| 927 | if (e != -1) { |
---|
| 928 | _data[e].dmin = ee - min2; |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | int w = _data[v].parent; |
---|
| 932 | _data[v].successor = _data[w].successor; |
---|
| 933 | _data[w].successor = -1; |
---|
| 934 | _data[v].parent = _data[w].parent; |
---|
| 935 | _data[w].parent = v; |
---|
| 936 | _data[w].left = _data[v].right; |
---|
| 937 | _data[v].right = w; |
---|
| 938 | if (_data[v].parent != -1){ |
---|
| 939 | if (_data[_data[v].parent].right == w) { |
---|
| 940 | _data[_data[v].parent].right = v; |
---|
| 941 | } else { |
---|
| 942 | _data[_data[v].parent].left = v; |
---|
| 943 | } |
---|
| 944 | } |
---|
| 945 | if (_data[w].left != -1){ |
---|
| 946 | _data[_data[w].left].parent = w; |
---|
| 947 | } |
---|
| 948 | } |
---|
| 949 | |
---|
| 950 | |
---|
| 951 | void zag(int v) { |
---|
| 952 | |
---|
| 953 | Value min = _data[_data[v].parent].dmin; |
---|
| 954 | |
---|
| 955 | int a = _data[v].parent; |
---|
| 956 | Value aa = _data[a].dcost; |
---|
| 957 | if (_tolerance.less(aa, _max_value)) { |
---|
| 958 | aa += min; |
---|
| 959 | } |
---|
| 960 | |
---|
| 961 | int b = v; |
---|
| 962 | Value ab = min + _data[b].dmin; |
---|
| 963 | Value bb = _data[b].dcost; |
---|
| 964 | if (_tolerance.less(bb, _max_value)) { |
---|
| 965 | bb += ab; |
---|
| 966 | } |
---|
| 967 | |
---|
| 968 | int c = -1; |
---|
| 969 | Value cc = _max_value; |
---|
| 970 | if (_data[a].left != -1){ |
---|
| 971 | c = _data[a].left; |
---|
| 972 | cc = min + _data[c].dmin; |
---|
| 973 | } |
---|
| 974 | |
---|
| 975 | int d = -1; |
---|
| 976 | Value dd = _max_value; |
---|
| 977 | if (_data[v].right!=-1) { |
---|
| 978 | d = _data[v].right; |
---|
| 979 | dd = _data[d].dmin; |
---|
| 980 | if (_tolerance.less(dd, _max_value)) { |
---|
| 981 | dd += ab; |
---|
| 982 | } |
---|
| 983 | } |
---|
| 984 | |
---|
| 985 | int e = -1; |
---|
| 986 | Value ee = _max_value; |
---|
| 987 | if (_data[v].left != -1){ |
---|
| 988 | e = _data[v].left; |
---|
| 989 | ee = ab + _data[e].dmin; |
---|
| 990 | } |
---|
| 991 | |
---|
| 992 | Value min2; |
---|
| 993 | if (_tolerance.less(0, _data[b].dmin) || |
---|
| 994 | (e != -1 && !_tolerance.less(0, _data[e].dmin))) { |
---|
| 995 | min2 = min; |
---|
| 996 | } else { |
---|
| 997 | if (_tolerance.less(aa, cc)) { |
---|
| 998 | if (_tolerance.less(aa, ee)) { |
---|
| 999 | min2 = aa; |
---|
| 1000 | } else { |
---|
| 1001 | min2 = ee; |
---|
| 1002 | } |
---|
| 1003 | } else if (_tolerance.less(cc, ee)) { |
---|
| 1004 | min2 = cc; |
---|
| 1005 | } else { |
---|
| 1006 | min2 = ee; |
---|
| 1007 | } |
---|
| 1008 | } |
---|
| 1009 | _data[a].dcost = aa; |
---|
| 1010 | if (_tolerance.less(aa, _max_value)) { |
---|
| 1011 | _data[a].dcost -= min2; |
---|
| 1012 | } |
---|
| 1013 | _data[a].dmin = min2; |
---|
| 1014 | if (_tolerance.less(min2, _max_value)) { |
---|
| 1015 | _data[a].dmin -= min; |
---|
| 1016 | } |
---|
| 1017 | _data[b].dcost = bb; |
---|
| 1018 | if (_tolerance.less(bb, _max_value)) { |
---|
| 1019 | _data[b].dcost -= min; |
---|
| 1020 | } |
---|
| 1021 | _data[b].dmin = min; |
---|
| 1022 | if (c != -1) { |
---|
| 1023 | _data[c].dmin = cc - min2; |
---|
| 1024 | } |
---|
| 1025 | if (d != -1) { |
---|
| 1026 | _data[d].dmin = dd; |
---|
| 1027 | if (_tolerance.less(dd, _max_value)) { |
---|
| 1028 | _data[d].dmin -= min; |
---|
| 1029 | } |
---|
| 1030 | } |
---|
| 1031 | if (e != -1) { |
---|
| 1032 | _data[e].dmin = ee - min2; |
---|
| 1033 | } |
---|
| 1034 | |
---|
| 1035 | int w = _data[v].parent; |
---|
| 1036 | _data[v].successor = _data[w].successor; |
---|
| 1037 | _data[w].successor = -1; |
---|
| 1038 | _data[v].parent = _data[w].parent; |
---|
| 1039 | _data[w].parent = v; |
---|
| 1040 | _data[w].right = _data[v].left; |
---|
| 1041 | _data[v].left = w; |
---|
| 1042 | if (_data[v].parent != -1){ |
---|
| 1043 | if (_data[_data[v].parent].left == w) { |
---|
| 1044 | _data[_data[v].parent].left = v; |
---|
| 1045 | } else { |
---|
| 1046 | _data[_data[v].parent].right = v; |
---|
| 1047 | } |
---|
| 1048 | } |
---|
| 1049 | if (_data[w].right != -1){ |
---|
| 1050 | _data[_data[w].right].parent = w; |
---|
| 1051 | } |
---|
| 1052 | } |
---|
| 1053 | |
---|
| 1054 | private: |
---|
| 1055 | |
---|
| 1056 | class ItemData { |
---|
| 1057 | public: |
---|
| 1058 | Item id; |
---|
| 1059 | int successor; |
---|
| 1060 | int parent; |
---|
| 1061 | int left; |
---|
| 1062 | int right; |
---|
| 1063 | Value dmin; |
---|
| 1064 | Value dcost; |
---|
| 1065 | |
---|
| 1066 | public: |
---|
| 1067 | ItemData(const Item &item) |
---|
| 1068 | : id(item), successor(), parent(-1), |
---|
| 1069 | left(-1), right(-1), dmin(0), dcost(0) {} |
---|
| 1070 | }; |
---|
| 1071 | |
---|
| 1072 | }; |
---|
| 1073 | |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | #endif |
---|