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