[463] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[357] | 2 | * |
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[463] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[357] | 4 | * |
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[956] | 5 | * Copyright (C) 2003-2010 |
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[357] | 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 | |
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| 19 | #ifndef LEMON_SUURBALLE_H |
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| 20 | #define LEMON_SUURBALLE_H |
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| 21 | |
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| 22 | ///\ingroup shortest_path |
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| 23 | ///\file |
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| 24 | ///\brief An algorithm for finding arc-disjoint paths between two |
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| 25 | /// nodes having minimum total length. |
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| 26 | |
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| 27 | #include <vector> |
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[670] | 28 | #include <limits> |
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[357] | 29 | #include <lemon/bin_heap.h> |
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| 30 | #include <lemon/path.h> |
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[566] | 31 | #include <lemon/list_graph.h> |
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[927] | 32 | #include <lemon/dijkstra.h> |
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[566] | 33 | #include <lemon/maps.h> |
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[357] | 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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[931] | 37 | /// \brief Default traits class of Suurballe algorithm. |
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| 38 | /// |
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| 39 | /// Default traits class of Suurballe algorithm. |
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| 40 | /// \tparam GR The digraph type the algorithm runs on. |
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| 41 | /// \tparam LEN The type of the length map. |
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| 42 | /// The default value is <tt>GR::ArcMap<int></tt>. |
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| 43 | #ifdef DOXYGEN |
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| 44 | template <typename GR, typename LEN> |
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| 45 | #else |
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| 46 | template < typename GR, |
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| 47 | typename LEN = typename GR::template ArcMap<int> > |
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| 48 | #endif |
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| 49 | struct SuurballeDefaultTraits |
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| 50 | { |
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| 51 | /// The type of the digraph. |
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| 52 | typedef GR Digraph; |
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| 53 | /// The type of the length map. |
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| 54 | typedef LEN LengthMap; |
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| 55 | /// The type of the lengths. |
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| 56 | typedef typename LEN::Value Length; |
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| 57 | /// The type of the flow map. |
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| 58 | typedef typename GR::template ArcMap<int> FlowMap; |
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| 59 | /// The type of the potential map. |
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| 60 | typedef typename GR::template NodeMap<Length> PotentialMap; |
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| 61 | |
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| 62 | /// \brief The path type |
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| 63 | /// |
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| 64 | /// The type used for storing the found arc-disjoint paths. |
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| 65 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 66 | /// and it must have an \c addBack() function. |
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| 67 | typedef lemon::Path<Digraph> Path; |
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[956] | 68 | |
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[931] | 69 | /// The cross reference type used for the heap. |
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| 70 | typedef typename GR::template NodeMap<int> HeapCrossRef; |
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| 71 | |
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| 72 | /// \brief The heap type used for internal Dijkstra computations. |
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| 73 | /// |
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| 74 | /// The type of the heap used for internal Dijkstra computations. |
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| 75 | /// It must conform to the \ref lemon::concepts::Heap "Heap" concept |
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| 76 | /// and its priority type must be \c Length. |
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| 77 | typedef BinHeap<Length, HeapCrossRef> Heap; |
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| 78 | }; |
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| 79 | |
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[357] | 80 | /// \addtogroup shortest_path |
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| 81 | /// @{ |
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| 82 | |
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[358] | 83 | /// \brief Algorithm for finding arc-disjoint paths between two nodes |
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| 84 | /// having minimum total length. |
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[357] | 85 | /// |
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| 86 | /// \ref lemon::Suurballe "Suurballe" implements an algorithm for |
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| 87 | /// finding arc-disjoint paths having minimum total length (cost) |
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[358] | 88 | /// from a given source node to a given target node in a digraph. |
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[357] | 89 | /// |
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[670] | 90 | /// Note that this problem is a special case of the \ref min_cost_flow |
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| 91 | /// "minimum cost flow problem". This implementation is actually an |
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| 92 | /// efficient specialized version of the \ref CapacityScaling |
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[926] | 93 | /// "successive shortest path" algorithm directly for this problem. |
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[670] | 94 | /// Therefore this class provides query functions for flow values and |
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| 95 | /// node potentials (the dual solution) just like the minimum cost flow |
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| 96 | /// algorithms. |
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[357] | 97 | /// |
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[606] | 98 | /// \tparam GR The digraph type the algorithm runs on. |
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[670] | 99 | /// \tparam LEN The type of the length map. |
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| 100 | /// The default value is <tt>GR::ArcMap<int></tt>. |
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[357] | 101 | /// |
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[925] | 102 | /// \warning Length values should be \e non-negative. |
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[357] | 103 | /// |
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[926] | 104 | /// \note For finding \e node-disjoint paths, this algorithm can be used |
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[670] | 105 | /// along with the \ref SplitNodes adaptor. |
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[358] | 106 | #ifdef DOXYGEN |
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[931] | 107 | template <typename GR, typename LEN, typename TR> |
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[358] | 108 | #else |
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[670] | 109 | template < typename GR, |
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[931] | 110 | typename LEN = typename GR::template ArcMap<int>, |
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| 111 | typename TR = SuurballeDefaultTraits<GR, LEN> > |
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[358] | 112 | #endif |
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[357] | 113 | class Suurballe |
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| 114 | { |
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[606] | 115 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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[357] | 116 | |
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| 117 | typedef ConstMap<Arc, int> ConstArcMap; |
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[606] | 118 | typedef typename GR::template NodeMap<Arc> PredMap; |
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[357] | 119 | |
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| 120 | public: |
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| 121 | |
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[931] | 122 | /// The type of the digraph. |
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| 123 | typedef typename TR::Digraph Digraph; |
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[606] | 124 | /// The type of the length map. |
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[931] | 125 | typedef typename TR::LengthMap LengthMap; |
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[606] | 126 | /// The type of the lengths. |
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[931] | 127 | typedef typename TR::Length Length; |
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| 128 | |
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[670] | 129 | /// The type of the flow map. |
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[931] | 130 | typedef typename TR::FlowMap FlowMap; |
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[670] | 131 | /// The type of the potential map. |
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[931] | 132 | typedef typename TR::PotentialMap PotentialMap; |
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| 133 | /// The type of the path structures. |
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| 134 | typedef typename TR::Path Path; |
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| 135 | /// The cross reference type used for the heap. |
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| 136 | typedef typename TR::HeapCrossRef HeapCrossRef; |
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| 137 | /// The heap type used for internal Dijkstra computations. |
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| 138 | typedef typename TR::Heap Heap; |
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[670] | 139 | |
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[931] | 140 | /// The \ref SuurballeDefaultTraits "traits class" of the algorithm. |
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| 141 | typedef TR Traits; |
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[357] | 142 | |
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| 143 | private: |
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[463] | 144 | |
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[670] | 145 | // ResidualDijkstra is a special implementation of the |
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| 146 | // Dijkstra algorithm for finding shortest paths in the |
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| 147 | // residual network with respect to the reduced arc lengths |
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| 148 | // and modifying the node potentials according to the |
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| 149 | // distance of the nodes. |
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[357] | 150 | class ResidualDijkstra |
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| 151 | { |
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| 152 | private: |
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| 153 | |
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| 154 | const Digraph &_graph; |
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[926] | 155 | const LengthMap &_length; |
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[357] | 156 | const FlowMap &_flow; |
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[926] | 157 | PotentialMap &_pi; |
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[357] | 158 | PredMap &_pred; |
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| 159 | Node _s; |
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| 160 | Node _t; |
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[956] | 161 | |
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[926] | 162 | PotentialMap _dist; |
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| 163 | std::vector<Node> _proc_nodes; |
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[357] | 164 | |
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| 165 | public: |
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| 166 | |
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[926] | 167 | // Constructor |
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| 168 | ResidualDijkstra(Suurballe &srb) : |
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| 169 | _graph(srb._graph), _length(srb._length), |
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[956] | 170 | _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred), |
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[926] | 171 | _s(srb._s), _t(srb._t), _dist(_graph) {} |
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[956] | 172 | |
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[926] | 173 | // Run the algorithm and return true if a path is found |
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| 174 | // from the source node to the target node. |
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| 175 | bool run(int cnt) { |
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| 176 | return cnt == 0 ? startFirst() : start(); |
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| 177 | } |
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[357] | 178 | |
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[926] | 179 | private: |
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[956] | 180 | |
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[926] | 181 | // Execute the algorithm for the first time (the flow and potential |
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| 182 | // functions have to be identically zero). |
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| 183 | bool startFirst() { |
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[357] | 184 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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| 185 | Heap heap(heap_cross_ref); |
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| 186 | heap.push(_s, 0); |
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| 187 | _pred[_s] = INVALID; |
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| 188 | _proc_nodes.clear(); |
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| 189 | |
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[358] | 190 | // Process nodes |
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[357] | 191 | while (!heap.empty() && heap.top() != _t) { |
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| 192 | Node u = heap.top(), v; |
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[926] | 193 | Length d = heap.prio(), dn; |
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[357] | 194 | _dist[u] = heap.prio(); |
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[926] | 195 | _proc_nodes.push_back(u); |
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[357] | 196 | heap.pop(); |
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[926] | 197 | |
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| 198 | // Traverse outgoing arcs |
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| 199 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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| 200 | v = _graph.target(e); |
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| 201 | switch(heap.state(v)) { |
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| 202 | case Heap::PRE_HEAP: |
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| 203 | heap.push(v, d + _length[e]); |
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| 204 | _pred[v] = e; |
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| 205 | break; |
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| 206 | case Heap::IN_HEAP: |
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| 207 | dn = d + _length[e]; |
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| 208 | if (dn < heap[v]) { |
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| 209 | heap.decrease(v, dn); |
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| 210 | _pred[v] = e; |
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| 211 | } |
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| 212 | break; |
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| 213 | case Heap::POST_HEAP: |
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| 214 | break; |
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| 215 | } |
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| 216 | } |
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| 217 | } |
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| 218 | if (heap.empty()) return false; |
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| 219 | |
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| 220 | // Update potentials of processed nodes |
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| 221 | Length t_dist = heap.prio(); |
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| 222 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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| 223 | _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist; |
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| 224 | return true; |
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| 225 | } |
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| 226 | |
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| 227 | // Execute the algorithm. |
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| 228 | bool start() { |
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| 229 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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| 230 | Heap heap(heap_cross_ref); |
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| 231 | heap.push(_s, 0); |
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| 232 | _pred[_s] = INVALID; |
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| 233 | _proc_nodes.clear(); |
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| 234 | |
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| 235 | // Process nodes |
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| 236 | while (!heap.empty() && heap.top() != _t) { |
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| 237 | Node u = heap.top(), v; |
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| 238 | Length d = heap.prio() + _pi[u], dn; |
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| 239 | _dist[u] = heap.prio(); |
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[357] | 240 | _proc_nodes.push_back(u); |
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[926] | 241 | heap.pop(); |
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[357] | 242 | |
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[358] | 243 | // Traverse outgoing arcs |
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[357] | 244 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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| 245 | if (_flow[e] == 0) { |
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| 246 | v = _graph.target(e); |
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| 247 | switch(heap.state(v)) { |
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[926] | 248 | case Heap::PRE_HEAP: |
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| 249 | heap.push(v, d + _length[e] - _pi[v]); |
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[357] | 250 | _pred[v] = e; |
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[926] | 251 | break; |
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| 252 | case Heap::IN_HEAP: |
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| 253 | dn = d + _length[e] - _pi[v]; |
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| 254 | if (dn < heap[v]) { |
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| 255 | heap.decrease(v, dn); |
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| 256 | _pred[v] = e; |
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| 257 | } |
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| 258 | break; |
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| 259 | case Heap::POST_HEAP: |
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| 260 | break; |
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[357] | 261 | } |
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| 262 | } |
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| 263 | } |
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| 264 | |
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[358] | 265 | // Traverse incoming arcs |
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[357] | 266 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
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| 267 | if (_flow[e] == 1) { |
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| 268 | v = _graph.source(e); |
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| 269 | switch(heap.state(v)) { |
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[926] | 270 | case Heap::PRE_HEAP: |
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| 271 | heap.push(v, d - _length[e] - _pi[v]); |
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[357] | 272 | _pred[v] = e; |
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[926] | 273 | break; |
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| 274 | case Heap::IN_HEAP: |
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| 275 | dn = d - _length[e] - _pi[v]; |
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| 276 | if (dn < heap[v]) { |
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| 277 | heap.decrease(v, dn); |
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| 278 | _pred[v] = e; |
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| 279 | } |
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| 280 | break; |
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| 281 | case Heap::POST_HEAP: |
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| 282 | break; |
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[357] | 283 | } |
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| 284 | } |
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| 285 | } |
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| 286 | } |
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| 287 | if (heap.empty()) return false; |
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| 288 | |
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[358] | 289 | // Update potentials of processed nodes |
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[357] | 290 | Length t_dist = heap.prio(); |
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| 291 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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[926] | 292 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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[357] | 293 | return true; |
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| 294 | } |
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| 295 | |
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| 296 | }; //class ResidualDijkstra |
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| 297 | |
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[931] | 298 | public: |
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| 299 | |
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| 300 | /// \name Named Template Parameters |
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| 301 | /// @{ |
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| 302 | |
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| 303 | template <typename T> |
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| 304 | struct SetFlowMapTraits : public Traits { |
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| 305 | typedef T FlowMap; |
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| 306 | }; |
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| 307 | |
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| 308 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 309 | /// \c FlowMap type. |
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| 310 | /// |
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| 311 | /// \ref named-templ-param "Named parameter" for setting |
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| 312 | /// \c FlowMap type. |
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| 313 | template <typename T> |
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| 314 | struct SetFlowMap |
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| 315 | : public Suurballe<GR, LEN, SetFlowMapTraits<T> > { |
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| 316 | typedef Suurballe<GR, LEN, SetFlowMapTraits<T> > Create; |
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| 317 | }; |
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| 318 | |
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| 319 | template <typename T> |
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| 320 | struct SetPotentialMapTraits : public Traits { |
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| 321 | typedef T PotentialMap; |
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| 322 | }; |
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| 323 | |
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| 324 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 325 | /// \c PotentialMap type. |
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| 326 | /// |
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| 327 | /// \ref named-templ-param "Named parameter" for setting |
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| 328 | /// \c PotentialMap type. |
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| 329 | template <typename T> |
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| 330 | struct SetPotentialMap |
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| 331 | : public Suurballe<GR, LEN, SetPotentialMapTraits<T> > { |
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| 332 | typedef Suurballe<GR, LEN, SetPotentialMapTraits<T> > Create; |
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| 333 | }; |
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| 334 | |
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| 335 | template <typename T> |
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| 336 | struct SetPathTraits : public Traits { |
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| 337 | typedef T Path; |
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| 338 | }; |
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| 339 | |
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| 340 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 341 | /// \c %Path type. |
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| 342 | /// |
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| 343 | /// \ref named-templ-param "Named parameter" for setting \c %Path type. |
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| 344 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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| 345 | /// and it must have an \c addBack() function. |
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| 346 | template <typename T> |
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| 347 | struct SetPath |
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| 348 | : public Suurballe<GR, LEN, SetPathTraits<T> > { |
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| 349 | typedef Suurballe<GR, LEN, SetPathTraits<T> > Create; |
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| 350 | }; |
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[956] | 351 | |
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[931] | 352 | template <typename H, typename CR> |
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| 353 | struct SetHeapTraits : public Traits { |
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| 354 | typedef H Heap; |
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| 355 | typedef CR HeapCrossRef; |
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| 356 | }; |
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| 357 | |
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| 358 | /// \brief \ref named-templ-param "Named parameter" for setting |
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| 359 | /// \c Heap and \c HeapCrossRef types. |
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| 360 | /// |
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| 361 | /// \ref named-templ-param "Named parameter" for setting \c Heap |
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[956] | 362 | /// and \c HeapCrossRef types with automatic allocation. |
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[931] | 363 | /// They will be used for internal Dijkstra computations. |
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| 364 | /// The heap type must conform to the \ref lemon::concepts::Heap "Heap" |
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| 365 | /// concept and its priority type must be \c Length. |
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| 366 | template <typename H, |
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| 367 | typename CR = typename Digraph::template NodeMap<int> > |
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| 368 | struct SetHeap |
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| 369 | : public Suurballe<GR, LEN, SetHeapTraits<H, CR> > { |
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| 370 | typedef Suurballe<GR, LEN, SetHeapTraits<H, CR> > Create; |
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| 371 | }; |
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| 372 | |
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| 373 | /// @} |
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| 374 | |
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[357] | 375 | private: |
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| 376 | |
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[358] | 377 | // The digraph the algorithm runs on |
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[357] | 378 | const Digraph &_graph; |
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| 379 | // The length map |
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| 380 | const LengthMap &_length; |
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[463] | 381 | |
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[357] | 382 | // Arc map of the current flow |
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| 383 | FlowMap *_flow; |
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| 384 | bool _local_flow; |
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| 385 | // Node map of the current potentials |
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| 386 | PotentialMap *_potential; |
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| 387 | bool _local_potential; |
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| 388 | |
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| 389 | // The source node |
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[926] | 390 | Node _s; |
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[357] | 391 | // The target node |
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[926] | 392 | Node _t; |
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[357] | 393 | |
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| 394 | // Container to store the found paths |
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[926] | 395 | std::vector<Path> _paths; |
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[357] | 396 | int _path_num; |
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| 397 | |
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| 398 | // The pred arc map |
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| 399 | PredMap _pred; |
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[956] | 400 | |
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[927] | 401 | // Data for full init |
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| 402 | PotentialMap *_init_dist; |
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| 403 | PredMap *_init_pred; |
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| 404 | bool _full_init; |
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[357] | 405 | |
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[941] | 406 | protected: |
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| 407 | |
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| 408 | Suurballe() {} |
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| 409 | |
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[357] | 410 | public: |
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| 411 | |
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| 412 | /// \brief Constructor. |
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| 413 | /// |
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| 414 | /// Constructor. |
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| 415 | /// |
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[670] | 416 | /// \param graph The digraph the algorithm runs on. |
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[357] | 417 | /// \param length The length (cost) values of the arcs. |
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[670] | 418 | Suurballe( const Digraph &graph, |
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| 419 | const LengthMap &length ) : |
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| 420 | _graph(graph), _length(length), _flow(0), _local_flow(false), |
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[927] | 421 | _potential(0), _local_potential(false), _pred(graph), |
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| 422 | _init_dist(0), _init_pred(0) |
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[925] | 423 | {} |
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[357] | 424 | |
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| 425 | /// Destructor. |
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| 426 | ~Suurballe() { |
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| 427 | if (_local_flow) delete _flow; |
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| 428 | if (_local_potential) delete _potential; |
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[927] | 429 | delete _init_dist; |
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| 430 | delete _init_pred; |
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[357] | 431 | } |
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| 432 | |
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[358] | 433 | /// \brief Set the flow map. |
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[357] | 434 | /// |
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[358] | 435 | /// This function sets the flow map. |
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[670] | 436 | /// If it is not used before calling \ref run() or \ref init(), |
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| 437 | /// an instance will be allocated automatically. The destructor |
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| 438 | /// deallocates this automatically allocated map, of course. |
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[357] | 439 | /// |
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[670] | 440 | /// The found flow contains only 0 and 1 values, since it is the |
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| 441 | /// union of the found arc-disjoint paths. |
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[357] | 442 | /// |
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[606] | 443 | /// \return <tt>(*this)</tt> |
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[357] | 444 | Suurballe& flowMap(FlowMap &map) { |
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| 445 | if (_local_flow) { |
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| 446 | delete _flow; |
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| 447 | _local_flow = false; |
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| 448 | } |
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| 449 | _flow = ↦ |
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| 450 | return *this; |
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| 451 | } |
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| 452 | |
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[358] | 453 | /// \brief Set the potential map. |
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[357] | 454 | /// |
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[358] | 455 | /// This function sets the potential map. |
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[670] | 456 | /// If it is not used before calling \ref run() or \ref init(), |
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| 457 | /// an instance will be allocated automatically. The destructor |
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| 458 | /// deallocates this automatically allocated map, of course. |
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[357] | 459 | /// |
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[670] | 460 | /// The node potentials provide the dual solution of the underlying |
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| 461 | /// \ref min_cost_flow "minimum cost flow problem". |
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[357] | 462 | /// |
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[606] | 463 | /// \return <tt>(*this)</tt> |
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[357] | 464 | Suurballe& potentialMap(PotentialMap &map) { |
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| 465 | if (_local_potential) { |
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| 466 | delete _potential; |
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| 467 | _local_potential = false; |
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| 468 | } |
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| 469 | _potential = ↦ |
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| 470 | return *this; |
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| 471 | } |
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| 472 | |
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[631] | 473 | /// \name Execution Control |
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[357] | 474 | /// The simplest way to execute the algorithm is to call the run() |
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[927] | 475 | /// function.\n |
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| 476 | /// If you need to execute the algorithm many times using the same |
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| 477 | /// source node, then you may call fullInit() once and start() |
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| 478 | /// for each target node.\n |
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[357] | 479 | /// If you only need the flow that is the union of the found |
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[927] | 480 | /// arc-disjoint paths, then you may call findFlow() instead of |
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| 481 | /// start(). |
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[357] | 482 | |
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| 483 | /// @{ |
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| 484 | |
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[358] | 485 | /// \brief Run the algorithm. |
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[357] | 486 | /// |
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[358] | 487 | /// This function runs the algorithm. |
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[357] | 488 | /// |
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[670] | 489 | /// \param s The source node. |
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| 490 | /// \param t The target node. |
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[357] | 491 | /// \param k The number of paths to be found. |
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| 492 | /// |
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[358] | 493 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 494 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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[357] | 495 | /// arc-disjoint paths found. |
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| 496 | /// |
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[670] | 497 | /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is |
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| 498 | /// just a shortcut of the following code. |
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[357] | 499 | /// \code |
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[670] | 500 | /// s.init(s); |
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[927] | 501 | /// s.start(t, k); |
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[357] | 502 | /// \endcode |
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[670] | 503 | int run(const Node& s, const Node& t, int k = 2) { |
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| 504 | init(s); |
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[927] | 505 | start(t, k); |
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[357] | 506 | return _path_num; |
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| 507 | } |
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| 508 | |
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[358] | 509 | /// \brief Initialize the algorithm. |
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[357] | 510 | /// |
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[927] | 511 | /// This function initializes the algorithm with the given source node. |
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[670] | 512 | /// |
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| 513 | /// \param s The source node. |
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| 514 | void init(const Node& s) { |
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[926] | 515 | _s = s; |
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[670] | 516 | |
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[358] | 517 | // Initialize maps |
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[357] | 518 | if (!_flow) { |
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| 519 | _flow = new FlowMap(_graph); |
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| 520 | _local_flow = true; |
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| 521 | } |
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| 522 | if (!_potential) { |
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| 523 | _potential = new PotentialMap(_graph); |
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| 524 | _local_potential = true; |
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| 525 | } |
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[927] | 526 | _full_init = false; |
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| 527 | } |
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| 528 | |
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| 529 | /// \brief Initialize the algorithm and perform Dijkstra. |
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| 530 | /// |
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| 531 | /// This function initializes the algorithm and performs a full |
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| 532 | /// Dijkstra search from the given source node. It makes consecutive |
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| 533 | /// executions of \ref start() "start(t, k)" faster, since they |
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| 534 | /// have to perform %Dijkstra only k-1 times. |
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| 535 | /// |
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| 536 | /// This initialization is usually worth using instead of \ref init() |
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| 537 | /// if the algorithm is executed many times using the same source node. |
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| 538 | /// |
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| 539 | /// \param s The source node. |
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| 540 | void fullInit(const Node& s) { |
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| 541 | // Initialize maps |
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| 542 | init(s); |
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| 543 | if (!_init_dist) { |
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| 544 | _init_dist = new PotentialMap(_graph); |
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| 545 | } |
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| 546 | if (!_init_pred) { |
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| 547 | _init_pred = new PredMap(_graph); |
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| 548 | } |
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| 549 | |
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| 550 | // Run a full Dijkstra |
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| 551 | typename Dijkstra<Digraph, LengthMap> |
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| 552 | ::template SetStandardHeap<Heap> |
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| 553 | ::template SetDistMap<PotentialMap> |
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| 554 | ::template SetPredMap<PredMap> |
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| 555 | ::Create dijk(_graph, _length); |
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| 556 | dijk.distMap(*_init_dist).predMap(*_init_pred); |
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| 557 | dijk.run(s); |
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[956] | 558 | |
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[927] | 559 | _full_init = true; |
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| 560 | } |
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| 561 | |
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| 562 | /// \brief Execute the algorithm. |
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| 563 | /// |
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| 564 | /// This function executes the algorithm. |
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| 565 | /// |
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| 566 | /// \param t The target node. |
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| 567 | /// \param k The number of paths to be found. |
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| 568 | /// |
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| 569 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 570 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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| 571 | /// arc-disjoint paths found. |
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| 572 | /// |
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| 573 | /// \note Apart from the return value, <tt>s.start(t, k)</tt> is |
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| 574 | /// just a shortcut of the following code. |
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| 575 | /// \code |
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| 576 | /// s.findFlow(t, k); |
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| 577 | /// s.findPaths(); |
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| 578 | /// \endcode |
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| 579 | int start(const Node& t, int k = 2) { |
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| 580 | findFlow(t, k); |
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| 581 | findPaths(); |
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| 582 | return _path_num; |
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[357] | 583 | } |
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| 584 | |
---|
[670] | 585 | /// \brief Execute the algorithm to find an optimal flow. |
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[357] | 586 | /// |
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[358] | 587 | /// This function executes the successive shortest path algorithm to |
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[670] | 588 | /// find a minimum cost flow, which is the union of \c k (or less) |
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[357] | 589 | /// arc-disjoint paths. |
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| 590 | /// |
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[670] | 591 | /// \param t The target node. |
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| 592 | /// \param k The number of paths to be found. |
---|
| 593 | /// |
---|
[358] | 594 | /// \return \c k if there are at least \c k arc-disjoint paths from |
---|
[670] | 595 | /// the source node to the given node \c t in the digraph. |
---|
| 596 | /// Otherwise it returns the number of arc-disjoint paths found. |
---|
[357] | 597 | /// |
---|
| 598 | /// \pre \ref init() must be called before using this function. |
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[670] | 599 | int findFlow(const Node& t, int k = 2) { |
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[926] | 600 | _t = t; |
---|
| 601 | ResidualDijkstra dijkstra(*this); |
---|
[956] | 602 | |
---|
[927] | 603 | // Initialization |
---|
| 604 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 605 | (*_flow)[e] = 0; |
---|
| 606 | } |
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| 607 | if (_full_init) { |
---|
| 608 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 609 | (*_potential)[n] = (*_init_dist)[n]; |
---|
| 610 | } |
---|
| 611 | Node u = _t; |
---|
| 612 | Arc e; |
---|
| 613 | while ((e = (*_init_pred)[u]) != INVALID) { |
---|
| 614 | (*_flow)[e] = 1; |
---|
| 615 | u = _graph.source(e); |
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[956] | 616 | } |
---|
[927] | 617 | _path_num = 1; |
---|
| 618 | } else { |
---|
| 619 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 620 | (*_potential)[n] = 0; |
---|
| 621 | } |
---|
| 622 | _path_num = 0; |
---|
| 623 | } |
---|
[670] | 624 | |
---|
[358] | 625 | // Find shortest paths |
---|
[357] | 626 | while (_path_num < k) { |
---|
[358] | 627 | // Run Dijkstra |
---|
[926] | 628 | if (!dijkstra.run(_path_num)) break; |
---|
[357] | 629 | ++_path_num; |
---|
| 630 | |
---|
[358] | 631 | // Set the flow along the found shortest path |
---|
[926] | 632 | Node u = _t; |
---|
[357] | 633 | Arc e; |
---|
| 634 | while ((e = _pred[u]) != INVALID) { |
---|
| 635 | if (u == _graph.target(e)) { |
---|
| 636 | (*_flow)[e] = 1; |
---|
| 637 | u = _graph.source(e); |
---|
| 638 | } else { |
---|
| 639 | (*_flow)[e] = 0; |
---|
| 640 | u = _graph.target(e); |
---|
| 641 | } |
---|
| 642 | } |
---|
| 643 | } |
---|
| 644 | return _path_num; |
---|
| 645 | } |
---|
[463] | 646 | |
---|
[358] | 647 | /// \brief Compute the paths from the flow. |
---|
[357] | 648 | /// |
---|
[926] | 649 | /// This function computes arc-disjoint paths from the found minimum |
---|
| 650 | /// cost flow, which is the union of them. |
---|
[357] | 651 | /// |
---|
| 652 | /// \pre \ref init() and \ref findFlow() must be called before using |
---|
| 653 | /// this function. |
---|
| 654 | void findPaths() { |
---|
| 655 | FlowMap res_flow(_graph); |
---|
[358] | 656 | for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; |
---|
[357] | 657 | |
---|
[926] | 658 | _paths.clear(); |
---|
| 659 | _paths.resize(_path_num); |
---|
[357] | 660 | for (int i = 0; i < _path_num; ++i) { |
---|
[926] | 661 | Node n = _s; |
---|
| 662 | while (n != _t) { |
---|
[357] | 663 | OutArcIt e(_graph, n); |
---|
| 664 | for ( ; res_flow[e] == 0; ++e) ; |
---|
| 665 | n = _graph.target(e); |
---|
[926] | 666 | _paths[i].addBack(e); |
---|
[357] | 667 | res_flow[e] = 0; |
---|
| 668 | } |
---|
| 669 | } |
---|
| 670 | } |
---|
| 671 | |
---|
| 672 | /// @} |
---|
| 673 | |
---|
| 674 | /// \name Query Functions |
---|
[358] | 675 | /// The results of the algorithm can be obtained using these |
---|
[357] | 676 | /// functions. |
---|
| 677 | /// \n The algorithm should be executed before using them. |
---|
| 678 | |
---|
| 679 | /// @{ |
---|
| 680 | |
---|
[670] | 681 | /// \brief Return the total length of the found paths. |
---|
| 682 | /// |
---|
| 683 | /// This function returns the total length of the found paths, i.e. |
---|
| 684 | /// the total cost of the found flow. |
---|
| 685 | /// The complexity of the function is O(e). |
---|
| 686 | /// |
---|
| 687 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 688 | /// this function. |
---|
| 689 | Length totalLength() const { |
---|
| 690 | Length c = 0; |
---|
| 691 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 692 | c += (*_flow)[e] * _length[e]; |
---|
| 693 | return c; |
---|
| 694 | } |
---|
| 695 | |
---|
| 696 | /// \brief Return the flow value on the given arc. |
---|
| 697 | /// |
---|
| 698 | /// This function returns the flow value on the given arc. |
---|
| 699 | /// It is \c 1 if the arc is involved in one of the found arc-disjoint |
---|
| 700 | /// paths, otherwise it is \c 0. |
---|
| 701 | /// |
---|
| 702 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 703 | /// this function. |
---|
| 704 | int flow(const Arc& arc) const { |
---|
| 705 | return (*_flow)[arc]; |
---|
| 706 | } |
---|
| 707 | |
---|
| 708 | /// \brief Return a const reference to an arc map storing the |
---|
[357] | 709 | /// found flow. |
---|
| 710 | /// |
---|
[670] | 711 | /// This function returns a const reference to an arc map storing |
---|
[358] | 712 | /// the flow that is the union of the found arc-disjoint paths. |
---|
[357] | 713 | /// |
---|
[358] | 714 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 715 | /// this function. |
---|
[357] | 716 | const FlowMap& flowMap() const { |
---|
| 717 | return *_flow; |
---|
| 718 | } |
---|
| 719 | |
---|
[358] | 720 | /// \brief Return the potential of the given node. |
---|
[357] | 721 | /// |
---|
[358] | 722 | /// This function returns the potential of the given node. |
---|
[670] | 723 | /// The node potentials provide the dual solution of the |
---|
| 724 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
---|
[357] | 725 | /// |
---|
[358] | 726 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 727 | /// this function. |
---|
[357] | 728 | Length potential(const Node& node) const { |
---|
| 729 | return (*_potential)[node]; |
---|
| 730 | } |
---|
| 731 | |
---|
[670] | 732 | /// \brief Return a const reference to a node map storing the |
---|
| 733 | /// found potentials (the dual solution). |
---|
[357] | 734 | /// |
---|
[670] | 735 | /// This function returns a const reference to a node map storing |
---|
| 736 | /// the found potentials that provide the dual solution of the |
---|
| 737 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
---|
[357] | 738 | /// |
---|
[358] | 739 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 740 | /// this function. |
---|
[670] | 741 | const PotentialMap& potentialMap() const { |
---|
| 742 | return *_potential; |
---|
[357] | 743 | } |
---|
| 744 | |
---|
[358] | 745 | /// \brief Return the number of the found paths. |
---|
[357] | 746 | /// |
---|
[358] | 747 | /// This function returns the number of the found paths. |
---|
[357] | 748 | /// |
---|
[358] | 749 | /// \pre \ref run() or \ref findFlow() must be called before using |
---|
| 750 | /// this function. |
---|
[357] | 751 | int pathNum() const { |
---|
| 752 | return _path_num; |
---|
| 753 | } |
---|
| 754 | |
---|
[358] | 755 | /// \brief Return a const reference to the specified path. |
---|
[357] | 756 | /// |
---|
[358] | 757 | /// This function returns a const reference to the specified path. |
---|
[357] | 758 | /// |
---|
[670] | 759 | /// \param i The function returns the <tt>i</tt>-th path. |
---|
[357] | 760 | /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>. |
---|
| 761 | /// |
---|
[358] | 762 | /// \pre \ref run() or \ref findPaths() must be called before using |
---|
| 763 | /// this function. |
---|
[924] | 764 | const Path& path(int i) const { |
---|
[926] | 765 | return _paths[i]; |
---|
[357] | 766 | } |
---|
| 767 | |
---|
| 768 | /// @} |
---|
| 769 | |
---|
| 770 | }; //class Suurballe |
---|
| 771 | |
---|
| 772 | ///@} |
---|
| 773 | |
---|
| 774 | } //namespace lemon |
---|
| 775 | |
---|
| 776 | #endif //LEMON_SUURBALLE_H |
---|