[726] | 1 | // -*- C++ -*- |
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[749] | 2 | #ifndef HUGO_MAX_FLOW_H |
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| 3 | #define HUGO_MAX_FLOW_H |
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[726] | 4 | |
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| 5 | #include <vector> |
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| 6 | #include <queue> |
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| 7 | |
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| 8 | #include <hugo/graph_wrapper.h> |
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| 9 | #include <hugo/invalid.h> |
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| 10 | #include <hugo/maps.h> |
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| 11 | |
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| 12 | /// \file |
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| 13 | /// \ingroup galgs |
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| 14 | |
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| 15 | namespace hugo { |
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| 16 | |
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| 17 | /// \addtogroup galgs |
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| 18 | /// @{ |
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| 19 | ///Maximum flow algorithms class. |
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| 20 | |
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| 21 | ///This class provides various algorithms for finding a flow of |
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| 22 | ///maximum value in a directed graph. The \e source node, the \e |
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| 23 | ///target node, the \e capacity of the edges and the \e starting \e |
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| 24 | ///flow value of the edges should be passed to the algorithm through the |
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| 25 | ///constructor. It is possible to change these quantities using the |
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| 26 | ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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| 27 | ///\ref resetFlow. Before any subsequent runs of any algorithm of |
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| 28 | ///the class \ref resetFlow should be called. |
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| 29 | |
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| 30 | ///After running an algorithm of the class, the actual flow value |
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| 31 | ///can be obtained by calling \ref flowValue(). The minimum |
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| 32 | ///value cut can be written into a \c node map of \c bools by |
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| 33 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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| 34 | ///the inclusionwise minimum and maximum of the minimum value |
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| 35 | ///cuts, resp.) |
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| 36 | ///\param Graph The directed graph type the algorithm runs on. |
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| 37 | ///\param Num The number type of the capacities and the flow values. |
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| 38 | ///\param CapMap The capacity map type. |
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| 39 | ///\param FlowMap The flow map type. |
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| 40 | ///\author Marton Makai, Jacint Szabo |
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| 41 | template <typename Graph, typename Num, |
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| 42 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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| 43 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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| 44 | class MaxFlow { |
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| 45 | protected: |
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| 46 | typedef typename Graph::Node Node; |
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| 47 | typedef typename Graph::NodeIt NodeIt; |
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| 48 | typedef typename Graph::EdgeIt EdgeIt; |
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| 49 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 50 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 51 | |
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| 52 | typedef typename std::vector<Node> VecFirst; |
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| 53 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 54 | typedef typename std::vector<Node> VecNode; |
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| 55 | |
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| 56 | const Graph* g; |
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| 57 | Node s; |
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| 58 | Node t; |
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| 59 | const CapMap* capacity; |
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| 60 | FlowMap* flow; |
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| 61 | int n; //the number of nodes of G |
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| 62 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 63 | //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 64 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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| 65 | typedef typename ResGW::Edge ResGWEdge; |
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| 66 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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| 67 | |
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| 68 | |
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| 69 | //level works as a bool map in augmenting path algorithms and is |
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| 70 | //used by bfs for storing reached information. In preflow, it |
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| 71 | //shows the levels of nodes. |
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| 72 | ReachedMap level; |
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| 73 | |
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| 74 | //excess is needed only in preflow |
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| 75 | typename Graph::template NodeMap<Num> excess; |
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| 76 | |
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| 77 | // constants used for heuristics |
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| 78 | static const int H0=20; |
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| 79 | static const int H1=1; |
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| 80 | |
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| 81 | public: |
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| 82 | |
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| 83 | ///Indicates the property of the starting flow. |
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| 84 | |
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| 85 | ///Indicates the property of the starting flow. The meanings are as follows: |
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| 86 | ///- \c ZERO_FLOW: constant zero flow |
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| 87 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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| 88 | ///the sum of the out-flows in every node except the \e source and |
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| 89 | ///the \e target. |
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| 90 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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| 91 | ///least the sum of the out-flows in every node except the \e source. |
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| 92 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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| 93 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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| 94 | enum FlowEnum{ |
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| 95 | ZERO_FLOW, |
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| 96 | GEN_FLOW, |
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| 97 | PRE_FLOW, |
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| 98 | NO_FLOW |
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| 99 | }; |
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| 100 | |
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| 101 | enum StatusEnum { |
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| 102 | AFTER_NOTHING, |
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| 103 | AFTER_AUGMENTING, |
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| 104 | AFTER_FAST_AUGMENTING, |
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| 105 | AFTER_PRE_FLOW_PHASE_1, |
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| 106 | AFTER_PRE_FLOW_PHASE_2 |
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| 107 | }; |
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| 108 | |
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[749] | 109 | /// Do not needle this flag only if necessary. |
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[726] | 110 | StatusEnum status; |
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| 111 | |
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| 112 | // int number_of_augmentations; |
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| 113 | |
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| 114 | |
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| 115 | // template<typename IntMap> |
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| 116 | // class TrickyReachedMap { |
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| 117 | // protected: |
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| 118 | // IntMap* map; |
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| 119 | // int* number_of_augmentations; |
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| 120 | // public: |
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| 121 | // TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
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| 122 | // map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
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| 123 | // void set(const Node& n, bool b) { |
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| 124 | // if (b) |
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| 125 | // map->set(n, *number_of_augmentations); |
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| 126 | // else |
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| 127 | // map->set(n, *number_of_augmentations-1); |
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| 128 | // } |
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| 129 | // bool operator[](const Node& n) const { |
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| 130 | // return (*map)[n]==*number_of_augmentations; |
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| 131 | // } |
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| 132 | // }; |
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| 133 | |
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| 134 | ///Constructor |
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| 135 | |
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| 136 | ///\todo Document, please. |
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| 137 | /// |
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| 138 | MaxFlow(const Graph& _G, Node _s, Node _t, |
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[745] | 139 | const CapMap& _capacity, FlowMap& _flow) : |
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[726] | 140 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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| 141 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), |
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| 142 | status(AFTER_NOTHING) { } |
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| 143 | |
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| 144 | ///Runs a maximum flow algorithm. |
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| 145 | |
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| 146 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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| 147 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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| 148 | ///\pre The starting flow must be |
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| 149 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 150 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 151 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 152 | /// - any map if \c fe is NO_FLOW. |
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| 153 | void run(FlowEnum fe=ZERO_FLOW) { |
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| 154 | preflow(fe); |
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| 155 | } |
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| 156 | |
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| 157 | |
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| 158 | ///Runs a preflow algorithm. |
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| 159 | |
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| 160 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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| 161 | ///fastest way to compute a maximum flow in a directed graph. |
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| 162 | ///\pre The starting flow must be |
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| 163 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 164 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 165 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 166 | /// - any map if \c fe is NO_FLOW. |
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| 167 | /// |
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| 168 | ///\todo NO_FLOW should be the default flow. |
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| 169 | void preflow(FlowEnum fe) { |
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| 170 | preflowPhase1(fe); |
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| 171 | preflowPhase2(); |
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| 172 | } |
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| 173 | // Heuristics: |
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| 174 | // 2 phase |
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| 175 | // gap |
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| 176 | // list 'level_list' on the nodes on level i implemented by hand |
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| 177 | // stack 'active' on the active nodes on level i |
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| 178 | // runs heuristic 'highest label' for H1*n relabels |
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| 179 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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| 180 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 181 | |
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| 182 | ///Runs the first phase of the preflow algorithm. |
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| 183 | |
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| 184 | ///The preflow algorithm consists of two phases, this method runs the |
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| 185 | ///first phase. After the first phase the maximum flow value and a |
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| 186 | ///minimum value cut can already be computed, though a maximum flow |
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[749] | 187 | ///is not yet obtained. So after calling this method \ref flowValue |
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[726] | 188 | ///and \ref actMinCut gives proper results. |
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| 189 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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| 190 | ///give minimum value cuts unless calling \ref preflowPhase2. |
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| 191 | ///\pre The starting flow must be |
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| 192 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 193 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 194 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 195 | /// - any map if \c fe is NO_FLOW. |
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| 196 | void preflowPhase1(FlowEnum fe) |
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| 197 | { |
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| 198 | |
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| 199 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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| 200 | int heur1=(int)(H1*n); //time while running 'highest label' |
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| 201 | int heur=heur1; //starting time interval (#of relabels) |
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| 202 | int numrelabel=0; |
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| 203 | |
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| 204 | bool what_heur=1; |
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| 205 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 206 | |
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| 207 | bool end=false; |
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| 208 | //Needed for 'bound decrease', true means no active nodes are above bound |
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| 209 | //b. |
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| 210 | |
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| 211 | int k=n-2; //bound on the highest level under n containing a node |
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| 212 | int b=k; //bound on the highest level under n of an active node |
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| 213 | |
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| 214 | VecFirst first(n, INVALID); |
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| 215 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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| 216 | |
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| 217 | NNMap left(*g, INVALID); |
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| 218 | NNMap right(*g, INVALID); |
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| 219 | VecNode level_list(n,INVALID); |
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| 220 | //List of the nodes in level i<n, set to n. |
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| 221 | |
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[745] | 222 | preflowPreproc(fe, next, first, level_list, left, right); |
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[726] | 223 | //End of preprocessing |
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| 224 | |
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| 225 | //Push/relabel on the highest level active nodes. |
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| 226 | while ( true ) { |
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| 227 | if ( b == 0 ) { |
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| 228 | if ( !what_heur && !end && k > 0 ) { |
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| 229 | b=k; |
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| 230 | end=true; |
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| 231 | } else break; |
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| 232 | } |
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| 233 | |
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[745] | 234 | if ( !g->valid(first[b]) ) --b; |
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[726] | 235 | else { |
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| 236 | end=false; |
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| 237 | Node w=first[b]; |
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| 238 | first[b]=next[w]; |
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[745] | 239 | int newlevel=push(w, next, first); |
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| 240 | if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list, |
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[726] | 241 | left, right, b, k, what_heur); |
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| 242 | |
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| 243 | ++numrelabel; |
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| 244 | if ( numrelabel >= heur ) { |
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| 245 | numrelabel=0; |
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| 246 | if ( what_heur ) { |
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| 247 | what_heur=0; |
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| 248 | heur=heur0; |
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| 249 | end=false; |
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| 250 | } else { |
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| 251 | what_heur=1; |
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| 252 | heur=heur1; |
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| 253 | b=k; |
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| 254 | } |
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| 255 | } |
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| 256 | } |
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| 257 | } |
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| 258 | |
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| 259 | status=AFTER_PRE_FLOW_PHASE_1; |
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| 260 | } |
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| 261 | |
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| 262 | |
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| 263 | ///Runs the second phase of the preflow algorithm. |
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| 264 | |
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| 265 | ///The preflow algorithm consists of two phases, this method runs |
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| 266 | ///the second phase. After calling \ref preflowPhase1 and then |
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| 267 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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| 268 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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| 269 | ///\pre \ref preflowPhase1 must be called before. |
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| 270 | void preflowPhase2() |
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| 271 | { |
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| 272 | |
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| 273 | int k=n-2; //bound on the highest level under n containing a node |
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| 274 | int b=k; //bound on the highest level under n of an active node |
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| 275 | |
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| 276 | |
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| 277 | VecFirst first(n, INVALID); |
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| 278 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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| 279 | level.set(s,0); |
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| 280 | std::queue<Node> bfs_queue; |
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| 281 | bfs_queue.push(s); |
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| 282 | |
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| 283 | while (!bfs_queue.empty()) { |
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| 284 | |
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| 285 | Node v=bfs_queue.front(); |
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| 286 | bfs_queue.pop(); |
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| 287 | int l=level[v]+1; |
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| 288 | |
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| 289 | InEdgeIt e; |
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| 290 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 291 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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| 292 | Node u=g->tail(e); |
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| 293 | if ( level[u] >= n ) { |
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| 294 | bfs_queue.push(u); |
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| 295 | level.set(u, l); |
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| 296 | if ( excess[u] > 0 ) { |
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| 297 | next.set(u,first[l]); |
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| 298 | first[l]=u; |
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| 299 | } |
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| 300 | } |
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| 301 | } |
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| 302 | |
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| 303 | OutEdgeIt f; |
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| 304 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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| 305 | if ( 0 >= (*flow)[f] ) continue; |
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| 306 | Node u=g->head(f); |
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| 307 | if ( level[u] >= n ) { |
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| 308 | bfs_queue.push(u); |
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| 309 | level.set(u, l); |
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| 310 | if ( excess[u] > 0 ) { |
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| 311 | next.set(u,first[l]); |
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| 312 | first[l]=u; |
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| 313 | } |
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| 314 | } |
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| 315 | } |
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| 316 | } |
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| 317 | b=n-2; |
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| 318 | |
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| 319 | while ( true ) { |
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| 320 | |
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| 321 | if ( b == 0 ) break; |
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| 322 | |
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[745] | 323 | if ( !g->valid(first[b]) ) --b; |
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[726] | 324 | else { |
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| 325 | |
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| 326 | Node w=first[b]; |
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| 327 | first[b]=next[w]; |
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| 328 | int newlevel=push(w,next, first/*active*/); |
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| 329 | |
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| 330 | //relabel |
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| 331 | if ( excess[w] > 0 ) { |
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| 332 | level.set(w,++newlevel); |
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| 333 | next.set(w,first[newlevel]); |
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| 334 | first[newlevel]=w; |
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| 335 | b=newlevel; |
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| 336 | } |
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[749] | 337 | } |
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[726] | 338 | } // while(true) |
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| 339 | |
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| 340 | status=AFTER_PRE_FLOW_PHASE_2; |
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| 341 | } |
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| 342 | |
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| 343 | |
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| 344 | /// Returns the maximum value of a flow. |
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| 345 | |
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| 346 | /// Returns the maximum value of a flow, by counting the |
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| 347 | /// over-flow of the target node \ref t. |
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| 348 | /// It can be called already after running \ref preflowPhase1. |
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| 349 | Num flowValue() const { |
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| 350 | Num a=0; |
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[735] | 351 | for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e]; |
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| 352 | for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e]; |
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[745] | 353 | return a; |
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[726] | 354 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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| 355 | } |
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[749] | 356 | |
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[726] | 357 | |
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| 358 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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| 359 | |
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| 360 | ///After the first phase of the preflow algorithm the maximum flow |
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| 361 | ///value and a minimum value cut can already be computed. This |
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| 362 | ///method can be called after running \ref preflowPhase1 for |
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| 363 | ///obtaining a minimum value cut. |
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| 364 | /// \warning Gives proper result only right after calling \ref |
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| 365 | /// preflowPhase1. |
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| 366 | /// \todo We have to make some status variable which shows the |
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| 367 | /// actual state |
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| 368 | /// of the class. This enables us to determine which methods are valid |
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| 369 | /// for MinCut computation |
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| 370 | template<typename _CutMap> |
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| 371 | void actMinCut(_CutMap& M) const { |
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| 372 | NodeIt v; |
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| 373 | switch (status) { |
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| 374 | case AFTER_PRE_FLOW_PHASE_1: |
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| 375 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 376 | if (level[v] < n) { |
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| 377 | M.set(v, false); |
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| 378 | } else { |
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| 379 | M.set(v, true); |
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| 380 | } |
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| 381 | } |
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| 382 | break; |
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| 383 | case AFTER_PRE_FLOW_PHASE_2: |
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| 384 | case AFTER_NOTHING: |
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[745] | 385 | case AFTER_AUGMENTING: |
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| 386 | case AFTER_FAST_AUGMENTING: |
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[726] | 387 | minMinCut(M); |
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| 388 | break; |
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| 389 | } |
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| 390 | } |
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| 391 | |
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| 392 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 393 | |
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| 394 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 395 | ///which is inclusionwise minimum. It is computed by processing |
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| 396 | ///a bfs from the source node \c s in the residual graph. |
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| 397 | ///\pre M should be a node map of bools initialized to false. |
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| 398 | ///\pre \c flow must be a maximum flow. |
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| 399 | template<typename _CutMap> |
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| 400 | void minMinCut(_CutMap& M) const { |
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| 401 | std::queue<Node> queue; |
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| 402 | |
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| 403 | M.set(s,true); |
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| 404 | queue.push(s); |
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| 405 | |
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| 406 | while (!queue.empty()) { |
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| 407 | Node w=queue.front(); |
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| 408 | queue.pop(); |
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| 409 | |
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| 410 | OutEdgeIt e; |
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| 411 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 412 | Node v=g->head(e); |
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| 413 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 414 | queue.push(v); |
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| 415 | M.set(v, true); |
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| 416 | } |
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| 417 | } |
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| 418 | |
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| 419 | InEdgeIt f; |
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| 420 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 421 | Node v=g->tail(f); |
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| 422 | if (!M[v] && (*flow)[f] > 0 ) { |
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| 423 | queue.push(v); |
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| 424 | M.set(v, true); |
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| 425 | } |
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| 426 | } |
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| 427 | } |
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| 428 | } |
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| 429 | |
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| 430 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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| 431 | |
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| 432 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 433 | ///which is inclusionwise maximum. It is computed by processing a |
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| 434 | ///backward bfs from the target node \c t in the residual graph. |
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| 435 | ///\pre M should be a node map of bools initialized to false. |
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| 436 | ///\pre \c flow must be a maximum flow. |
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| 437 | template<typename _CutMap> |
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| 438 | void maxMinCut(_CutMap& M) const { |
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| 439 | |
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| 440 | NodeIt v; |
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| 441 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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| 442 | M.set(v, true); |
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| 443 | } |
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| 444 | |
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| 445 | std::queue<Node> queue; |
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| 446 | |
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| 447 | M.set(t,false); |
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| 448 | queue.push(t); |
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| 449 | |
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| 450 | while (!queue.empty()) { |
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| 451 | Node w=queue.front(); |
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| 452 | queue.pop(); |
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| 453 | |
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| 454 | InEdgeIt e; |
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| 455 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 456 | Node v=g->tail(e); |
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| 457 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 458 | queue.push(v); |
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| 459 | M.set(v, false); |
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| 460 | } |
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| 461 | } |
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| 462 | |
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| 463 | OutEdgeIt f; |
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| 464 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 465 | Node v=g->head(f); |
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| 466 | if (M[v] && (*flow)[f] > 0 ) { |
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| 467 | queue.push(v); |
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| 468 | M.set(v, false); |
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| 469 | } |
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| 470 | } |
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| 471 | } |
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| 472 | } |
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| 473 | |
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| 474 | ///Returns a minimum value cut. |
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| 475 | |
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| 476 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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| 477 | ///\pre M should be a node map of bools initialized to false. |
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| 478 | ///\pre \c flow must be a maximum flow. |
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| 479 | template<typename CutMap> |
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| 480 | void minCut(CutMap& M) const { minMinCut(M); } |
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| 481 | |
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| 482 | ///Resets the source node to \c _s. |
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| 483 | |
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| 484 | ///Resets the source node to \c _s. |
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| 485 | /// |
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| 486 | void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; } |
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| 487 | |
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| 488 | ///Resets the target node to \c _t. |
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| 489 | |
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| 490 | ///Resets the target node to \c _t. |
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| 491 | /// |
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| 492 | void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; } |
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| 493 | |
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| 494 | /// Resets the edge map of the capacities to _cap. |
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| 495 | |
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| 496 | /// Resets the edge map of the capacities to _cap. |
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| 497 | /// |
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| 498 | void resetCap(const CapMap& _cap) |
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| 499 | { capacity=&_cap; status=AFTER_NOTHING; } |
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| 500 | |
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| 501 | /// Resets the edge map of the flows to _flow. |
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| 502 | |
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| 503 | /// Resets the edge map of the flows to _flow. |
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| 504 | /// |
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| 505 | void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; } |
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| 506 | |
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| 507 | |
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| 508 | private: |
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| 509 | |
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| 510 | int push(Node w, NNMap& next, VecFirst& first) { |
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| 511 | |
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| 512 | int lev=level[w]; |
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| 513 | Num exc=excess[w]; |
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| 514 | int newlevel=n; //bound on the next level of w |
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| 515 | |
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| 516 | OutEdgeIt e; |
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| 517 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 518 | |
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| 519 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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| 520 | Node v=g->head(e); |
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| 521 | |
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| 522 | if( lev > level[v] ) { //Push is allowed now |
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| 523 | |
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| 524 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 525 | next.set(v,first[level[v]]); |
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| 526 | first[level[v]]=v; |
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| 527 | } |
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| 528 | |
---|
| 529 | Num cap=(*capacity)[e]; |
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| 530 | Num flo=(*flow)[e]; |
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| 531 | Num remcap=cap-flo; |
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| 532 | |
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| 533 | if ( remcap >= exc ) { //A nonsaturating push. |
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| 534 | |
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| 535 | flow->set(e, flo+exc); |
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| 536 | excess.set(v, excess[v]+exc); |
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| 537 | exc=0; |
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| 538 | break; |
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| 539 | |
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| 540 | } else { //A saturating push. |
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| 541 | flow->set(e, cap); |
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| 542 | excess.set(v, excess[v]+remcap); |
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| 543 | exc-=remcap; |
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| 544 | } |
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| 545 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 546 | } //for out edges wv |
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| 547 | |
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| 548 | if ( exc > 0 ) { |
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| 549 | InEdgeIt e; |
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| 550 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 551 | |
---|
| 552 | if( (*flow)[e] <= 0 ) continue; |
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| 553 | Node v=g->tail(e); |
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| 554 | |
---|
| 555 | if( lev > level[v] ) { //Push is allowed now |
---|
| 556 | |
---|
| 557 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 558 | next.set(v,first[level[v]]); |
---|
| 559 | first[level[v]]=v; |
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| 560 | } |
---|
| 561 | |
---|
| 562 | Num flo=(*flow)[e]; |
---|
| 563 | |
---|
| 564 | if ( flo >= exc ) { //A nonsaturating push. |
---|
| 565 | |
---|
| 566 | flow->set(e, flo-exc); |
---|
| 567 | excess.set(v, excess[v]+exc); |
---|
| 568 | exc=0; |
---|
| 569 | break; |
---|
| 570 | } else { //A saturating push. |
---|
| 571 | |
---|
| 572 | excess.set(v, excess[v]+flo); |
---|
| 573 | exc-=flo; |
---|
| 574 | flow->set(e,0); |
---|
| 575 | } |
---|
| 576 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 577 | } //for in edges vw |
---|
| 578 | |
---|
| 579 | } // if w still has excess after the out edge for cycle |
---|
| 580 | |
---|
| 581 | excess.set(w, exc); |
---|
| 582 | |
---|
| 583 | return newlevel; |
---|
| 584 | } |
---|
| 585 | |
---|
| 586 | |
---|
[749] | 587 | |
---|
[726] | 588 | void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first, |
---|
| 589 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
| 590 | { |
---|
[749] | 591 | switch (fe) { //setting excess |
---|
| 592 | case NO_FLOW: |
---|
| 593 | { |
---|
| 594 | EdgeIt e; |
---|
| 595 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
---|
| 596 | |
---|
| 597 | NodeIt v; |
---|
| 598 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 599 | break; |
---|
| 600 | } |
---|
| 601 | case ZERO_FLOW: |
---|
| 602 | { |
---|
| 603 | NodeIt v; |
---|
| 604 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 605 | break; |
---|
| 606 | } |
---|
| 607 | case GEN_FLOW: |
---|
| 608 | { |
---|
| 609 | NodeIt v; |
---|
| 610 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 611 | |
---|
| 612 | Num exc=0; |
---|
| 613 | InEdgeIt e; |
---|
| 614 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
| 615 | OutEdgeIt f; |
---|
| 616 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
| 617 | excess.set(t,exc); |
---|
| 618 | break; |
---|
| 619 | } |
---|
| 620 | default: break; |
---|
| 621 | } |
---|
| 622 | |
---|
| 623 | NodeIt v; |
---|
| 624 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
---|
| 625 | //setting each node to level n |
---|
| 626 | |
---|
[726] | 627 | std::queue<Node> bfs_queue; |
---|
| 628 | |
---|
[749] | 629 | |
---|
[726] | 630 | switch (fe) { |
---|
[749] | 631 | case NO_FLOW: //flow is already set to const zero |
---|
[726] | 632 | case ZERO_FLOW: |
---|
| 633 | { |
---|
| 634 | //Reverse_bfs from t, to find the starting level. |
---|
| 635 | level.set(t,0); |
---|
| 636 | bfs_queue.push(t); |
---|
| 637 | |
---|
| 638 | while (!bfs_queue.empty()) { |
---|
| 639 | |
---|
| 640 | Node v=bfs_queue.front(); |
---|
| 641 | bfs_queue.pop(); |
---|
| 642 | int l=level[v]+1; |
---|
| 643 | |
---|
| 644 | InEdgeIt e; |
---|
| 645 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 646 | Node w=g->tail(e); |
---|
| 647 | if ( level[w] == n && w != s ) { |
---|
| 648 | bfs_queue.push(w); |
---|
| 649 | Node z=level_list[l]; |
---|
| 650 | if ( g->valid(z) ) left.set(z,w); |
---|
| 651 | right.set(w,z); |
---|
| 652 | level_list[l]=w; |
---|
| 653 | level.set(w, l); |
---|
| 654 | } |
---|
| 655 | } |
---|
| 656 | } |
---|
| 657 | |
---|
| 658 | //the starting flow |
---|
| 659 | OutEdgeIt e; |
---|
| 660 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
| 661 | { |
---|
| 662 | Num c=(*capacity)[e]; |
---|
| 663 | if ( c <= 0 ) continue; |
---|
| 664 | Node w=g->head(e); |
---|
| 665 | if ( level[w] < n ) { |
---|
[749] | 666 | if ( excess[w] <= 0 && w!=t ) //putting into the stack |
---|
| 667 | { |
---|
[726] | 668 | next.set(w,first[level[w]]); |
---|
| 669 | first[level[w]]=w; |
---|
| 670 | } |
---|
| 671 | flow->set(e, c); |
---|
| 672 | excess.set(w, excess[w]+c); |
---|
| 673 | } |
---|
| 674 | } |
---|
| 675 | break; |
---|
| 676 | } |
---|
| 677 | |
---|
| 678 | case GEN_FLOW: |
---|
[749] | 679 | { |
---|
| 680 | //Reverse_bfs from t in the residual graph, |
---|
| 681 | //to find the starting level. |
---|
| 682 | level.set(t,0); |
---|
| 683 | bfs_queue.push(t); |
---|
| 684 | |
---|
| 685 | while (!bfs_queue.empty()) { |
---|
| 686 | |
---|
| 687 | Node v=bfs_queue.front(); |
---|
| 688 | bfs_queue.pop(); |
---|
| 689 | int l=level[v]+1; |
---|
| 690 | |
---|
| 691 | InEdgeIt e; |
---|
| 692 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 693 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 694 | Node w=g->tail(e); |
---|
| 695 | if ( level[w] == n && w != s ) { |
---|
| 696 | bfs_queue.push(w); |
---|
| 697 | Node z=level_list[l]; |
---|
| 698 | if ( g->valid(z) ) left.set(z,w); |
---|
| 699 | right.set(w,z); |
---|
| 700 | level_list[l]=w; |
---|
| 701 | level.set(w, l); |
---|
| 702 | } |
---|
| 703 | } |
---|
| 704 | |
---|
| 705 | OutEdgeIt f; |
---|
| 706 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 707 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 708 | Node w=g->head(f); |
---|
| 709 | if ( level[w] == n && w != s ) { |
---|
| 710 | bfs_queue.push(w); |
---|
| 711 | Node z=level_list[l]; |
---|
| 712 | if ( g->valid(z) ) left.set(z,w); |
---|
| 713 | right.set(w,z); |
---|
| 714 | level_list[l]=w; |
---|
| 715 | level.set(w, l); |
---|
| 716 | } |
---|
| 717 | } |
---|
| 718 | } |
---|
| 719 | |
---|
| 720 | //the starting flow |
---|
| 721 | OutEdgeIt e; |
---|
| 722 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
| 723 | { |
---|
| 724 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
| 725 | if ( rem <= 0 ) continue; |
---|
| 726 | Node w=g->head(e); |
---|
| 727 | if ( level[w] < n ) { |
---|
| 728 | if ( excess[w] <= 0 && w!=t ) //putting into the stack |
---|
| 729 | { |
---|
| 730 | next.set(w,first[level[w]]); |
---|
| 731 | first[level[w]]=w; |
---|
| 732 | } |
---|
| 733 | flow->set(e, (*capacity)[e]); |
---|
| 734 | excess.set(w, excess[w]+rem); |
---|
| 735 | } |
---|
| 736 | } |
---|
| 737 | |
---|
| 738 | InEdgeIt f; |
---|
| 739 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
| 740 | { |
---|
| 741 | if ( (*flow)[f] <= 0 ) continue; |
---|
| 742 | Node w=g->tail(f); |
---|
| 743 | if ( level[w] < n ) { |
---|
| 744 | if ( excess[w] <= 0 && w!=t ) |
---|
| 745 | { |
---|
| 746 | next.set(w,first[level[w]]); |
---|
| 747 | first[level[w]]=w; |
---|
| 748 | } |
---|
| 749 | excess.set(w, excess[w]+(*flow)[f]); |
---|
| 750 | flow->set(f, 0); |
---|
| 751 | } |
---|
| 752 | } |
---|
| 753 | break; |
---|
| 754 | } //case GEN_FLOW |
---|
| 755 | |
---|
[726] | 756 | case PRE_FLOW: |
---|
| 757 | { |
---|
| 758 | //Reverse_bfs from t in the residual graph, |
---|
| 759 | //to find the starting level. |
---|
| 760 | level.set(t,0); |
---|
| 761 | bfs_queue.push(t); |
---|
| 762 | |
---|
| 763 | while (!bfs_queue.empty()) { |
---|
| 764 | |
---|
| 765 | Node v=bfs_queue.front(); |
---|
| 766 | bfs_queue.pop(); |
---|
| 767 | int l=level[v]+1; |
---|
| 768 | |
---|
| 769 | InEdgeIt e; |
---|
| 770 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 771 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 772 | Node w=g->tail(e); |
---|
| 773 | if ( level[w] == n && w != s ) { |
---|
| 774 | bfs_queue.push(w); |
---|
| 775 | Node z=level_list[l]; |
---|
| 776 | if ( g->valid(z) ) left.set(z,w); |
---|
| 777 | right.set(w,z); |
---|
| 778 | level_list[l]=w; |
---|
| 779 | level.set(w, l); |
---|
| 780 | } |
---|
| 781 | } |
---|
| 782 | |
---|
| 783 | OutEdgeIt f; |
---|
| 784 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 785 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 786 | Node w=g->head(f); |
---|
| 787 | if ( level[w] == n && w != s ) { |
---|
| 788 | bfs_queue.push(w); |
---|
| 789 | Node z=level_list[l]; |
---|
| 790 | if ( g->valid(z) ) left.set(z,w); |
---|
| 791 | right.set(w,z); |
---|
| 792 | level_list[l]=w; |
---|
| 793 | level.set(w, l); |
---|
| 794 | } |
---|
| 795 | } |
---|
| 796 | } |
---|
| 797 | |
---|
| 798 | |
---|
| 799 | //the starting flow |
---|
| 800 | OutEdgeIt e; |
---|
| 801 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
| 802 | { |
---|
| 803 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
| 804 | if ( rem <= 0 ) continue; |
---|
| 805 | Node w=g->head(e); |
---|
| 806 | if ( level[w] < n ) { |
---|
| 807 | flow->set(e, (*capacity)[e]); |
---|
| 808 | excess.set(w, excess[w]+rem); |
---|
| 809 | } |
---|
| 810 | } |
---|
| 811 | |
---|
| 812 | InEdgeIt f; |
---|
| 813 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
| 814 | { |
---|
| 815 | if ( (*flow)[f] <= 0 ) continue; |
---|
| 816 | Node w=g->tail(f); |
---|
| 817 | if ( level[w] < n ) { |
---|
| 818 | excess.set(w, excess[w]+(*flow)[f]); |
---|
| 819 | flow->set(f, 0); |
---|
| 820 | } |
---|
| 821 | } |
---|
[749] | 822 | |
---|
| 823 | NodeIt w; //computing the excess |
---|
| 824 | for(g->first(w); g->valid(w); g->next(w)) { |
---|
| 825 | Num exc=0; |
---|
| 826 | |
---|
| 827 | InEdgeIt e; |
---|
| 828 | for(g->first(e,w); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
| 829 | OutEdgeIt f; |
---|
| 830 | for(g->first(f,w); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
| 831 | |
---|
| 832 | excess.set(w,exc); |
---|
| 833 | |
---|
| 834 | //putting the active nodes into the stack |
---|
| 835 | int lev=level[w]; |
---|
| 836 | if ( exc > 0 && lev < n && w != t ) |
---|
| 837 | { |
---|
| 838 | next.set(w,first[lev]); |
---|
| 839 | first[lev]=w; |
---|
| 840 | } |
---|
| 841 | } |
---|
[726] | 842 | break; |
---|
| 843 | } //case PRE_FLOW |
---|
| 844 | } |
---|
| 845 | } //preflowPreproc |
---|
| 846 | |
---|
| 847 | |
---|
| 848 | void relabel(Node w, int newlevel, NNMap& next, VecFirst& first, |
---|
| 849 | VecNode& level_list, NNMap& left, |
---|
| 850 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
| 851 | { |
---|
| 852 | |
---|
| 853 | Num lev=level[w]; |
---|
| 854 | |
---|
| 855 | Node right_n=right[w]; |
---|
| 856 | Node left_n=left[w]; |
---|
| 857 | |
---|
| 858 | //unlacing starts |
---|
| 859 | if ( g->valid(right_n) ) { |
---|
| 860 | if ( g->valid(left_n) ) { |
---|
| 861 | right.set(left_n, right_n); |
---|
| 862 | left.set(right_n, left_n); |
---|
| 863 | } else { |
---|
| 864 | level_list[lev]=right_n; |
---|
| 865 | left.set(right_n, INVALID); |
---|
| 866 | } |
---|
| 867 | } else { |
---|
| 868 | if ( g->valid(left_n) ) { |
---|
| 869 | right.set(left_n, INVALID); |
---|
| 870 | } else { |
---|
| 871 | level_list[lev]=INVALID; |
---|
| 872 | } |
---|
| 873 | } |
---|
| 874 | //unlacing ends |
---|
| 875 | |
---|
| 876 | if ( !g->valid(level_list[lev]) ) { |
---|
| 877 | |
---|
| 878 | //gapping starts |
---|
| 879 | for (int i=lev; i!=k ; ) { |
---|
| 880 | Node v=level_list[++i]; |
---|
| 881 | while ( g->valid(v) ) { |
---|
| 882 | level.set(v,n); |
---|
| 883 | v=right[v]; |
---|
| 884 | } |
---|
| 885 | level_list[i]=INVALID; |
---|
| 886 | if ( !what_heur ) first[i]=INVALID; |
---|
| 887 | } |
---|
| 888 | |
---|
| 889 | level.set(w,n); |
---|
| 890 | b=lev-1; |
---|
| 891 | k=b; |
---|
| 892 | //gapping ends |
---|
| 893 | |
---|
| 894 | } else { |
---|
| 895 | |
---|
| 896 | if ( newlevel == n ) level.set(w,n); |
---|
| 897 | else { |
---|
| 898 | level.set(w,++newlevel); |
---|
| 899 | next.set(w,first[newlevel]); |
---|
| 900 | first[newlevel]=w; |
---|
| 901 | if ( what_heur ) b=newlevel; |
---|
| 902 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 903 | Node z=level_list[newlevel]; |
---|
| 904 | if ( g->valid(z) ) left.set(z,w); |
---|
| 905 | right.set(w,z); |
---|
| 906 | left.set(w,INVALID); |
---|
| 907 | level_list[newlevel]=w; |
---|
| 908 | } |
---|
| 909 | } |
---|
| 910 | } //relabel |
---|
[749] | 911 | |
---|
| 912 | void printexcess() {//// |
---|
| 913 | std::cout << "Excesses:" <<std::endl; |
---|
| 914 | |
---|
| 915 | NodeIt v; |
---|
| 916 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
| 917 | std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | |
---|
| 921 | void printlevel() {//// |
---|
| 922 | std::cout << "Levels:" <<std::endl; |
---|
| 923 | |
---|
| 924 | NodeIt v; |
---|
| 925 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
| 926 | std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; |
---|
| 927 | } |
---|
| 928 | } |
---|
| 929 | |
---|
| 930 | void printactive() {//// |
---|
| 931 | std::cout << "Levels:" <<std::endl; |
---|
| 932 | |
---|
| 933 | NodeIt v; |
---|
| 934 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
| 935 | std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; |
---|
| 936 | } |
---|
| 937 | } |
---|
| 938 | |
---|
| 939 | |
---|
[726] | 940 | }; //class MaxFlow |
---|
| 941 | } //namespace hugo |
---|
| 942 | |
---|
| 943 | #endif //HUGO_MAX_FLOW_H |
---|
| 944 | |
---|
| 945 | |
---|
| 946 | |
---|
| 947 | |
---|