[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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| 28 | #include <lemon/bin_heap.h> |
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| 29 | #include <lemon/path.h> |
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[519] | 30 | #include <lemon/list_graph.h> |
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| 31 | #include <lemon/maps.h> |
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[345] | 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | /// \addtogroup shortest_path |
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| 36 | /// @{ |
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| 37 | |
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[346] | 38 | /// \brief Algorithm for finding arc-disjoint paths between two nodes |
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| 39 | /// having minimum total length. |
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[345] | 40 | /// |
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| 41 | /// \ref lemon::Suurballe "Suurballe" implements an algorithm for |
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| 42 | /// finding arc-disjoint paths having minimum total length (cost) |
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[346] | 43 | /// from a given source node to a given target node in a digraph. |
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[345] | 44 | /// |
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| 45 | /// In fact, this implementation is the specialization of the |
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| 46 | /// \ref CapacityScaling "successive shortest path" algorithm. |
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| 47 | /// |
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[346] | 48 | /// \tparam Digraph The digraph type the algorithm runs on. |
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| 49 | /// The default value is \c ListDigraph. |
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[345] | 50 | /// \tparam LengthMap The type of the length (cost) map. |
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[346] | 51 | /// The default value is <tt>Digraph::ArcMap<int></tt>. |
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[345] | 52 | /// |
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| 53 | /// \warning Length values should be \e non-negative \e integers. |
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| 54 | /// |
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| 55 | /// \note For finding node-disjoint paths this algorithm can be used |
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[425] | 56 | /// with \ref SplitNodes. |
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[346] | 57 | #ifdef DOXYGEN |
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| 58 | template <typename Digraph, typename LengthMap> |
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| 59 | #else |
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| 60 | template < typename Digraph = ListDigraph, |
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[345] | 61 | typename LengthMap = typename Digraph::template ArcMap<int> > |
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[346] | 62 | #endif |
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[345] | 63 | class Suurballe |
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| 64 | { |
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| 65 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 66 | |
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| 67 | typedef typename LengthMap::Value Length; |
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| 68 | typedef ConstMap<Arc, int> ConstArcMap; |
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| 69 | typedef typename Digraph::template NodeMap<Arc> PredMap; |
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| 70 | |
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| 71 | public: |
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| 72 | |
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| 73 | /// The type of the flow map. |
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| 74 | typedef typename Digraph::template ArcMap<int> FlowMap; |
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| 75 | /// The type of the potential map. |
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| 76 | typedef typename Digraph::template NodeMap<Length> PotentialMap; |
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| 77 | /// The type of the path structures. |
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| 78 | typedef SimplePath<Digraph> Path; |
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| 79 | |
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| 80 | private: |
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[440] | 81 | |
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[346] | 82 | /// \brief Special implementation of the Dijkstra algorithm |
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[345] | 83 | /// for finding shortest paths in the residual network. |
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| 84 | /// |
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| 85 | /// \ref ResidualDijkstra is a special implementation of the |
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| 86 | /// \ref Dijkstra algorithm for finding shortest paths in the |
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| 87 | /// residual network of the digraph with respect to the reduced arc |
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| 88 | /// lengths and modifying the node potentials according to the |
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| 89 | /// distance of the nodes. |
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| 90 | class ResidualDijkstra |
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| 91 | { |
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| 92 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
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| 93 | typedef BinHeap<Length, HeapCrossRef> Heap; |
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| 94 | |
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| 95 | private: |
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| 96 | |
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[346] | 97 | // The digraph the algorithm runs on |
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[345] | 98 | const Digraph &_graph; |
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| 99 | |
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| 100 | // The main maps |
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| 101 | const FlowMap &_flow; |
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| 102 | const LengthMap &_length; |
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| 103 | PotentialMap &_potential; |
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| 104 | |
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| 105 | // The distance map |
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| 106 | PotentialMap _dist; |
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| 107 | // The pred arc map |
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| 108 | PredMap &_pred; |
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| 109 | // The processed (i.e. permanently labeled) nodes |
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| 110 | std::vector<Node> _proc_nodes; |
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[440] | 111 | |
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[345] | 112 | Node _s; |
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| 113 | Node _t; |
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| 114 | |
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| 115 | public: |
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| 116 | |
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| 117 | /// Constructor. |
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| 118 | ResidualDijkstra( const Digraph &digraph, |
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| 119 | const FlowMap &flow, |
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| 120 | const LengthMap &length, |
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| 121 | PotentialMap &potential, |
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| 122 | PredMap &pred, |
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| 123 | Node s, Node t ) : |
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| 124 | _graph(digraph), _flow(flow), _length(length), _potential(potential), |
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| 125 | _dist(digraph), _pred(pred), _s(s), _t(t) {} |
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| 126 | |
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[346] | 127 | /// \brief Run the algorithm. It returns \c true if a path is found |
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[345] | 128 | /// from the source node to the target node. |
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| 129 | bool run() { |
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| 130 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
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| 131 | Heap heap(heap_cross_ref); |
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| 132 | heap.push(_s, 0); |
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| 133 | _pred[_s] = INVALID; |
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| 134 | _proc_nodes.clear(); |
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| 135 | |
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[346] | 136 | // Process nodes |
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[345] | 137 | while (!heap.empty() && heap.top() != _t) { |
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| 138 | Node u = heap.top(), v; |
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| 139 | Length d = heap.prio() + _potential[u], nd; |
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| 140 | _dist[u] = heap.prio(); |
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| 141 | heap.pop(); |
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| 142 | _proc_nodes.push_back(u); |
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| 143 | |
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[346] | 144 | // Traverse outgoing arcs |
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[345] | 145 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
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| 146 | if (_flow[e] == 0) { |
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| 147 | v = _graph.target(e); |
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| 148 | switch(heap.state(v)) { |
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| 149 | case Heap::PRE_HEAP: |
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| 150 | heap.push(v, d + _length[e] - _potential[v]); |
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| 151 | _pred[v] = e; |
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| 152 | break; |
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| 153 | case Heap::IN_HEAP: |
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| 154 | nd = d + _length[e] - _potential[v]; |
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| 155 | if (nd < heap[v]) { |
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| 156 | heap.decrease(v, nd); |
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| 157 | _pred[v] = e; |
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| 158 | } |
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| 159 | break; |
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| 160 | case Heap::POST_HEAP: |
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| 161 | break; |
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| 162 | } |
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| 163 | } |
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| 164 | } |
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| 165 | |
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[346] | 166 | // Traverse incoming arcs |
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[345] | 167 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
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| 168 | if (_flow[e] == 1) { |
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| 169 | v = _graph.source(e); |
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| 170 | switch(heap.state(v)) { |
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| 171 | case Heap::PRE_HEAP: |
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| 172 | heap.push(v, d - _length[e] - _potential[v]); |
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| 173 | _pred[v] = e; |
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| 174 | break; |
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| 175 | case Heap::IN_HEAP: |
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| 176 | nd = d - _length[e] - _potential[v]; |
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| 177 | if (nd < heap[v]) { |
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| 178 | heap.decrease(v, nd); |
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| 179 | _pred[v] = e; |
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| 180 | } |
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| 181 | break; |
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| 182 | case Heap::POST_HEAP: |
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| 183 | break; |
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| 184 | } |
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| 185 | } |
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| 186 | } |
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| 187 | } |
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| 188 | if (heap.empty()) return false; |
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| 189 | |
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[346] | 190 | // Update potentials of processed nodes |
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[345] | 191 | Length t_dist = heap.prio(); |
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| 192 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
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| 193 | _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
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| 194 | return true; |
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| 195 | } |
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| 196 | |
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| 197 | }; //class ResidualDijkstra |
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| 198 | |
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| 199 | private: |
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| 200 | |
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[346] | 201 | // The digraph the algorithm runs on |
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[345] | 202 | const Digraph &_graph; |
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| 203 | // The length map |
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| 204 | const LengthMap &_length; |
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[440] | 205 | |
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[345] | 206 | // Arc map of the current flow |
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| 207 | FlowMap *_flow; |
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| 208 | bool _local_flow; |
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| 209 | // Node map of the current potentials |
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| 210 | PotentialMap *_potential; |
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| 211 | bool _local_potential; |
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| 212 | |
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| 213 | // The source node |
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| 214 | Node _source; |
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| 215 | // The target node |
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| 216 | Node _target; |
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| 217 | |
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| 218 | // Container to store the found paths |
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| 219 | std::vector< SimplePath<Digraph> > paths; |
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| 220 | int _path_num; |
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| 221 | |
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| 222 | // The pred arc map |
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| 223 | PredMap _pred; |
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| 224 | // Implementation of the Dijkstra algorithm for finding augmenting |
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| 225 | // shortest paths in the residual network |
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| 226 | ResidualDijkstra *_dijkstra; |
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| 227 | |
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| 228 | public: |
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| 229 | |
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| 230 | /// \brief Constructor. |
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| 231 | /// |
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| 232 | /// Constructor. |
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| 233 | /// |
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[346] | 234 | /// \param digraph The digraph the algorithm runs on. |
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[345] | 235 | /// \param length The length (cost) values of the arcs. |
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| 236 | /// \param s The source node. |
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| 237 | /// \param t The target node. |
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| 238 | Suurballe( const Digraph &digraph, |
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| 239 | const LengthMap &length, |
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| 240 | Node s, Node t ) : |
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| 241 | _graph(digraph), _length(length), _flow(0), _local_flow(false), |
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| 242 | _potential(0), _local_potential(false), _source(s), _target(t), |
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| 243 | _pred(digraph) {} |
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| 244 | |
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| 245 | /// Destructor. |
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| 246 | ~Suurballe() { |
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| 247 | if (_local_flow) delete _flow; |
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| 248 | if (_local_potential) delete _potential; |
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| 249 | delete _dijkstra; |
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| 250 | } |
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| 251 | |
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[346] | 252 | /// \brief Set the flow map. |
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[345] | 253 | /// |
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[346] | 254 | /// This function sets the flow map. |
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[345] | 255 | /// |
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| 256 | /// The found flow contains only 0 and 1 values. It is the union of |
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| 257 | /// the found arc-disjoint paths. |
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| 258 | /// |
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| 259 | /// \return \c (*this) |
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| 260 | Suurballe& flowMap(FlowMap &map) { |
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| 261 | if (_local_flow) { |
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| 262 | delete _flow; |
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| 263 | _local_flow = false; |
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| 264 | } |
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| 265 | _flow = ↦ |
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| 266 | return *this; |
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| 267 | } |
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| 268 | |
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[346] | 269 | /// \brief Set the potential map. |
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[345] | 270 | /// |
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[346] | 271 | /// This function sets the potential map. |
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[345] | 272 | /// |
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[440] | 273 | /// The potentials provide the dual solution of the underlying |
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[345] | 274 | /// minimum cost flow problem. |
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| 275 | /// |
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| 276 | /// \return \c (*this) |
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| 277 | Suurballe& potentialMap(PotentialMap &map) { |
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| 278 | if (_local_potential) { |
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| 279 | delete _potential; |
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| 280 | _local_potential = false; |
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| 281 | } |
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| 282 | _potential = ↦ |
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| 283 | return *this; |
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| 284 | } |
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| 285 | |
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| 286 | /// \name Execution control |
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| 287 | /// The simplest way to execute the algorithm is to call the run() |
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| 288 | /// function. |
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| 289 | /// \n |
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| 290 | /// If you only need the flow that is the union of the found |
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| 291 | /// arc-disjoint paths, you may call init() and findFlow(). |
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| 292 | |
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| 293 | /// @{ |
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| 294 | |
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[346] | 295 | /// \brief Run the algorithm. |
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[345] | 296 | /// |
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[346] | 297 | /// This function runs the algorithm. |
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[345] | 298 | /// |
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| 299 | /// \param k The number of paths to be found. |
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| 300 | /// |
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[346] | 301 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 302 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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[345] | 303 | /// arc-disjoint paths found. |
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| 304 | /// |
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| 305 | /// \note Apart from the return value, <tt>s.run(k)</tt> is just a |
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| 306 | /// shortcut of the following code. |
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| 307 | /// \code |
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| 308 | /// s.init(); |
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| 309 | /// s.findFlow(k); |
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| 310 | /// s.findPaths(); |
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| 311 | /// \endcode |
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| 312 | int run(int k = 2) { |
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| 313 | init(); |
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| 314 | findFlow(k); |
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| 315 | findPaths(); |
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| 316 | return _path_num; |
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| 317 | } |
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| 318 | |
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[346] | 319 | /// \brief Initialize the algorithm. |
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[345] | 320 | /// |
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[346] | 321 | /// This function initializes the algorithm. |
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[345] | 322 | void init() { |
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[346] | 323 | // Initialize maps |
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[345] | 324 | if (!_flow) { |
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| 325 | _flow = new FlowMap(_graph); |
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| 326 | _local_flow = true; |
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| 327 | } |
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| 328 | if (!_potential) { |
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| 329 | _potential = new PotentialMap(_graph); |
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| 330 | _local_potential = true; |
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| 331 | } |
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| 332 | for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; |
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| 333 | for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; |
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| 334 | |
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[440] | 335 | _dijkstra = new ResidualDijkstra( _graph, *_flow, _length, |
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[345] | 336 | *_potential, _pred, |
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| 337 | _source, _target ); |
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| 338 | } |
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| 339 | |
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[346] | 340 | /// \brief Execute the successive shortest path algorithm to find |
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[345] | 341 | /// an optimal flow. |
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| 342 | /// |
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[346] | 343 | /// This function executes the successive shortest path algorithm to |
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| 344 | /// find a minimum cost flow, which is the union of \c k or less |
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[345] | 345 | /// arc-disjoint paths. |
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| 346 | /// |
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[346] | 347 | /// \return \c k if there are at least \c k arc-disjoint paths from |
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| 348 | /// \c s to \c t in the digraph. Otherwise it returns the number of |
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[345] | 349 | /// arc-disjoint paths found. |
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| 350 | /// |
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| 351 | /// \pre \ref init() must be called before using this function. |
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| 352 | int findFlow(int k = 2) { |
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[346] | 353 | // Find shortest paths |
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[345] | 354 | _path_num = 0; |
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| 355 | while (_path_num < k) { |
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[346] | 356 | // Run Dijkstra |
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[345] | 357 | if (!_dijkstra->run()) break; |
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| 358 | ++_path_num; |
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| 359 | |
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[346] | 360 | // Set the flow along the found shortest path |
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[345] | 361 | Node u = _target; |
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| 362 | Arc e; |
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| 363 | while ((e = _pred[u]) != INVALID) { |
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| 364 | if (u == _graph.target(e)) { |
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| 365 | (*_flow)[e] = 1; |
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| 366 | u = _graph.source(e); |
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| 367 | } else { |
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| 368 | (*_flow)[e] = 0; |
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| 369 | u = _graph.target(e); |
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| 370 | } |
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| 371 | } |
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| 372 | } |
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| 373 | return _path_num; |
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| 374 | } |
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[440] | 375 | |
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[346] | 376 | /// \brief Compute the paths from the flow. |
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[345] | 377 | /// |
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[346] | 378 | /// This function computes the paths from the flow. |
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[345] | 379 | /// |
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| 380 | /// \pre \ref init() and \ref findFlow() must be called before using |
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| 381 | /// this function. |
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| 382 | void findPaths() { |
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[346] | 383 | // Create the residual flow map (the union of the paths not found |
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| 384 | // so far) |
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[345] | 385 | FlowMap res_flow(_graph); |
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[346] | 386 | for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a]; |
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[345] | 387 | |
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| 388 | paths.clear(); |
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| 389 | paths.resize(_path_num); |
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| 390 | for (int i = 0; i < _path_num; ++i) { |
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| 391 | Node n = _source; |
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| 392 | while (n != _target) { |
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| 393 | OutArcIt e(_graph, n); |
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| 394 | for ( ; res_flow[e] == 0; ++e) ; |
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| 395 | n = _graph.target(e); |
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| 396 | paths[i].addBack(e); |
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| 397 | res_flow[e] = 0; |
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| 398 | } |
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| 399 | } |
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| 400 | } |
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| 401 | |
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| 402 | /// @} |
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| 403 | |
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| 404 | /// \name Query Functions |
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[346] | 405 | /// The results of the algorithm can be obtained using these |
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[345] | 406 | /// functions. |
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| 407 | /// \n The algorithm should be executed before using them. |
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| 408 | |
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| 409 | /// @{ |
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| 410 | |
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[346] | 411 | /// \brief Return a const reference to the arc map storing the |
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[345] | 412 | /// found flow. |
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| 413 | /// |
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[346] | 414 | /// This function returns a const reference to the arc map storing |
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| 415 | /// the flow that is the union of the found arc-disjoint paths. |
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[345] | 416 | /// |
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[346] | 417 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 418 | /// this function. |
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[345] | 419 | const FlowMap& flowMap() const { |
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| 420 | return *_flow; |
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| 421 | } |
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| 422 | |
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[346] | 423 | /// \brief Return a const reference to the node map storing the |
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[345] | 424 | /// found potentials (the dual solution). |
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| 425 | /// |
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[346] | 426 | /// This function returns a const reference to the node map storing |
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| 427 | /// the found potentials that provide the dual solution of the |
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| 428 | /// underlying minimum cost flow problem. |
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[345] | 429 | /// |
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[346] | 430 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 431 | /// this function. |
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[345] | 432 | const PotentialMap& potentialMap() const { |
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| 433 | return *_potential; |
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| 434 | } |
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| 435 | |
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[346] | 436 | /// \brief Return the flow on the given arc. |
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[345] | 437 | /// |
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[346] | 438 | /// This function returns the flow on the given arc. |
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[345] | 439 | /// It is \c 1 if the arc is involved in one of the found paths, |
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| 440 | /// otherwise it is \c 0. |
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| 441 | /// |
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[346] | 442 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 443 | /// this function. |
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[345] | 444 | int flow(const Arc& arc) const { |
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| 445 | return (*_flow)[arc]; |
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| 446 | } |
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| 447 | |
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[346] | 448 | /// \brief Return the potential of the given node. |
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[345] | 449 | /// |
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[346] | 450 | /// This function returns the potential of the given node. |
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[345] | 451 | /// |
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[346] | 452 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 453 | /// this function. |
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[345] | 454 | Length potential(const Node& node) const { |
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| 455 | return (*_potential)[node]; |
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| 456 | } |
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| 457 | |
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[346] | 458 | /// \brief Return the total length (cost) of the found paths (flow). |
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[345] | 459 | /// |
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[346] | 460 | /// This function returns the total length (cost) of the found paths |
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| 461 | /// (flow). The complexity of the function is \f$ O(e) \f$. |
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[345] | 462 | /// |
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[346] | 463 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 464 | /// this function. |
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[345] | 465 | Length totalLength() const { |
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| 466 | Length c = 0; |
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| 467 | for (ArcIt e(_graph); e != INVALID; ++e) |
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| 468 | c += (*_flow)[e] * _length[e]; |
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| 469 | return c; |
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| 470 | } |
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| 471 | |
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[346] | 472 | /// \brief Return the number of the found paths. |
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[345] | 473 | /// |
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[346] | 474 | /// This function returns the number of the found paths. |
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[345] | 475 | /// |
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[346] | 476 | /// \pre \ref run() or \ref findFlow() must be called before using |
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| 477 | /// this function. |
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[345] | 478 | int pathNum() const { |
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| 479 | return _path_num; |
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| 480 | } |
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| 481 | |
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[346] | 482 | /// \brief Return a const reference to the specified path. |
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[345] | 483 | /// |
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[346] | 484 | /// This function returns a const reference to the specified path. |
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[345] | 485 | /// |
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| 486 | /// \param i The function returns the \c i-th path. |
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| 487 | /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>. |
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| 488 | /// |
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[346] | 489 | /// \pre \ref run() or \ref findPaths() must be called before using |
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| 490 | /// this function. |
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[345] | 491 | Path path(int i) const { |
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| 492 | return paths[i]; |
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| 493 | } |
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| 494 | |
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| 495 | /// @} |
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| 496 | |
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| 497 | }; //class Suurballe |
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| 498 | |
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| 499 | ///@} |
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| 500 | |
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| 501 | } //namespace lemon |
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| 502 | |
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| 503 | #endif //LEMON_SUURBALLE_H |
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