[478] | 1 | // -*- C++ -*- |
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| 2 | |
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| 3 | /* |
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[485] | 4 | Heuristics: |
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| 5 | 2 phase |
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| 6 | gap |
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| 7 | list 'level_list' on the nodes on level i implemented by hand |
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| 8 | stack 'active' on the active nodes on level i |
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| 9 | runs heuristic 'highest label' for H1*n relabels |
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| 10 | runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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[478] | 11 | |
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[485] | 12 | Parameters H0 and H1 are initialized to 20 and 1. |
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[478] | 13 | |
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[485] | 14 | Constructors: |
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[478] | 15 | |
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[485] | 16 | Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if |
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| 17 | FlowMap is not constant zero, and should be true if it is |
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[478] | 18 | |
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[485] | 19 | Members: |
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[478] | 20 | |
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[485] | 21 | void run() |
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[478] | 22 | |
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[485] | 23 | Num flowValue() : returns the value of a maximum flow |
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[478] | 24 | |
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[485] | 25 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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| 26 | minimum min cut. M should be a map of bools initialized to false. ??Is it OK? |
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[478] | 27 | |
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[485] | 28 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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| 29 | maximum min cut. M should be a map of bools initialized to false. |
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[478] | 30 | |
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[485] | 31 | void minCut(CutMap& M) : sets M to the characteristic vector of |
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| 32 | a min cut. M should be a map of bools initialized to false. |
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[478] | 33 | |
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| 34 | */ |
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| 35 | |
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[480] | 36 | #ifndef HUGO_MAX_FLOW_H |
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| 37 | #define HUGO_MAX_FLOW_H |
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[478] | 38 | |
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| 39 | #define H0 20 |
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| 40 | #define H1 1 |
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| 41 | |
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| 42 | #include <vector> |
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| 43 | #include <queue> |
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| 44 | #include <stack> |
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| 45 | |
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| 46 | #include <graph_wrapper.h> |
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| 47 | #include <bfs_iterator.h> |
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| 48 | #include <invalid.h> |
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| 49 | #include <maps.h> |
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| 50 | #include <for_each_macros.h> |
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| 51 | |
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| 52 | |
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| 53 | namespace hugo { |
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| 54 | |
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[485] | 55 | ///\author Marton Makai, Jacint Szabo |
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[478] | 56 | template <typename Graph, typename Num, |
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| 57 | typename CapMap=typename Graph::template EdgeMap<Num>, |
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| 58 | typename FlowMap=typename Graph::template EdgeMap<Num> > |
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| 59 | class MaxFlow { |
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| 60 | |
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| 61 | typedef typename Graph::Node Node; |
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| 62 | typedef typename Graph::NodeIt NodeIt; |
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| 63 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 64 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 65 | |
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| 66 | typedef typename std::vector<std::stack<Node> > VecStack; |
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| 67 | typedef typename Graph::template NodeMap<Node> NNMap; |
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| 68 | typedef typename std::vector<Node> VecNode; |
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| 69 | |
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| 70 | const Graph* g; |
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| 71 | Node s; |
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| 72 | Node t; |
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| 73 | const CapMap* capacity; |
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| 74 | FlowMap* flow; |
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| 75 | int n; //the number of nodes of G |
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| 76 | typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW; |
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| 77 | typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt; |
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| 78 | typedef typename ResGW::Edge ResGWEdge; |
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| 79 | //typedef typename ResGW::template NodeMap<bool> ReachedMap; |
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| 80 | typedef typename Graph::template NodeMap<int> ReachedMap; |
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| 81 | ReachedMap level; |
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| 82 | //level works as a bool map in augmenting path algorithms |
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| 83 | //and is used by bfs for storing reached information. |
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| 84 | //In preflow, it shows levels of nodes. |
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| 85 | //typename Graph::template NodeMap<int> level; |
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| 86 | typename Graph::template NodeMap<Num> excess; |
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| 87 | |
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| 88 | public: |
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| 89 | |
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[487] | 90 | ///\todo Document this |
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[478] | 91 | enum flowEnum{ |
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| 92 | ZERO_FLOW=0, |
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| 93 | GEN_FLOW=1, |
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| 94 | PREFLOW=2 |
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| 95 | }; |
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| 96 | |
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| 97 | MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, |
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| 98 | FlowMap& _flow) : |
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| 99 | g(&_G), s(_s), t(_t), capacity(&_capacity), |
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| 100 | flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {} |
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| 101 | |
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[485] | 102 | /// A max flow algorithm is run. |
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| 103 | ///\pre the flow have to be 0 at the beginning. |
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[478] | 104 | void run() { |
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| 105 | preflow( ZERO_FLOW ); |
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| 106 | } |
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| 107 | |
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[487] | 108 | /// A preflow algorithm is run. |
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| 109 | ///\pre The initial edge-map have to be a |
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| 110 | /// zero flow if \c fe is \c ZERO_FLOW, |
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| 111 | /// a flow if \c fe is \c GEN_FLOW, |
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| 112 | /// and a pre-flow it is \c PREFLOW. |
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[478] | 113 | void preflow( flowEnum fe ) { |
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| 114 | preflowPhase0(fe); |
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| 115 | preflowPhase1(); |
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| 116 | } |
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| 117 | |
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[485] | 118 | /// Run the first phase of preflow, starting from a 0 flow, from a flow, |
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| 119 | /// or from a preflow, according to \c fe. |
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[478] | 120 | void preflowPhase0( flowEnum fe ); |
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| 121 | |
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[485] | 122 | /// Second phase of preflow. |
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[478] | 123 | void preflowPhase1(); |
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| 124 | |
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[485] | 125 | /// Starting from a flow, this method searches for an augmenting path |
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| 126 | /// according to the Edmonds-Karp algorithm |
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| 127 | /// and augments the flow on if any. |
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[487] | 128 | /// The return value shows if the augmentation was succesful. |
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[478] | 129 | bool augmentOnShortestPath(); |
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| 130 | |
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[485] | 131 | /// Starting from a flow, this method searches for an augmenting blockin |
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| 132 | /// flow according to Dinits' algorithm and augments the flow on if any. |
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| 133 | /// The blocking flow is computed in a physically constructed |
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| 134 | /// residual graph of type \c Mutablegraph. |
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[487] | 135 | /// The return value show sif the augmentation was succesful. |
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[478] | 136 | template<typename MutableGraph> bool augmentOnBlockingFlow(); |
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| 137 | |
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[485] | 138 | /// The same as \c augmentOnBlockingFlow<MutableGraph> but the |
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| 139 | /// residual graph is not constructed physically. |
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[487] | 140 | /// The return value shows if the augmentation was succesful. |
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[478] | 141 | bool augmentOnBlockingFlow2(); |
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| 142 | |
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| 143 | /// Returns the actual flow value. |
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| 144 | /// More precisely, it returns the negative excess of s, thus |
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| 145 | /// this works also for preflows. |
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| 146 | Num flowValue() { |
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| 147 | Num a=0; |
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| 148 | FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e]; |
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| 149 | FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e]; |
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| 150 | return a; |
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| 151 | } |
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| 152 | |
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[485] | 153 | /// Should be used between preflowPhase0 and preflowPhase1. |
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| 154 | ///\todo We have to make some status variable which shows the actual state |
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| 155 | /// of the class. This enables us to determine which methods are valid |
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| 156 | /// for MinCut computation |
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[478] | 157 | template<typename _CutMap> |
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| 158 | void actMinCut(_CutMap& M) { |
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| 159 | NodeIt v; |
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[485] | 160 | for(g->first(v); g->valid(v); g->next(v)) { |
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| 161 | if ( level[v] < n ) { |
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| 162 | M.set(v,false); |
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| 163 | } else { |
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| 164 | M.set(v,true); |
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| 165 | } |
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[478] | 166 | } |
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| 167 | } |
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| 168 | |
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[485] | 169 | /// The unique inclusionwise minimum cut is computed by |
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| 170 | /// processing a bfs from s in the residual graph. |
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| 171 | ///\pre flow have to be a max flow otherwise it will the whole node-set. |
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[478] | 172 | template<typename _CutMap> |
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| 173 | void minMinCut(_CutMap& M) { |
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| 174 | |
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| 175 | std::queue<Node> queue; |
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| 176 | |
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| 177 | M.set(s,true); |
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| 178 | queue.push(s); |
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| 179 | |
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| 180 | while (!queue.empty()) { |
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| 181 | Node w=queue.front(); |
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| 182 | queue.pop(); |
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| 183 | |
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| 184 | OutEdgeIt e; |
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| 185 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 186 | Node v=g->head(e); |
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| 187 | if (!M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 188 | queue.push(v); |
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| 189 | M.set(v, true); |
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| 190 | } |
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| 191 | } |
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| 192 | |
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| 193 | InEdgeIt f; |
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| 194 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 195 | Node v=g->tail(f); |
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| 196 | if (!M[v] && (*flow)[f] > 0 ) { |
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| 197 | queue.push(v); |
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| 198 | M.set(v, true); |
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| 199 | } |
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| 200 | } |
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| 201 | } |
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| 202 | } |
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| 203 | |
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| 204 | |
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[485] | 205 | /// The unique inclusionwise maximum cut is computed by |
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| 206 | /// processing a reverse bfs from t in the residual graph. |
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| 207 | ///\pre flow have to be a max flow otherwise it will be empty. |
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[478] | 208 | template<typename _CutMap> |
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| 209 | void maxMinCut(_CutMap& M) { |
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| 210 | |
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| 211 | NodeIt v; |
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| 212 | for(g->first(v) ; g->valid(v); g->next(v)) { |
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| 213 | M.set(v, true); |
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| 214 | } |
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| 215 | |
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| 216 | std::queue<Node> queue; |
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| 217 | |
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| 218 | M.set(t,false); |
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| 219 | queue.push(t); |
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| 220 | |
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| 221 | while (!queue.empty()) { |
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| 222 | Node w=queue.front(); |
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| 223 | queue.pop(); |
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| 224 | |
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| 225 | |
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| 226 | InEdgeIt e; |
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| 227 | for(g->first(e,w) ; g->valid(e); g->next(e)) { |
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| 228 | Node v=g->tail(e); |
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| 229 | if (M[v] && (*flow)[e] < (*capacity)[e] ) { |
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| 230 | queue.push(v); |
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| 231 | M.set(v, false); |
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| 232 | } |
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| 233 | } |
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| 234 | |
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| 235 | OutEdgeIt f; |
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| 236 | for(g->first(f,w) ; g->valid(f); g->next(f)) { |
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| 237 | Node v=g->head(f); |
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| 238 | if (M[v] && (*flow)[f] > 0 ) { |
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| 239 | queue.push(v); |
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| 240 | M.set(v, false); |
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| 241 | } |
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| 242 | } |
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| 243 | } |
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| 244 | } |
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| 245 | |
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| 246 | |
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[485] | 247 | /// A minimum cut is computed. |
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[478] | 248 | template<typename CutMap> |
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[485] | 249 | void minCut(CutMap& M) { minMinCut(M); } |
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[478] | 250 | |
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[485] | 251 | /// |
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[487] | 252 | void resetSource(Node _s) { s=_s; } |
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| 253 | /// |
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| 254 | void resetTarget(Node _t) { t=_t; } |
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[478] | 255 | |
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[485] | 256 | /// capacity-map is changed. |
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| 257 | void resetCap(const CapMap& _cap) { capacity=&_cap; } |
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[478] | 258 | |
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[485] | 259 | /// flow-map is changed. |
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| 260 | void resetFlow(FlowMap& _flow) { flow=&_flow; } |
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[478] | 261 | |
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| 262 | |
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| 263 | private: |
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| 264 | |
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| 265 | int push(Node w, VecStack& active) { |
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| 266 | |
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| 267 | int lev=level[w]; |
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| 268 | Num exc=excess[w]; |
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| 269 | int newlevel=n; //bound on the next level of w |
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| 270 | |
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| 271 | OutEdgeIt e; |
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| 272 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 273 | |
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| 274 | if ( (*flow)[e] >= (*capacity)[e] ) continue; |
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| 275 | Node v=g->head(e); |
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| 276 | |
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| 277 | if( lev > level[v] ) { //Push is allowed now |
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| 278 | |
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| 279 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 280 | int lev_v=level[v]; |
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| 281 | active[lev_v].push(v); |
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| 282 | } |
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| 283 | |
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| 284 | Num cap=(*capacity)[e]; |
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| 285 | Num flo=(*flow)[e]; |
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| 286 | Num remcap=cap-flo; |
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| 287 | |
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| 288 | if ( remcap >= exc ) { //A nonsaturating push. |
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| 289 | |
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| 290 | flow->set(e, flo+exc); |
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| 291 | excess.set(v, excess[v]+exc); |
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| 292 | exc=0; |
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| 293 | break; |
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| 294 | |
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| 295 | } else { //A saturating push. |
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| 296 | flow->set(e, cap); |
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| 297 | excess.set(v, excess[v]+remcap); |
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| 298 | exc-=remcap; |
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| 299 | } |
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| 300 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 301 | } //for out edges wv |
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| 302 | |
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| 303 | if ( exc > 0 ) { |
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| 304 | InEdgeIt e; |
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| 305 | for(g->first(e,w); g->valid(e); g->next(e)) { |
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| 306 | |
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| 307 | if( (*flow)[e] <= 0 ) continue; |
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| 308 | Node v=g->tail(e); |
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| 309 | |
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| 310 | if( lev > level[v] ) { //Push is allowed now |
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| 311 | |
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| 312 | if ( excess[v]<=0 && v!=t && v!=s ) { |
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| 313 | int lev_v=level[v]; |
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| 314 | active[lev_v].push(v); |
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| 315 | } |
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| 316 | |
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| 317 | Num flo=(*flow)[e]; |
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| 318 | |
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| 319 | if ( flo >= exc ) { //A nonsaturating push. |
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| 320 | |
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| 321 | flow->set(e, flo-exc); |
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| 322 | excess.set(v, excess[v]+exc); |
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| 323 | exc=0; |
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| 324 | break; |
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| 325 | } else { //A saturating push. |
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| 326 | |
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| 327 | excess.set(v, excess[v]+flo); |
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| 328 | exc-=flo; |
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| 329 | flow->set(e,0); |
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| 330 | } |
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| 331 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
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| 332 | } //for in edges vw |
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| 333 | |
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| 334 | } // if w still has excess after the out edge for cycle |
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| 335 | |
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| 336 | excess.set(w, exc); |
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| 337 | |
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| 338 | return newlevel; |
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[485] | 339 | } |
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[478] | 340 | |
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| 341 | |
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| 342 | void preflowPreproc ( flowEnum fe, VecStack& active, |
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| 343 | VecNode& level_list, NNMap& left, NNMap& right ) { |
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| 344 | |
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[485] | 345 | std::queue<Node> bfs_queue; |
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[478] | 346 | |
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[485] | 347 | switch ( fe ) { |
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| 348 | case ZERO_FLOW: |
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| 349 | { |
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| 350 | //Reverse_bfs from t, to find the starting level. |
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| 351 | level.set(t,0); |
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| 352 | bfs_queue.push(t); |
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[478] | 353 | |
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[485] | 354 | while (!bfs_queue.empty()) { |
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[478] | 355 | |
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[485] | 356 | Node v=bfs_queue.front(); |
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| 357 | bfs_queue.pop(); |
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| 358 | int l=level[v]+1; |
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[478] | 359 | |
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[485] | 360 | InEdgeIt e; |
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| 361 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 362 | Node w=g->tail(e); |
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| 363 | if ( level[w] == n && w != s ) { |
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| 364 | bfs_queue.push(w); |
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| 365 | Node first=level_list[l]; |
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| 366 | if ( g->valid(first) ) left.set(first,w); |
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| 367 | right.set(w,first); |
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| 368 | level_list[l]=w; |
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| 369 | level.set(w, l); |
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| 370 | } |
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| 371 | } |
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| 372 | } |
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[478] | 373 | |
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[485] | 374 | //the starting flow |
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| 375 | OutEdgeIt e; |
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| 376 | for(g->first(e,s); g->valid(e); g->next(e)) |
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| 377 | { |
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| 378 | Num c=(*capacity)[e]; |
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| 379 | if ( c <= 0 ) continue; |
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| 380 | Node w=g->head(e); |
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| 381 | if ( level[w] < n ) { |
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| 382 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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| 383 | flow->set(e, c); |
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| 384 | excess.set(w, excess[w]+c); |
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| 385 | } |
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| 386 | } |
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| 387 | break; |
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| 388 | } |
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[478] | 389 | |
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[485] | 390 | case GEN_FLOW: |
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| 391 | case PREFLOW: |
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| 392 | { |
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| 393 | //Reverse_bfs from t in the residual graph, |
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| 394 | //to find the starting level. |
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| 395 | level.set(t,0); |
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| 396 | bfs_queue.push(t); |
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[478] | 397 | |
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[485] | 398 | while (!bfs_queue.empty()) { |
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[478] | 399 | |
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[485] | 400 | Node v=bfs_queue.front(); |
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| 401 | bfs_queue.pop(); |
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| 402 | int l=level[v]+1; |
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[478] | 403 | |
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[485] | 404 | InEdgeIt e; |
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| 405 | for(g->first(e,v); g->valid(e); g->next(e)) { |
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| 406 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
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| 407 | Node w=g->tail(e); |
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| 408 | if ( level[w] == n && w != s ) { |
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| 409 | bfs_queue.push(w); |
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| 410 | Node first=level_list[l]; |
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| 411 | if ( g->valid(first) ) left.set(first,w); |
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| 412 | right.set(w,first); |
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| 413 | level_list[l]=w; |
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| 414 | level.set(w, l); |
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| 415 | } |
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| 416 | } |
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[478] | 417 | |
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[485] | 418 | OutEdgeIt f; |
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| 419 | for(g->first(f,v); g->valid(f); g->next(f)) { |
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| 420 | if ( 0 >= (*flow)[f] ) continue; |
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| 421 | Node w=g->head(f); |
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| 422 | if ( level[w] == n && w != s ) { |
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| 423 | bfs_queue.push(w); |
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| 424 | Node first=level_list[l]; |
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| 425 | if ( g->valid(first) ) left.set(first,w); |
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| 426 | right.set(w,first); |
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| 427 | level_list[l]=w; |
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| 428 | level.set(w, l); |
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| 429 | } |
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| 430 | } |
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| 431 | } |
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[478] | 432 | |
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| 433 | |
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[485] | 434 | //the starting flow |
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| 435 | OutEdgeIt e; |
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| 436 | for(g->first(e,s); g->valid(e); g->next(e)) |
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| 437 | { |
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| 438 | Num rem=(*capacity)[e]-(*flow)[e]; |
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| 439 | if ( rem <= 0 ) continue; |
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| 440 | Node w=g->head(e); |
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| 441 | if ( level[w] < n ) { |
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| 442 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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| 443 | flow->set(e, (*capacity)[e]); |
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| 444 | excess.set(w, excess[w]+rem); |
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| 445 | } |
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| 446 | } |
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[478] | 447 | |
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[485] | 448 | InEdgeIt f; |
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| 449 | for(g->first(f,s); g->valid(f); g->next(f)) |
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| 450 | { |
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| 451 | if ( (*flow)[f] <= 0 ) continue; |
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| 452 | Node w=g->tail(f); |
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| 453 | if ( level[w] < n ) { |
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| 454 | if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w); |
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| 455 | excess.set(w, excess[w]+(*flow)[f]); |
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| 456 | flow->set(f, 0); |
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| 457 | } |
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| 458 | } |
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| 459 | break; |
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| 460 | } //case PREFLOW |
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| 461 | } |
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| 462 | } //preflowPreproc |
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[478] | 463 | |
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| 464 | |
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| 465 | |
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| 466 | void relabel(Node w, int newlevel, VecStack& active, |
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| 467 | VecNode& level_list, NNMap& left, |
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| 468 | NNMap& right, int& b, int& k, bool what_heur ) |
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| 469 | { |
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| 470 | |
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| 471 | Num lev=level[w]; |
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| 472 | |
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| 473 | Node right_n=right[w]; |
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| 474 | Node left_n=left[w]; |
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| 475 | |
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| 476 | //unlacing starts |
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| 477 | if ( g->valid(right_n) ) { |
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| 478 | if ( g->valid(left_n) ) { |
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| 479 | right.set(left_n, right_n); |
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| 480 | left.set(right_n, left_n); |
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| 481 | } else { |
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| 482 | level_list[lev]=right_n; |
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| 483 | left.set(right_n, INVALID); |
---|
| 484 | } |
---|
| 485 | } else { |
---|
| 486 | if ( g->valid(left_n) ) { |
---|
| 487 | right.set(left_n, INVALID); |
---|
| 488 | } else { |
---|
| 489 | level_list[lev]=INVALID; |
---|
| 490 | } |
---|
| 491 | } |
---|
| 492 | //unlacing ends |
---|
| 493 | |
---|
| 494 | if ( !g->valid(level_list[lev]) ) { |
---|
| 495 | |
---|
| 496 | //gapping starts |
---|
| 497 | for (int i=lev; i!=k ; ) { |
---|
| 498 | Node v=level_list[++i]; |
---|
| 499 | while ( g->valid(v) ) { |
---|
| 500 | level.set(v,n); |
---|
| 501 | v=right[v]; |
---|
| 502 | } |
---|
| 503 | level_list[i]=INVALID; |
---|
| 504 | if ( !what_heur ) { |
---|
| 505 | while ( !active[i].empty() ) { |
---|
| 506 | active[i].pop(); //FIXME: ezt szebben kene |
---|
| 507 | } |
---|
| 508 | } |
---|
| 509 | } |
---|
| 510 | |
---|
| 511 | level.set(w,n); |
---|
| 512 | b=lev-1; |
---|
| 513 | k=b; |
---|
| 514 | //gapping ends |
---|
| 515 | |
---|
| 516 | } else { |
---|
| 517 | |
---|
| 518 | if ( newlevel == n ) level.set(w,n); |
---|
| 519 | else { |
---|
| 520 | level.set(w,++newlevel); |
---|
| 521 | active[newlevel].push(w); |
---|
| 522 | if ( what_heur ) b=newlevel; |
---|
| 523 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
| 524 | Node first=level_list[newlevel]; |
---|
| 525 | if ( g->valid(first) ) left.set(first,w); |
---|
| 526 | right.set(w,first); |
---|
| 527 | left.set(w,INVALID); |
---|
| 528 | level_list[newlevel]=w; |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | |
---|
| 532 | } //relabel |
---|
| 533 | |
---|
| 534 | |
---|
| 535 | template<typename MapGraphWrapper> |
---|
| 536 | class DistanceMap { |
---|
| 537 | protected: |
---|
| 538 | const MapGraphWrapper* g; |
---|
| 539 | typename MapGraphWrapper::template NodeMap<int> dist; |
---|
| 540 | public: |
---|
| 541 | DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { } |
---|
| 542 | void set(const typename MapGraphWrapper::Node& n, int a) { |
---|
| 543 | dist.set(n, a); |
---|
| 544 | } |
---|
| 545 | int operator[](const typename MapGraphWrapper::Node& n) |
---|
[485] | 546 | { return dist[n]; } |
---|
| 547 | // int get(const typename MapGraphWrapper::Node& n) const { |
---|
| 548 | // return dist[n]; } |
---|
| 549 | // bool get(const typename MapGraphWrapper::Edge& e) const { |
---|
| 550 | // return (dist.get(g->tail(e))<dist.get(g->head(e))); } |
---|
[478] | 551 | bool operator[](const typename MapGraphWrapper::Edge& e) const { |
---|
| 552 | return (dist[g->tail(e)]<dist[g->head(e)]); |
---|
| 553 | } |
---|
| 554 | }; |
---|
| 555 | |
---|
| 556 | }; |
---|
| 557 | |
---|
| 558 | |
---|
| 559 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 560 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase0( flowEnum fe ) |
---|
| 561 | { |
---|
| 562 | |
---|
[485] | 563 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
---|
| 564 | int heur1=(int)(H1*n); //time while running 'highest label' |
---|
| 565 | int heur=heur1; //starting time interval (#of relabels) |
---|
| 566 | int numrelabel=0; |
---|
[478] | 567 | |
---|
[485] | 568 | bool what_heur=1; |
---|
| 569 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
[478] | 570 | |
---|
[485] | 571 | bool end=false; |
---|
| 572 | //Needed for 'bound decrease', true means no active nodes are above bound b. |
---|
[478] | 573 | |
---|
[485] | 574 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 575 | int b=k; //bound on the highest level under n of an active node |
---|
[478] | 576 | |
---|
[485] | 577 | VecStack active(n); |
---|
[478] | 578 | |
---|
[485] | 579 | NNMap left(*g, INVALID); |
---|
| 580 | NNMap right(*g, INVALID); |
---|
| 581 | VecNode level_list(n,INVALID); |
---|
| 582 | //List of the nodes in level i<n, set to n. |
---|
[478] | 583 | |
---|
[485] | 584 | NodeIt v; |
---|
| 585 | for(g->first(v); g->valid(v); g->next(v)) level.set(v,n); |
---|
| 586 | //setting each node to level n |
---|
[478] | 587 | |
---|
[485] | 588 | switch ( fe ) { |
---|
| 589 | case PREFLOW: |
---|
| 590 | { |
---|
| 591 | //counting the excess |
---|
| 592 | NodeIt v; |
---|
| 593 | for(g->first(v); g->valid(v); g->next(v)) { |
---|
[478] | 594 | Num exc=0; |
---|
| 595 | |
---|
| 596 | InEdgeIt e; |
---|
[485] | 597 | for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
[478] | 598 | OutEdgeIt f; |
---|
[485] | 599 | for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
| 600 | |
---|
| 601 | excess.set(v,exc); |
---|
| 602 | |
---|
| 603 | //putting the active nodes into the stack |
---|
| 604 | int lev=level[v]; |
---|
| 605 | if ( exc > 0 && lev < n && v != t ) active[lev].push(v); |
---|
[478] | 606 | } |
---|
| 607 | break; |
---|
| 608 | } |
---|
[485] | 609 | case GEN_FLOW: |
---|
| 610 | { |
---|
| 611 | //Counting the excess of t |
---|
| 612 | Num exc=0; |
---|
| 613 | |
---|
| 614 | InEdgeIt e; |
---|
| 615 | for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e]; |
---|
| 616 | OutEdgeIt f; |
---|
| 617 | for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f]; |
---|
| 618 | |
---|
| 619 | excess.set(t,exc); |
---|
| 620 | |
---|
| 621 | break; |
---|
| 622 | } |
---|
| 623 | default: |
---|
| 624 | break; |
---|
| 625 | } |
---|
[478] | 626 | |
---|
[485] | 627 | preflowPreproc( fe, active, level_list, left, right ); |
---|
| 628 | //End of preprocessing |
---|
[478] | 629 | |
---|
| 630 | |
---|
[485] | 631 | //Push/relabel on the highest level active nodes. |
---|
| 632 | while ( true ) { |
---|
| 633 | if ( b == 0 ) { |
---|
| 634 | if ( !what_heur && !end && k > 0 ) { |
---|
| 635 | b=k; |
---|
| 636 | end=true; |
---|
| 637 | } else break; |
---|
| 638 | } |
---|
| 639 | |
---|
| 640 | if ( active[b].empty() ) --b; |
---|
| 641 | else { |
---|
| 642 | end=false; |
---|
| 643 | Node w=active[b].top(); |
---|
| 644 | active[b].pop(); |
---|
| 645 | int newlevel=push(w,active); |
---|
| 646 | if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, |
---|
| 647 | left, right, b, k, what_heur); |
---|
| 648 | |
---|
| 649 | ++numrelabel; |
---|
| 650 | if ( numrelabel >= heur ) { |
---|
| 651 | numrelabel=0; |
---|
| 652 | if ( what_heur ) { |
---|
| 653 | what_heur=0; |
---|
| 654 | heur=heur0; |
---|
| 655 | end=false; |
---|
| 656 | } else { |
---|
| 657 | what_heur=1; |
---|
| 658 | heur=heur1; |
---|
| 659 | b=k; |
---|
| 660 | } |
---|
[478] | 661 | } |
---|
| 662 | } |
---|
[485] | 663 | } |
---|
| 664 | } |
---|
[478] | 665 | |
---|
| 666 | |
---|
| 667 | |
---|
| 668 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 669 | void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1() |
---|
| 670 | { |
---|
| 671 | |
---|
[485] | 672 | int k=n-2; //bound on the highest level under n containing a node |
---|
| 673 | int b=k; //bound on the highest level under n of an active node |
---|
[478] | 674 | |
---|
[485] | 675 | VecStack active(n); |
---|
| 676 | level.set(s,0); |
---|
| 677 | std::queue<Node> bfs_queue; |
---|
| 678 | bfs_queue.push(s); |
---|
[478] | 679 | |
---|
[485] | 680 | while (!bfs_queue.empty()) { |
---|
[478] | 681 | |
---|
[485] | 682 | Node v=bfs_queue.front(); |
---|
| 683 | bfs_queue.pop(); |
---|
| 684 | int l=level[v]+1; |
---|
[478] | 685 | |
---|
[485] | 686 | InEdgeIt e; |
---|
| 687 | for(g->first(e,v); g->valid(e); g->next(e)) { |
---|
| 688 | if ( (*capacity)[e] <= (*flow)[e] ) continue; |
---|
| 689 | Node u=g->tail(e); |
---|
| 690 | if ( level[u] >= n ) { |
---|
| 691 | bfs_queue.push(u); |
---|
| 692 | level.set(u, l); |
---|
| 693 | if ( excess[u] > 0 ) active[l].push(u); |
---|
[478] | 694 | } |
---|
| 695 | } |
---|
[485] | 696 | |
---|
| 697 | OutEdgeIt f; |
---|
| 698 | for(g->first(f,v); g->valid(f); g->next(f)) { |
---|
| 699 | if ( 0 >= (*flow)[f] ) continue; |
---|
| 700 | Node u=g->head(f); |
---|
| 701 | if ( level[u] >= n ) { |
---|
| 702 | bfs_queue.push(u); |
---|
| 703 | level.set(u, l); |
---|
| 704 | if ( excess[u] > 0 ) active[l].push(u); |
---|
| 705 | } |
---|
| 706 | } |
---|
| 707 | } |
---|
| 708 | b=n-2; |
---|
[478] | 709 | |
---|
[485] | 710 | while ( true ) { |
---|
[478] | 711 | |
---|
[485] | 712 | if ( b == 0 ) break; |
---|
[478] | 713 | |
---|
[485] | 714 | if ( active[b].empty() ) --b; |
---|
| 715 | else { |
---|
| 716 | Node w=active[b].top(); |
---|
| 717 | active[b].pop(); |
---|
| 718 | int newlevel=push(w,active); |
---|
[478] | 719 | |
---|
[485] | 720 | //relabel |
---|
| 721 | if ( excess[w] > 0 ) { |
---|
| 722 | level.set(w,++newlevel); |
---|
| 723 | active[newlevel].push(w); |
---|
| 724 | b=newlevel; |
---|
| 725 | } |
---|
| 726 | } // if stack[b] is nonempty |
---|
| 727 | } // while(true) |
---|
| 728 | } |
---|
[478] | 729 | |
---|
| 730 | |
---|
| 731 | |
---|
| 732 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 733 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() |
---|
| 734 | { |
---|
[485] | 735 | ResGW res_graph(*g, *capacity, *flow); |
---|
| 736 | bool _augment=false; |
---|
[478] | 737 | |
---|
[485] | 738 | //ReachedMap level(res_graph); |
---|
| 739 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 740 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 741 | bfs.pushAndSetReached(s); |
---|
[478] | 742 | |
---|
[485] | 743 | typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); |
---|
| 744 | pred.set(s, INVALID); |
---|
[478] | 745 | |
---|
[485] | 746 | typename ResGW::template NodeMap<Num> free(res_graph); |
---|
[478] | 747 | |
---|
[485] | 748 | //searching for augmenting path |
---|
| 749 | while ( !bfs.finished() ) { |
---|
| 750 | ResGWOutEdgeIt e=bfs; |
---|
| 751 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 752 | Node v=res_graph.tail(e); |
---|
| 753 | Node w=res_graph.head(e); |
---|
| 754 | pred.set(w, e); |
---|
| 755 | if (res_graph.valid(pred[v])) { |
---|
| 756 | free.set(w, std::min(free[v], res_graph.resCap(e))); |
---|
| 757 | } else { |
---|
| 758 | free.set(w, res_graph.resCap(e)); |
---|
[478] | 759 | } |
---|
[485] | 760 | if (res_graph.head(e)==t) { _augment=true; break; } |
---|
| 761 | } |
---|
[478] | 762 | |
---|
[485] | 763 | ++bfs; |
---|
| 764 | } //end of searching augmenting path |
---|
[478] | 765 | |
---|
[485] | 766 | if (_augment) { |
---|
| 767 | Node n=t; |
---|
| 768 | Num augment_value=free[t]; |
---|
| 769 | while (res_graph.valid(pred[n])) { |
---|
| 770 | ResGWEdge e=pred[n]; |
---|
| 771 | res_graph.augment(e, augment_value); |
---|
| 772 | n=res_graph.tail(e); |
---|
[478] | 773 | } |
---|
[485] | 774 | } |
---|
[478] | 775 | |
---|
[485] | 776 | return _augment; |
---|
| 777 | } |
---|
[478] | 778 | |
---|
| 779 | |
---|
| 780 | |
---|
| 781 | |
---|
| 782 | |
---|
| 783 | |
---|
| 784 | |
---|
| 785 | |
---|
| 786 | |
---|
| 787 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 788 | template<typename MutableGraph> |
---|
| 789 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() |
---|
| 790 | { |
---|
[485] | 791 | typedef MutableGraph MG; |
---|
| 792 | bool _augment=false; |
---|
[478] | 793 | |
---|
[485] | 794 | ResGW res_graph(*g, *capacity, *flow); |
---|
[478] | 795 | |
---|
[485] | 796 | //bfs for distances on the residual graph |
---|
| 797 | //ReachedMap level(res_graph); |
---|
| 798 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 799 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
| 800 | bfs.pushAndSetReached(s); |
---|
| 801 | typename ResGW::template NodeMap<int> |
---|
| 802 | dist(res_graph); //filled up with 0's |
---|
[478] | 803 | |
---|
[485] | 804 | //F will contain the physical copy of the residual graph |
---|
| 805 | //with the set of edges which are on shortest paths |
---|
| 806 | MG F; |
---|
| 807 | typename ResGW::template NodeMap<typename MG::Node> |
---|
| 808 | res_graph_to_F(res_graph); |
---|
| 809 | { |
---|
| 810 | typename ResGW::NodeIt n; |
---|
| 811 | for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) { |
---|
| 812 | res_graph_to_F.set(n, F.addNode()); |
---|
[478] | 813 | } |
---|
[485] | 814 | } |
---|
[478] | 815 | |
---|
[485] | 816 | typename MG::Node sF=res_graph_to_F[s]; |
---|
| 817 | typename MG::Node tF=res_graph_to_F[t]; |
---|
| 818 | typename MG::template EdgeMap<ResGWEdge> original_edge(F); |
---|
| 819 | typename MG::template EdgeMap<Num> residual_capacity(F); |
---|
[478] | 820 | |
---|
[485] | 821 | while ( !bfs.finished() ) { |
---|
| 822 | ResGWOutEdgeIt e=bfs; |
---|
| 823 | if (res_graph.valid(e)) { |
---|
| 824 | if (bfs.isBNodeNewlyReached()) { |
---|
| 825 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
| 826 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]); |
---|
| 827 | original_edge.update(); |
---|
| 828 | original_edge.set(f, e); |
---|
| 829 | residual_capacity.update(); |
---|
| 830 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 831 | } else { |
---|
| 832 | if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) { |
---|
[478] | 833 | typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]); |
---|
| 834 | original_edge.update(); |
---|
| 835 | original_edge.set(f, e); |
---|
| 836 | residual_capacity.update(); |
---|
| 837 | residual_capacity.set(f, res_graph.resCap(e)); |
---|
| 838 | } |
---|
| 839 | } |
---|
[485] | 840 | } |
---|
| 841 | ++bfs; |
---|
| 842 | } //computing distances from s in the residual graph |
---|
[478] | 843 | |
---|
[485] | 844 | bool __augment=true; |
---|
[478] | 845 | |
---|
[485] | 846 | while (__augment) { |
---|
| 847 | __augment=false; |
---|
| 848 | //computing blocking flow with dfs |
---|
| 849 | DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F); |
---|
| 850 | typename MG::template NodeMap<typename MG::Edge> pred(F); |
---|
| 851 | pred.set(sF, INVALID); |
---|
| 852 | //invalid iterators for sources |
---|
[478] | 853 | |
---|
[485] | 854 | typename MG::template NodeMap<Num> free(F); |
---|
[478] | 855 | |
---|
[485] | 856 | dfs.pushAndSetReached(sF); |
---|
| 857 | while (!dfs.finished()) { |
---|
| 858 | ++dfs; |
---|
| 859 | if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) { |
---|
| 860 | if (dfs.isBNodeNewlyReached()) { |
---|
| 861 | typename MG::Node v=F.aNode(dfs); |
---|
| 862 | typename MG::Node w=F.bNode(dfs); |
---|
| 863 | pred.set(w, dfs); |
---|
| 864 | if (F.valid(pred[v])) { |
---|
| 865 | free.set(w, std::min(free[v], residual_capacity[dfs])); |
---|
| 866 | } else { |
---|
| 867 | free.set(w, residual_capacity[dfs]); |
---|
| 868 | } |
---|
| 869 | if (w==tF) { |
---|
| 870 | __augment=true; |
---|
| 871 | _augment=true; |
---|
| 872 | break; |
---|
| 873 | } |
---|
[478] | 874 | |
---|
[485] | 875 | } else { |
---|
| 876 | F.erase(/*typename MG::OutEdgeIt*/(dfs)); |
---|
| 877 | } |
---|
| 878 | } |
---|
| 879 | } |
---|
| 880 | |
---|
| 881 | if (__augment) { |
---|
| 882 | typename MG::Node n=tF; |
---|
| 883 | Num augment_value=free[tF]; |
---|
| 884 | while (F.valid(pred[n])) { |
---|
| 885 | typename MG::Edge e=pred[n]; |
---|
| 886 | res_graph.augment(original_edge[e], augment_value); |
---|
| 887 | n=F.tail(e); |
---|
| 888 | if (residual_capacity[e]==augment_value) |
---|
| 889 | F.erase(e); |
---|
| 890 | else |
---|
| 891 | residual_capacity.set(e, residual_capacity[e]-augment_value); |
---|
[478] | 892 | } |
---|
[485] | 893 | } |
---|
[478] | 894 | |
---|
[485] | 895 | } |
---|
[478] | 896 | |
---|
[485] | 897 | return _augment; |
---|
| 898 | } |
---|
[478] | 899 | |
---|
| 900 | |
---|
| 901 | |
---|
| 902 | |
---|
| 903 | |
---|
| 904 | |
---|
| 905 | template <typename Graph, typename Num, typename CapMap, typename FlowMap> |
---|
| 906 | bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() |
---|
| 907 | { |
---|
[485] | 908 | bool _augment=false; |
---|
[478] | 909 | |
---|
[485] | 910 | ResGW res_graph(*g, *capacity, *flow); |
---|
[478] | 911 | |
---|
[485] | 912 | //ReachedMap level(res_graph); |
---|
| 913 | FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); |
---|
| 914 | BfsIterator<ResGW, ReachedMap> bfs(res_graph, level); |
---|
[478] | 915 | |
---|
[485] | 916 | bfs.pushAndSetReached(s); |
---|
| 917 | DistanceMap<ResGW> dist(res_graph); |
---|
| 918 | while ( !bfs.finished() ) { |
---|
| 919 | ResGWOutEdgeIt e=bfs; |
---|
| 920 | if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) { |
---|
| 921 | dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1); |
---|
| 922 | } |
---|
| 923 | ++bfs; |
---|
| 924 | } //computing distances from s in the residual graph |
---|
[478] | 925 | |
---|
| 926 | //Subgraph containing the edges on some shortest paths |
---|
[485] | 927 | ConstMap<typename ResGW::Node, bool> true_map(true); |
---|
| 928 | typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, |
---|
| 929 | DistanceMap<ResGW> > FilterResGW; |
---|
| 930 | FilterResGW filter_res_graph(res_graph, true_map, dist); |
---|
[478] | 931 | |
---|
[485] | 932 | //Subgraph, which is able to delete edges which are already |
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| 933 | //met by the dfs |
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| 934 | typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> |
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| 935 | first_out_edges(filter_res_graph); |
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| 936 | typename FilterResGW::NodeIt v; |
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| 937 | for(filter_res_graph.first(v); filter_res_graph.valid(v); |
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| 938 | filter_res_graph.next(v)) |
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[478] | 939 | { |
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| 940 | typename FilterResGW::OutEdgeIt e; |
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| 941 | filter_res_graph.first(e, v); |
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| 942 | first_out_edges.set(v, e); |
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| 943 | } |
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[485] | 944 | typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW:: |
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| 945 | template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW; |
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| 946 | ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges); |
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[478] | 947 | |
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[485] | 948 | bool __augment=true; |
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[478] | 949 | |
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[485] | 950 | while (__augment) { |
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[478] | 951 | |
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[485] | 952 | __augment=false; |
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| 953 | //computing blocking flow with dfs |
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| 954 | DfsIterator< ErasingResGW, |
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| 955 | typename ErasingResGW::template NodeMap<bool> > |
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| 956 | dfs(erasing_res_graph); |
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| 957 | typename ErasingResGW:: |
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| 958 | template NodeMap<typename ErasingResGW::OutEdgeIt> |
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| 959 | pred(erasing_res_graph); |
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| 960 | pred.set(s, INVALID); |
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| 961 | //invalid iterators for sources |
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[478] | 962 | |
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[485] | 963 | typename ErasingResGW::template NodeMap<Num> |
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| 964 | free1(erasing_res_graph); |
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[478] | 965 | |
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[485] | 966 | dfs.pushAndSetReached( |
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| 967 | typename ErasingResGW::Node( |
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| 968 | typename FilterResGW::Node( |
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| 969 | typename ResGW::Node(s) |
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| 970 | ) |
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| 971 | ) |
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| 972 | ); |
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| 973 | while (!dfs.finished()) { |
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| 974 | ++dfs; |
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| 975 | if (erasing_res_graph.valid( |
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| 976 | typename ErasingResGW::OutEdgeIt(dfs))) |
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[478] | 977 | { |
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| 978 | if (dfs.isBNodeNewlyReached()) { |
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| 979 | |
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| 980 | typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs); |
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| 981 | typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs); |
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| 982 | |
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| 983 | pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs)); |
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| 984 | if (erasing_res_graph.valid(pred[v])) { |
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| 985 | free1.set(w, std::min(free1[v], res_graph.resCap( |
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[485] | 986 | typename ErasingResGW::OutEdgeIt(dfs)))); |
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[478] | 987 | } else { |
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| 988 | free1.set(w, res_graph.resCap( |
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[485] | 989 | typename ErasingResGW::OutEdgeIt(dfs))); |
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[478] | 990 | } |
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| 991 | |
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| 992 | if (w==t) { |
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| 993 | __augment=true; |
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| 994 | _augment=true; |
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| 995 | break; |
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| 996 | } |
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| 997 | } else { |
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| 998 | erasing_res_graph.erase(dfs); |
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| 999 | } |
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| 1000 | } |
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[485] | 1001 | } |
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[478] | 1002 | |
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[485] | 1003 | if (__augment) { |
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| 1004 | typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t)); |
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| 1005 | // typename ResGW::NodeMap<Num> a(res_graph); |
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| 1006 | // typename ResGW::Node b; |
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| 1007 | // Num j=a[b]; |
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| 1008 | // typename FilterResGW::NodeMap<Num> a1(filter_res_graph); |
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| 1009 | // typename FilterResGW::Node b1; |
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| 1010 | // Num j1=a1[b1]; |
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| 1011 | // typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph); |
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| 1012 | // typename ErasingResGW::Node b2; |
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| 1013 | // Num j2=a2[b2]; |
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| 1014 | Num augment_value=free1[n]; |
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| 1015 | while (erasing_res_graph.valid(pred[n])) { |
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| 1016 | typename ErasingResGW::OutEdgeIt e=pred[n]; |
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| 1017 | res_graph.augment(e, augment_value); |
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| 1018 | n=erasing_res_graph.tail(e); |
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| 1019 | if (res_graph.resCap(e)==0) |
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| 1020 | erasing_res_graph.erase(e); |
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[478] | 1021 | } |
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| 1022 | } |
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| 1023 | |
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[485] | 1024 | } //while (__augment) |
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[478] | 1025 | |
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[485] | 1026 | return _augment; |
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| 1027 | } |
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[478] | 1028 | |
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| 1029 | |
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| 1030 | |
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| 1031 | |
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| 1032 | } //namespace hugo |
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| 1033 | |
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[480] | 1034 | #endif //HUGO_MAX_FLOW_H |
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[478] | 1035 | |
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| 1036 | |
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| 1037 | |
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| 1038 | |
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