[102] | 1 | // -*- C++ -*- |
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| 2 | /* |
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[109] | 3 | preflow_h5.h |
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[102] | 4 | by jacint. |
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[109] | 5 | Heuristics: |
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| 6 | 2 phase |
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| 7 | gap |
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| 8 | list 'level_list' on the nodes on level i implemented by hand |
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| 9 | highest label |
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| 10 | relevel: in phase 0, after BFS*n relabels, it runs a reverse |
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| 11 | bfs from t in the res graph to relevel the nodes reachable from t. |
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| 12 | BFS is initialized to 20 |
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[102] | 13 | |
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[109] | 14 | Due to the last heuristic, this algorithm is quite fast on very |
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| 15 | sparse graphs, but relatively bad on even the dense graphs. |
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[102] | 16 | |
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[109] | 17 | 'NodeMap<bool> cut' is a member, in this way we can count it fast, after |
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| 18 | the algorithm was run. |
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[102] | 19 | |
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[109] | 20 | The constructor runs the algorithm. |
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[102] | 21 | |
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[109] | 22 | Members: |
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[102] | 23 | |
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[109] | 24 | T maxFlow() : returns the value of a maximum flow |
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[102] | 25 | |
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[109] | 26 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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[102] | 27 | |
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[109] | 28 | FlowMap Flow() : returns the fixed maximum flow x |
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[102] | 29 | |
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[109] | 30 | void Flow(FlowMap& _flow ) : returns the fixed maximum flow x |
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[102] | 31 | |
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[109] | 32 | void minMinCut(CutMap& M) : sets M to the characteristic vector of the |
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[102] | 33 | minimum min cut. M should be a map of bools initialized to false. |
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| 34 | |
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[109] | 35 | void maxMinCut(CutMap& M) : sets M to the characteristic vector of the |
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[102] | 36 | maximum min cut. M should be a map of bools initialized to false. |
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| 37 | |
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[109] | 38 | void minCut(CutMap& M) : fast function, sets M to the characteristic |
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| 39 | vector of a minimum cut. |
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| 40 | |
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| 41 | Different member from the other preflow_hl-s (here we have a member |
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| 42 | 'NodeMap<bool> cut'). |
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| 43 | |
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| 44 | CutMap minCut() : fast function, giving the characteristic |
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| 45 | vector of a minimum cut. |
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| 46 | |
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| 47 | |
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[102] | 48 | */ |
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| 49 | |
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| 50 | #ifndef PREFLOW_HL4_H |
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| 51 | #define PREFLOW_HL4_H |
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| 52 | |
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[109] | 53 | #define BFS 20 |
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| 54 | |
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[102] | 55 | #include <vector> |
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| 56 | #include <queue> |
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| 57 | |
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[109] | 58 | #include <time_measure.h> //for test |
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| 59 | |
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[105] | 60 | namespace hugo { |
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[102] | 61 | |
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| 62 | template <typename Graph, typename T, |
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| 63 | typename FlowMap=typename Graph::EdgeMap<T>, |
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[109] | 64 | typename CutMap=typename Graph::NodeMap<bool>, |
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[102] | 65 | typename CapMap=typename Graph::EdgeMap<T> > |
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| 66 | class preflow_hl4 { |
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| 67 | |
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| 68 | typedef typename Graph::NodeIt NodeIt; |
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| 69 | typedef typename Graph::EdgeIt EdgeIt; |
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| 70 | typedef typename Graph::EachNodeIt EachNodeIt; |
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| 71 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 72 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 73 | |
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| 74 | Graph& G; |
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| 75 | NodeIt s; |
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| 76 | NodeIt t; |
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| 77 | FlowMap flow; |
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| 78 | CapMap& capacity; |
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[109] | 79 | CutMap cut; |
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[102] | 80 | T value; |
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| 81 | |
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| 82 | public: |
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| 83 | |
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[109] | 84 | double time; |
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| 85 | |
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[102] | 86 | preflow_hl4(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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[109] | 87 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), |
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| 88 | cut(G, false) { |
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[102] | 89 | |
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[109] | 90 | bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd |
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[102] | 91 | int n=G.nodeNum(); |
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[109] | 92 | int relabel=0; |
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| 93 | int heur=(int)BFS*n; |
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[102] | 94 | int k=n-2; |
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| 95 | int b=k; |
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| 96 | /* |
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| 97 | b is a bound on the highest level of the stack. |
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| 98 | k is a bound on the highest nonempty level i < n. |
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| 99 | */ |
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| 100 | |
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| 101 | typename Graph::NodeMap<int> level(G,n); |
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| 102 | typename Graph::NodeMap<T> excess(G); |
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[109] | 103 | |
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| 104 | std::vector<NodeIt> active(n); |
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| 105 | typename Graph::NodeMap<NodeIt> next(G); |
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[102] | 106 | //Stack of the active nodes in level i < n. |
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| 107 | //We use it in both phases. |
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| 108 | |
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| 109 | typename Graph::NodeMap<NodeIt> left(G); |
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| 110 | typename Graph::NodeMap<NodeIt> right(G); |
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| 111 | std::vector<NodeIt> level_list(n); |
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| 112 | /* |
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| 113 | Needed for the list of the nodes in level i. |
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| 114 | */ |
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| 115 | |
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| 116 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 117 | level.set(t,0); |
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| 118 | std::queue<NodeIt> bfs_queue; |
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| 119 | bfs_queue.push(t); |
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| 120 | |
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| 121 | while (!bfs_queue.empty()) { |
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| 122 | |
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| 123 | NodeIt v=bfs_queue.front(); |
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| 124 | bfs_queue.pop(); |
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| 125 | int l=level.get(v)+1; |
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| 126 | |
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| 127 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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| 128 | NodeIt w=G.tail(e); |
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[109] | 129 | if ( level.get(w) == n && w !=s ) { |
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[102] | 130 | bfs_queue.push(w); |
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| 131 | NodeIt first=level_list[l]; |
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| 132 | if ( first != 0 ) left.set(first,w); |
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| 133 | right.set(w,first); |
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| 134 | level_list[l]=w; |
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| 135 | level.set(w, l); |
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| 136 | } |
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| 137 | } |
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| 138 | } |
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| 139 | |
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| 140 | level.set(s,n); |
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| 141 | |
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| 142 | |
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| 143 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 144 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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| 145 | { |
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| 146 | T c=capacity.get(e); |
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| 147 | if ( c == 0 ) continue; |
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| 148 | NodeIt w=G.head(e); |
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| 149 | if ( level.get(w) < n ) { |
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[109] | 150 | if ( excess.get(w) == 0 && w!=t ) { |
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| 151 | next.set(w,active[level.get(w)]); |
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| 152 | active[level.get(w)]=w; |
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| 153 | } |
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[102] | 154 | flow.set(e, c); |
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| 155 | excess.set(w, excess.get(w)+c); |
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| 156 | } |
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| 157 | } |
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| 158 | /* |
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| 159 | End of preprocessing |
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| 160 | */ |
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| 161 | |
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| 162 | |
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| 163 | /* |
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| 164 | Push/relabel on the highest level active nodes. |
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| 165 | */ |
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| 166 | while ( true ) { |
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| 167 | |
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| 168 | if ( b == 0 ) { |
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| 169 | if ( phase ) break; |
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| 170 | |
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| 171 | /* |
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| 172 | In the end of phase 0 we apply a bfs from s in |
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| 173 | the residual graph. |
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| 174 | */ |
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| 175 | phase=1; |
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[109] | 176 | |
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| 177 | //Now have a min cut. |
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| 178 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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| 179 | v.valid(); ++v) |
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| 180 | if (level.get(v) >= n ) cut.set(v,true); |
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| 181 | |
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| 182 | time=currTime(); |
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[102] | 183 | level.set(s,0); |
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| 184 | std::queue<NodeIt> bfs_queue; |
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| 185 | bfs_queue.push(s); |
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| 186 | |
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| 187 | while (!bfs_queue.empty()) { |
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| 188 | |
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| 189 | NodeIt v=bfs_queue.front(); |
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| 190 | bfs_queue.pop(); |
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| 191 | int l=level.get(v)+1; |
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| 192 | |
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| 193 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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| 194 | if ( capacity.get(e) == flow.get(e) ) continue; |
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| 195 | NodeIt u=G.tail(e); |
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| 196 | if ( level.get(u) >= n ) { |
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| 197 | bfs_queue.push(u); |
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| 198 | level.set(u, l); |
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[109] | 199 | if ( excess.get(u) > 0 ) { |
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| 200 | next.set(u,active[l]); |
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| 201 | active[l]=u; |
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| 202 | } |
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[102] | 203 | } |
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| 204 | } |
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| 205 | |
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| 206 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) { |
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| 207 | if ( 0 == flow.get(e) ) continue; |
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| 208 | NodeIt u=G.head(e); |
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| 209 | if ( level.get(u) >= n ) { |
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| 210 | bfs_queue.push(u); |
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| 211 | level.set(u, l); |
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[109] | 212 | if ( excess.get(u) > 0 ) { |
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| 213 | next.set(u,active[l]); |
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| 214 | active[l]=u; |
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| 215 | } |
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[102] | 216 | } |
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| 217 | } |
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| 218 | } |
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| 219 | b=n-2; |
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| 220 | } |
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| 221 | |
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| 222 | |
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[109] | 223 | if ( active[b] == 0 ) --b; |
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[102] | 224 | else { |
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| 225 | |
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[109] | 226 | NodeIt w=active[b]; |
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| 227 | active[b]=next.get(w); |
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[102] | 228 | int lev=level.get(w); |
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| 229 | T exc=excess.get(w); |
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[109] | 230 | int newlevel=n; //bound on the next level of w. |
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[102] | 231 | |
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| 232 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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| 233 | |
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| 234 | if ( flow.get(e) == capacity.get(e) ) continue; |
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| 235 | NodeIt v=G.head(e); |
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| 236 | //e=wv |
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| 237 | |
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| 238 | if( lev > level.get(v) ) { |
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| 239 | /*Push is allowed now*/ |
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| 240 | |
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[109] | 241 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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| 242 | int lev_v=level.get(v); |
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| 243 | next.set(v,active[lev_v]); |
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| 244 | active[lev_v]=v; |
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| 245 | } |
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[102] | 246 | |
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| 247 | T cap=capacity.get(e); |
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| 248 | T flo=flow.get(e); |
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| 249 | T remcap=cap-flo; |
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| 250 | |
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| 251 | if ( remcap >= exc ) { |
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| 252 | /*A nonsaturating push.*/ |
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| 253 | |
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| 254 | flow.set(e, flo+exc); |
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| 255 | excess.set(v, excess.get(v)+exc); |
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| 256 | exc=0; |
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| 257 | break; |
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| 258 | |
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| 259 | } else { |
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| 260 | /*A saturating push.*/ |
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| 261 | |
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| 262 | flow.set(e, cap); |
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| 263 | excess.set(v, excess.get(v)+remcap); |
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| 264 | exc-=remcap; |
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| 265 | } |
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| 266 | } else if ( newlevel > level.get(v) ){ |
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| 267 | newlevel = level.get(v); |
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| 268 | } |
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| 269 | |
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| 270 | } //for out edges wv |
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| 271 | |
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| 272 | |
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| 273 | if ( exc > 0 ) { |
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| 274 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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| 275 | |
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| 276 | if( flow.get(e) == 0 ) continue; |
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| 277 | NodeIt v=G.tail(e); |
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| 278 | //e=vw |
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| 279 | |
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| 280 | if( lev > level.get(v) ) { |
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| 281 | /*Push is allowed now*/ |
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| 282 | |
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[109] | 283 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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| 284 | int lev_v=level.get(v); |
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| 285 | next.set(v,active[lev_v]); |
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| 286 | active[lev_v]=v; |
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| 287 | } |
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[102] | 288 | |
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| 289 | T flo=flow.get(e); |
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| 290 | |
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| 291 | if ( flo >= exc ) { |
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| 292 | /*A nonsaturating push.*/ |
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| 293 | |
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| 294 | flow.set(e, flo-exc); |
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| 295 | excess.set(v, excess.get(v)+exc); |
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| 296 | exc=0; |
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| 297 | break; |
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| 298 | } else { |
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| 299 | /*A saturating push.*/ |
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| 300 | |
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| 301 | excess.set(v, excess.get(v)+flo); |
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| 302 | exc-=flo; |
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| 303 | flow.set(e,0); |
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| 304 | } |
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| 305 | } else if ( newlevel > level.get(v) ) { |
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| 306 | newlevel = level.get(v); |
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| 307 | } |
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| 308 | } //for in edges vw |
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| 309 | |
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| 310 | } // if w still has excess after the out edge for cycle |
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| 311 | |
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| 312 | excess.set(w, exc); |
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| 313 | |
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| 314 | /* |
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| 315 | Relabel |
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| 316 | */ |
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| 317 | |
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| 318 | if ( exc > 0 ) { |
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| 319 | //now 'lev' is the old level of w |
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| 320 | |
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| 321 | if ( phase ) { |
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| 322 | level.set(w,++newlevel); |
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[109] | 323 | next.set(w,active[newlevel]); |
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| 324 | active[newlevel]=w; |
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[102] | 325 | b=newlevel; |
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| 326 | } else { |
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| 327 | //unlacing |
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| 328 | NodeIt right_n=right.get(w); |
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| 329 | NodeIt left_n=left.get(w); |
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| 330 | |
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| 331 | if ( right_n != 0 ) { |
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| 332 | if ( left_n != 0 ) { |
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| 333 | right.set(left_n, right_n); |
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| 334 | left.set(right_n, left_n); |
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| 335 | } else { |
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| 336 | level_list[lev]=right_n; |
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| 337 | left.set(right_n, 0); |
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| 338 | } |
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| 339 | } else { |
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| 340 | if ( left_n != 0 ) { |
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| 341 | right.set(left_n, 0); |
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| 342 | } else { |
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| 343 | level_list[lev]=0; |
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| 344 | } |
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| 345 | } |
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[109] | 346 | //unlacing ends |
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[102] | 347 | |
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| 348 | |
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| 349 | if ( level_list[lev]==0 ) { |
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| 350 | |
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| 351 | for (int i=lev; i!=k ; ) { |
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| 352 | NodeIt v=level_list[++i]; |
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| 353 | while ( v != 0 ) { |
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| 354 | level.set(v,n); |
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| 355 | v=right.get(v); |
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| 356 | } |
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| 357 | level_list[i]=0; |
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| 358 | } |
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| 359 | |
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| 360 | level.set(w,n); |
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| 361 | |
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| 362 | b=--lev; |
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| 363 | k=b; |
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| 364 | |
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| 365 | } else { |
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| 366 | |
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| 367 | if ( newlevel == n ) { |
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| 368 | level.set(w,n); |
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| 369 | } else { |
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| 370 | |
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| 371 | level.set(w,++newlevel); |
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[109] | 372 | next.set(w,active[newlevel]); |
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| 373 | active[newlevel]=w; |
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[102] | 374 | b=newlevel; |
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| 375 | if ( k < newlevel ) ++k; |
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| 376 | NodeIt first=level_list[newlevel]; |
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| 377 | if ( first != 0 ) left.set(first,w); |
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| 378 | right.set(w,first); |
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| 379 | left.set(w,0); |
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| 380 | level_list[newlevel]=w; |
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| 381 | } |
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| 382 | } |
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[109] | 383 | |
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| 384 | ++relabel; |
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| 385 | if ( relabel >= heur ) { |
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| 386 | relabel=0; |
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| 387 | b=n-2; |
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| 388 | k=b; |
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| 389 | |
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| 390 | for ( int i=1; i!=n; ++i ) { |
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| 391 | active[i]=0; |
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| 392 | level_list[i]=0; |
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| 393 | } |
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| 394 | |
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| 395 | //bfs from t in the res graph to relevel the nodes |
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| 396 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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| 397 | v.valid(); ++v) level.set(v,n); |
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| 398 | |
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| 399 | level.set(t,0); |
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| 400 | std::queue<NodeIt> bfs_queue; |
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| 401 | bfs_queue.push(t); |
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| 402 | |
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| 403 | while (!bfs_queue.empty()) { |
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| 404 | |
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| 405 | NodeIt v=bfs_queue.front(); |
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| 406 | bfs_queue.pop(); |
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| 407 | int l=level.get(v)+1; |
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| 408 | |
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| 409 | for(InEdgeIt e=G.template first<InEdgeIt>(v); |
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| 410 | e.valid(); ++e) { |
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| 411 | if ( capacity.get(e) == flow.get(e) ) continue; |
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| 412 | NodeIt u=G.tail(e); |
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| 413 | if ( level.get(u) == n ) { |
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| 414 | bfs_queue.push(u); |
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| 415 | level.set(u, l); |
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| 416 | if ( excess.get(u) > 0 ) { |
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| 417 | next.set(u,active[l]); |
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| 418 | active[l]=u; |
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| 419 | } |
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| 420 | NodeIt first=level_list[l]; |
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| 421 | if ( first != 0 ) left.set(first,w); |
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| 422 | right.set(w,first); |
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| 423 | left.set(w,0); |
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| 424 | level_list[l]=w; |
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| 425 | } |
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| 426 | } |
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| 427 | |
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| 428 | |
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| 429 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); |
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| 430 | e.valid(); ++e) { |
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| 431 | if ( 0 == flow.get(e) ) continue; |
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| 432 | NodeIt u=G.head(e); |
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| 433 | if ( level.get(u) == n ) { |
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| 434 | bfs_queue.push(u); |
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| 435 | level.set(u, l); |
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| 436 | if ( excess.get(u) > 0 ) { |
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| 437 | next.set(u,active[l]); |
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| 438 | active[l]=u; |
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| 439 | } |
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| 440 | NodeIt first=level_list[l]; |
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| 441 | if ( first != 0 ) left.set(first,w); |
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| 442 | right.set(w,first); |
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| 443 | left.set(w,0); |
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| 444 | level_list[l]=w; |
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| 445 | } |
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| 446 | } |
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| 447 | } |
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| 448 | |
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| 449 | level.set(s,n); |
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| 450 | } |
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| 451 | |
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[102] | 452 | } //phase 0 |
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| 453 | } // if ( exc > 0 ) |
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[109] | 454 | |
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[102] | 455 | |
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| 456 | } // if stack[b] is nonempty |
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| 457 | |
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| 458 | } // while(true) |
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| 459 | |
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| 460 | |
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| 461 | value = excess.get(t); |
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| 462 | /*Max flow value.*/ |
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| 463 | |
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| 464 | |
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| 465 | } //void run() |
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| 466 | |
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| 467 | |
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| 468 | |
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| 469 | |
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| 470 | |
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| 471 | /* |
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| 472 | Returns the maximum value of a flow. |
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| 473 | */ |
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| 474 | |
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[109] | 475 | T maxFlow() { |
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[102] | 476 | return value; |
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| 477 | } |
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| 478 | |
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| 479 | |
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| 480 | |
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| 481 | /* |
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| 482 | For the maximum flow x found by the algorithm, it returns the flow value on Edge e, i.e. x(e). |
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| 483 | */ |
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| 484 | |
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[109] | 485 | T flowOnEdge(EdgeIt e) { |
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[102] | 486 | return flow.get(e); |
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| 487 | } |
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| 488 | |
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| 489 | |
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| 490 | |
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[109] | 491 | FlowMap Flow() { |
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[102] | 492 | return flow; |
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| 493 | } |
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| 494 | |
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| 495 | |
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| 496 | |
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[109] | 497 | void Flow(FlowMap& _flow ) { |
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[102] | 498 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) |
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| 499 | _flow.set(v,flow.get(v)); |
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| 500 | } |
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| 501 | |
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| 502 | |
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| 503 | |
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| 504 | /* |
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| 505 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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| 506 | */ |
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| 507 | |
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[109] | 508 | template<typename _CutMap> |
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| 509 | void minMinCut(_CutMap& M) { |
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[102] | 510 | |
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| 511 | std::queue<NodeIt> queue; |
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| 512 | |
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| 513 | M.set(s,true); |
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| 514 | queue.push(s); |
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| 515 | |
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| 516 | while (!queue.empty()) { |
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| 517 | NodeIt w=queue.front(); |
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| 518 | queue.pop(); |
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| 519 | |
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| 520 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 521 | NodeIt v=G.head(e); |
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| 522 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 523 | queue.push(v); |
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| 524 | M.set(v, true); |
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| 525 | } |
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| 526 | } |
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| 527 | |
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| 528 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 529 | NodeIt v=G.tail(e); |
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| 530 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 531 | queue.push(v); |
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| 532 | M.set(v, true); |
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| 533 | } |
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| 534 | } |
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| 535 | |
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| 536 | } |
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| 537 | |
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| 538 | } |
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| 539 | |
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| 540 | |
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| 541 | |
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| 542 | /* |
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| 543 | Returns the maximum min cut, by a reverse bfs |
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| 544 | from t in the residual graph. |
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| 545 | */ |
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| 546 | |
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[109] | 547 | template<typename _CutMap> |
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| 548 | void maxMinCut(_CutMap& M) { |
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[102] | 549 | |
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| 550 | std::queue<NodeIt> queue; |
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| 551 | |
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| 552 | M.set(t,true); |
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| 553 | queue.push(t); |
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| 554 | |
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| 555 | while (!queue.empty()) { |
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| 556 | NodeIt w=queue.front(); |
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| 557 | queue.pop(); |
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| 558 | |
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| 559 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 560 | NodeIt v=G.tail(e); |
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| 561 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 562 | queue.push(v); |
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| 563 | M.set(v, true); |
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| 564 | } |
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| 565 | } |
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| 566 | |
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| 567 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 568 | NodeIt v=G.head(e); |
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| 569 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 570 | queue.push(v); |
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| 571 | M.set(v, true); |
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| 572 | } |
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| 573 | } |
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| 574 | } |
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| 575 | |
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| 576 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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| 577 | M.set(v, !M.get(v)); |
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| 578 | } |
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| 579 | |
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| 580 | } |
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| 581 | |
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| 582 | |
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[109] | 583 | template<typename _CutMap> |
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| 584 | void minCut(_CutMap& M) { |
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| 585 | for( EachNodeIt v=G.template first<EachNodeIt>(); |
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| 586 | v.valid(); ++v) |
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| 587 | M.set(v, cut.get(v)); |
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[102] | 588 | } |
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| 589 | |
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[109] | 590 | |
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| 591 | CutMap minCut() { |
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| 592 | return cut; |
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| 593 | } |
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[102] | 594 | |
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| 595 | |
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| 596 | }; |
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[109] | 597 | }//namespace marci |
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[102] | 598 | #endif |
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| 599 | |
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| 600 | |
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| 601 | |
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| 602 | |
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