[906] | 1 | /* -*- C++ -*- |
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| 2 | * |
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[1956] | 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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[1359] | 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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[906] | 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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[921] | 19 | #ifndef LEMON_MIN_COST_FLOW_H |
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| 20 | #define LEMON_MIN_COST_FLOW_H |
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[899] | 21 | |
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| 22 | ///\ingroup flowalgs |
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| 23 | ///\file |
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| 24 | ///\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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| 25 | |
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| 26 | |
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[921] | 27 | #include <lemon/dijkstra.h> |
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[1401] | 28 | #include <lemon/graph_adaptor.h> |
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[921] | 29 | #include <lemon/maps.h> |
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[899] | 30 | #include <vector> |
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| 31 | |
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[921] | 32 | namespace lemon { |
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[899] | 33 | |
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| 34 | /// \addtogroup flowalgs |
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| 35 | /// @{ |
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| 36 | |
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| 37 | ///\brief Implementation of an algorithm for finding a flow of value \c k |
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| 38 | ///(for small values of \c k) having minimal total cost between 2 nodes |
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| 39 | /// |
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| 40 | /// |
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[1270] | 41 | /// The class \ref lemon::MinCostFlow "MinCostFlow" implements an |
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| 42 | /// algorithm for finding a flow of value \c k having minimal total |
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[1527] | 43 | /// cost from a given source node to a given target node in a |
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| 44 | /// directed graph with a cost function on the edges. To |
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| 45 | /// this end, the edge-capacities and edge-costs have to be |
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| 46 | /// nonnegative. The edge-capacities should be integers, but the |
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| 47 | /// edge-costs can be integers, reals or of other comparable |
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| 48 | /// numeric type. This algorithm is intended to be used only for |
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| 49 | /// small values of \c k, since it is only polynomial in k, not in |
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| 50 | /// the length of k (which is log k): in order to find the minimum |
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| 51 | /// cost flow of value \c k it finds the minimum cost flow of value |
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| 52 | /// \c i for every \c i between 0 and \c k. |
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[899] | 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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[987] | 62 | typedef typename LengthMap::Value Length; |
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[899] | 63 | |
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| 64 | //Warning: this should be integer type |
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[987] | 65 | typedef typename CapacityMap::Value Capacity; |
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[899] | 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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[1401] | 73 | typedef ResGraphAdaptor<const Graph,int,CapacityMap,EdgeIntMap> ResGW; |
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[910] | 74 | typedef typename ResGW::Edge ResGraphEdge; |
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[899] | 75 | |
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[941] | 76 | protected: |
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| 77 | |
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| 78 | const Graph& g; |
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| 79 | const LengthMap& length; |
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| 80 | const CapacityMap& capacity; |
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| 81 | |
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| 82 | EdgeIntMap flow; |
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| 83 | typedef typename Graph::template NodeMap<Length> PotentialMap; |
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| 84 | PotentialMap potential; |
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| 85 | |
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| 86 | Node s; |
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| 87 | Node t; |
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| 88 | |
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| 89 | Length total_length; |
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| 90 | |
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[899] | 91 | class ModLengthMap { |
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| 92 | typedef typename Graph::template NodeMap<Length> NodeMap; |
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[941] | 93 | const ResGW& g; |
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| 94 | const LengthMap &length; |
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[899] | 95 | const NodeMap &pot; |
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| 96 | public : |
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[987] | 97 | typedef typename LengthMap::Key Key; |
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| 98 | typedef typename LengthMap::Value Value; |
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[941] | 99 | |
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| 100 | ModLengthMap(const ResGW& _g, |
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| 101 | const LengthMap &_length, const NodeMap &_pot) : |
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| 102 | g(_g), /*rev(_rev),*/ length(_length), pot(_pot) { } |
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[899] | 103 | |
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[987] | 104 | Value operator[](typename ResGW::Edge e) const { |
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[941] | 105 | if (g.forward(e)) |
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[986] | 106 | return length[e]-(pot[g.target(e)]-pot[g.source(e)]); |
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[899] | 107 | else |
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[986] | 108 | return -length[e]-(pot[g.target(e)]-pot[g.source(e)]); |
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[899] | 109 | } |
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| 110 | |
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[941] | 111 | }; //ModLengthMap |
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[899] | 112 | |
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[941] | 113 | ResGW res_graph; |
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| 114 | ModLengthMap mod_length; |
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| 115 | Dijkstra<ResGW, ModLengthMap> dijkstra; |
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[899] | 116 | |
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| 117 | public : |
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| 118 | |
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[941] | 119 | /*! \brief The constructor of the class. |
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[899] | 120 | |
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[941] | 121 | \param _g The directed graph the algorithm runs on. |
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[1527] | 122 | \param _length The length (cost) of the edges. |
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[941] | 123 | \param _cap The capacity of the edges. |
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| 124 | \param _s Source node. |
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| 125 | \param _t Target node. |
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| 126 | */ |
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| 127 | MinCostFlow(Graph& _g, LengthMap& _length, CapacityMap& _cap, |
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| 128 | Node _s, Node _t) : |
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| 129 | g(_g), length(_length), capacity(_cap), flow(_g), potential(_g), |
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| 130 | s(_s), t(_t), |
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| 131 | res_graph(g, capacity, flow), |
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| 132 | mod_length(res_graph, length, potential), |
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| 133 | dijkstra(res_graph, mod_length) { |
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| 134 | reset(); |
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| 135 | } |
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[899] | 136 | |
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[941] | 137 | /*! Tries to augment the flow between s and t by 1. |
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| 138 | The return value shows if the augmentation is successful. |
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| 139 | */ |
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| 140 | bool augment() { |
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| 141 | dijkstra.run(s); |
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| 142 | if (!dijkstra.reached(t)) { |
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[899] | 143 | |
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[941] | 144 | //Unsuccessful augmentation. |
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| 145 | return false; |
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| 146 | } else { |
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[899] | 147 | |
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[941] | 148 | //We have to change the potential |
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| 149 | for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n) |
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[1027] | 150 | potential.set(n, potential[n]+dijkstra.distMap()[n]); |
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[899] | 151 | |
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[1270] | 152 | //Augmenting on the shortest path |
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[899] | 153 | Node n=t; |
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| 154 | ResGraphEdge e; |
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| 155 | while (n!=s){ |
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[1763] | 156 | e = dijkstra.predEdge(n); |
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[899] | 157 | n = dijkstra.predNode(n); |
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| 158 | res_graph.augment(e,1); |
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| 159 | //Let's update the total length |
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| 160 | if (res_graph.forward(e)) |
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| 161 | total_length += length[e]; |
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| 162 | else |
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| 163 | total_length -= length[e]; |
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| 164 | } |
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| 165 | |
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[941] | 166 | return true; |
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[899] | 167 | } |
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[941] | 168 | } |
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| 169 | |
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| 170 | /*! \brief Runs the algorithm. |
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| 171 | |
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| 172 | Runs the algorithm. |
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| 173 | Returns k if there is a flow of value at least k from s to t. |
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| 174 | Otherwise it returns the maximum value of a flow from s to t. |
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| 175 | |
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| 176 | \param k The value of the flow we are looking for. |
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| 177 | |
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| 178 | \todo May be it does make sense to be able to start with a nonzero |
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| 179 | feasible primal-dual solution pair as well. |
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| 180 | |
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| 181 | \todo If the actual flow value is bigger than k, then everything is |
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| 182 | cleared and the algorithm starts from zero flow. Is it a good approach? |
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| 183 | */ |
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| 184 | int run(int k) { |
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| 185 | if (flowValue()>k) reset(); |
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| 186 | while (flowValue()<k && augment()) { } |
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| 187 | return flowValue(); |
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| 188 | } |
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[899] | 189 | |
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[941] | 190 | /*! \brief The class is reset to zero flow and potential. |
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| 191 | The class is reset to zero flow and potential. |
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| 192 | */ |
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| 193 | void reset() { |
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| 194 | total_length=0; |
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| 195 | for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0); |
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| 196 | for (typename Graph::NodeIt n(g); n!=INVALID; ++n) potential.set(n, 0); |
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| 197 | } |
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| 198 | |
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| 199 | /*! Returns the value of the actual flow. |
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| 200 | */ |
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| 201 | int flowValue() const { |
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| 202 | int i=0; |
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| 203 | for (typename Graph::OutEdgeIt e(g, s); e!=INVALID; ++e) i+=flow[e]; |
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| 204 | for (typename Graph::InEdgeIt e(g, s); e!=INVALID; ++e) i-=flow[e]; |
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[899] | 205 | return i; |
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| 206 | } |
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| 207 | |
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[1527] | 208 | /// Total cost of the found flow. |
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[899] | 209 | |
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[1527] | 210 | /// This function gives back the total cost of the found flow. |
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[899] | 211 | Length totalLength(){ |
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| 212 | return total_length; |
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| 213 | } |
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| 214 | |
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| 215 | ///Returns a const reference to the EdgeMap \c flow. |
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| 216 | |
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| 217 | ///Returns a const reference to the EdgeMap \c flow. |
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| 218 | const EdgeIntMap &getFlow() const { return flow;} |
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| 219 | |
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[941] | 220 | /*! \brief Returns a const reference to the NodeMap \c potential (the dual solution). |
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[899] | 221 | |
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[941] | 222 | Returns a const reference to the NodeMap \c potential (the dual solution). |
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| 223 | */ |
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[899] | 224 | const PotentialMap &getPotential() const { return potential;} |
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| 225 | |
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[941] | 226 | /*! \brief Checking the complementary slackness optimality criteria. |
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[899] | 227 | |
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[941] | 228 | This function checks, whether the given flow and potential |
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[1270] | 229 | satisfy the complementary slackness conditions (i.e. these are optimal). |
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[941] | 230 | This function only checks optimality, doesn't bother with feasibility. |
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| 231 | For testing purpose. |
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| 232 | */ |
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[899] | 233 | bool checkComplementarySlackness(){ |
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| 234 | Length mod_pot; |
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| 235 | Length fl_e; |
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[941] | 236 | for(typename Graph::EdgeIt e(g); e!=INVALID; ++e) { |
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[899] | 237 | //C^{\Pi}_{i,j} |
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[986] | 238 | mod_pot = length[e]-potential[g.target(e)]+potential[g.source(e)]; |
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[899] | 239 | fl_e = flow[e]; |
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| 240 | if (0<fl_e && fl_e<capacity[e]) { |
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| 241 | /// \todo better comparison is needed for real types, moreover, |
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| 242 | /// this comparison here is superfluous. |
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| 243 | if (mod_pot != 0) |
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| 244 | return false; |
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| 245 | } |
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| 246 | else { |
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| 247 | if (mod_pot > 0 && fl_e != 0) |
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| 248 | return false; |
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| 249 | if (mod_pot < 0 && fl_e != capacity[e]) |
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| 250 | return false; |
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| 251 | } |
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| 252 | } |
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| 253 | return true; |
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| 254 | } |
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| 255 | |
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| 256 | }; //class MinCostFlow |
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| 257 | |
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| 258 | ///@} |
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| 259 | |
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[921] | 260 | } //namespace lemon |
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[899] | 261 | |
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[921] | 262 | #endif //LEMON_MIN_COST_FLOW_H |
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