[131] | 1 | // -*- C++ -*- |
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| 2 | /* |
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| 3 | preflow.h with 'j_graph interface' |
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| 4 | by jacint. |
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| 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 | stack 'active' on the active nodes on level i implemented by hand |
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| 10 | runs heuristic 'highest label' for H1*n relabels |
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| 11 | runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label' |
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| 12 | |
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| 13 | Parameters H0 and H1 are initialized to 20 and 10. |
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| 14 | |
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| 15 | The best preflow I could ever write. |
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| 16 | |
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| 17 | The constructor runs the algorithm. |
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| 18 | |
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| 19 | Members: |
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| 20 | |
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| 21 | T maxFlow() : returns the value of a maximum flow |
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| 22 | |
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| 23 | T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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| 24 | |
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| 25 | FlowMap Flow() : returns the fixed maximum flow x |
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| 26 | |
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| 27 | void minMinCut(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 maxMinCut(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 | void minCut(CutMap& M) : sets M to the characteristic vector of |
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| 34 | a min cut. M should be a map of bools initialized to false. |
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| 35 | |
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| 36 | */ |
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| 37 | |
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| 38 | #ifndef PREFLOW_H |
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| 39 | #define PREFLOW_H |
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| 40 | |
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| 41 | #define H0 20 |
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| 42 | #define H1 1 |
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| 43 | |
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| 44 | #include <vector> |
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| 45 | #include <queue> |
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| 46 | |
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| 47 | #include<iostream> |
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| 48 | |
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| 49 | #include <time_measure.h> |
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| 50 | |
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| 51 | namespace hugo { |
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| 52 | |
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| 53 | template <typename Graph, typename T, |
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| 54 | typename FlowMap=typename Graph::EdgeMap<T>, |
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| 55 | typename CapMap=typename Graph::EdgeMap<T> > |
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| 56 | class preflow { |
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| 57 | |
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| 58 | typedef typename Graph::TrivNodeIt NodeIt; |
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| 59 | typedef typename Graph::TrivEdgeIt EdgeIt; |
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| 60 | typedef typename Graph::NodeIt EachNodeIt; |
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| 61 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 62 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 63 | |
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| 64 | Graph& G; |
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| 65 | NodeIt s; |
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| 66 | NodeIt t; |
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| 67 | FlowMap flow; |
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| 68 | CapMap& capacity; |
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| 69 | T value; |
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| 70 | |
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| 71 | public: |
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| 72 | double time; |
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| 73 | preflow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) : |
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| 74 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) |
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| 75 | { |
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| 76 | |
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| 77 | bool phase=0; //phase 0 is the 1st phase, phase 1 is the 2nd |
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| 78 | int n=G.numNodes(); |
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| 79 | int heur0=(int)(H0*n); //time while running 'bound decrease' |
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| 80 | int heur1=(int)(H1*n); //time while running 'highest label' |
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| 81 | int heur=heur1; //starting time interval (#of relabels) |
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| 82 | bool what_heur=1; |
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| 83 | /* |
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| 84 | what_heur is 0 in case 'bound decrease' |
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| 85 | and 1 in case 'highest label' |
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| 86 | */ |
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| 87 | bool end=false; |
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| 88 | /* |
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| 89 | Needed for 'bound decrease', 'true' |
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| 90 | means no active nodes are above bound b. |
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| 91 | */ |
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| 92 | int relabel=0; |
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| 93 | int k=n-2; //bound on the highest level under n containing a node |
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| 94 | int b=k; //bound on the highest level under n of an active node |
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| 95 | |
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| 96 | typename Graph::NodeMap<int> level(G,n); |
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| 97 | typename Graph::NodeMap<T> excess(G); |
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| 98 | |
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| 99 | std::vector<NodeIt> active(n); |
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| 100 | typename Graph::NodeMap<NodeIt> next(G); |
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| 101 | //Stack of the active nodes in level i < n. |
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| 102 | //We use it in both phases. |
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| 103 | |
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| 104 | typename Graph::NodeMap<NodeIt> left(G); |
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| 105 | typename Graph::NodeMap<NodeIt> right(G); |
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| 106 | std::vector<NodeIt> level_list(n); |
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| 107 | /* |
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| 108 | List of the nodes in level i<n. |
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| 109 | */ |
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| 110 | |
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| 111 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 112 | level.set(t,0); |
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| 113 | std::queue<NodeIt> bfs_queue; |
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| 114 | bfs_queue.push(t); |
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| 115 | |
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| 116 | while (!bfs_queue.empty()) { |
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| 117 | |
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| 118 | NodeIt v=bfs_queue.front(); |
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| 119 | bfs_queue.pop(); |
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| 120 | int l=level.get(v)+1; |
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| 121 | |
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| 122 | for(InEdgeIt e=G.firstIn(v); e; G.next(e)) { |
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| 123 | NodeIt w=G.tail(e); |
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| 124 | if ( level.get(w) == n && w != s ) { |
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| 125 | bfs_queue.push(w); |
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| 126 | NodeIt first=level_list[l]; |
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| 127 | if ( first ) left.set(first,w); |
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| 128 | right.set(w,first); |
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| 129 | level_list[l]=w; |
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| 130 | level.set(w, l); |
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| 131 | } |
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| 132 | } |
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| 133 | } |
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| 134 | |
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| 135 | level.set(s,n); |
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| 136 | |
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| 137 | |
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| 138 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 139 | for(OutEdgeIt e=G.firstOut(s); e; G.next(e)) |
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| 140 | { |
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| 141 | T c=capacity.get(e); |
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| 142 | if ( c == 0 ) continue; |
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| 143 | NodeIt w=G.head(e); |
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| 144 | if ( level.get(w) < n ) { |
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| 145 | if ( excess.get(w) == 0 && w!=t ) { |
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| 146 | next.set(w,active[level.get(w)]); |
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| 147 | active[level.get(w)]=w; |
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| 148 | } |
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| 149 | flow.set(e, c); |
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| 150 | excess.set(w, excess.get(w)+c); |
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| 151 | } |
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| 152 | } |
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| 153 | |
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| 154 | /* |
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| 155 | End of preprocessing |
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| 156 | */ |
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| 157 | |
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| 158 | |
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| 159 | |
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| 160 | /* |
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| 161 | Push/relabel on the highest level active nodes. |
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| 162 | */ |
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| 163 | while ( true ) { |
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| 164 | |
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| 165 | if ( b == 0 ) { |
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| 166 | if ( phase ) break; |
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| 167 | |
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| 168 | if ( !what_heur && !end && k > 0 ) { |
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| 169 | b=k; |
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| 170 | end=true; |
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| 171 | } else { |
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| 172 | phase=1; |
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| 173 | time=currTime(); |
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| 174 | level.set(s,0); |
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| 175 | std::queue<NodeIt> bfs_queue; |
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| 176 | bfs_queue.push(s); |
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| 177 | |
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| 178 | while (!bfs_queue.empty()) { |
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| 179 | |
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| 180 | NodeIt v=bfs_queue.front(); |
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| 181 | bfs_queue.pop(); |
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| 182 | int l=level.get(v)+1; |
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| 183 | |
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| 184 | for(InEdgeIt e=G.firstIn(v); e; G.next(e)) { |
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| 185 | if ( capacity.get(e) == flow.get(e) ) continue; |
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| 186 | NodeIt u=G.tail(e); |
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| 187 | if ( level.get(u) >= n ) { |
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| 188 | bfs_queue.push(u); |
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| 189 | level.set(u, l); |
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| 190 | if ( excess.get(u) > 0 ) { |
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| 191 | next.set(u,active[l]); |
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| 192 | active[l]=u; |
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| 193 | } |
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| 194 | } |
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| 195 | } |
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| 196 | |
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| 197 | for(OutEdgeIt e=G.firstOut(v); e; G.next(e)) { |
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| 198 | if ( 0 == flow.get(e) ) continue; |
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| 199 | NodeIt u=G.head(e); |
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| 200 | if ( level.get(u) >= n ) { |
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| 201 | bfs_queue.push(u); |
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| 202 | level.set(u, l); |
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| 203 | if ( excess.get(u) > 0 ) { |
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| 204 | next.set(u,active[l]); |
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| 205 | active[l]=u; |
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| 206 | } |
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| 207 | } |
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| 208 | } |
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| 209 | } |
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| 210 | b=n-2; |
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| 211 | } |
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| 212 | |
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| 213 | } |
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| 214 | |
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| 215 | |
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| 216 | if ( !active[b] ) --b; |
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| 217 | else { |
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| 218 | end=false; |
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| 219 | |
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| 220 | NodeIt w=active[b]; |
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| 221 | active[b]=next.get(w); |
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| 222 | int lev=level.get(w); |
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| 223 | T exc=excess.get(w); |
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| 224 | int newlevel=n; //bound on the next level of w |
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| 225 | |
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| 226 | for(OutEdgeIt e=G.firstOut(w); e; G.next(e)) { |
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| 227 | |
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| 228 | if ( flow.get(e) == capacity.get(e) ) continue; |
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| 229 | NodeIt v=G.head(e); |
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| 230 | //e=wv |
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| 231 | |
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| 232 | if( lev > level.get(v) ) { |
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| 233 | /*Push is allowed now*/ |
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| 234 | |
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| 235 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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| 236 | int lev_v=level.get(v); |
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| 237 | next.set(v,active[lev_v]); |
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| 238 | active[lev_v]=v; |
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| 239 | } |
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| 240 | |
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| 241 | T cap=capacity.get(e); |
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| 242 | T flo=flow.get(e); |
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| 243 | T remcap=cap-flo; |
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| 244 | |
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| 245 | if ( remcap >= exc ) { |
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| 246 | /*A nonsaturating push.*/ |
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| 247 | |
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| 248 | flow.set(e, flo+exc); |
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| 249 | excess.set(v, excess.get(v)+exc); |
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| 250 | exc=0; |
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| 251 | break; |
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| 252 | |
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| 253 | } else { |
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| 254 | /*A saturating push.*/ |
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| 255 | |
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| 256 | flow.set(e, cap); |
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| 257 | excess.set(v, excess.get(v)+remcap); |
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| 258 | exc-=remcap; |
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| 259 | } |
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| 260 | } else if ( newlevel > level.get(v) ){ |
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| 261 | newlevel = level.get(v); |
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| 262 | } |
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| 263 | |
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| 264 | } //for out edges wv |
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| 265 | |
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| 266 | |
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| 267 | if ( exc > 0 ) { |
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| 268 | for( InEdgeIt e=G.firstIn(w); e; G.next(e)) { |
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| 269 | |
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| 270 | if( flow.get(e) == 0 ) continue; |
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| 271 | NodeIt v=G.tail(e); |
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| 272 | //e=vw |
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| 273 | |
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| 274 | if( lev > level.get(v) ) { |
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| 275 | /*Push is allowed now*/ |
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| 276 | |
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| 277 | if ( excess.get(v)==0 && v!=t && v!=s ) { |
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| 278 | int lev_v=level.get(v); |
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| 279 | next.set(v,active[lev_v]); |
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| 280 | active[lev_v]=v; |
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| 281 | } |
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| 282 | |
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| 283 | T flo=flow.get(e); |
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| 284 | |
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| 285 | if ( flo >= exc ) { |
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| 286 | /*A nonsaturating push.*/ |
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| 287 | |
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| 288 | flow.set(e, flo-exc); |
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| 289 | excess.set(v, excess.get(v)+exc); |
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| 290 | exc=0; |
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| 291 | break; |
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| 292 | } else { |
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| 293 | /*A saturating push.*/ |
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| 294 | |
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| 295 | excess.set(v, excess.get(v)+flo); |
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| 296 | exc-=flo; |
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| 297 | flow.set(e,0); |
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| 298 | } |
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| 299 | } else if ( newlevel > level.get(v) ) { |
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| 300 | newlevel = level.get(v); |
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| 301 | } |
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| 302 | } //for in edges vw |
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| 303 | |
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| 304 | } // if w still has excess after the out edge for cycle |
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| 305 | |
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| 306 | excess.set(w, exc); |
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| 307 | |
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| 308 | /* |
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| 309 | Relabel |
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| 310 | */ |
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| 311 | |
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| 312 | |
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| 313 | if ( exc > 0 ) { |
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| 314 | //now 'lev' is the old level of w |
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| 315 | |
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| 316 | if ( phase ) { |
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| 317 | level.set(w,++newlevel); |
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| 318 | next.set(w,active[newlevel]); |
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| 319 | active[newlevel]=w; |
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| 320 | b=newlevel; |
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| 321 | } else { |
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| 322 | //unlacing starts |
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| 323 | NodeIt right_n=right.get(w); |
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| 324 | NodeIt left_n=left.get(w); |
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| 325 | |
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| 326 | if ( right_n ) { |
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| 327 | if ( left_n ) { |
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| 328 | right.set(left_n, right_n); |
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| 329 | left.set(right_n, left_n); |
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| 330 | } else { |
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| 331 | level_list[lev]=right_n; |
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| 332 | left.set(right_n, NodeIt()); |
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| 333 | } |
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| 334 | } else { |
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| 335 | if ( left_n ) { |
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| 336 | right.set(left_n, NodeIt()); |
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| 337 | } else { |
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| 338 | level_list[lev]=NodeIt(); |
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| 339 | |
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| 340 | } |
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| 341 | } |
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| 342 | //unlacing ends |
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| 343 | |
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| 344 | //gapping starts |
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| 345 | if ( !level_list[lev] ) { |
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| 346 | |
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| 347 | for (int i=lev; i!=k ; ) { |
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| 348 | NodeIt v=level_list[++i]; |
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| 349 | while ( v ) { |
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| 350 | level.set(v,n); |
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| 351 | v=right.get(v); |
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| 352 | } |
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| 353 | level_list[i]=NodeIt(); |
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| 354 | if ( !what_heur ) active[i]=NodeIt(); |
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| 355 | } |
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| 356 | |
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| 357 | level.set(w,n); |
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| 358 | b=lev-1; |
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| 359 | k=b; |
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| 360 | //gapping ends |
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| 361 | } else { |
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| 362 | |
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| 363 | if ( newlevel == n ) level.set(w,n); |
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| 364 | else { |
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| 365 | level.set(w,++newlevel); |
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| 366 | next.set(w,active[newlevel]); |
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| 367 | active[newlevel]=w; |
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| 368 | if ( what_heur ) b=newlevel; |
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| 369 | if ( k < newlevel ) ++k; |
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| 370 | NodeIt first=level_list[newlevel]; |
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| 371 | if ( first ) left.set(first,w); |
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| 372 | right.set(w,first); |
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| 373 | left.set(w,NodeIt()); |
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| 374 | level_list[newlevel]=w; |
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| 375 | } |
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| 376 | } |
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| 377 | |
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| 378 | |
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| 379 | ++relabel; |
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| 380 | if ( relabel >= heur ) { |
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| 381 | relabel=0; |
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| 382 | if ( what_heur ) { |
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| 383 | what_heur=0; |
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| 384 | heur=heur0; |
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| 385 | end=false; |
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| 386 | } else { |
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| 387 | what_heur=1; |
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| 388 | heur=heur1; |
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| 389 | b=k; |
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| 390 | } |
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| 391 | } |
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| 392 | } //phase 0 |
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| 393 | |
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| 394 | |
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| 395 | } // if ( exc > 0 ) |
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| 396 | |
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| 397 | |
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| 398 | } // if stack[b] is nonempty |
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| 399 | |
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| 400 | } // while(true) |
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| 401 | |
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| 402 | |
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| 403 | value = excess.get(t); |
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| 404 | /*Max flow value.*/ |
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| 405 | |
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| 406 | } //void run() |
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| 407 | |
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| 408 | |
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| 409 | |
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| 410 | |
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| 411 | |
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| 412 | /* |
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| 413 | Returns the maximum value of a flow. |
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| 414 | */ |
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| 415 | |
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| 416 | T maxFlow() { |
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| 417 | return value; |
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| 418 | } |
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| 419 | |
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| 420 | |
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| 421 | |
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| 422 | /* |
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| 423 | For the maximum flow x found by the algorithm, |
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| 424 | it returns the flow value on edge e, i.e. x(e). |
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| 425 | */ |
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| 426 | |
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| 427 | T flowOnEdge(EdgeIt e) { |
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| 428 | return flow.get(e); |
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| 429 | } |
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| 430 | |
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| 431 | |
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| 432 | |
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| 433 | FlowMap Flow() { |
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| 434 | return flow; |
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| 435 | } |
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| 436 | |
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| 437 | |
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| 438 | |
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| 439 | void Flow(FlowMap& _flow ) { |
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| 440 | for(EachNodeIt v=G.firstNode() ; v; G.next(v)) |
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| 441 | _flow.set(v,flow.get(v)); |
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| 442 | } |
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| 443 | |
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| 444 | |
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| 445 | |
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| 446 | /* |
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| 447 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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| 448 | */ |
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| 449 | |
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| 450 | template<typename _CutMap> |
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| 451 | void minMinCut(_CutMap& M) { |
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| 452 | |
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| 453 | std::queue<NodeIt> queue; |
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| 454 | |
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| 455 | M.set(s,true); |
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| 456 | queue.push(s); |
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| 457 | |
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| 458 | while (!queue.empty()) { |
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| 459 | NodeIt w=queue.front(); |
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| 460 | queue.pop(); |
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| 461 | |
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| 462 | for(OutEdgeIt e=G.firstOut(w) ; e; G.next(e)) { |
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| 463 | NodeIt v=G.head(e); |
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| 464 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 465 | queue.push(v); |
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| 466 | M.set(v, true); |
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| 467 | } |
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| 468 | } |
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| 469 | |
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| 470 | for(InEdgeIt e=G.firstIn(w) ; e; G.next(e)) { |
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| 471 | NodeIt v=G.tail(e); |
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| 472 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 473 | queue.push(v); |
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| 474 | M.set(v, true); |
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| 475 | } |
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| 476 | } |
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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 | /* |
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| 483 | Returns the maximum min cut, by a reverse bfs |
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| 484 | from t in the residual graph. |
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| 485 | */ |
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| 486 | |
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| 487 | template<typename _CutMap> |
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| 488 | void maxMinCut(_CutMap& M) { |
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| 489 | |
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| 490 | std::queue<NodeIt> queue; |
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| 491 | |
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| 492 | M.set(t,true); |
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| 493 | queue.push(t); |
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| 494 | |
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| 495 | while (!queue.empty()) { |
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| 496 | NodeIt w=queue.front(); |
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| 497 | queue.pop(); |
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| 498 | |
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| 499 | for(InEdgeIt e=G.firstIn(w) ; e; G.next(e)) { |
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| 500 | NodeIt v=G.tail(e); |
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| 501 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 502 | queue.push(v); |
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| 503 | M.set(v, true); |
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| 504 | } |
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| 505 | } |
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| 506 | |
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| 507 | for(OutEdgeIt e=G.firstOut(w) ; e; G.next(e)) { |
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| 508 | NodeIt v=G.head(e); |
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| 509 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 510 | queue.push(v); |
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| 511 | M.set(v, true); |
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| 512 | } |
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| 513 | } |
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| 514 | } |
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| 515 | |
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| 516 | for(EachNodeIt v=G.firstNode() ; v; G.next(v)) { |
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| 517 | M.set(v, !M.get(v)); |
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| 518 | } |
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| 519 | |
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| 520 | } |
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| 521 | |
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| 522 | |
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| 523 | |
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| 524 | template<typename CutMap> |
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| 525 | void minCut(CutMap& M) { |
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| 526 | minMinCut(M); |
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| 527 | } |
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| 528 | |
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| 529 | |
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| 530 | }; |
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| 531 | }//namespace marci |
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| 532 | #endif |
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| 533 | |
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| 534 | |
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| 535 | |
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| 536 | |
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