[98] | 1 | // -*- C++ -*- |
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| 2 | /* |
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| 3 | preflow_hl2.h |
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| 4 | by jacint. |
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| 5 | Runs the highest label variant of the preflow push algorithm with |
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| 6 | running time O(n^2\sqrt(m)), with the 'empty level' and with the |
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| 7 | heuristic that the bound b on the active nodes is not increased |
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| 8 | only when b=0, when we put b=2*n-2. |
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| 9 | |
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| 10 | 'A' is a parameter for the empty_level heuristic |
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| 11 | |
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| 12 | Member functions: |
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| 13 | |
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| 14 | void run() : runs the algorithm |
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| 15 | |
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| 16 | The following functions should be used after run() was already run. |
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| 17 | |
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| 18 | T maxflow() : returns the value of a maximum flow |
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| 19 | |
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| 20 | T flowonedge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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| 21 | |
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| 22 | FlowMap allflow() : returns the fixed maximum flow x |
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| 23 | |
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| 24 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
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| 25 | minimum cut. M should be a map of bools initialized to false. |
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| 26 | |
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| 27 | void min_mincut(CutMap& M) : sets M to the characteristic vector of the |
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| 28 | minimum min cut. M should be a map of bools initialized to false. |
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| 29 | |
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| 30 | void max_mincut(CutMap& M) : sets M to the characteristic vector of the |
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| 31 | maximum min cut. M should be a map of bools initialized to false. |
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| 32 | |
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| 33 | */ |
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| 34 | |
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| 35 | #ifndef PREFLOW_HL2_H |
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| 36 | #define PREFLOW_HL2_H |
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| 37 | |
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| 38 | #define A 1 |
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| 39 | |
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| 40 | #include <vector> |
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| 41 | #include <stack> |
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| 42 | #include <queue> |
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| 43 | |
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| 44 | namespace marci { |
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| 45 | |
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| 46 | template <typename Graph, typename T, |
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| 47 | typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, |
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| 48 | typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> > |
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| 49 | class preflow_hl2 { |
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| 50 | |
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| 51 | typedef typename Graph::NodeIt NodeIt; |
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| 52 | typedef typename Graph::EdgeIt EdgeIt; |
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| 53 | typedef typename Graph::EachNodeIt EachNodeIt; |
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| 54 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 55 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 56 | |
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| 57 | Graph& G; |
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| 58 | NodeIt s; |
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| 59 | NodeIt t; |
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| 60 | FlowMap flow; |
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| 61 | CapMap& capacity; |
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| 62 | T value; |
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| 63 | |
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| 64 | public: |
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| 65 | |
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| 66 | preflow_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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| 67 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { } |
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| 68 | |
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| 69 | |
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| 70 | void run() { |
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| 71 | |
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| 72 | bool no_end=true; |
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| 73 | int n=G.nodeNum(); |
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| 74 | int b=n-2; |
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| 75 | /* |
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| 76 | b is a bound on the highest level of an active node. |
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| 77 | In the beginning it is at most n-2. |
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| 78 | */ |
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| 79 | |
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| 80 | IntMap level(G,n); |
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| 81 | TMap excess(G); |
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| 82 | |
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| 83 | std::vector<int> numb(n+1); |
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| 84 | /* |
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| 85 | The number of nodes on level i < n. It is |
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| 86 | initialized to n+1, because of the reverse_bfs-part. |
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| 87 | */ |
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| 88 | |
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| 89 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
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| 90 | //Stack of the active nodes in level i. |
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| 91 | |
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| 92 | |
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| 93 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 94 | level.set(t,0); |
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| 95 | std::queue<NodeIt> bfs_queue; |
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| 96 | bfs_queue.push(t); |
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| 97 | |
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| 98 | while (!bfs_queue.empty()) { |
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| 99 | |
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| 100 | NodeIt v=bfs_queue.front(); |
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| 101 | bfs_queue.pop(); |
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| 102 | int l=level.get(v)+1; |
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| 103 | |
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| 104 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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| 105 | NodeIt w=G.tail(e); |
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| 106 | if ( level.get(w) == n ) { |
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| 107 | bfs_queue.push(w); |
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| 108 | ++numb[l]; |
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| 109 | level.set(w, l); |
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| 110 | } |
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| 111 | } |
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| 112 | } |
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| 113 | |
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| 114 | level.set(s,n); |
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| 115 | |
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| 116 | |
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| 117 | |
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| 118 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 119 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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| 120 | { |
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| 121 | if ( capacity.get(e) == 0 ) continue; |
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| 122 | NodeIt w=G.head(e); |
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| 123 | if ( w!=s ) { |
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| 124 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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| 125 | flow.set(e, capacity.get(e)); |
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| 126 | excess.set(w, excess.get(w)+capacity.get(e)); |
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| 127 | } |
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| 128 | } |
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| 129 | |
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| 130 | /* |
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| 131 | End of preprocessing |
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| 132 | */ |
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| 133 | |
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| 134 | |
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| 135 | |
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| 136 | /* |
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| 137 | Push/relabel on the highest level active nodes. |
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| 138 | */ |
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| 139 | /*While there exists an active node.*/ |
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| 140 | while (b) { |
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| 141 | if ( stack[b].empty() ) { |
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| 142 | if ( b==1 ) { |
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| 143 | if ( !no_end ) break; |
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| 144 | else { |
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| 145 | b=2*n-2; |
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| 146 | no_end=false; |
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| 147 | } |
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| 148 | } |
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| 149 | --b; |
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| 150 | } else { |
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| 151 | |
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| 152 | no_end=true; |
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| 153 | |
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| 154 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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| 155 | stack[b].pop(); |
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| 156 | int lev=level.get(w); |
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| 157 | int exc=excess.get(w); |
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| 158 | int newlevel=2*n-2; //In newlevel we bound the next level of w. |
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| 159 | |
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| 160 | // if ( level.get(w) < n ) { //Nem tudom ez mukodik-e |
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| 161 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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| 162 | |
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| 163 | if ( flow.get(e) == capacity.get(e) ) continue; |
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| 164 | NodeIt v=G.head(e); |
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| 165 | //e=wv |
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| 166 | |
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| 167 | if( lev > level.get(v) ) { |
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| 168 | /*Push is allowed now*/ |
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| 169 | |
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| 170 | if ( excess.get(v)==0 && v != s && v !=t ) |
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| 171 | stack[level.get(v)].push(v); |
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| 172 | /*v becomes active.*/ |
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| 173 | |
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| 174 | int cap=capacity.get(e); |
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| 175 | int flo=flow.get(e); |
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| 176 | int remcap=cap-flo; |
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| 177 | |
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| 178 | if ( remcap >= exc ) { |
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| 179 | /*A nonsaturating push.*/ |
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| 180 | |
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| 181 | flow.set(e, flo+exc); |
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| 182 | excess.set(v, excess.get(v)+exc); |
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| 183 | exc=0; |
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| 184 | break; |
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| 185 | |
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| 186 | } else { |
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| 187 | /*A saturating push.*/ |
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| 188 | |
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| 189 | flow.set(e, cap ); |
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| 190 | excess.set(v, excess.get(v)+remcap); |
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| 191 | exc-=remcap; |
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| 192 | } |
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| 193 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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| 194 | |
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| 195 | } //for out edges wv |
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| 196 | |
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| 197 | |
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| 198 | if ( exc > 0 ) { |
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| 199 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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| 200 | |
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| 201 | if( flow.get(e) == 0 ) continue; |
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| 202 | NodeIt v=G.tail(e); |
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| 203 | //e=vw |
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| 204 | |
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| 205 | if( lev > level.get(v) ) { |
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| 206 | /*Push is allowed now*/ |
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| 207 | |
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| 208 | if ( excess.get(v)==0 && v != s && v !=t) |
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| 209 | stack[level.get(v)].push(v); |
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| 210 | /*v becomes active.*/ |
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| 211 | |
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| 212 | int flo=flow.get(e); |
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| 213 | |
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| 214 | if ( flo >= exc ) { |
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| 215 | /*A nonsaturating push.*/ |
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| 216 | |
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| 217 | flow.set(e, flo-exc); |
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| 218 | excess.set(v, excess.get(v)+exc); |
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| 219 | exc=0; |
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| 220 | break; |
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| 221 | } else { |
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| 222 | /*A saturating push.*/ |
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| 223 | |
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| 224 | excess.set(v, excess.get(v)+flo); |
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| 225 | exc-=flo; |
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| 226 | flow.set(e,0); |
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| 227 | } |
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| 228 | } else if ( newlevel > level.get(v) ) newlevel = level.get(v); |
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| 229 | |
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| 230 | } //for in edges vw |
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| 231 | |
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| 232 | } // if w still has excess after the out edge for cycle |
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| 233 | |
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| 234 | excess.set(w, exc); |
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| 235 | |
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| 236 | |
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| 237 | /* |
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| 238 | Relabel |
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| 239 | */ |
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| 240 | |
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| 241 | if ( exc > 0 ) { |
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| 242 | //now 'lev' is the old level of w |
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| 243 | level.set(w,++newlevel); |
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| 244 | |
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| 245 | if ( lev < n ) { |
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| 246 | --numb[lev]; |
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| 247 | |
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| 248 | if ( !numb[lev] && lev < A*n ) { //If the level of w gets empty. |
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| 249 | |
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| 250 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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| 251 | if (level.get(v) > lev && level.get(v) < n ) level.set(v,n); |
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| 252 | } |
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| 253 | for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; |
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| 254 | if ( newlevel < n ) newlevel=n; |
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| 255 | } else { |
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| 256 | if ( newlevel < n ) ++numb[newlevel]; |
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| 257 | } |
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| 258 | } |
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| 259 | |
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| 260 | stack[newlevel].push(w); |
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| 261 | |
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| 262 | } |
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| 263 | |
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| 264 | } // if stack[b] is nonempty |
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| 265 | |
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| 266 | } // while(b) |
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| 267 | |
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| 268 | |
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| 269 | value = excess.get(t); |
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| 270 | /*Max flow value.*/ |
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| 271 | |
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| 272 | |
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| 273 | } //void run() |
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| 274 | |
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| 275 | |
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| 276 | |
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| 277 | |
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| 278 | |
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| 279 | /* |
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| 280 | Returns the maximum value of a flow. |
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| 281 | */ |
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| 282 | |
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| 283 | T maxflow() { |
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| 284 | return value; |
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| 285 | } |
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| 286 | |
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| 287 | |
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| 288 | |
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| 289 | /* |
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| 290 | 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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| 291 | */ |
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| 292 | |
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| 293 | T flowonedge(EdgeIt e) { |
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| 294 | return flow.get(e); |
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| 295 | } |
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| 296 | |
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| 297 | |
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| 298 | |
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| 299 | /* |
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| 300 | Returns the maximum flow x found by the algorithm. |
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| 301 | */ |
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| 302 | |
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| 303 | FlowMap allflow() { |
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| 304 | return flow; |
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| 305 | } |
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| 306 | |
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| 307 | |
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| 308 | |
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| 309 | |
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| 310 | /* |
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| 311 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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| 312 | */ |
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| 313 | |
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| 314 | template<typename CutMap> |
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| 315 | void mincut(CutMap& M) { |
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| 316 | |
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| 317 | std::queue<NodeIt> queue; |
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| 318 | |
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| 319 | M.set(s,true); |
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| 320 | queue.push(s); |
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| 321 | |
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| 322 | while (!queue.empty()) { |
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| 323 | NodeIt w=queue.front(); |
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| 324 | queue.pop(); |
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| 325 | |
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| 326 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 327 | NodeIt v=G.head(e); |
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| 328 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 329 | queue.push(v); |
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| 330 | M.set(v, true); |
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| 331 | } |
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| 332 | } |
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| 333 | |
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| 334 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 335 | NodeIt v=G.tail(e); |
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| 336 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 337 | queue.push(v); |
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| 338 | M.set(v, true); |
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| 339 | } |
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| 340 | } |
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| 341 | |
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| 342 | } |
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| 343 | |
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| 344 | } |
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| 345 | |
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| 346 | |
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| 347 | |
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| 348 | /* |
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| 349 | Returns the maximum min cut, by a reverse bfs |
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| 350 | from t in the residual graph. |
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| 351 | */ |
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| 352 | |
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| 353 | template<typename CutMap> |
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| 354 | void max_mincut(CutMap& M) { |
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| 355 | |
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| 356 | std::queue<NodeIt> queue; |
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| 357 | |
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| 358 | M.set(t,true); |
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| 359 | queue.push(t); |
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| 360 | |
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| 361 | while (!queue.empty()) { |
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| 362 | NodeIt w=queue.front(); |
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| 363 | queue.pop(); |
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| 364 | |
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| 365 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 366 | NodeIt v=G.tail(e); |
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| 367 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 368 | queue.push(v); |
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| 369 | M.set(v, true); |
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| 370 | } |
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| 371 | } |
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| 372 | |
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| 373 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 374 | NodeIt v=G.head(e); |
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| 375 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 376 | queue.push(v); |
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| 377 | M.set(v, true); |
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| 378 | } |
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| 379 | } |
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| 380 | } |
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| 381 | |
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| 382 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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| 383 | M.set(v, !M.get(v)); |
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| 384 | } |
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| 385 | |
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| 386 | } |
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| 387 | |
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| 388 | |
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| 389 | |
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| 390 | template<typename CutMap> |
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| 391 | void min_mincut(CutMap& M) { |
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| 392 | mincut(M); |
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| 393 | } |
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| 394 | |
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| 395 | |
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| 396 | |
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| 397 | }; |
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| 398 | }//namespace marci |
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| 399 | #endif |
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| 400 | |
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| 401 | |
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| 402 | |
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| 403 | |
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