[440] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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[345] | 2 | * |
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[440] | 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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[345] | 4 | * |
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[440] | 5 | * Copyright (C) 2003-2009 |
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[345] | 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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[623] | 28 | #include <limits> |
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[345] | 29 | #include <lemon/bin_heap.h> |
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| 30 | #include <lemon/path.h> |
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[519] | 31 | #include <lemon/list_graph.h> |
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[854] | 32 | #include <lemon/dijkstra.h> |
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[519] | 33 | #include <lemon/maps.h> |
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[345] | 34 | |
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| 35 | namespace lemon { |
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| 36 | |
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| 37 | /// \addtogroup shortest_path |
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| 38 | /// @{ |
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| 39 | |
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[346] | 40 | /// \brief Algorithm for finding arc-disjoint paths between two nodes |
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| 41 | /// having minimum total length. |
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[345] | 42 | /// |
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| 43 | /// \ref lemon::Suurballe "Suurballe" implements an algorithm for |
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| 44 | /// finding arc-disjoint paths having minimum total length (cost) |
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[346] | 45 | /// from a given source node to a given target node in a digraph. |
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[345] | 46 | /// |
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[623] | 47 | /// Note that this problem is a special case of the \ref min_cost_flow |
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| 48 | /// "minimum cost flow problem". This implementation is actually an |
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| 49 | /// efficient specialized version of the \ref CapacityScaling |
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[853] | 50 | /// "successive shortest path" algorithm directly for this problem. |
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[623] | 51 | /// Therefore this class provides query functions for flow values and |
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| 52 | /// node potentials (the dual solution) just like the minimum cost flow |
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| 53 | /// algorithms. |
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[345] | 54 | /// |
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[559] | 55 | /// \tparam GR The digraph type the algorithm runs on. |
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[623] | 56 | /// \tparam LEN The type of the length map. |
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| 57 | /// The default value is <tt>GR::ArcMap<int></tt>. |
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[345] | 58 | /// |
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[852] | 59 | /// \warning Length values should be \e non-negative. |
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[345] | 60 | /// |
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[853] | 61 | /// \note For finding \e node-disjoint paths, this algorithm can be used |
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[623] | 62 | /// along with the \ref SplitNodes adaptor. |
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[346] | 63 | #ifdef DOXYGEN |
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[559] | 64 | template <typename GR, typename LEN> |
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[346] | 65 | #else |
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[623] | 66 | template < typename GR, |
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[559] | 67 | typename LEN = typename GR::template ArcMap<int> > |
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[346] | 68 | #endif |
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[345] | 69 | class Suurballe |
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| 70 | { |
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[559] | 71 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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[345] | 72 | |
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| 73 | typedef ConstMap<Arc, int> ConstArcMap; |
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[559] | 74 | typedef typename GR::template NodeMap<Arc> PredMap; |
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[345] | 75 | |
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| 76 | public: |
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| 77 | |
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[559] | 78 | /// The type of the digraph the algorithm runs on. |
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| 79 | typedef GR Digraph; |
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| 80 | /// The type of the length map. |
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| 81 | typedef LEN LengthMap; |
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| 82 | /// The type of the lengths. |
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| 83 | typedef typename LengthMap::Value Length; |
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[623] | 84 | #ifdef DOXYGEN |
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| 85 | /// The type of the flow map. |
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| 86 | typedef GR::ArcMap<int> FlowMap; |
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| 87 | /// The type of the potential map. |
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| 88 | typedef GR::NodeMap<Length> PotentialMap; |
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| 89 | #else |
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[345] | 90 | /// The type of the flow map. |
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| 91 | typedef typename Digraph::template ArcMap<int> FlowMap; |
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| 92 | /// The type of the potential map. |
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| 93 | typedef typename Digraph::template NodeMap<Length> PotentialMap; |
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[623] | 94 | #endif |
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| 95 | |
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[345] | 96 | /// The type of the path structures. |
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[623] | 97 | typedef SimplePath<GR> Path; |
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[345] | 98 | |
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| 99 | private: |
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[440] | 100 | |
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[854] | 101 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
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| 102 | typedef BinHeap<Length, HeapCrossRef> Heap; |
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| 103 | |
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[623] | 104 | // ResidualDijkstra is a special implementation of the |
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| 105 | // Dijkstra algorithm for finding shortest paths in the |
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| 106 | // residual network with respect to the reduced arc lengths |
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| 107 | // and modifying the node potentials according to the |
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| 108 | // distance of the nodes. |
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[345] | 109 | class ResidualDijkstra |
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| 110 | { |
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| 111 | private: |
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| 112 | |
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| 113 | const Digraph &_graph; |
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[853] | 114 | const LengthMap &_length; |
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[345] | 115 | const FlowMap &_flow; |
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[853] | 116 | PotentialMap &_pi; |
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[345] | 117 | PredMap &_pred; |
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| 118 | Node _s; |
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| 119 | Node _t; |
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[853] | 120 | |
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| 121 | PotentialMap _dist; |
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| 122 | std::vector<Node> _proc_nodes; |
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[345] | 123 | |
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| 124 | public: |
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| 125 | |
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[853] | 126 | // Constructor |
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| 127 | ResidualDijkstra(Suurballe &srb) : |
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| 128 | _graph(srb._graph), _length(srb._length), |
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| 129 | _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred), |
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| 130 | _s(srb._s), _t(srb._t), _dist(_graph) {} |
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| 131 | |
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| 132 | // Run the algorithm and return true if a path is found |
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| 133 | // from the source node to the target node. |
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| 134 | bool run(int cnt) { |
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| 135 | return cnt == 0 ? startFirst() : start(); |
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| 136 | } |
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[345] | 137 | |
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[853] | 138 | private: |
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| 139 | |
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| 140 | // Execute the algorithm for the first time (the flow and potential |
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| 141 | // functions have to be identically zero). |
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| 142 | bool startFirst() { |
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[345] | 143 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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| 144 | Heap heap(heap_cross_ref); |
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| 145 | heap.push(_s, 0); |
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| 146 | _pred[_s] = INVALID; |
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| 147 | _proc_nodes.clear(); |
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| 148 | |
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[346] | 149 | // Process nodes |
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[345] | 150 | while (!heap.empty() && heap.top() != _t) { |
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| 151 | Node u = heap.top(), v; |
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[853] | 152 | Length d = heap.prio(), dn; |
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[345] | 153 | _dist[u] = heap.prio(); |
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[853] | 154 | _proc_nodes.push_back(u); |
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[345] | 155 | heap.pop(); |
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[853] | 156 | |
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| 157 | // Traverse outgoing arcs |
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| 158 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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| 159 | v = _graph.target(e); |
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| 160 | switch(heap.state(v)) { |
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| 161 | case Heap::PRE_HEAP: |
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| 162 | heap.push(v, d + _length[e]); |
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| 163 | _pred[v] = e; |
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| 164 | break; |
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| 165 | case Heap::IN_HEAP: |
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| 166 | dn = d + _length[e]; |
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| 167 | if (dn < heap[v]) { |
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| 168 | heap.decrease(v, dn); |
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| 169 | _pred[v] = e; |
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| 170 | } |
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| 171 | break; |
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| 172 | case Heap::POST_HEAP: |
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| 173 | break; |
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| 174 | } |
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| 175 | } |
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| 176 | } |
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| 177 | if (heap.empty()) return false; |
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| 178 | |
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| 179 | // Update potentials of processed nodes |
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| 180 | Length t_dist = heap.prio(); |
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| 181 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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| 182 | _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist; |
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| 183 | return true; |
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| 184 | } |
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| 185 | |
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| 186 | // Execute the algorithm. |
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| 187 | bool start() { |
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| 188 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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| 189 | Heap heap(heap_cross_ref); |
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| 190 | heap.push(_s, 0); |
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| 191 | _pred[_s] = INVALID; |
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| 192 | _proc_nodes.clear(); |
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| 193 | |
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| 194 | // Process nodes |
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| 195 | while (!heap.empty() && heap.top() != _t) { |
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| 196 | Node u = heap.top(), v; |
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| 197 | Length d = heap.prio() + _pi[u], dn; |
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| 198 | _dist[u] = heap.prio(); |
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[345] | 199 | _proc_nodes.push_back(u); |
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[853] | 200 | heap.pop(); |
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[345] | 201 | |
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[346] | 202 | // Traverse outgoing arcs |
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[345] | 203 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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| 204 | if (_flow[e] == 0) { |
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| 205 | v = _graph.target(e); |
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| 206 | switch(heap.state(v)) { |
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[853] | 207 | case Heap::PRE_HEAP: |
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| 208 | heap.push(v, d + _length[e] - _pi[v]); |
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[345] | 209 | _pred[v] = e; |
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[853] | 210 | break; |
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| 211 | case Heap::IN_HEAP: |
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| 212 | dn = d + _length[e] - _pi[v]; |
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| 213 | if (dn < heap[v]) { |
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| 214 | heap.decrease(v, dn); |
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| 215 | _pred[v] = e; |
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| 216 | } |
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| 217 | break; |
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| 218 | case Heap::POST_HEAP: |
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| 219 | break; |
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[345] | 220 | } |
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| 221 | } |
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| 222 | } |
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| 223 | |
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[346] | 224 | // Traverse incoming arcs |
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[345] | 225 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
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| 226 | if (_flow[e] == 1) { |
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| 227 | v = _graph.source(e); |
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| 228 | switch(heap.state(v)) { |
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[853] | 229 | case Heap::PRE_HEAP: |
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| 230 | heap.push(v, d - _length[e] - _pi[v]); |
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[345] | 231 | _pred[v] = e; |
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[853] | 232 | break; |
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| 233 | case Heap::IN_HEAP: |
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| 234 | dn = d - _length[e] - _pi[v]; |
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| 235 | if (dn < heap[v]) { |
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| 236 | heap.decrease(v, dn); |
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| 237 | _pred[v] = e; |
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| 238 | } |
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| 239 | break; |
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| 240 | case Heap::POST_HEAP: |
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| 241 | break; |
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[345] | 242 | } |
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| 243 | } |
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| 244 | } |
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| 245 | } |
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| 246 | if (heap.empty()) return false; |
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| 247 | |
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[346] | 248 | // Update potentials of processed nodes |
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[345] | 249 | Length t_dist = heap.prio(); |
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| 250 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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[853] | 251 | _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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[345] | 252 | return true; |
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| 253 | } |
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| 254 | |
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| 255 | }; //class ResidualDijkstra |
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| 256 | |
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| 257 | private: |
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| 258 | |
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[346] | 259 | // The digraph the algorithm runs on |
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[345] | 260 | const Digraph &_graph; |
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| 261 | // The length map |
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| 262 | const LengthMap &_length; |
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[440] | 263 | |
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[345] | 264 | // Arc map of the current flow |
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| 265 | FlowMap *_flow; |
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| 266 | bool _local_flow; |
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| 267 | // Node map of the current potentials |
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| 268 | PotentialMap *_potential; |
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| 269 | bool _local_potential; |
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| 270 | |
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| 271 | // The source node |
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[853] | 272 | Node _s; |
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[345] | 273 | // The target node |
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[853] | 274 | Node _t; |
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[345] | 275 | |
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| 276 | // Container to store the found paths |
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[853] | 277 | std::vector<Path> _paths; |
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[345] | 278 | int _path_num; |
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| 279 | |
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| 280 | // The pred arc map |
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| 281 | PredMap _pred; |
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[854] | 282 | |
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| 283 | // Data for full init |
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| 284 | PotentialMap *_init_dist; |
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| 285 | PredMap *_init_pred; |
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| 286 | bool _full_init; |
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[345] | 287 | |
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| 288 | public: |
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| 289 | |
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| 290 | /// \brief Constructor. |
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| 291 | /// |
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| 292 | /// Constructor. |
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| 293 | /// |
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[623] | 294 | /// \param graph The digraph the algorithm runs on. |
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[345] | 295 | /// \param length The length (cost) values of the arcs. |
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[623] | 296 | Suurballe( const Digraph &graph, |
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| 297 | const LengthMap &length ) : |
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| 298 | _graph(graph), _length(length), _flow(0), _local_flow(false), |
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[854] | 299 | _potential(0), _local_potential(false), _pred(graph), |
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| 300 | _init_dist(0), _init_pred(0) |
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[852] | 301 | {} |
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[345] | 302 | |
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| 303 | /// Destructor. |
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| 304 | ~Suurballe() { |
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| 305 | if (_local_flow) delete _flow; |
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| 306 | if (_local_potential) delete _potential; |
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[854] | 307 | delete _init_dist; |
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| 308 | delete _init_pred; |
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[345] | 309 | } |
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| 310 | |
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[346] | 311 | /// \brief Set the flow map. |
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[345] | 312 | /// |
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[346] | 313 | /// This function sets the flow map. |
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[623] | 314 | /// If it is not used before calling \ref run() or \ref init(), |
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| 315 | /// an instance will be allocated automatically. The destructor |
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| 316 | /// deallocates this automatically allocated map, of course. |
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[345] | 317 | /// |
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[623] | 318 | /// The found flow contains only 0 and 1 values, since it is the |
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| 319 | /// union of the found arc-disjoint paths. |
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[345] | 320 | /// |
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[559] | 321 | /// \return <tt>(*this)</tt> |
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[345] | 322 | Suurballe& flowMap(FlowMap &map) { |
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| 323 | if (_local_flow) { |
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| 324 | delete _flow; |
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| 325 | _local_flow = false; |
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| 326 | } |
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| 327 | _flow = ↦ |
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| 328 | return *this; |
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| 329 | } |
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| 330 | |
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[346] | 331 | /// \brief Set the potential map. |
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[345] | 332 | /// |
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[346] | 333 | /// This function sets the potential map. |
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[623] | 334 | /// If it is not used before calling \ref run() or \ref init(), |
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| 335 | /// an instance will be allocated automatically. The destructor |
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| 336 | /// deallocates this automatically allocated map, of course. |
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[345] | 337 | /// |
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[623] | 338 | /// The node potentials provide the dual solution of the underlying |
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| 339 | /// \ref min_cost_flow "minimum cost flow problem". |
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[345] | 340 | /// |
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[559] | 341 | /// \return <tt>(*this)</tt> |
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[345] | 342 | Suurballe& potentialMap(PotentialMap &map) { |
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| 343 | if (_local_potential) { |
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| 344 | delete _potential; |
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| 345 | _local_potential = false; |
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| 346 | } |
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| 347 | _potential = ↦ |
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| 348 | return *this; |
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| 349 | } |
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| 350 | |
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[584] | 351 | /// \name Execution Control |
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[345] | 352 | /// The simplest way to execute the algorithm is to call the run() |
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[854] | 353 | /// function.\n |
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| 354 | /// If you need to execute the algorithm many times using the same |
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| 355 | /// source node, then you may call fullInit() once and start() |
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| 356 | /// for each target node.\n |
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[345] | 357 | /// If you only need the flow that is the union of the found |
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[854] | 358 | /// arc-disjoint paths, then you may call findFlow() instead of |
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| 359 | /// start(). |
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[345] | 360 | |
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| 361 | /// @{ |
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| 362 | |
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[346] | 363 | /// \brief Run the algorithm. |
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[345] | 364 | /// |
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[346] | 365 | /// This function runs the algorithm. |
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[345] | 366 | /// |
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[623] | 367 | /// \param s The source node. |
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| 368 | /// \param t The target node. |
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[345] | 369 | /// \param k The number of paths to be found. |
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| 370 | /// |
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[346] | 371 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 372 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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[345] | 373 | /// arc-disjoint paths found. |
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| 374 | /// |
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[623] | 375 | /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is |
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| 376 | /// just a shortcut of the following code. |
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[345] | 377 | /// \code |
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[623] | 378 | /// s.init(s); |
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[854] | 379 | /// s.start(t, k); |
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[345] | 380 | /// \endcode |
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[623] | 381 | int run(const Node& s, const Node& t, int k = 2) { |
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| 382 | init(s); |
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[854] | 383 | start(t, k); |
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[345] | 384 | return _path_num; |
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| 385 | } |
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| 386 | |
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[346] | 387 | /// \brief Initialize the algorithm. |
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[345] | 388 | /// |
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[854] | 389 | /// This function initializes the algorithm with the given source node. |
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[623] | 390 | /// |
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| 391 | /// \param s The source node. |
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| 392 | void init(const Node& s) { |
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[853] | 393 | _s = s; |
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[623] | 394 | |
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[346] | 395 | // Initialize maps |
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[345] | 396 | if (!_flow) { |
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| 397 | _flow = new FlowMap(_graph); |
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| 398 | _local_flow = true; |
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| 399 | } |
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| 400 | if (!_potential) { |
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| 401 | _potential = new PotentialMap(_graph); |
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| 402 | _local_potential = true; |
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| 403 | } |
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[854] | 404 | _full_init = false; |
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| 405 | } |
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| 406 | |
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| 407 | /// \brief Initialize the algorithm and perform Dijkstra. |
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| 408 | /// |
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| 409 | /// This function initializes the algorithm and performs a full |
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| 410 | /// Dijkstra search from the given source node. It makes consecutive |
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| 411 | /// executions of \ref start() "start(t, k)" faster, since they |
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| 412 | /// have to perform %Dijkstra only k-1 times. |
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| 413 | /// |
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| 414 | /// This initialization is usually worth using instead of \ref init() |
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| 415 | /// if the algorithm is executed many times using the same source node. |
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| 416 | /// |
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| 417 | /// \param s The source node. |
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| 418 | void fullInit(const Node& s) { |
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| 419 | // Initialize maps |
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| 420 | init(s); |
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| 421 | if (!_init_dist) { |
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| 422 | _init_dist = new PotentialMap(_graph); |
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| 423 | } |
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| 424 | if (!_init_pred) { |
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| 425 | _init_pred = new PredMap(_graph); |
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| 426 | } |
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| 427 | |
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| 428 | // Run a full Dijkstra |
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| 429 | typename Dijkstra<Digraph, LengthMap> |
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| 430 | ::template SetStandardHeap<Heap> |
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| 431 | ::template SetDistMap<PotentialMap> |
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| 432 | ::template SetPredMap<PredMap> |
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| 433 | ::Create dijk(_graph, _length); |
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| 434 | dijk.distMap(*_init_dist).predMap(*_init_pred); |
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| 435 | dijk.run(s); |
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| 436 | |
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| 437 | _full_init = true; |
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| 438 | } |
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| 439 | |
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| 440 | /// \brief Execute the algorithm. |
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| 441 | /// |
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| 442 | /// This function executes the algorithm. |
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| 443 | /// |
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| 444 | /// \param t The target node. |
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| 445 | /// \param k The number of paths to be found. |
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| 446 | /// |
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| 447 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 448 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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| 449 | /// arc-disjoint paths found. |
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| 450 | /// |
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| 451 | /// \note Apart from the return value, <tt>s.start(t, k)</tt> is |
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| 452 | /// just a shortcut of the following code. |
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| 453 | /// \code |
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| 454 | /// s.findFlow(t, k); |
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| 455 | /// s.findPaths(); |
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| 456 | /// \endcode |
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| 457 | int start(const Node& t, int k = 2) { |
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| 458 | findFlow(t, k); |
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| 459 | findPaths(); |
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| 460 | return _path_num; |
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[345] | 461 | } |
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| 462 | |
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[623] | 463 | /// \brief Execute the algorithm to find an optimal flow. |
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[345] | 464 | /// |
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[346] | 465 | /// This function executes the successive shortest path algorithm to |
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[623] | 466 | /// find a minimum cost flow, which is the union of \c k (or less) |
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[345] | 467 | /// arc-disjoint paths. |
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| 468 | /// |
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[623] | 469 | /// \param t The target node. |
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| 470 | /// \param k The number of paths to be found. |
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| 471 | /// |
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[346] | 472 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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[623] | 473 | /// the source node to the given node \c t in the digraph. |
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| 474 | /// Otherwise it returns the number of arc-disjoint paths found. |
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[345] | 475 | /// |
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| 476 | /// \pre \ref init() must be called before using this function. |
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[623] | 477 | int findFlow(const Node& t, int k = 2) { |
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[853] | 478 | _t = t; |
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| 479 | ResidualDijkstra dijkstra(*this); |
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[854] | 480 | |
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| 481 | // Initialization |
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| 482 | for (ArcIt e(_graph); e != INVALID; ++e) { |
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| 483 | (*_flow)[e] = 0; |
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| 484 | } |
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| 485 | if (_full_init) { |
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| 486 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 487 | (*_potential)[n] = (*_init_dist)[n]; |
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| 488 | } |
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| 489 | Node u = _t; |
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| 490 | Arc e; |
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| 491 | while ((e = (*_init_pred)[u]) != INVALID) { |
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| 492 | (*_flow)[e] = 1; |
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| 493 | u = _graph.source(e); |
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| 494 | } |
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| 495 | _path_num = 1; |
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| 496 | } else { |
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| 497 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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| 498 | (*_potential)[n] = 0; |
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| 499 | } |
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| 500 | _path_num = 0; |
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| 501 | } |
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[623] | 502 | |
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[346] | 503 | // Find shortest paths |
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[345] | 504 | while (_path_num < k) { |
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[346] | 505 | // Run Dijkstra |
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[853] | 506 | if (!dijkstra.run(_path_num)) break; |
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[345] | 507 | ++_path_num; |
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| 508 | |
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[346] | 509 | // Set the flow along the found shortest path |
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[853] | 510 | Node u = _t; |
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[345] | 511 | Arc e; |
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| 512 | while ((e = _pred[u]) != INVALID) { |
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| 513 | if (u == _graph.target(e)) { |
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| 514 | (*_flow)[e] = 1; |
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| 515 | u = _graph.source(e); |
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| 516 | } else { |
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| 517 | (*_flow)[e] = 0; |
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| 518 | u = _graph.target(e); |
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| 519 | } |
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| 520 | } |
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| 521 | } |
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| 522 | return _path_num; |
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| 523 | } |
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[440] | 524 | |
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[346] | 525 | /// \brief Compute the paths from the flow. |
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[345] | 526 | /// |
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[853] | 527 | /// This function computes arc-disjoint paths from the found minimum |
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| 528 | /// cost flow, which is the union of them. |
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[345] | 529 | /// |
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| 530 | /// \pre \ref init() and \ref findFlow() must be called before using |
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| 531 | /// this function. |
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| 532 | void findPaths() { |
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| 533 | FlowMap res_flow(_graph); |
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[346] | 534 | for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; |
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[345] | 535 | |
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[853] | 536 | _paths.clear(); |
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| 537 | _paths.resize(_path_num); |
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[345] | 538 | for (int i = 0; i < _path_num; ++i) { |
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[853] | 539 | Node n = _s; |
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| 540 | while (n != _t) { |
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[345] | 541 | OutArcIt e(_graph, n); |
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| 542 | for ( ; res_flow[e] == 0; ++e) ; |
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| 543 | n = _graph.target(e); |
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[853] | 544 | _paths[i].addBack(e); |
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[345] | 545 | res_flow[e] = 0; |
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| 546 | } |
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| 547 | } |
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| 548 | } |
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| 549 | |
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| 550 | /// @} |
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| 551 | |
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| 552 | /// \name Query Functions |
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[346] | 553 | /// The results of the algorithm can be obtained using these |
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[345] | 554 | /// functions. |
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| 555 | /// \n The algorithm should be executed before using them. |
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| 556 | |
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| 557 | /// @{ |
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| 558 | |
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[623] | 559 | /// \brief Return the total length of the found paths. |
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| 560 | /// |
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| 561 | /// This function returns the total length of the found paths, i.e. |
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| 562 | /// the total cost of the found flow. |
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| 563 | /// The complexity of the function is O(e). |
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| 564 | /// |
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| 565 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 566 | /// this function. |
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| 567 | Length totalLength() const { |
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| 568 | Length c = 0; |
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| 569 | for (ArcIt e(_graph); e != INVALID; ++e) |
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| 570 | c += (*_flow)[e] * _length[e]; |
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| 571 | return c; |
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| 572 | } |
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| 573 | |
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| 574 | /// \brief Return the flow value on the given arc. |
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| 575 | /// |
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| 576 | /// This function returns the flow value on the given arc. |
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| 577 | /// It is \c 1 if the arc is involved in one of the found arc-disjoint |
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| 578 | /// paths, otherwise it is \c 0. |
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| 579 | /// |
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| 580 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 581 | /// this function. |
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| 582 | int flow(const Arc& arc) const { |
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| 583 | return (*_flow)[arc]; |
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| 584 | } |
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| 585 | |
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| 586 | /// \brief Return a const reference to an arc map storing the |
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[345] | 587 | /// found flow. |
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| 588 | /// |
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[623] | 589 | /// This function returns a const reference to an arc map storing |
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[346] | 590 | /// the flow that is the union of the found arc-disjoint paths. |
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[345] | 591 | /// |
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[346] | 592 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 593 | /// this function. |
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[345] | 594 | const FlowMap& flowMap() const { |
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| 595 | return *_flow; |
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| 596 | } |
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| 597 | |
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[346] | 598 | /// \brief Return the potential of the given node. |
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[345] | 599 | /// |
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[346] | 600 | /// This function returns the potential of the given node. |
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[623] | 601 | /// The node potentials provide the dual solution of the |
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| 602 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
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[345] | 603 | /// |
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[346] | 604 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 605 | /// this function. |
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[345] | 606 | Length potential(const Node& node) const { |
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| 607 | return (*_potential)[node]; |
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| 608 | } |
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| 609 | |
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[623] | 610 | /// \brief Return a const reference to a node map storing the |
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| 611 | /// found potentials (the dual solution). |
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[345] | 612 | /// |
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[623] | 613 | /// This function returns a const reference to a node map storing |
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| 614 | /// the found potentials that provide the dual solution of the |
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| 615 | /// underlying \ref min_cost_flow "minimum cost flow problem". |
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[345] | 616 | /// |
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[346] | 617 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 618 | /// this function. |
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[623] | 619 | const PotentialMap& potentialMap() const { |
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| 620 | return *_potential; |
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[345] | 621 | } |
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| 622 | |
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[346] | 623 | /// \brief Return the number of the found paths. |
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[345] | 624 | /// |
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[346] | 625 | /// This function returns the number of the found paths. |
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[345] | 626 | /// |
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[346] | 627 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 628 | /// this function. |
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[345] | 629 | int pathNum() const { |
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| 630 | return _path_num; |
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| 631 | } |
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| 632 | |
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[346] | 633 | /// \brief Return a const reference to the specified path. |
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[345] | 634 | /// |
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[346] | 635 | /// This function returns a const reference to the specified path. |
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[345] | 636 | /// |
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[623] | 637 | /// \param i The function returns the <tt>i</tt>-th path. |
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[345] | 638 | /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>. |
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| 639 | /// |
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[346] | 640 | /// \pre \ref run() or \ref findPaths() must be called before using |
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| 641 | /// this function. |
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[851] | 642 | const Path& path(int i) const { |
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[853] | 643 | return _paths[i]; |
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[345] | 644 | } |
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| 645 | |
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| 646 | /// @} |
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| 647 | |
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| 648 | }; //class Suurballe |
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| 649 | |
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| 650 | ///@} |
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| 651 | |
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| 652 | } //namespace lemon |
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| 653 | |
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| 654 | #endif //LEMON_SUURBALLE_H |
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