[726] | 1 | // -*- C++ -*- |
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| 2 | #ifndef HUGO_MAX_FLOW_NO_STACK_H |
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| 3 | #define HUGO_MAX_FLOW_NO_STACK_H |
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| 4 | |
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| 5 | #include <vector> |
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| 6 | #include <queue> |
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| 7 | //#include <stack> |
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| 8 | |
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| 9 | #include <hugo/graph_wrapper.h> |
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| 10 | #include <hugo/invalid.h> |
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| 11 | #include <hugo/maps.h> |
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| 12 | |
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| 13 | /// \file |
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| 14 | /// \brief The same as max_flow.h, but without using stl stack for the active nodes. Only for test. |
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| 15 | /// \ingroup galgs |
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| 16 | |
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| 17 | namespace hugo { |
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| 18 | |
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| 19 | /// \addtogroup galgs |
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| 20 | /// @{ |
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| 21 | ///Maximum flow algorithms class. |
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| 22 | |
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| 23 | ///This class provides various algorithms for finding a flow of |
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| 24 | ///maximum value in a directed graph. The \e source node, the \e |
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| 25 | ///target node, the \e capacity of the edges and the \e starting \e |
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| 26 | ///flow value of the edges should be passed to the algorithm through the |
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| 27 | ///constructor. It is possible to change these quantities using the |
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| 28 | ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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| 29 | ///\ref resetFlow. Before any subsequent runs of any algorithm of |
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| 30 | ///the class \ref resetFlow should be called. |
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| 31 | |
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| 32 | ///After running an algorithm of the class, the actual flow value |
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| 33 | ///can be obtained by calling \ref flowValue(). The minimum |
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| 34 | ///value cut can be written into a \c node map of \c bools by |
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| 35 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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| 36 | ///the inclusionwise minimum and maximum of the minimum value |
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| 37 | ///cuts, resp.) |
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| 38 | ///\param Graph The directed graph type the algorithm runs on. |
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| 39 | ///\param Num The number type of the capacities and the flow values. |
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| 40 | ///\param CapMap The capacity map type. |
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| 41 | ///\param FlowMap The flow map type. |
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| 42 | ///\author Marton Makai, Jacint Szabo |
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| 43 | template <typename Graph, typename Num, |
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| 44 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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| 45 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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| 46 | class MaxFlow { |
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| 47 | protected: |
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| 48 | typedef typename Graph::Node Node; |
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| 49 | typedef typename Graph::NodeIt NodeIt; |
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| 50 | typedef typename Graph::EdgeIt EdgeIt; |
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| 51 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 52 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 53 | |
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| 54 | // typedef typename std::vector<std::stack<Node> > VecStack; |
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| 55 | typedef typename std::vector<Node> VecFirst; |
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| 56 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 57 | typedef typename std::vector<Node> VecNode; |
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| 58 | |
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| 59 | const Graph* g; |
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| 60 | Node s; |
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| 61 | Node t; |
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| 62 | const CapMap* capacity; |
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| 63 | FlowMap* flow; |
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| 64 | int n; //the number of nodes of G |
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| 65 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 66 | //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 67 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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| 68 | typedef typename ResGW::Edge ResGWEdge; |
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| 69 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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| 70 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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| 71 | |
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| 72 | |
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| 73 | //level works as a bool map in augmenting path algorithms and is |
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| 74 | //used by bfs for storing reached information. In preflow, it |
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| 75 | //shows the levels of nodes. |
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| 76 | ReachedMap level; |
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| 77 | |
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| 78 | //excess is needed only in preflow |
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| 79 | typename Graph::template NodeMap<Num> excess; |
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| 80 | |
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| 81 | // constants used for heuristics |
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| 82 | static const int H0=20; |
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| 83 | static const int H1=1; |
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| 84 | |
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| 85 | public: |
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| 86 | |
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| 87 | ///Indicates the property of the starting flow. |
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| 88 | |
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| 89 | ///Indicates the property of the starting flow. The meanings are as follows: |
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| 90 | ///- \c ZERO_FLOW: constant zero flow |
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| 91 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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| 92 | ///the sum of the out-flows in every node except the \e source and |
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| 93 | ///the \e target. |
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| 94 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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| 95 | ///least the sum of the out-flows in every node except the \e source. |
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| 96 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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| 97 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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| 98 | enum FlowEnum{ |
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| 99 | ZERO_FLOW, |
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| 100 | GEN_FLOW, |
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| 101 | PRE_FLOW, |
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| 102 | NO_FLOW |
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| 103 | }; |
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| 104 | |
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| 105 | enum StatusEnum { |
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| 106 | AFTER_NOTHING, |
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| 107 | AFTER_AUGMENTING, |
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| 108 | AFTER_FAST_AUGMENTING, |
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| 109 | AFTER_PRE_FLOW_PHASE_1, |
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| 110 | AFTER_PRE_FLOW_PHASE_2 |
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| 111 | }; |
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| 112 | |
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| 113 | /// Don not needle this flag only if necessary. |
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| 114 | StatusEnum status; |
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| 115 | |
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| 116 | // int number_of_augmentations; |
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| 117 | |
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| 118 | |
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| 119 | // template<typename IntMap> |
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| 120 | // class TrickyReachedMap { |
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| 121 | // protected: |
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| 122 | // IntMap* map; |
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| 123 | // int* number_of_augmentations; |
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| 124 | // public: |
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| 125 | // TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
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| 126 | // map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
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| 127 | // void set(const Node& n, bool b) { |
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| 128 | // if (b) |
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| 129 | // map->set(n, *number_of_augmentations); |
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| 130 | // else |
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| 131 | // map->set(n, *number_of_augmentations-1); |
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| 132 | // } |
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| 133 | // bool operator[](const Node& n) const { |
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| 134 | // return (*map)[n]==*number_of_augmentations; |
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| 135 | // } |
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| 136 | // }; |
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| 137 | |
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| 138 | ///Constructor |
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| 139 | |
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| 140 | ///\todo Document, please. |
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| 141 | /// |
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| 142 | MaxFlow(const Graph& _G, Node _s, Node _t, |
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[745] | 143 | const CapMap& _capacity, FlowMap& _flow) : |
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[726] | 144 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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| 145 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), |
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| 146 | status(AFTER_NOTHING) { } |
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| 147 | |
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| 148 | ///Runs a maximum flow algorithm. |
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| 149 | |
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| 150 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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| 151 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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| 152 | ///\pre The starting flow must be |
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| 153 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 154 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 155 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 156 | /// - any map if \c fe is NO_FLOW. |
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| 157 | void run(FlowEnum fe=ZERO_FLOW) { |
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| 158 | preflow(fe); |
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| 159 | } |
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| 160 | |
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| 161 | |
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| 162 | ///Runs a preflow algorithm. |
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| 163 | |
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| 164 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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| 165 | ///fastest way to compute a maximum flow in a directed graph. |
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| 166 | ///\pre The starting flow must be |
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| 167 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 168 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 169 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 170 | /// - any map if \c fe is NO_FLOW. |
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| 171 | /// |
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| 172 | ///\todo NO_FLOW should be the default flow. |
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| 173 | void preflow(FlowEnum fe) { |
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| 174 | preflowPhase1(fe); |
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| 175 | preflowPhase2(); |
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| 176 | } |
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| 177 | // Heuristics: |
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| 178 | // 2 phase |
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| 179 | // gap |
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| 180 | // list 'level_list' on the nodes on level i implemented by hand |
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| 181 | // stack 'active' on the active nodes on level i |
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| 182 | // runs heuristic 'highest label' for H1*n relabels |
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| 183 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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| 184 | // Parameters H0 and H1 are initialized to 20 and 1. |
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| 185 | |
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| 186 | ///Runs the first phase of the preflow algorithm. |
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| 187 | |
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| 188 | ///The preflow algorithm consists of two phases, this method runs the |
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| 189 | ///first phase. After the first phase the maximum flow value and a |
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| 190 | ///minimum value cut can already be computed, though a maximum flow |
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| 191 | ///is net yet obtained. So after calling this method \ref flowValue |
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| 192 | ///and \ref actMinCut gives proper results. |
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| 193 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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| 194 | ///give minimum value cuts unless calling \ref preflowPhase2. |
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| 195 | ///\pre The starting flow must be |
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| 196 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 197 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 198 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 199 | /// - any map if \c fe is NO_FLOW. |
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| 200 | void preflowPhase1(FlowEnum fe) |
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| 201 | { |
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| 202 | |
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| 203 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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| 204 | int heur1=(int)(H1*n); //time while running 'highest label' |
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| 205 | int heur=heur1; //starting time interval (#of relabels) |
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| 206 | int numrelabel=0; |
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| 207 | |
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| 208 | bool what_heur=1; |
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| 209 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
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| 210 | |
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| 211 | bool end=false; |
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| 212 | //Needed for 'bound decrease', true means no active nodes are above bound |
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| 213 | //b. |
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| 214 | |
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| 215 | int k=n-2; //bound on the highest level under n containing a node |
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| 216 | int b=k; //bound on the highest level under n of an active node |
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| 217 | |
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| 218 | VecFirst first(n, INVALID); |
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| 219 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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| 220 | |
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| 221 | NNMap left(*g, INVALID); |
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| 222 | NNMap right(*g, INVALID); |
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| 223 | VecNode level_list(n,INVALID); |
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| 224 | //List of the nodes in level i<n, set to n. |
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| 225 | |
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| 226 | NodeIt v; |
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| 227 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
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| 228 | //setting each node to level n |
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| 229 | |
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| 230 | if ( fe == NO_FLOW ) { |
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| 231 | EdgeIt e; |
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| 232 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
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| 233 | } |
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| 234 | |
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| 235 | switch (fe) { //computing the excess |
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| 236 | case PRE_FLOW: |
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| 237 | { |
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| 238 | NodeIt v; |
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| 239 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 240 | Num exc=0; |
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| 241 | |
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| 242 | InEdgeIt e; |
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| 243 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
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| 244 | OutEdgeIt f; |
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| 245 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
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| 246 | |
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| 247 | excess.set(v,exc); |
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| 248 | |
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| 249 | //putting the active nodes into the stack |
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| 250 | int lev=level[v]; |
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| 251 | if ( exc > 0 && lev < n && v != t ) |
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| 252 | { |
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| 253 | next.set(v,first[lev]); |
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| 254 | first[lev]=v; |
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| 255 | } |
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| 256 | } |
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| 257 | break; |
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| 258 | } |
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| 259 | case GEN_FLOW: |
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| 260 | { |
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| 261 | NodeIt v; |
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| 262 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
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| 263 | |
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| 264 | Num exc=0; |
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| 265 | InEdgeIt e; |
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| 266 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
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| 267 | OutEdgeIt f; |
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| 268 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
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| 269 | excess.set(t,exc); |
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| 270 | break; |
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| 271 | } |
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| 272 | case ZERO_FLOW: |
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| 273 | case NO_FLOW: |
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| 274 | { |
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| 275 | NodeIt v; |
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| 276 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
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| 277 | break; |
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| 278 | } |
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| 279 | } |
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| 280 | |
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[745] | 281 | preflowPreproc(fe, next, first, level_list, left, right); |
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[726] | 282 | //End of preprocessing |
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| 283 | |
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| 284 | |
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| 285 | //Push/relabel on the highest level active nodes. |
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| 286 | while ( true ) { |
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| 287 | if ( b == 0 ) { |
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| 288 | if ( !what_heur && !end && k > 0 ) { |
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| 289 | b=k; |
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| 290 | end=true; |
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| 291 | } else break; |
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| 292 | } |
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| 293 | |
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[745] | 294 | if ( !g->valid(first[b]) ) --b; |
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[726] | 295 | else { |
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| 296 | end=false; |
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| 297 | Node w=first[b]; |
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| 298 | first[b]=next[w]; |
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[745] | 299 | int newlevel=push(w, next, first); |
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| 300 | if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list, |
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[726] | 301 | left, right, b, k, what_heur); |
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| 302 | |
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| 303 | ++numrelabel; |
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| 304 | if ( numrelabel >= heur ) { |
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| 305 | numrelabel=0; |
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| 306 | if ( what_heur ) { |
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| 307 | what_heur=0; |
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| 308 | heur=heur0; |
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| 309 | end=false; |
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| 310 | } else { |
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| 311 | what_heur=1; |
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| 312 | heur=heur1; |
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| 313 | b=k; |
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| 314 | } |
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| 315 | } |
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| 316 | } |
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| 317 | } |
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| 318 | |
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| 319 | status=AFTER_PRE_FLOW_PHASE_1; |
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| 320 | } |
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| 321 | |
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| 322 | |
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| 323 | ///Runs the second phase of the preflow algorithm. |
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| 324 | |
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| 325 | ///The preflow algorithm consists of two phases, this method runs |
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| 326 | ///the second phase. After calling \ref preflowPhase1 and then |
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| 327 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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| 328 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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| 329 | ///\pre \ref preflowPhase1 must be called before. |
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| 330 | void preflowPhase2() |
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| 331 | { |
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| 332 | |
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| 333 | int k=n-2; //bound on the highest level under n containing a node |
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| 334 | int b=k; //bound on the highest level under n of an active node |
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| 335 | |
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| 336 | |
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| 337 | VecFirst first(n, INVALID); |
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| 338 | NNMap next(*g, INVALID); //maybe INVALID is not needed |
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| 339 | level.set(s,0); |
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| 340 | std::queue<Node> bfs_queue; |
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| 341 | bfs_queue.push(s); |
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| 342 | |
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| 343 | while (!bfs_queue.empty()) { |
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| 344 | |
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| 345 | Node v=bfs_queue.front(); |
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| 346 | bfs_queue.pop(); |
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| 347 | int l=level[v]+1; |
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| 348 | |
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| 349 | InEdgeIt e; |
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| 350 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 351 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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| 352 | Node u=g->tail(e); |
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| 353 | if ( level[u] >= n ) { |
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| 354 | bfs_queue.push(u); |
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| 355 | level.set(u, l); |
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| 356 | if ( excess[u] > 0 ) { |
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| 357 | next.set(u,first[l]); |
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| 358 | first[l]=u; |
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| 359 | } |
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| 360 | } |
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| 361 | } |
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| 362 | |
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| 363 | OutEdgeIt f; |
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| 364 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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| 365 | if ( 0 >= (*flow)[f] ) continue; |
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| 366 | Node u=g->head(f); |
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| 367 | if ( level[u] >= n ) { |
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| 368 | bfs_queue.push(u); |
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| 369 | level.set(u, l); |
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| 370 | if ( excess[u] > 0 ) { |
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| 371 | next.set(u,first[l]); |
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| 372 | first[l]=u; |
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| 373 | } |
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| 374 | } |
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| 375 | } |
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| 376 | } |
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| 377 | b=n-2; |
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| 378 | |
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| 379 | while ( true ) { |
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| 380 | |
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| 381 | if ( b == 0 ) break; |
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| 382 | |
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[745] | 383 | if ( !g->valid(first[b]) ) --b; |
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[726] | 384 | else { |
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| 385 | |
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| 386 | Node w=first[b]; |
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| 387 | first[b]=next[w]; |
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| 388 | int newlevel=push(w,next, first/*active*/); |
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| 389 | |
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| 390 | //relabel |
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| 391 | if ( excess[w] > 0 ) { |
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| 392 | level.set(w,++newlevel); |
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| 393 | next.set(w,first[newlevel]); |
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| 394 | first[newlevel]=w; |
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| 395 | b=newlevel; |
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| 396 | } |
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| 397 | } // if stack[b] is nonempty |
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| 398 | } // while(true) |
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| 399 | |
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| 400 | status=AFTER_PRE_FLOW_PHASE_2; |
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| 401 | } |
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| 402 | |
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| 403 | |
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| 404 | /// Returns the maximum value of a flow. |
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| 405 | |
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| 406 | /// Returns the maximum value of a flow, by counting the |
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| 407 | /// over-flow of the target node \ref t. |
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| 408 | /// It can be called already after running \ref preflowPhase1. |
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| 409 | Num flowValue() const { |
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| 410 | Num a=0; |
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[735] | 411 | for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e]; |
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| 412 | for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e]; |
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[745] | 413 | return a; |
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[726] | 414 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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| 415 | } |
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[745] | 416 | Num flowValue2() const { |
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| 417 | return excess[t]; |
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| 418 | // Num a=0; |
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| 419 | // for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e]; |
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| 420 | // for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e]; |
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| 421 | // return a; |
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| 422 | // //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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| 423 | |
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| 424 | } |
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[726] | 425 | |
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| 426 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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| 427 | |
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| 428 | ///After the first phase of the preflow algorithm the maximum flow |
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| 429 | ///value and a minimum value cut can already be computed. This |
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| 430 | ///method can be called after running \ref preflowPhase1 for |
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| 431 | ///obtaining a minimum value cut. |
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| 432 | /// \warning Gives proper result only right after calling \ref |
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| 433 | /// preflowPhase1. |
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| 434 | /// \todo We have to make some status variable which shows the |
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| 435 | /// actual state |
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| 436 | /// of the class. This enables us to determine which methods are valid |
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| 437 | /// for MinCut computation |
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| 438 | template<typename _CutMap> |
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| 439 | void actMinCut(_CutMap& M) const { |
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| 440 | NodeIt v; |
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| 441 | switch (status) { |
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| 442 | case AFTER_PRE_FLOW_PHASE_1: |
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| 443 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 444 | if (level[v] < n) { |
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| 445 | M.set(v, false); |
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| 446 | } else { |
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| 447 | M.set(v, true); |
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| 448 | } |
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| 449 | } |
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| 450 | break; |
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| 451 | case AFTER_PRE_FLOW_PHASE_2: |
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| 452 | case AFTER_NOTHING: |
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[745] | 453 | case AFTER_AUGMENTING: |
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| 454 | case AFTER_FAST_AUGMENTING: |
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[726] | 455 | minMinCut(M); |
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| 456 | break; |
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| 457 | } |
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| 458 | } |
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| 459 | |
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| 460 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 461 | |
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| 462 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 463 | ///which is inclusionwise minimum. It is computed by processing |
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| 464 | ///a bfs from the source node \c s in the residual graph. |
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| 465 | ///\pre M should be a node map of bools initialized to false. |
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| 466 | ///\pre \c flow must be a maximum flow. |
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| 467 | template<typename _CutMap> |
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| 468 | void minMinCut(_CutMap& M) const { |
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| 469 | std::queue<Node> queue; |
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| 470 | |
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| 471 | M.set(s,true); |
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| 472 | queue.push(s); |
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| 473 | |
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| 474 | while (!queue.empty()) { |
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| 475 | Node w=queue.front(); |
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| 476 | queue.pop(); |
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| 477 | |
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| 478 | OutEdgeIt e; |
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| 479 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 480 | Node v=g->head(e); |
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| 481 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 482 | queue.push(v); |
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| 483 | M.set(v, true); |
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| 484 | } |
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| 485 | } |
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| 486 | |
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| 487 | InEdgeIt f; |
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| 488 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 489 | Node v=g->tail(f); |
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| 490 | if (!M[v] && (*flow)[f] > 0 ) { |
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| 491 | queue.push(v); |
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| 492 | M.set(v, true); |
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| 493 | } |
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| 494 | } |
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| 495 | } |
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| 496 | } |
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| 497 | |
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| 498 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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| 499 | |
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| 500 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 501 | ///which is inclusionwise maximum. It is computed by processing a |
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| 502 | ///backward bfs from the target node \c t in the residual graph. |
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| 503 | ///\pre M should be a node map of bools initialized to false. |
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| 504 | ///\pre \c flow must be a maximum flow. |
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| 505 | template<typename _CutMap> |
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| 506 | void maxMinCut(_CutMap& M) const { |
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| 507 | |
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| 508 | NodeIt v; |
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| 509 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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| 510 | M.set(v, true); |
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| 511 | } |
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| 512 | |
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| 513 | std::queue<Node> queue; |
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| 514 | |
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| 515 | M.set(t,false); |
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| 516 | queue.push(t); |
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| 517 | |
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| 518 | while (!queue.empty()) { |
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| 519 | Node w=queue.front(); |
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| 520 | queue.pop(); |
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| 521 | |
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| 522 | InEdgeIt e; |
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| 523 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 524 | Node v=g->tail(e); |
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| 525 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 526 | queue.push(v); |
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| 527 | M.set(v, false); |
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| 528 | } |
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| 529 | } |
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| 530 | |
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| 531 | OutEdgeIt f; |
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| 532 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 533 | Node v=g->head(f); |
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| 534 | if (M[v] && (*flow)[f] > 0 ) { |
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| 535 | queue.push(v); |
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| 536 | M.set(v, false); |
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| 537 | } |
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| 538 | } |
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| 539 | } |
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| 540 | } |
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| 541 | |
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| 542 | ///Returns a minimum value cut. |
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| 543 | |
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| 544 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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| 545 | ///\pre M should be a node map of bools initialized to false. |
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| 546 | ///\pre \c flow must be a maximum flow. |
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| 547 | template<typename CutMap> |
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| 548 | void minCut(CutMap& M) const { minMinCut(M); } |
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| 549 | |
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| 550 | ///Resets the source node to \c _s. |
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| 551 | |
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| 552 | ///Resets the source node to \c _s. |
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| 553 | /// |
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| 554 | void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; } |
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| 555 | |
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| 556 | ///Resets the target node to \c _t. |
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| 557 | |
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| 558 | ///Resets the target node to \c _t. |
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| 559 | /// |
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| 560 | void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; } |
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| 561 | |
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| 562 | /// Resets the edge map of the capacities to _cap. |
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| 563 | |
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| 564 | /// Resets the edge map of the capacities to _cap. |
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| 565 | /// |
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| 566 | void resetCap(const CapMap& _cap) |
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| 567 | { capacity=&_cap; status=AFTER_NOTHING; } |
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| 568 | |
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| 569 | /// Resets the edge map of the flows to _flow. |
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| 570 | |
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| 571 | /// Resets the edge map of the flows to _flow. |
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| 572 | /// |
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| 573 | void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; } |
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| 574 | |
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| 575 | |
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| 576 | private: |
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| 577 | |
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| 578 | int push(Node w, NNMap& next, VecFirst& first) { |
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| 579 | |
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| 580 | int lev=level[w]; |
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| 581 | Num exc=excess[w]; |
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| 582 | int newlevel=n; //bound on the next level of w |
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| 583 | |
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| 584 | OutEdgeIt e; |
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| 585 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 586 | |
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| 587 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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| 588 | Node v=g->head(e); |
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| 589 | |
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| 590 | if( lev > level[v] ) { //Push is allowed now |
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| 591 | |
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| 592 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 593 | next.set(v,first[level[v]]); |
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| 594 | first[level[v]]=v; |
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| 595 | } |
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| 596 | |
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| 597 | Num cap=(*capacity)[e]; |
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| 598 | Num flo=(*flow)[e]; |
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| 599 | Num remcap=cap-flo; |
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| 600 | |
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| 601 | if ( remcap >= exc ) { //A nonsaturating push. |
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| 602 | |
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| 603 | flow->set(e, flo+exc); |
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| 604 | excess.set(v, excess[v]+exc); |
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| 605 | exc=0; |
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| 606 | break; |
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| 607 | |
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| 608 | } else { //A saturating push. |
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| 609 | flow->set(e, cap); |
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| 610 | excess.set(v, excess[v]+remcap); |
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| 611 | exc-=remcap; |
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| 612 | } |
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| 613 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 614 | } //for out edges wv |
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| 615 | |
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| 616 | if ( exc > 0 ) { |
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| 617 | InEdgeIt e; |
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| 618 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 619 | |
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| 620 | if( (*flow)[e] <= 0 ) continue; |
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| 621 | Node v=g->tail(e); |
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| 622 | |
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| 623 | if( lev > level[v] ) { //Push is allowed now |
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| 624 | |
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| 625 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 626 | next.set(v,first[level[v]]); |
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| 627 | first[level[v]]=v; |
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| 628 | } |
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| 629 | |
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| 630 | Num flo=(*flow)[e]; |
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| 631 | |
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| 632 | if ( flo >= exc ) { //A nonsaturating push. |
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| 633 | |
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| 634 | flow->set(e, flo-exc); |
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| 635 | excess.set(v, excess[v]+exc); |
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| 636 | exc=0; |
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| 637 | break; |
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| 638 | } else { //A saturating push. |
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| 639 | |
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| 640 | excess.set(v, excess[v]+flo); |
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| 641 | exc-=flo; |
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| 642 | flow->set(e,0); |
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| 643 | } |
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| 644 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 645 | } //for in edges vw |
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| 646 | |
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| 647 | } // if w still has excess after the out edge for cycle |
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| 648 | |
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| 649 | excess.set(w, exc); |
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| 650 | |
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| 651 | return newlevel; |
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| 652 | } |
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| 653 | |
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| 654 | |
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| 655 | void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first, |
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| 656 | VecNode& level_list, NNMap& left, NNMap& right) |
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| 657 | { |
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| 658 | std::queue<Node> bfs_queue; |
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| 659 | |
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| 660 | switch (fe) { |
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| 661 | case NO_FLOW: //flow is already set to const zero in this case |
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| 662 | case ZERO_FLOW: |
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| 663 | { |
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| 664 | //Reverse_bfs from t, to find the starting level. |
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| 665 | level.set(t,0); |
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| 666 | bfs_queue.push(t); |
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| 667 | |
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| 668 | while (!bfs_queue.empty()) { |
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| 669 | |
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| 670 | Node v=bfs_queue.front(); |
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| 671 | bfs_queue.pop(); |
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| 672 | int l=level[v]+1; |
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| 673 | |
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| 674 | InEdgeIt e; |
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| 675 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 676 | Node w=g->tail(e); |
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| 677 | if ( level[w] == n && w != s ) { |
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| 678 | bfs_queue.push(w); |
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| 679 | Node z=level_list[l]; |
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| 680 | if ( g->valid(z) ) left.set(z,w); |
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| 681 | right.set(w,z); |
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| 682 | level_list[l]=w; |
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| 683 | level.set(w, l); |
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| 684 | } |
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| 685 | } |
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| 686 | } |
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| 687 | |
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| 688 | //the starting flow |
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| 689 | OutEdgeIt e; |
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| 690 | for(g->first(e,s); g->valid(e); g->next(e)) |
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| 691 | { |
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| 692 | Num c=(*capacity)[e]; |
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| 693 | if ( c <= 0 ) continue; |
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| 694 | Node w=g->head(e); |
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| 695 | if ( level[w] < n ) { |
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| 696 | if ( excess[w] <= 0 && w!=t ) |
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| 697 | { |
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| 698 | next.set(w,first[level[w]]); |
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| 699 | first[level[w]]=w; |
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| 700 | } |
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| 701 | flow->set(e, c); |
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| 702 | excess.set(w, excess[w]+c); |
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| 703 | } |
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| 704 | } |
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| 705 | break; |
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| 706 | } |
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| 707 | |
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| 708 | case GEN_FLOW: |
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| 709 | case PRE_FLOW: |
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| 710 | { |
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| 711 | //Reverse_bfs from t in the residual graph, |
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| 712 | //to find the starting level. |
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| 713 | level.set(t,0); |
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| 714 | bfs_queue.push(t); |
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| 715 | |
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| 716 | while (!bfs_queue.empty()) { |
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| 717 | |
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| 718 | Node v=bfs_queue.front(); |
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| 719 | bfs_queue.pop(); |
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| 720 | int l=level[v]+1; |
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| 721 | |
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| 722 | InEdgeIt e; |
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| 723 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 724 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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| 725 | Node w=g->tail(e); |
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| 726 | if ( level[w] == n && w != s ) { |
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| 727 | bfs_queue.push(w); |
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| 728 | Node z=level_list[l]; |
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| 729 | if ( g->valid(z) ) left.set(z,w); |
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| 730 | right.set(w,z); |
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| 731 | level_list[l]=w; |
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| 732 | level.set(w, l); |
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| 733 | } |
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| 734 | } |
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| 735 | |
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| 736 | OutEdgeIt f; |
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| 737 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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| 738 | if ( 0 >= (*flow)[f] ) continue; |
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| 739 | Node w=g->head(f); |
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| 740 | if ( level[w] == n && w != s ) { |
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| 741 | bfs_queue.push(w); |
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| 742 | Node z=level_list[l]; |
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| 743 | if ( g->valid(z) ) left.set(z,w); |
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| 744 | right.set(w,z); |
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| 745 | level_list[l]=w; |
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| 746 | level.set(w, l); |
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| 747 | } |
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| 748 | } |
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| 749 | } |
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| 750 | |
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| 751 | |
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| 752 | //the starting flow |
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| 753 | OutEdgeIt e; |
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| 754 | for(g->first(e,s); g->valid(e); g->next(e)) |
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| 755 | { |
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| 756 | Num rem=(*capacity)[e]-(*flow)[e]; |
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| 757 | if ( rem <= 0 ) continue; |
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| 758 | Node w=g->head(e); |
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| 759 | if ( level[w] < n ) { |
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| 760 | if ( excess[w] <= 0 && w!=t ) |
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| 761 | { |
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| 762 | next.set(w,first[level[w]]); |
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| 763 | first[level[w]]=w; |
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| 764 | } |
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| 765 | flow->set(e, (*capacity)[e]); |
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| 766 | excess.set(w, excess[w]+rem); |
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| 767 | } |
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| 768 | } |
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| 769 | |
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| 770 | InEdgeIt f; |
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| 771 | for(g->first(f,s); g->valid(f); g->next(f)) |
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| 772 | { |
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| 773 | if ( (*flow)[f] <= 0 ) continue; |
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| 774 | Node w=g->tail(f); |
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| 775 | if ( level[w] < n ) { |
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| 776 | if ( excess[w] <= 0 && w!=t ) |
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| 777 | { |
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| 778 | next.set(w,first[level[w]]); |
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| 779 | first[level[w]]=w; |
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| 780 | } |
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| 781 | excess.set(w, excess[w]+(*flow)[f]); |
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| 782 | flow->set(f, 0); |
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| 783 | } |
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| 784 | } |
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| 785 | break; |
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| 786 | } //case PRE_FLOW |
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| 787 | } |
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| 788 | } //preflowPreproc |
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| 789 | |
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| 790 | |
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| 791 | |
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| 792 | void relabel(Node w, int newlevel, NNMap& next, VecFirst& first, |
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| 793 | VecNode& level_list, NNMap& left, |
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| 794 | NNMap& right, int& b, int& k, bool what_heur ) |
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| 795 | { |
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| 796 | |
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| 797 | Num lev=level[w]; |
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| 798 | |
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| 799 | Node right_n=right[w]; |
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| 800 | Node left_n=left[w]; |
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| 801 | |
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| 802 | //unlacing starts |
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| 803 | if ( g->valid(right_n) ) { |
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| 804 | if ( g->valid(left_n) ) { |
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| 805 | right.set(left_n, right_n); |
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| 806 | left.set(right_n, left_n); |
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| 807 | } else { |
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| 808 | level_list[lev]=right_n; |
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| 809 | left.set(right_n, INVALID); |
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| 810 | } |
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| 811 | } else { |
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| 812 | if ( g->valid(left_n) ) { |
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| 813 | right.set(left_n, INVALID); |
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| 814 | } else { |
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| 815 | level_list[lev]=INVALID; |
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| 816 | } |
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| 817 | } |
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| 818 | //unlacing ends |
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| 819 | |
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| 820 | if ( !g->valid(level_list[lev]) ) { |
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| 821 | |
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| 822 | //gapping starts |
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| 823 | for (int i=lev; i!=k ; ) { |
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| 824 | Node v=level_list[++i]; |
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| 825 | while ( g->valid(v) ) { |
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| 826 | level.set(v,n); |
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| 827 | v=right[v]; |
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| 828 | } |
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| 829 | level_list[i]=INVALID; |
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| 830 | if ( !what_heur ) first[i]=INVALID; |
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| 831 | } |
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| 832 | |
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| 833 | level.set(w,n); |
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| 834 | b=lev-1; |
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| 835 | k=b; |
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| 836 | //gapping ends |
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| 837 | |
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| 838 | } else { |
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| 839 | |
---|
| 840 | if ( newlevel == n ) level.set(w,n); |
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| 841 | else { |
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| 842 | level.set(w,++newlevel); |
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| 843 | next.set(w,first[newlevel]); |
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| 844 | first[newlevel]=w; |
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| 845 | if ( what_heur ) b=newlevel; |
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| 846 | if ( k < newlevel ) ++k; //now k=newlevel |
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| 847 | Node z=level_list[newlevel]; |
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| 848 | if ( g->valid(z) ) left.set(z,w); |
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| 849 | right.set(w,z); |
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| 850 | left.set(w,INVALID); |
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| 851 | level_list[newlevel]=w; |
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| 852 | } |
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| 853 | } |
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| 854 | } //relabel |
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| 855 | }; //class MaxFlow |
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| 856 | } //namespace hugo |
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| 857 | |
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| 858 | #endif //HUGO_MAX_FLOW_H |
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| 859 | |
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| 860 | |
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| 861 | |
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| 862 | |
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