[478] | 1 | // -*- C++ -*- |
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[480] | 2 | #ifndef HUGO_MAX_FLOW_H |
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| 3 | #define HUGO_MAX_FLOW_H |
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[478] | 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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[557] | 9 | #include <hugo/graph_wrapper.h> |
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[602] | 10 | #include <bfs_dfs.h> |
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[555] | 11 | #include <hugo/invalid.h> |
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| 12 | #include <hugo/maps.h> |
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[640] | 13 | #include <hugo/for_each_macros.h> |
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[478] | 14 | |
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[488] | 15 | /// \file |
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[631] | 16 | /// \brief Maximum flow algorithms. |
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[615] | 17 | /// \ingroup galgs |
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[478] | 18 | |
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| 19 | namespace hugo { |
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| 20 | |
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[631] | 21 | /// \addtogroup galgs |
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| 22 | /// @{ |
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| 23 | ///Maximum flow algorithms class. |
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[488] | 24 | |
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[631] | 25 | ///This class provides various algorithms for finding a flow of |
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| 26 | ///maximum value in a directed graph. The \e source node, the \e |
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| 27 | ///target node, the \e capacity of the edges and the \e starting \e |
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[647] | 28 | ///flow value of the edges should be passed to the algorithm through the |
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[631] | 29 | ///constructor. It is possible to change these quantities using the |
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| 30 | ///functions \ref resetSource, \ref resetTarget, \ref resetCap and |
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| 31 | ///\ref resetFlow. Before any subsequent runs of any algorithm of |
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[647] | 32 | ///the class \ref resetFlow should be called. |
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| 33 | |
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| 34 | ///After running an algorithm of the class, the actual flow value |
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| 35 | ///can be obtained by calling \ref flowValue(). The minimum |
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[631] | 36 | ///value cut can be written into a \c node map of \c bools by |
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| 37 | ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes |
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| 38 | ///the inclusionwise minimum and maximum of the minimum value |
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| 39 | ///cuts, resp.) |
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[632] | 40 | ///\param Graph The directed graph type the algorithm runs on. |
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[631] | 41 | ///\param Num The number type of the capacities and the flow values. |
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[647] | 42 | ///\param CapMap The capacity map type. |
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| 43 | ///\param FlowMap The flow map type. |
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[631] | 44 | ///\author Marton Makai, Jacint Szabo |
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[615] | 45 | template <typename Graph, typename Num, |
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| 46 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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[478] | 47 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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| 48 | class MaxFlow { |
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[615] | 49 | protected: |
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[478] | 50 | typedef typename Graph::Node Node; |
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| 51 | typedef typename Graph::NodeIt NodeIt; |
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[631] | 52 | typedef typename Graph::EdgeIt EdgeIt; |
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[478] | 53 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 54 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 55 | |
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| 56 | typedef typename std::vector<std::stack<Node> > VecStack; |
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| 57 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 58 | typedef typename std::vector<Node> VecNode; |
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| 59 | |
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| 60 | const Graph* g; |
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| 61 | Node s; |
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| 62 | Node t; |
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[615] | 63 | const CapMap* capacity; |
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[478] | 64 | FlowMap* flow; |
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| 65 | int n; //the number of nodes of G |
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[650] | 66 | // typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 67 | typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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[478] | 68 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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| 69 | typedef typename ResGW::Edge ResGWEdge; |
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| 70 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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| 71 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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[631] | 72 | |
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| 73 | |
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| 74 | //level works as a bool map in augmenting path algorithms and is |
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| 75 | //used by bfs for storing reached information. In preflow, it |
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| 76 | //shows the levels of nodes. |
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[478] | 77 | ReachedMap level; |
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[631] | 78 | |
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| 79 | //excess is needed only in preflow |
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[615] | 80 | typename Graph::template NodeMap<Num> excess; |
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[631] | 81 | |
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| 82 | //fixme |
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| 83 | // protected: |
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[602] | 84 | // MaxFlow() { } |
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[615] | 85 | // void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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| 86 | // FlowMap& _flow) |
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[602] | 87 | // { |
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[615] | 88 | // g=&_G; |
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| 89 | // s=_s; |
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| 90 | // t=_t; |
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[602] | 91 | // capacity=&_capacity; |
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| 92 | // flow=&_flow; |
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| 93 | // n=_G.nodeNum; |
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[615] | 94 | // level.set (_G); //kellene vmi ilyesmi fv |
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[602] | 95 | // excess(_G,0); //itt is |
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| 96 | // } |
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[478] | 97 | |
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[615] | 98 | // constants used for heuristics |
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| 99 | static const int H0=20; |
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| 100 | static const int H1=1; |
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| 101 | |
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[478] | 102 | public: |
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[615] | 103 | |
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[631] | 104 | ///Indicates the property of the starting flow. |
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| 105 | |
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| 106 | ///Indicates the property of the starting flow. The meanings are as follows: |
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| 107 | ///- \c ZERO_FLOW: constant zero flow |
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| 108 | ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to |
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| 109 | ///the sum of the out-flows in every node except the \e source and |
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| 110 | ///the \e target. |
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| 111 | ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at |
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| 112 | ///least the sum of the out-flows in every node except the \e source. |
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| 113 | ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be |
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| 114 | ///set to the constant zero flow in the beginning of the algorithm in this case. |
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[647] | 115 | enum FlowEnum{ |
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[615] | 116 | ZERO_FLOW, |
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| 117 | GEN_FLOW, |
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| 118 | PRE_FLOW, |
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| 119 | NO_FLOW |
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[478] | 120 | }; |
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| 121 | |
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[647] | 122 | enum StatusEnum { |
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| 123 | AFTER_NOTHING, |
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| 124 | AFTER_AUGMENTING, |
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| 125 | AFTER_PRE_FLOW_PHASE_1, |
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| 126 | AFTER_PRE_FLOW_PHASE_2 |
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| 127 | }; |
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| 128 | |
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| 129 | /// Don not needle this flag only if necessary. |
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| 130 | StatusEnum status; |
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| 131 | int number_of_augmentations; |
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| 132 | |
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| 133 | |
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| 134 | template<typename IntMap> |
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| 135 | class TrickyReachedMap { |
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| 136 | protected: |
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| 137 | IntMap* map; |
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| 138 | int* number_of_augmentations; |
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| 139 | public: |
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| 140 | TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : |
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| 141 | map(&_map), number_of_augmentations(&_number_of_augmentations) { } |
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| 142 | void set(const Node& n, bool b) { |
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[650] | 143 | if (b) |
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| 144 | map->set(n, *number_of_augmentations); |
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| 145 | else |
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| 146 | map->set(n, *number_of_augmentations-1); |
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[647] | 147 | } |
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| 148 | bool operator[](const Node& n) const { |
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| 149 | return (*map)[n]==*number_of_augmentations; |
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| 150 | } |
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| 151 | }; |
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| 152 | |
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[615] | 153 | MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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[478] | 154 | FlowMap& _flow) : |
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[615] | 155 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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[647] | 156 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), |
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| 157 | status(AFTER_NOTHING), number_of_augmentations(0) { } |
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[478] | 158 | |
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[631] | 159 | ///Runs a maximum flow algorithm. |
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| 160 | |
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| 161 | ///Runs a preflow algorithm, which is the fastest maximum flow |
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| 162 | ///algorithm up-to-date. The default for \c fe is ZERO_FLOW. |
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| 163 | ///\pre The starting flow must be |
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| 164 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 165 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 166 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 167 | /// - any map if \c fe is NO_FLOW. |
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[647] | 168 | void run(FlowEnum fe=ZERO_FLOW) { |
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[615] | 169 | preflow(fe); |
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[478] | 170 | } |
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[615] | 171 | |
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[647] | 172 | |
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[631] | 173 | ///Runs a preflow algorithm. |
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| 174 | |
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| 175 | ///Runs a preflow algorithm. The preflow algorithms provide the |
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| 176 | ///fastest way to compute a maximum flow in a directed graph. |
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| 177 | ///\pre The starting flow must be |
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| 178 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 179 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 180 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 181 | /// - any map if \c fe is NO_FLOW. |
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[647] | 182 | void preflow(FlowEnum fe) { |
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[631] | 183 | preflowPhase1(fe); |
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| 184 | preflowPhase2(); |
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[478] | 185 | } |
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[631] | 186 | // Heuristics: |
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| 187 | // 2 phase |
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| 188 | // gap |
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| 189 | // list 'level_list' on the nodes on level i implemented by hand |
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| 190 | // stack 'active' on the active nodes on level i |
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| 191 | // runs heuristic 'highest label' for H1*n relabels |
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| 192 | // runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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| 193 | // Parameters H0 and H1 are initialized to 20 and 1. |
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[478] | 194 | |
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[631] | 195 | ///Runs the first phase of the preflow algorithm. |
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[478] | 196 | |
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[631] | 197 | ///The preflow algorithm consists of two phases, this method runs the |
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| 198 | ///first phase. After the first phase the maximum flow value and a |
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| 199 | ///minimum value cut can already be computed, though a maximum flow |
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| 200 | ///is net yet obtained. So after calling this method \ref flowValue |
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| 201 | ///and \ref actMinCut gives proper results. |
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| 202 | ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not |
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| 203 | ///give minimum value cuts unless calling \ref preflowPhase2. |
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| 204 | ///\pre The starting flow must be |
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| 205 | /// - a constant zero flow if \c fe is \c ZERO_FLOW, |
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| 206 | /// - an arbitary flow if \c fe is \c GEN_FLOW, |
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| 207 | /// - an arbitary preflow if \c fe is \c PRE_FLOW, |
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| 208 | /// - any map if \c fe is NO_FLOW. |
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[647] | 209 | void preflowPhase1(FlowEnum fe); |
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[631] | 210 | |
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| 211 | ///Runs the second phase of the preflow algorithm. |
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| 212 | |
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| 213 | ///The preflow algorithm consists of two phases, this method runs |
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| 214 | ///the second phase. After calling \ref preflowPhase1 and then |
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| 215 | ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut, |
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| 216 | ///\ref minMinCut and \ref maxMinCut give proper results. |
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| 217 | ///\pre \ref preflowPhase1 must be called before. |
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| 218 | void preflowPhase2(); |
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[478] | 219 | |
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[615] | 220 | /// Starting from a flow, this method searches for an augmenting path |
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| 221 | /// according to the Edmonds-Karp algorithm |
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| 222 | /// and augments the flow on if any. |
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[487] | 223 | /// The return value shows if the augmentation was succesful. |
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[478] | 224 | bool augmentOnShortestPath(); |
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[647] | 225 | bool augmentOnShortestPath2(); |
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[478] | 226 | |
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[615] | 227 | /// Starting from a flow, this method searches for an augmenting blocking |
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| 228 | /// flow according to Dinits' algorithm and augments the flow on if any. |
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| 229 | /// The blocking flow is computed in a physically constructed |
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[485] | 230 | /// residual graph of type \c Mutablegraph. |
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[487] | 231 | /// The return value show sif the augmentation was succesful. |
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[478] | 232 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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| 233 | |
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[615] | 234 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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[485] | 235 | /// residual graph is not constructed physically. |
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[487] | 236 | /// The return value shows if the augmentation was succesful. |
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[478] | 237 | bool augmentOnBlockingFlow2(); |
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| 238 | |
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[631] | 239 | /// Returns the maximum value of a flow. |
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| 240 | |
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| 241 | /// Returns the maximum value of a flow, by counting the |
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| 242 | /// over-flow of the target node \ref t. |
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| 243 | /// It can be called already after running \ref preflowPhase1. |
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[647] | 244 | Num flowValue() const { |
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[478] | 245 | Num a=0; |
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[615] | 246 | FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e]; |
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| 247 | FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e]; |
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[478] | 248 | return a; |
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[631] | 249 | //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan |
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[478] | 250 | } |
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| 251 | |
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[631] | 252 | ///Returns a minimum value cut after calling \ref preflowPhase1. |
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| 253 | |
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| 254 | ///After the first phase of the preflow algorithm the maximum flow |
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| 255 | ///value and a minimum value cut can already be computed. This |
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| 256 | ///method can be called after running \ref preflowPhase1 for |
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| 257 | ///obtaining a minimum value cut. |
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| 258 | /// \warning Gives proper result only right after calling \ref |
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| 259 | /// preflowPhase1. |
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[615] | 260 | /// \todo We have to make some status variable which shows the |
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| 261 | /// actual state |
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| 262 | /// of the class. This enables us to determine which methods are valid |
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[485] | 263 | /// for MinCut computation |
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[478] | 264 | template<typename _CutMap> |
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[647] | 265 | void actMinCut(_CutMap& M) const { |
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[478] | 266 | NodeIt v; |
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[647] | 267 | switch (status) { |
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| 268 | case AFTER_PRE_FLOW_PHASE_1: |
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| 269 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 270 | if (level[v] < n) { |
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| 271 | M.set(v, false); |
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| 272 | } else { |
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| 273 | M.set(v, true); |
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| 274 | } |
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[485] | 275 | } |
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[647] | 276 | break; |
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| 277 | case AFTER_PRE_FLOW_PHASE_2: |
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| 278 | case AFTER_NOTHING: |
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| 279 | minMinCut(M); |
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| 280 | break; |
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| 281 | case AFTER_AUGMENTING: |
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| 282 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 283 | if (level[v]) { |
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| 284 | M.set(v, true); |
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| 285 | } else { |
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| 286 | M.set(v, false); |
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| 287 | } |
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| 288 | } |
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| 289 | break; |
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[478] | 290 | } |
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| 291 | } |
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| 292 | |
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[631] | 293 | ///Returns the inclusionwise minimum of the minimum value cuts. |
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| 294 | |
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| 295 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 296 | ///which is inclusionwise minimum. It is computed by processing |
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| 297 | ///a bfs from the source node \c s in the residual graph. |
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| 298 | ///\pre M should be a node map of bools initialized to false. |
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| 299 | ///\pre \c flow must be a maximum flow. |
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[478] | 300 | template<typename _CutMap> |
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[647] | 301 | void minMinCut(_CutMap& M) const { |
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[478] | 302 | std::queue<Node> queue; |
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[615] | 303 | |
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| 304 | M.set(s,true); |
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[478] | 305 | queue.push(s); |
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| 306 | |
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| 307 | while (!queue.empty()) { |
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| 308 | Node w=queue.front(); |
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| 309 | queue.pop(); |
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| 310 | |
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| 311 | OutEdgeIt e; |
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| 312 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 313 | Node v=g->head(e); |
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| 314 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 315 | queue.push(v); |
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| 316 | M.set(v, true); |
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| 317 | } |
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[615] | 318 | } |
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[478] | 319 | |
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| 320 | InEdgeIt f; |
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| 321 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 322 | Node v=g->tail(f); |
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| 323 | if (!M[v] && (*flow)[f] > 0 ) { |
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| 324 | queue.push(v); |
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| 325 | M.set(v, true); |
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| 326 | } |
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[615] | 327 | } |
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[478] | 328 | } |
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| 329 | } |
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| 330 | |
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[631] | 331 | ///Returns the inclusionwise maximum of the minimum value cuts. |
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[478] | 332 | |
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[631] | 333 | ///Sets \c M to the characteristic vector of the minimum value cut |
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| 334 | ///which is inclusionwise maximum. It is computed by processing a |
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| 335 | ///backward bfs from the target node \c t in the residual graph. |
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| 336 | ///\pre M should be a node map of bools initialized to false. |
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| 337 | ///\pre \c flow must be a maximum flow. |
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[478] | 338 | template<typename _CutMap> |
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[647] | 339 | void maxMinCut(_CutMap& M) const { |
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[478] | 340 | |
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| 341 | NodeIt v; |
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| 342 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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| 343 | M.set(v, true); |
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| 344 | } |
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| 345 | |
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| 346 | std::queue<Node> queue; |
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[615] | 347 | |
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| 348 | M.set(t,false); |
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[478] | 349 | queue.push(t); |
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| 350 | |
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| 351 | while (!queue.empty()) { |
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| 352 | Node w=queue.front(); |
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| 353 | queue.pop(); |
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| 354 | |
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| 355 | InEdgeIt e; |
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| 356 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 357 | Node v=g->tail(e); |
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| 358 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 359 | queue.push(v); |
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| 360 | M.set(v, false); |
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| 361 | } |
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| 362 | } |
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[615] | 363 | |
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[478] | 364 | OutEdgeIt f; |
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| 365 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 366 | Node v=g->head(f); |
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| 367 | if (M[v] && (*flow)[f] > 0 ) { |
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| 368 | queue.push(v); |
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| 369 | M.set(v, false); |
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| 370 | } |
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| 371 | } |
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| 372 | } |
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| 373 | } |
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| 374 | |
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[631] | 375 | ///Returns a minimum value cut. |
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[478] | 376 | |
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[631] | 377 | ///Sets \c M to the characteristic vector of a minimum value cut. |
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| 378 | ///\pre M should be a node map of bools initialized to false. |
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| 379 | ///\pre \c flow must be a maximum flow. |
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[478] | 380 | template<typename CutMap> |
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[647] | 381 | void minCut(CutMap& M) const { minMinCut(M); } |
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[478] | 382 | |
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[631] | 383 | ///Resets the source node to \c _s. |
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| 384 | |
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| 385 | ///Resets the source node to \c _s. |
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| 386 | /// |
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[647] | 387 | void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; } |
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[631] | 388 | |
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| 389 | ///Resets the target node to \c _t. |
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| 390 | |
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| 391 | ///Resets the target node to \c _t. |
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[487] | 392 | /// |
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[647] | 393 | void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; } |
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[615] | 394 | |
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[631] | 395 | /// Resets the edge map of the capacities to _cap. |
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| 396 | |
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| 397 | /// Resets the edge map of the capacities to _cap. |
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| 398 | /// |
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[647] | 399 | void resetCap(const CapMap& _cap) { capacity=&_cap; status=AFTER_NOTHING; } |
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[615] | 400 | |
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[631] | 401 | /// Resets the edge map of the flows to _flow. |
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| 402 | |
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| 403 | /// Resets the edge map of the flows to _flow. |
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| 404 | /// |
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[647] | 405 | void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; } |
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[478] | 406 | |
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| 407 | |
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| 408 | private: |
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| 409 | |
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| 410 | int push(Node w, VecStack& active) { |
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[615] | 411 | |
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[478] | 412 | int lev=level[w]; |
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| 413 | Num exc=excess[w]; |
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| 414 | int newlevel=n; //bound on the next level of w |
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[615] | 415 | |
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[478] | 416 | OutEdgeIt e; |
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| 417 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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[615] | 418 | |
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| 419 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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| 420 | Node v=g->head(e); |
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| 421 | |
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[478] | 422 | if( lev > level[v] ) { //Push is allowed now |
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[615] | 423 | |
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[478] | 424 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 425 | int lev_v=level[v]; |
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| 426 | active[lev_v].push(v); |
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| 427 | } |
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[615] | 428 | |
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[478] | 429 | Num cap=(*capacity)[e]; |
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| 430 | Num flo=(*flow)[e]; |
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| 431 | Num remcap=cap-flo; |
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[615] | 432 | |
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[478] | 433 | if ( remcap >= exc ) { //A nonsaturating push. |
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[615] | 434 | |
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[478] | 435 | flow->set(e, flo+exc); |
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| 436 | excess.set(v, excess[v]+exc); |
---|
| 437 | exc=0; |
---|
[615] | 438 | break; |
---|
| 439 | |
---|
[478] | 440 | } else { //A saturating push. |
---|
| 441 | flow->set(e, cap); |
---|
| 442 | excess.set(v, excess[v]+remcap); |
---|
| 443 | exc-=remcap; |
---|
| 444 | } |
---|
| 445 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
[615] | 446 | } //for out edges wv |
---|
| 447 | |
---|
| 448 | if ( exc > 0 ) { |
---|
[478] | 449 | InEdgeIt e; |
---|
| 450 | for(g->first(e,w); g->valid(e); g->next(e)) { |
---|
[615] | 451 | |
---|
| 452 | if( (*flow)[e] <= 0 ) continue; |
---|
| 453 | Node v=g->tail(e); |
---|
| 454 | |
---|
[478] | 455 | if( lev > level[v] ) { //Push is allowed now |
---|
[615] | 456 | |
---|
[478] | 457 | if ( excess[v]<=0 && v!=t && v!=s ) { |
---|
| 458 | int lev_v=level[v]; |
---|
| 459 | active[lev_v].push(v); |
---|
| 460 | } |
---|
[615] | 461 | |
---|
[478] | 462 | Num flo=(*flow)[e]; |
---|
[615] | 463 | |
---|
[478] | 464 | if ( flo >= exc ) { //A nonsaturating push. |
---|
[615] | 465 | |
---|
[478] | 466 | flow->set(e, flo-exc); |
---|
| 467 | excess.set(v, excess[v]+exc); |
---|
| 468 | exc=0; |
---|
[615] | 469 | break; |
---|
[478] | 470 | } else { //A saturating push. |
---|
[615] | 471 | |
---|
[478] | 472 | excess.set(v, excess[v]+flo); |
---|
| 473 | exc-=flo; |
---|
| 474 | flow->set(e,0); |
---|
[615] | 475 | } |
---|
[478] | 476 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
| 477 | } //for in edges vw |
---|
[615] | 478 | |
---|
[478] | 479 | } // if w still has excess after the out edge for cycle |
---|
[615] | 480 | |
---|
[478] | 481 | excess.set(w, exc); |
---|
[615] | 482 | |
---|
[478] | 483 | return newlevel; |
---|
[485] | 484 | } |
---|
[478] | 485 | |
---|
| 486 | |
---|
[647] | 487 | void preflowPreproc(FlowEnum fe, VecStack& active, |
---|
[615] | 488 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
[602] | 489 | { |
---|
[615] | 490 | std::queue<Node> bfs_queue; |
---|
[478] | 491 | |
---|
[615] | 492 | switch (fe) { |
---|
[631] | 493 | case NO_FLOW: //flow is already set to const zero in this case |
---|
[615] | 494 | case ZERO_FLOW: |
---|
[602] | 495 | { |
---|
| 496 | //Reverse_bfs from t, to find the starting level. |
---|
| 497 | level.set(t,0); |
---|
| 498 | bfs_queue.push(t); |
---|
[615] | 499 | |
---|
[602] | 500 | while (!bfs_queue.empty()) { |
---|
[615] | 501 | |
---|
| 502 | Node v=bfs_queue.front(); |
---|
[602] | 503 | bfs_queue.pop(); |
---|
| 504 | int l=level[v]+1; |
---|
[615] | 505 | |
---|
[602] | 506 | InEdgeIt e; |
---|
| 507 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 508 | Node w=g->tail(e); |
---|
| 509 | if ( level[w] == n && w != s ) { |
---|
| 510 | bfs_queue.push(w); |
---|
| 511 | Node first=level_list[l]; |
---|
| 512 | if ( g->valid(first) ) left.set(first,w); |
---|
| 513 | right.set(w,first); |
---|
| 514 | level_list[l]=w; |
---|
| 515 | level.set(w, l); |
---|
| 516 | } |
---|
| 517 | } |
---|
| 518 | } |
---|
[615] | 519 | |
---|
[602] | 520 | //the starting flow |
---|
| 521 | OutEdgeIt e; |
---|
[615] | 522 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
[602] | 523 | { |
---|
| 524 | Num c=(*capacity)[e]; |
---|
| 525 | if ( c <= 0 ) continue; |
---|
| 526 | Node w=g->head(e); |
---|
[615] | 527 | if ( level[w] < n ) { |
---|
[602] | 528 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
[615] | 529 | flow->set(e, c); |
---|
[602] | 530 | excess.set(w, excess[w]+c); |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | break; |
---|
| 534 | } |
---|
[615] | 535 | |
---|
[602] | 536 | case GEN_FLOW: |
---|
[615] | 537 | case PRE_FLOW: |
---|
[602] | 538 | { |
---|
[615] | 539 | //Reverse_bfs from t in the residual graph, |
---|
[602] | 540 | //to find the starting level. |
---|
| 541 | level.set(t,0); |
---|
| 542 | bfs_queue.push(t); |
---|
[615] | 543 | |
---|
[602] | 544 | while (!bfs_queue.empty()) { |
---|
[615] | 545 | |
---|
| 546 | Node v=bfs_queue.front(); |
---|
[602] | 547 | bfs_queue.pop(); |
---|
| 548 | int l=level[v]+1; |
---|
[615] | 549 | |
---|
[602] | 550 | InEdgeIt e; |
---|
| 551 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 552 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 553 | Node w=g->tail(e); |
---|
| 554 | if ( level[w] == n && w != s ) { |
---|
| 555 | bfs_queue.push(w); |
---|
| 556 | Node first=level_list[l]; |
---|
| 557 | if ( g->valid(first) ) left.set(first,w); |
---|
| 558 | right.set(w,first); |
---|
| 559 | level_list[l]=w; |
---|
| 560 | level.set(w, l); |
---|
| 561 | } |
---|
| 562 | } |
---|
[615] | 563 | |
---|
[602] | 564 | OutEdgeIt f; |
---|
| 565 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 566 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 567 | Node w=g->head(f); |
---|
| 568 | if ( level[w] == n && w != s ) { |
---|
| 569 | bfs_queue.push(w); |
---|
| 570 | Node first=level_list[l]; |
---|
| 571 | if ( g->valid(first) ) left.set(first,w); |
---|
| 572 | right.set(w,first); |
---|
| 573 | level_list[l]=w; |
---|
| 574 | level.set(w, l); |
---|
| 575 | } |
---|
| 576 | } |
---|
| 577 | } |
---|
[615] | 578 | |
---|
| 579 | |
---|
[602] | 580 | //the starting flow |
---|
| 581 | OutEdgeIt e; |
---|
[615] | 582 | for(g->first(e,s); g->valid(e); g->next(e)) |
---|
[602] | 583 | { |
---|
| 584 | Num rem=(*capacity)[e]-(*flow)[e]; |
---|
| 585 | if ( rem <= 0 ) continue; |
---|
| 586 | Node w=g->head(e); |
---|
[615] | 587 | if ( level[w] < n ) { |
---|
[602] | 588 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
[615] | 589 | flow->set(e, (*capacity)[e]); |
---|
[602] | 590 | excess.set(w, excess[w]+rem); |
---|
| 591 | } |
---|
| 592 | } |
---|
[615] | 593 | |
---|
[602] | 594 | InEdgeIt f; |
---|
[615] | 595 | for(g->first(f,s); g->valid(f); g->next(f)) |
---|
[602] | 596 | { |
---|
| 597 | if ( (*flow)[f] <= 0 ) continue; |
---|
| 598 | Node w=g->tail(f); |
---|
[615] | 599 | if ( level[w] < n ) { |
---|
[602] | 600 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
---|
| 601 | excess.set(w, excess[w]+(*flow)[f]); |
---|
[615] | 602 | flow->set(f, 0); |
---|
[602] | 603 | } |
---|
[615] | 604 | } |
---|
[602] | 605 | break; |
---|
[615] | 606 | } //case PRE_FLOW |
---|
[602] | 607 | } |
---|
| 608 | } //preflowPreproc |
---|
[478] | 609 | |
---|
| 610 | |
---|
| 611 | |
---|
[615] | 612 | void relabel(Node w, int newlevel, VecStack& active, |
---|
| 613 | VecNode& level_list, NNMap& left, |
---|
| 614 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
[478] | 615 | { |
---|
| 616 | |
---|
[615] | 617 | Num lev=level[w]; |
---|
| 618 | |
---|
[478] | 619 | Node right_n=right[w]; |
---|
| 620 | Node left_n=left[w]; |
---|
[615] | 621 | |
---|
[478] | 622 | //unlacing starts |
---|
| 623 | if ( g->valid(right_n) ) { |
---|
| 624 | if ( g->valid(left_n) ) { |
---|
| 625 | right.set(left_n, right_n); |
---|
| 626 | left.set(right_n, left_n); |
---|
| 627 | } else { |
---|
[615] | 628 | level_list[lev]=right_n; |
---|
[478] | 629 | left.set(right_n, INVALID); |
---|
[615] | 630 | } |
---|
[478] | 631 | } else { |
---|
| 632 | if ( g->valid(left_n) ) { |
---|
| 633 | right.set(left_n, INVALID); |
---|
[615] | 634 | } else { |
---|
| 635 | level_list[lev]=INVALID; |
---|
| 636 | } |
---|
| 637 | } |
---|
[478] | 638 | //unlacing ends |
---|
[615] | 639 | |
---|
[478] | 640 | if ( !g->valid(level_list[lev]) ) { |
---|
[615] | 641 | |
---|
[478] | 642 | //gapping starts |
---|
| 643 | for (int i=lev; i!=k ; ) { |
---|
| 644 | Node v=level_list[++i]; |
---|
| 645 | while ( g->valid(v) ) { |
---|
| 646 | level.set(v,n); |
---|
| 647 | v=right[v]; |
---|
| 648 | } |
---|
| 649 | level_list[i]=INVALID; |
---|
| 650 | if ( !what_heur ) { |
---|
| 651 | while ( !active[i].empty() ) { |
---|
| 652 | active[i].pop(); //FIXME: ezt szebben kene |
---|
| 653 | } |
---|
[615] | 654 | } |
---|
[478] | 655 | } |
---|
[615] | 656 | |
---|
[478] | 657 | level.set(w,n); |
---|
| 658 | b=lev-1; |
---|
| 659 | k=b; |
---|
| 660 | //gapping ends |
---|
[615] | 661 | |
---|
[478] | 662 | } else { |
---|
[615] | 663 | |
---|
| 664 | if ( newlevel == n ) level.set(w,n); |
---|
[478] | 665 | else { |
---|
| 666 | level.set(w,++newlevel); |
---|
| 667 | active[newlevel].push(w); |
---|
| 668 | if ( what_heur ) b=newlevel; |
---|
| 669 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 670 | Node first=level_list[newlevel]; |
---|
| 671 | if ( g->valid(first) ) left.set(first,w); |
---|
| 672 | right.set(w,first); |
---|
| 673 | left.set(w,INVALID); |
---|
| 674 | level_list[newlevel]=w; |
---|
| 675 | } |
---|
| 676 | } |
---|
[615] | 677 | |
---|
[478] | 678 | } //relabel |
---|
| 679 | |
---|
| 680 | |
---|
[615] | 681 | template<typename MapGraphWrapper> |
---|
[478] | 682 | class DistanceMap { |
---|
| 683 | protected: |
---|
| 684 | const MapGraphWrapper* g; |
---|
[615] | 685 | typename MapGraphWrapper::template NodeMap<int> dist; |
---|
[478] | 686 | public: |
---|
| 687 | DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
---|
[615] | 688 | void set(const typename MapGraphWrapper::Node& n, int a) { |
---|
| 689 | dist.set(n, a); |
---|
[478] | 690 | } |
---|
[647] | 691 | int operator[](const typename MapGraphWrapper::Node& n) const { |
---|
| 692 | return dist[n]; |
---|
| 693 | } |
---|
[615] | 694 | // int get(const typename MapGraphWrapper::Node& n) const { |
---|
[485] | 695 | // return dist[n]; } |
---|
[615] | 696 | // bool get(const typename MapGraphWrapper::Edge& e) const { |
---|
[485] | 697 | // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
---|
[615] | 698 | bool operator[](const typename MapGraphWrapper::Edge& e) const { |
---|
| 699 | return (dist[g->tail(e)]<dist[g->head(e)]); |
---|
[478] | 700 | } |
---|
| 701 | }; |
---|
[615] | 702 | |
---|
[478] | 703 | }; |
---|
| 704 | |
---|
| 705 | |
---|
| 706 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[647] | 707 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1(FlowEnum fe) |
---|
[478] | 708 | { |
---|
[615] | 709 | |
---|
| 710 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
[485] | 711 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
| 712 | int heur=heur1; //starting time interval (#of relabels) |
---|
| 713 | int numrelabel=0; |
---|
[615] | 714 | |
---|
| 715 | bool what_heur=1; |
---|
[485] | 716 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
[478] | 717 | |
---|
[615] | 718 | bool end=false; |
---|
| 719 | //Needed for 'bound decrease', true means no active nodes are above bound |
---|
| 720 | //b. |
---|
[478] | 721 | |
---|
[485] | 722 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 723 | int b=k; //bound on the highest level under n of an active node |
---|
[615] | 724 | |
---|
[485] | 725 | VecStack active(n); |
---|
[615] | 726 | |
---|
[485] | 727 | NNMap left(*g, INVALID); |
---|
| 728 | NNMap right(*g, INVALID); |
---|
| 729 | VecNode level_list(n,INVALID); |
---|
| 730 | //List of the nodes in level i<n, set to n. |
---|
[478] | 731 | |
---|
[485] | 732 | NodeIt v; |
---|
| 733 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
---|
| 734 | //setting each node to level n |
---|
[615] | 735 | |
---|
[631] | 736 | if ( fe == NO_FLOW ) { |
---|
| 737 | EdgeIt e; |
---|
| 738 | for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0); |
---|
| 739 | } |
---|
| 740 | |
---|
| 741 | switch (fe) { //computing the excess |
---|
[615] | 742 | case PRE_FLOW: |
---|
[485] | 743 | { |
---|
| 744 | NodeIt v; |
---|
| 745 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
[478] | 746 | Num exc=0; |
---|
[615] | 747 | |
---|
[478] | 748 | InEdgeIt e; |
---|
[485] | 749 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
[478] | 750 | OutEdgeIt f; |
---|
[485] | 751 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
[615] | 752 | |
---|
| 753 | excess.set(v,exc); |
---|
| 754 | |
---|
[485] | 755 | //putting the active nodes into the stack |
---|
| 756 | int lev=level[v]; |
---|
| 757 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
---|
[478] | 758 | } |
---|
| 759 | break; |
---|
| 760 | } |
---|
[485] | 761 | case GEN_FLOW: |
---|
| 762 | { |
---|
[631] | 763 | NodeIt v; |
---|
| 764 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 765 | |
---|
[485] | 766 | Num exc=0; |
---|
| 767 | InEdgeIt e; |
---|
| 768 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
| 769 | OutEdgeIt f; |
---|
| 770 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
[615] | 771 | excess.set(t,exc); |
---|
[485] | 772 | break; |
---|
| 773 | } |
---|
[631] | 774 | case ZERO_FLOW: |
---|
| 775 | case NO_FLOW: |
---|
| 776 | { |
---|
| 777 | NodeIt v; |
---|
| 778 | for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0); |
---|
| 779 | break; |
---|
| 780 | } |
---|
[485] | 781 | } |
---|
[615] | 782 | |
---|
| 783 | preflowPreproc(fe, active, level_list, left, right); |
---|
| 784 | //End of preprocessing |
---|
| 785 | |
---|
| 786 | |
---|
[485] | 787 | //Push/relabel on the highest level active nodes. |
---|
| 788 | while ( true ) { |
---|
| 789 | if ( b == 0 ) { |
---|
| 790 | if ( !what_heur && !end && k > 0 ) { |
---|
| 791 | b=k; |
---|
| 792 | end=true; |
---|
| 793 | } else break; |
---|
| 794 | } |
---|
[615] | 795 | |
---|
| 796 | if ( active[b].empty() ) --b; |
---|
[485] | 797 | else { |
---|
[615] | 798 | end=false; |
---|
[485] | 799 | Node w=active[b].top(); |
---|
| 800 | active[b].pop(); |
---|
| 801 | int newlevel=push(w,active); |
---|
[615] | 802 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
---|
[485] | 803 | left, right, b, k, what_heur); |
---|
[615] | 804 | |
---|
| 805 | ++numrelabel; |
---|
[485] | 806 | if ( numrelabel >= heur ) { |
---|
| 807 | numrelabel=0; |
---|
| 808 | if ( what_heur ) { |
---|
| 809 | what_heur=0; |
---|
| 810 | heur=heur0; |
---|
| 811 | end=false; |
---|
| 812 | } else { |
---|
| 813 | what_heur=1; |
---|
| 814 | heur=heur1; |
---|
[615] | 815 | b=k; |
---|
[485] | 816 | } |
---|
[478] | 817 | } |
---|
[615] | 818 | } |
---|
| 819 | } |
---|
[647] | 820 | |
---|
| 821 | status=AFTER_PRE_FLOW_PHASE_1; |
---|
[485] | 822 | } |
---|
[478] | 823 | |
---|
| 824 | |
---|
| 825 | |
---|
| 826 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[631] | 827 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() |
---|
[478] | 828 | { |
---|
[615] | 829 | |
---|
[485] | 830 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 831 | int b=k; //bound on the highest level under n of an active node |
---|
[615] | 832 | |
---|
[485] | 833 | VecStack active(n); |
---|
| 834 | level.set(s,0); |
---|
| 835 | std::queue<Node> bfs_queue; |
---|
| 836 | bfs_queue.push(s); |
---|
[615] | 837 | |
---|
[485] | 838 | while (!bfs_queue.empty()) { |
---|
[615] | 839 | |
---|
| 840 | Node v=bfs_queue.front(); |
---|
[485] | 841 | bfs_queue.pop(); |
---|
| 842 | int l=level[v]+1; |
---|
[615] | 843 | |
---|
[485] | 844 | InEdgeIt e; |
---|
| 845 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 846 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 847 | Node u=g->tail(e); |
---|
[615] | 848 | if ( level[u] >= n ) { |
---|
[485] | 849 | bfs_queue.push(u); |
---|
| 850 | level.set(u, l); |
---|
| 851 | if ( excess[u] > 0 ) active[l].push(u); |
---|
[478] | 852 | } |
---|
| 853 | } |
---|
[615] | 854 | |
---|
[485] | 855 | OutEdgeIt f; |
---|
| 856 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 857 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 858 | Node u=g->head(f); |
---|
[615] | 859 | if ( level[u] >= n ) { |
---|
[485] | 860 | bfs_queue.push(u); |
---|
| 861 | level.set(u, l); |
---|
| 862 | if ( excess[u] > 0 ) active[l].push(u); |
---|
| 863 | } |
---|
| 864 | } |
---|
| 865 | } |
---|
| 866 | b=n-2; |
---|
[478] | 867 | |
---|
[485] | 868 | while ( true ) { |
---|
[615] | 869 | |
---|
[485] | 870 | if ( b == 0 ) break; |
---|
[478] | 871 | |
---|
[615] | 872 | if ( active[b].empty() ) --b; |
---|
[485] | 873 | else { |
---|
| 874 | Node w=active[b].top(); |
---|
| 875 | active[b].pop(); |
---|
[615] | 876 | int newlevel=push(w,active); |
---|
[478] | 877 | |
---|
[485] | 878 | //relabel |
---|
| 879 | if ( excess[w] > 0 ) { |
---|
| 880 | level.set(w,++newlevel); |
---|
| 881 | active[newlevel].push(w); |
---|
| 882 | b=newlevel; |
---|
| 883 | } |
---|
| 884 | } // if stack[b] is nonempty |
---|
| 885 | } // while(true) |
---|
[647] | 886 | |
---|
| 887 | status=AFTER_PRE_FLOW_PHASE_2; |
---|
[485] | 888 | } |
---|
[478] | 889 | |
---|
| 890 | |
---|
| 891 | |
---|
| 892 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 893 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
---|
[478] | 894 | { |
---|
[485] | 895 | ResGW res_graph(*g, *capacity, *flow); |
---|
| 896 | bool _augment=false; |
---|
[615] | 897 | |
---|
[485] | 898 | //ReachedMap level(res_graph); |
---|
| 899 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 900 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 901 | bfs.pushAndSetReached(s); |
---|
[615] | 902 | |
---|
| 903 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
[485] | 904 | pred.set(s, INVALID); |
---|
[615] | 905 | |
---|
[485] | 906 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
[615] | 907 | |
---|
[485] | 908 | //searching for augmenting path |
---|
[615] | 909 | while ( !bfs.finished() ) { |
---|
[485] | 910 | ResGWOutEdgeIt e=bfs; |
---|
| 911 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 912 | Node v=res_graph.tail(e); |
---|
| 913 | Node w=res_graph.head(e); |
---|
| 914 | pred.set(w, e); |
---|
| 915 | if (res_graph.valid(pred[v])) { |
---|
| 916 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
| 917 | } else { |
---|
[615] | 918 | free.set(w, res_graph.resCap(e)); |
---|
[478] | 919 | } |
---|
[485] | 920 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
| 921 | } |
---|
[615] | 922 | |
---|
[485] | 923 | ++bfs; |
---|
| 924 | } //end of searching augmenting path |
---|
[478] | 925 | |
---|
[485] | 926 | if (_augment) { |
---|
| 927 | Node n=t; |
---|
| 928 | Num augment_value=free[t]; |
---|
[615] | 929 | while (res_graph.valid(pred[n])) { |
---|
[485] | 930 | ResGWEdge e=pred[n]; |
---|
[615] | 931 | res_graph.augment(e, augment_value); |
---|
[485] | 932 | n=res_graph.tail(e); |
---|
[478] | 933 | } |
---|
[485] | 934 | } |
---|
[478] | 935 | |
---|
[647] | 936 | status=AFTER_AUGMENTING; |
---|
[485] | 937 | return _augment; |
---|
| 938 | } |
---|
[478] | 939 | |
---|
| 940 | |
---|
[647] | 941 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 942 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2() |
---|
| 943 | { |
---|
| 944 | ResGW res_graph(*g, *capacity, *flow); |
---|
| 945 | bool _augment=false; |
---|
[478] | 946 | |
---|
[647] | 947 | if (status!=AFTER_AUGMENTING) { |
---|
[650] | 948 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 3*n); |
---|
| 949 | number_of_augmentations=3*n+1; |
---|
[647] | 950 | } else { |
---|
| 951 | ++number_of_augmentations; |
---|
| 952 | } |
---|
| 953 | TrickyReachedMap<ReachedMap> |
---|
| 954 | tricky_reached_map(level, number_of_augmentations); |
---|
| 955 | //ReachedMap level(res_graph); |
---|
| 956 | // FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 957 | BfsIterator<ResGW, TrickyReachedMap<ReachedMap> > |
---|
| 958 | bfs(res_graph, tricky_reached_map); |
---|
| 959 | bfs.pushAndSetReached(s); |
---|
[478] | 960 | |
---|
[647] | 961 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
| 962 | pred.set(s, INVALID); |
---|
[478] | 963 | |
---|
[647] | 964 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
| 965 | |
---|
| 966 | //searching for augmenting path |
---|
| 967 | while ( !bfs.finished() ) { |
---|
| 968 | ResGWOutEdgeIt e=bfs; |
---|
| 969 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 970 | Node v=res_graph.tail(e); |
---|
| 971 | Node w=res_graph.head(e); |
---|
| 972 | pred.set(w, e); |
---|
| 973 | if (res_graph.valid(pred[v])) { |
---|
| 974 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
| 975 | } else { |
---|
| 976 | free.set(w, res_graph.resCap(e)); |
---|
| 977 | } |
---|
| 978 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
| 979 | } |
---|
| 980 | |
---|
| 981 | ++bfs; |
---|
| 982 | } //end of searching augmenting path |
---|
| 983 | |
---|
| 984 | if (_augment) { |
---|
| 985 | Node n=t; |
---|
| 986 | Num augment_value=free[t]; |
---|
| 987 | while (res_graph.valid(pred[n])) { |
---|
| 988 | ResGWEdge e=pred[n]; |
---|
| 989 | res_graph.augment(e, augment_value); |
---|
| 990 | n=res_graph.tail(e); |
---|
| 991 | } |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 | status=AFTER_AUGMENTING; |
---|
| 995 | return _augment; |
---|
| 996 | } |
---|
[478] | 997 | |
---|
| 998 | |
---|
| 999 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 1000 | template<typename MutableGraph> |
---|
| 1001 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
---|
| 1002 | { |
---|
[485] | 1003 | typedef MutableGraph MG; |
---|
| 1004 | bool _augment=false; |
---|
[478] | 1005 | |
---|
[485] | 1006 | ResGW res_graph(*g, *capacity, *flow); |
---|
[478] | 1007 | |
---|
[485] | 1008 | //bfs for distances on the residual graph |
---|
| 1009 | //ReachedMap level(res_graph); |
---|
| 1010 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 1011 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 1012 | bfs.pushAndSetReached(s); |
---|
[615] | 1013 | typename ResGW::template NodeMap<int> |
---|
[485] | 1014 | dist(res_graph); //filled up with 0's |
---|
[478] | 1015 | |
---|
[485] | 1016 | //F will contain the physical copy of the residual graph |
---|
| 1017 | //with the set of edges which are on shortest paths |
---|
| 1018 | MG F; |
---|
[615] | 1019 | typename ResGW::template NodeMap<typename MG::Node> |
---|
[485] | 1020 | res_graph_to_F(res_graph); |
---|
| 1021 | { |
---|
| 1022 | typename ResGW::NodeIt n; |
---|
| 1023 | for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
---|
| 1024 | res_graph_to_F.set(n, F.addNode()); |
---|
[478] | 1025 | } |
---|
[485] | 1026 | } |
---|
[478] | 1027 | |
---|
[485] | 1028 | typename MG::Node sF=res_graph_to_F[s]; |
---|
| 1029 | typename MG::Node tF=res_graph_to_F[t]; |
---|
| 1030 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
---|
| 1031 | typename MG::template EdgeMap<Num> residual_capacity(F); |
---|
[478] | 1032 | |
---|
[615] | 1033 | while ( !bfs.finished() ) { |
---|
[485] | 1034 | ResGWOutEdgeIt e=bfs; |
---|
| 1035 | if (res_graph.valid(e)) { |
---|
| 1036 | if (bfs.isBNodeNewlyReached()) { |
---|
| 1037 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
[615] | 1038 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
| 1039 | res_graph_to_F[res_graph.head(e)]); |
---|
[485] | 1040 | original_edge.update(); |
---|
| 1041 | original_edge.set(f, e); |
---|
| 1042 | residual_capacity.update(); |
---|
| 1043 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 1044 | } else { |
---|
| 1045 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
---|
[615] | 1046 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], |
---|
| 1047 | res_graph_to_F[res_graph.head(e)]); |
---|
[478] | 1048 | original_edge.update(); |
---|
| 1049 | original_edge.set(f, e); |
---|
| 1050 | residual_capacity.update(); |
---|
| 1051 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 1052 | } |
---|
| 1053 | } |
---|
[485] | 1054 | } |
---|
| 1055 | ++bfs; |
---|
| 1056 | } //computing distances from s in the residual graph |
---|
[478] | 1057 | |
---|
[485] | 1058 | bool __augment=true; |
---|
[478] | 1059 | |
---|
[485] | 1060 | while (__augment) { |
---|
| 1061 | __augment=false; |
---|
| 1062 | //computing blocking flow with dfs |
---|
| 1063 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
---|
| 1064 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
---|
| 1065 | pred.set(sF, INVALID); |
---|
| 1066 | //invalid iterators for sources |
---|
[478] | 1067 | |
---|
[485] | 1068 | typename MG::template NodeMap<Num> free(F); |
---|
[478] | 1069 | |
---|
[615] | 1070 | dfs.pushAndSetReached(sF); |
---|
[485] | 1071 | while (!dfs.finished()) { |
---|
| 1072 | ++dfs; |
---|
| 1073 | if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
---|
| 1074 | if (dfs.isBNodeNewlyReached()) { |
---|
| 1075 | typename MG::Node v=F.aNode(dfs); |
---|
| 1076 | typename MG::Node w=F.bNode(dfs); |
---|
| 1077 | pred.set(w, dfs); |
---|
| 1078 | if (F.valid(pred[v])) { |
---|
| 1079 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
---|
| 1080 | } else { |
---|
[615] | 1081 | free.set(w, residual_capacity[dfs]); |
---|
[485] | 1082 | } |
---|
[615] | 1083 | if (w==tF) { |
---|
| 1084 | __augment=true; |
---|
[485] | 1085 | _augment=true; |
---|
[615] | 1086 | break; |
---|
[485] | 1087 | } |
---|
[615] | 1088 | |
---|
[485] | 1089 | } else { |
---|
| 1090 | F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
---|
| 1091 | } |
---|
[615] | 1092 | } |
---|
[485] | 1093 | } |
---|
| 1094 | |
---|
| 1095 | if (__augment) { |
---|
| 1096 | typename MG::Node n=tF; |
---|
| 1097 | Num augment_value=free[tF]; |
---|
[615] | 1098 | while (F.valid(pred[n])) { |
---|
[485] | 1099 | typename MG::Edge e=pred[n]; |
---|
[615] | 1100 | res_graph.augment(original_edge[e], augment_value); |
---|
[485] | 1101 | n=F.tail(e); |
---|
[615] | 1102 | if (residual_capacity[e]==augment_value) |
---|
| 1103 | F.erase(e); |
---|
| 1104 | else |
---|
[485] | 1105 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
---|
[478] | 1106 | } |
---|
[485] | 1107 | } |
---|
[615] | 1108 | |
---|
[485] | 1109 | } |
---|
[615] | 1110 | |
---|
[647] | 1111 | status=AFTER_AUGMENTING; |
---|
[485] | 1112 | return _augment; |
---|
| 1113 | } |
---|
[478] | 1114 | |
---|
| 1115 | |
---|
| 1116 | |
---|
| 1117 | |
---|
| 1118 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
[615] | 1119 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
---|
[478] | 1120 | { |
---|
[485] | 1121 | bool _augment=false; |
---|
[478] | 1122 | |
---|
[485] | 1123 | ResGW res_graph(*g, *capacity, *flow); |
---|
[615] | 1124 | |
---|
[485] | 1125 | //ReachedMap level(res_graph); |
---|
| 1126 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 1127 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
[478] | 1128 | |
---|
[485] | 1129 | bfs.pushAndSetReached(s); |
---|
| 1130 | DistanceMap<ResGW> dist(res_graph); |
---|
[615] | 1131 | while ( !bfs.finished() ) { |
---|
[485] | 1132 | ResGWOutEdgeIt e=bfs; |
---|
| 1133 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 1134 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
| 1135 | } |
---|
| 1136 | ++bfs; |
---|
| 1137 | } //computing distances from s in the residual graph |
---|
[478] | 1138 | |
---|
| 1139 | //Subgraph containing the edges on some shortest paths |
---|
[485] | 1140 | ConstMap<typename ResGW::Node, bool> true_map(true); |
---|
[615] | 1141 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
---|
[485] | 1142 | DistanceMap<ResGW> > FilterResGW; |
---|
| 1143 | FilterResGW filter_res_graph(res_graph, true_map, dist); |
---|
[478] | 1144 | |
---|
[615] | 1145 | //Subgraph, which is able to delete edges which are already |
---|
[485] | 1146 | //met by the dfs |
---|
[615] | 1147 | typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
---|
[485] | 1148 | first_out_edges(filter_res_graph); |
---|
| 1149 | typename FilterResGW::NodeIt v; |
---|
[615] | 1150 | for(filter_res_graph.first(v); filter_res_graph.valid(v); |
---|
| 1151 | filter_res_graph.next(v)) |
---|
[478] | 1152 | { |
---|
| 1153 | typename FilterResGW::OutEdgeIt e; |
---|
| 1154 | filter_res_graph.first(e, v); |
---|
| 1155 | first_out_edges.set(v, e); |
---|
| 1156 | } |
---|
[485] | 1157 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
---|
| 1158 | template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
---|
| 1159 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
---|
[478] | 1160 | |
---|
[485] | 1161 | bool __augment=true; |
---|
[478] | 1162 | |
---|
[485] | 1163 | while (__augment) { |
---|
[478] | 1164 | |
---|
[485] | 1165 | __augment=false; |
---|
| 1166 | //computing blocking flow with dfs |
---|
[615] | 1167 | DfsIterator< ErasingResGW, |
---|
| 1168 | typename ErasingResGW::template NodeMap<bool> > |
---|
[485] | 1169 | dfs(erasing_res_graph); |
---|
| 1170 | typename ErasingResGW:: |
---|
[615] | 1171 | template NodeMap<typename ErasingResGW::OutEdgeIt> |
---|
| 1172 | pred(erasing_res_graph); |
---|
[485] | 1173 | pred.set(s, INVALID); |
---|
| 1174 | //invalid iterators for sources |
---|
[478] | 1175 | |
---|
[615] | 1176 | typename ErasingResGW::template NodeMap<Num> |
---|
[485] | 1177 | free1(erasing_res_graph); |
---|
[478] | 1178 | |
---|
[615] | 1179 | dfs.pushAndSetReached |
---|
| 1180 | ///\bug hugo 0.2 |
---|
| 1181 | (typename ErasingResGW::Node |
---|
| 1182 | (typename FilterResGW::Node |
---|
| 1183 | (typename ResGW::Node(s) |
---|
| 1184 | ) |
---|
| 1185 | ) |
---|
| 1186 | ); |
---|
[485] | 1187 | while (!dfs.finished()) { |
---|
| 1188 | ++dfs; |
---|
[615] | 1189 | if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs))) |
---|
| 1190 | { |
---|
[478] | 1191 | if (dfs.isBNodeNewlyReached()) { |
---|
[615] | 1192 | |
---|
[478] | 1193 | typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
---|
| 1194 | typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
---|
| 1195 | |
---|
| 1196 | pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
---|
| 1197 | if (erasing_res_graph.valid(pred[v])) { |
---|
[615] | 1198 | free1.set |
---|
| 1199 | (w, std::min(free1[v], res_graph.resCap |
---|
| 1200 | (typename ErasingResGW::OutEdgeIt(dfs)))); |
---|
[478] | 1201 | } else { |
---|
[615] | 1202 | free1.set |
---|
| 1203 | (w, res_graph.resCap |
---|
| 1204 | (typename ErasingResGW::OutEdgeIt(dfs))); |
---|
[478] | 1205 | } |
---|
[615] | 1206 | |
---|
| 1207 | if (w==t) { |
---|
| 1208 | __augment=true; |
---|
[478] | 1209 | _augment=true; |
---|
[615] | 1210 | break; |
---|
[478] | 1211 | } |
---|
| 1212 | } else { |
---|
| 1213 | erasing_res_graph.erase(dfs); |
---|
| 1214 | } |
---|
| 1215 | } |
---|
[615] | 1216 | } |
---|
[478] | 1217 | |
---|
[485] | 1218 | if (__augment) { |
---|
[615] | 1219 | typename ErasingResGW::Node |
---|
| 1220 | n=typename FilterResGW::Node(typename ResGW::Node(t)); |
---|
[485] | 1221 | // typename ResGW::NodeMap<Num> a(res_graph); |
---|
| 1222 | // typename ResGW::Node b; |
---|
| 1223 | // Num j=a[b]; |
---|
| 1224 | // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
---|
| 1225 | // typename FilterResGW::Node b1; |
---|
| 1226 | // Num j1=a1[b1]; |
---|
| 1227 | // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
---|
| 1228 | // typename ErasingResGW::Node b2; |
---|
| 1229 | // Num j2=a2[b2]; |
---|
| 1230 | Num augment_value=free1[n]; |
---|
[615] | 1231 | while (erasing_res_graph.valid(pred[n])) { |
---|
[485] | 1232 | typename ErasingResGW::OutEdgeIt e=pred[n]; |
---|
| 1233 | res_graph.augment(e, augment_value); |
---|
| 1234 | n=erasing_res_graph.tail(e); |
---|
| 1235 | if (res_graph.resCap(e)==0) |
---|
| 1236 | erasing_res_graph.erase(e); |
---|
[478] | 1237 | } |
---|
| 1238 | } |
---|
[615] | 1239 | |
---|
| 1240 | } //while (__augment) |
---|
| 1241 | |
---|
[647] | 1242 | status=AFTER_AUGMENTING; |
---|
[485] | 1243 | return _augment; |
---|
| 1244 | } |
---|
[478] | 1245 | |
---|
| 1246 | |
---|
| 1247 | } //namespace hugo |
---|
| 1248 | |
---|
[480] | 1249 | #endif //HUGO_MAX_FLOW_H |
---|
[478] | 1250 | |
---|
| 1251 | |
---|
| 1252 | |
---|
| 1253 | |
---|