[906] | 1 | /* -*- C++ -*- |
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[921] | 2 | * src/lemon/min_cost_flow.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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| 4 | * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Combinatorial Optimization Research Group, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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[921] | 17 | #ifndef LEMON_MIN_COST_FLOW_H |
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| 18 | #define LEMON_MIN_COST_FLOW_H |
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[899] | 19 | |
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| 20 | ///\ingroup flowalgs |
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| 21 | ///\file |
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| 22 | ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost |
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| 23 | |
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| 24 | |
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[921] | 25 | #include <lemon/dijkstra.h> |
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| 26 | #include <lemon/graph_wrapper.h> |
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| 27 | #include <lemon/maps.h> |
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[899] | 28 | #include <vector> |
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| 29 | |
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[921] | 30 | namespace lemon { |
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[899] | 31 | |
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| 32 | /// \addtogroup flowalgs |
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| 33 | /// @{ |
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| 34 | |
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| 35 | ///\brief Implementation of an algorithm for finding a flow of value \c k |
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| 36 | ///(for small values of \c k) having minimal total cost between 2 nodes |
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| 37 | /// |
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| 38 | /// |
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[921] | 39 | /// The class \ref lemon::MinCostFlow "MinCostFlow" implements |
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[899] | 40 | /// an algorithm for finding a flow of value \c k |
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| 41 | /// having minimal total cost |
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| 42 | /// from a given source node to a given target node in an |
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| 43 | /// edge-weighted directed graph. To this end, |
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| 44 | /// the edge-capacities and edge-weitghs have to be nonnegative. |
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| 45 | /// The edge-capacities should be integers, but the edge-weights can be |
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| 46 | /// integers, reals or of other comparable numeric type. |
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| 47 | /// This algorithm is intended to use only for small values of \c k, |
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| 48 | /// since it is only polynomial in k, |
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| 49 | /// not in the length of k (which is log k). |
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| 50 | /// In order to find the minimum cost flow of value \c k it |
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| 51 | /// finds the minimum cost flow of value \c i for every |
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| 52 | /// \c i between 0 and \c k. |
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| 53 | /// |
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| 54 | ///\param Graph The directed graph type the algorithm runs on. |
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| 55 | ///\param LengthMap The type of the length map. |
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| 56 | ///\param CapacityMap The capacity map type. |
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| 57 | /// |
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| 58 | ///\author Attila Bernath |
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| 59 | template <typename Graph, typename LengthMap, typename CapacityMap> |
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| 60 | class MinCostFlow { |
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| 61 | |
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| 62 | typedef typename LengthMap::ValueType Length; |
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| 63 | |
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| 64 | //Warning: this should be integer type |
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| 65 | typedef typename CapacityMap::ValueType Capacity; |
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| 66 | |
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| 67 | typedef typename Graph::Node Node; |
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| 68 | typedef typename Graph::NodeIt NodeIt; |
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| 69 | typedef typename Graph::Edge Edge; |
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| 70 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 71 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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| 72 | |
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| 73 | |
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[910] | 74 | typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGW; |
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| 75 | typedef typename ResGW::Edge ResGraphEdge; |
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[899] | 76 | |
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| 77 | class ModLengthMap { |
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| 78 | typedef typename Graph::template NodeMap<Length> NodeMap; |
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[910] | 79 | const ResGW& G; |
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[899] | 80 | const LengthMap &ol; |
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| 81 | const NodeMap &pot; |
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| 82 | public : |
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| 83 | typedef typename LengthMap::KeyType KeyType; |
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| 84 | typedef typename LengthMap::ValueType ValueType; |
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| 85 | |
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[910] | 86 | ValueType operator[](typename ResGW::Edge e) const { |
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[899] | 87 | if (G.forward(e)) |
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| 88 | return ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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| 89 | else |
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| 90 | return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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| 91 | } |
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| 92 | |
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[910] | 93 | ModLengthMap(const ResGW& _G, |
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[899] | 94 | const LengthMap &o, const NodeMap &p) : |
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| 95 | G(_G), /*rev(_rev),*/ ol(o), pot(p){}; |
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| 96 | };//ModLengthMap |
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| 97 | |
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| 98 | |
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| 99 | protected: |
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| 100 | |
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| 101 | //Input |
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| 102 | const Graph& G; |
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| 103 | const LengthMap& length; |
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| 104 | const CapacityMap& capacity; |
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| 105 | |
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| 106 | |
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| 107 | //auxiliary variables |
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| 108 | |
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| 109 | //To store the flow |
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| 110 | EdgeIntMap flow; |
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| 111 | //To store the potential (dual variables) |
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| 112 | typedef typename Graph::template NodeMap<Length> PotentialMap; |
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| 113 | PotentialMap potential; |
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| 114 | |
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| 115 | |
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| 116 | Length total_length; |
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| 117 | |
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| 118 | |
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| 119 | public : |
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| 120 | |
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| 121 | /// The constructor of the class. |
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| 122 | |
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| 123 | ///\param _G The directed graph the algorithm runs on. |
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| 124 | ///\param _length The length (weight or cost) of the edges. |
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| 125 | ///\param _cap The capacity of the edges. |
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| 126 | MinCostFlow(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), |
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| 127 | length(_length), capacity(_cap), flow(_G), potential(_G){ } |
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| 128 | |
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| 129 | |
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| 130 | ///Runs the algorithm. |
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| 131 | |
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| 132 | ///Runs the algorithm. |
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| 133 | ///Returns k if there is a flow of value at least k edge-disjoint |
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| 134 | ///from s to t. |
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| 135 | ///Otherwise it returns the maximum value of a flow from s to t. |
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| 136 | /// |
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| 137 | ///\param s The source node. |
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| 138 | ///\param t The target node. |
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| 139 | ///\param k The value of the flow we are looking for. |
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| 140 | /// |
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| 141 | ///\todo May be it does make sense to be able to start with a nonzero |
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| 142 | /// feasible primal-dual solution pair as well. |
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| 143 | int run(Node s, Node t, int k) { |
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| 144 | |
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| 145 | //Resetting variables from previous runs |
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| 146 | total_length = 0; |
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| 147 | |
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| 148 | for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0); |
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| 149 | |
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| 150 | //Initialize the potential to zero |
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| 151 | for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0); |
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| 152 | |
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| 153 | |
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| 154 | //We need a residual graph |
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[910] | 155 | ResGW res_graph(G, capacity, flow); |
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[899] | 156 | |
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| 157 | |
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| 158 | ModLengthMap mod_length(res_graph, length, potential); |
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| 159 | |
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[910] | 160 | Dijkstra<ResGW, ModLengthMap> dijkstra(res_graph, mod_length); |
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[899] | 161 | |
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| 162 | int i; |
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| 163 | for (i=0; i<k; ++i){ |
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| 164 | dijkstra.run(s); |
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| 165 | if (!dijkstra.reached(t)){ |
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| 166 | //There are no flow of value k from s to t |
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| 167 | break; |
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| 168 | }; |
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| 169 | |
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| 170 | //We have to change the potential |
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[910] | 171 | for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n) |
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[899] | 172 | potential[n] += dijkstra.distMap()[n]; |
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| 173 | |
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| 174 | |
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| 175 | //Augmenting on the sortest path |
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| 176 | Node n=t; |
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| 177 | ResGraphEdge e; |
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| 178 | while (n!=s){ |
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| 179 | e = dijkstra.pred(n); |
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| 180 | n = dijkstra.predNode(n); |
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| 181 | res_graph.augment(e,1); |
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| 182 | //Let's update the total length |
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| 183 | if (res_graph.forward(e)) |
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| 184 | total_length += length[e]; |
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| 185 | else |
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| 186 | total_length -= length[e]; |
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| 187 | } |
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| 188 | |
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| 189 | |
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| 190 | } |
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| 191 | |
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| 192 | |
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| 193 | return i; |
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| 194 | } |
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| 195 | |
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| 196 | |
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| 197 | |
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| 198 | /// Gives back the total weight of the found flow. |
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| 199 | |
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| 200 | ///This function gives back the total weight of the found flow. |
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| 201 | ///Assumes that \c run() has been run and nothing changed since then. |
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| 202 | Length totalLength(){ |
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| 203 | return total_length; |
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| 204 | } |
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| 205 | |
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| 206 | ///Returns a const reference to the EdgeMap \c flow. |
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| 207 | |
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| 208 | ///Returns a const reference to the EdgeMap \c flow. |
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| 209 | ///\pre \ref run() must |
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| 210 | ///be called before using this function. |
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| 211 | const EdgeIntMap &getFlow() const { return flow;} |
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| 212 | |
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| 213 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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| 214 | |
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| 215 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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| 216 | /// \pre \ref run() must be called before using this function. |
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| 217 | const PotentialMap &getPotential() const { return potential;} |
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| 218 | |
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| 219 | /// Checking the complementary slackness optimality criteria |
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| 220 | |
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| 221 | ///This function checks, whether the given solution is optimal |
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| 222 | ///If executed after the call of \c run() then it should return with true. |
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| 223 | ///This function only checks optimality, doesn't bother with feasibility. |
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| 224 | ///It is meant for testing purposes. |
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| 225 | /// |
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| 226 | bool checkComplementarySlackness(){ |
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| 227 | Length mod_pot; |
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| 228 | Length fl_e; |
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| 229 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) { |
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| 230 | //C^{\Pi}_{i,j} |
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| 231 | mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)]; |
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| 232 | fl_e = flow[e]; |
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| 233 | if (0<fl_e && fl_e<capacity[e]) { |
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| 234 | /// \todo better comparison is needed for real types, moreover, |
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| 235 | /// this comparison here is superfluous. |
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| 236 | if (mod_pot != 0) |
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| 237 | return false; |
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| 238 | } |
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| 239 | else { |
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| 240 | if (mod_pot > 0 && fl_e != 0) |
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| 241 | return false; |
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| 242 | if (mod_pot < 0 && fl_e != capacity[e]) |
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| 243 | return false; |
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| 244 | } |
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| 245 | } |
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| 246 | return true; |
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| 247 | } |
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| 248 | |
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| 249 | |
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| 250 | }; //class MinCostFlow |
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| 251 | |
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| 252 | ///@} |
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| 253 | |
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[921] | 254 | } //namespace lemon |
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[899] | 255 | |
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[921] | 256 | #endif //LEMON_MIN_COST_FLOW_H |
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