[102] | 1 | // -*- C++ -*- |
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| 2 | /* |
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| 3 | preflow_hl4.h |
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| 4 | by jacint. |
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| 5 | Runs the two phase highest label preflow push algorithm. In phase 0 |
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| 6 | we maintain in a list the nodes in level i < n, and we maintain a |
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| 7 | bound k on the max level i < n containing a node, so we can do |
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| 8 | the gap heuristic fast. Phase 1 is the same. (The algorithm is the |
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| 9 | same as preflow.hl3, the only diff is that here we use the gap |
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| 10 | heuristic with the list of the nodes on level i, and not a bfs form the |
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| 11 | upgraded node.) |
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| 12 | |
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| 13 | In phase 1 we shift everything downwards by n. |
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| 14 | |
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| 15 | Member functions: |
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| 16 | |
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| 17 | void run() : runs the algorithm |
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| 18 | |
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| 19 | The following functions should be used after run() was already run. |
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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 allflow() : returns a maximum flow |
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| 26 | |
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| 27 | void allflow(FlowMap& _flow ) : returns a maximum flow |
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| 28 | |
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| 29 | void mincut(CutMap& M) : sets M to the characteristic vector of a |
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| 30 | minimum cut. M should be a map of bools initialized to false. |
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| 31 | |
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| 32 | void min_mincut(CutMap& M) : sets M to the characteristic vector of the |
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| 33 | minimum min cut. M should be a map of bools initialized to false. |
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| 34 | |
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| 35 | void max_mincut(CutMap& M) : sets M to the characteristic vector of the |
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| 36 | maximum min cut. M should be a map of bools initialized to false. |
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| 37 | |
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| 38 | */ |
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| 39 | |
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| 40 | #ifndef PREFLOW_HL4_H |
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| 41 | #define PREFLOW_HL4_H |
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| 42 | |
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| 43 | #include <vector> |
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| 44 | #include <stack> |
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| 45 | #include <queue> |
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| 46 | |
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| 47 | namespace marci { |
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| 48 | |
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| 49 | template <typename Graph, typename T, |
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| 50 | typename FlowMap=typename Graph::EdgeMap<T>, |
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| 51 | typename CapMap=typename Graph::EdgeMap<T> > |
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| 52 | class preflow_hl4 { |
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| 53 | |
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| 54 | typedef typename Graph::NodeIt NodeIt; |
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| 55 | typedef typename Graph::EdgeIt EdgeIt; |
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| 56 | typedef typename Graph::EachNodeIt EachNodeIt; |
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| 57 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 58 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 59 | |
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| 60 | Graph& G; |
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| 61 | NodeIt s; |
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| 62 | NodeIt t; |
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| 63 | FlowMap flow; |
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| 64 | CapMap& capacity; |
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| 65 | T value; |
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| 66 | |
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| 67 | public: |
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| 68 | |
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| 69 | preflow_hl4(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) : |
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| 70 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { } |
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| 71 | |
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| 72 | |
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| 73 | void run() { |
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| 74 | |
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| 75 | bool phase=0; |
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| 76 | int n=G.nodeNum(); |
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| 77 | int k=n-2; |
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| 78 | int b=k; |
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| 79 | /* |
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| 80 | b is a bound on the highest level of the stack. |
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| 81 | k is a bound on the highest nonempty level i < n. |
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| 82 | */ |
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| 83 | |
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| 84 | typename Graph::NodeMap<int> level(G,n); |
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| 85 | typename Graph::NodeMap<T> excess(G); |
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| 86 | std::vector<std::stack<NodeIt> > stack(n); |
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| 87 | //Stack of the active nodes in level i < n. |
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| 88 | //We use it in both phases. |
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| 89 | |
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| 90 | typename Graph::NodeMap<NodeIt> left(G); |
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| 91 | typename Graph::NodeMap<NodeIt> right(G); |
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| 92 | std::vector<NodeIt> level_list(n); |
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| 93 | /* |
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| 94 | Needed for the list of the nodes in level i. |
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| 95 | */ |
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| 96 | |
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| 97 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 98 | level.set(t,0); |
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| 99 | std::queue<NodeIt> bfs_queue; |
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| 100 | bfs_queue.push(t); |
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| 101 | |
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| 102 | while (!bfs_queue.empty()) { |
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| 103 | |
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| 104 | NodeIt v=bfs_queue.front(); |
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| 105 | bfs_queue.pop(); |
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| 106 | int l=level.get(v)+1; |
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| 107 | |
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| 108 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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| 109 | NodeIt w=G.tail(e); |
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| 110 | if ( level.get(w) == n ) { |
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| 111 | bfs_queue.push(w); |
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| 112 | NodeIt first=level_list[l]; |
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| 113 | if ( first != 0 ) left.set(first,w); |
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| 114 | right.set(w,first); |
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| 115 | level_list[l]=w; |
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| 116 | level.set(w, l); |
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| 117 | } |
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| 118 | } |
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| 119 | } |
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| 120 | |
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| 121 | level.set(s,n); |
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| 122 | |
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| 123 | |
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| 124 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 125 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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| 126 | { |
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| 127 | T c=capacity.get(e); |
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| 128 | if ( c == 0 ) continue; |
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| 129 | NodeIt w=G.head(e); |
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| 130 | if ( level.get(w) < n ) { |
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| 131 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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| 132 | flow.set(e, c); |
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| 133 | excess.set(w, excess.get(w)+c); |
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| 134 | } |
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| 135 | } |
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| 136 | /* |
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| 137 | End of preprocessing |
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| 138 | */ |
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| 139 | |
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| 140 | |
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| 141 | /* |
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| 142 | Push/relabel on the highest level active nodes. |
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| 143 | */ |
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| 144 | while ( true ) { |
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| 145 | |
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| 146 | if ( b == 0 ) { |
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| 147 | if ( phase ) break; |
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| 148 | |
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| 149 | /* |
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| 150 | In the end of phase 0 we apply a bfs from s in |
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| 151 | the residual graph. |
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| 152 | */ |
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| 153 | phase=1; |
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| 154 | level.set(s,0); |
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| 155 | std::queue<NodeIt> bfs_queue; |
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| 156 | bfs_queue.push(s); |
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| 157 | |
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| 158 | while (!bfs_queue.empty()) { |
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| 159 | |
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| 160 | NodeIt v=bfs_queue.front(); |
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| 161 | bfs_queue.pop(); |
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| 162 | int l=level.get(v)+1; |
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| 163 | |
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| 164 | for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) { |
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| 165 | if ( capacity.get(e) == flow.get(e) ) continue; |
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| 166 | NodeIt u=G.tail(e); |
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| 167 | if ( level.get(u) >= n ) { |
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| 168 | bfs_queue.push(u); |
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| 169 | level.set(u, l); |
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| 170 | if ( excess.get(u) > 0 ) stack[l].push(u); |
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| 171 | } |
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| 172 | } |
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| 173 | |
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| 174 | for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) { |
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| 175 | if ( 0 == flow.get(e) ) continue; |
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| 176 | NodeIt u=G.head(e); |
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| 177 | if ( level.get(u) >= n ) { |
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| 178 | bfs_queue.push(u); |
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| 179 | level.set(u, l); |
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| 180 | if ( excess.get(u) > 0 ) stack[l].push(u); |
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| 181 | } |
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| 182 | } |
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| 183 | } |
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| 184 | b=n-2; |
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| 185 | } |
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| 186 | |
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| 187 | |
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| 188 | if ( stack[b].empty() ) --b; |
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| 189 | else { |
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| 190 | |
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| 191 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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| 192 | stack[b].pop(); |
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| 193 | int lev=level.get(w); |
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| 194 | T exc=excess.get(w); |
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| 195 | int newlevel=n; //In newlevel we bound the next level of w. |
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| 196 | |
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| 197 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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| 198 | |
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| 199 | if ( flow.get(e) == capacity.get(e) ) continue; |
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| 200 | NodeIt v=G.head(e); |
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| 201 | //e=wv |
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| 202 | |
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| 203 | if( lev > level.get(v) ) { |
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| 204 | /*Push is allowed now*/ |
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| 205 | |
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| 206 | if ( excess.get(v)==0 && v!=t && v!=s ) |
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| 207 | stack[level.get(v)].push(v); |
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| 208 | /*v becomes active.*/ |
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| 209 | |
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| 210 | T cap=capacity.get(e); |
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| 211 | T flo=flow.get(e); |
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| 212 | T remcap=cap-flo; |
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| 213 | |
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| 214 | if ( remcap >= 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 | |
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| 222 | } else { |
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| 223 | /*A saturating push.*/ |
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| 224 | |
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| 225 | flow.set(e, cap); |
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| 226 | excess.set(v, excess.get(v)+remcap); |
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| 227 | exc-=remcap; |
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| 228 | } |
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| 229 | } else if ( newlevel > level.get(v) ){ |
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| 230 | newlevel = level.get(v); |
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| 231 | } |
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| 232 | |
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| 233 | } //for out edges wv |
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| 234 | |
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| 235 | |
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| 236 | if ( exc > 0 ) { |
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| 237 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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| 238 | |
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| 239 | if( flow.get(e) == 0 ) continue; |
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| 240 | NodeIt v=G.tail(e); |
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| 241 | //e=vw |
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| 242 | |
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| 243 | if( lev > level.get(v) ) { |
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| 244 | /*Push is allowed now*/ |
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| 245 | |
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| 246 | if ( excess.get(v)==0 && v!=t && v!=s ) |
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| 247 | stack[level.get(v)].push(v); |
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| 248 | /*v becomes active.*/ |
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| 249 | |
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| 250 | T flo=flow.get(e); |
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| 251 | |
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| 252 | if ( flo >= exc ) { |
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| 253 | /*A nonsaturating push.*/ |
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| 254 | |
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| 255 | flow.set(e, flo-exc); |
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| 256 | excess.set(v, excess.get(v)+exc); |
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| 257 | exc=0; |
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| 258 | break; |
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| 259 | } else { |
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| 260 | /*A saturating push.*/ |
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| 261 | |
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| 262 | excess.set(v, excess.get(v)+flo); |
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| 263 | exc-=flo; |
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| 264 | flow.set(e,0); |
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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 | } //for in edges vw |
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| 270 | |
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| 271 | } // if w still has excess after the out edge for cycle |
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| 272 | |
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| 273 | excess.set(w, exc); |
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| 274 | |
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| 275 | /* |
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| 276 | Relabel |
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| 277 | */ |
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| 278 | |
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| 279 | if ( exc > 0 ) { |
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| 280 | //now 'lev' is the old level of w |
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| 281 | |
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| 282 | if ( phase ) { |
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| 283 | level.set(w,++newlevel); |
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| 284 | stack[newlevel].push(w); |
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| 285 | b=newlevel; |
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| 286 | } else { |
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| 287 | //unlacing |
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| 288 | NodeIt right_n=right.get(w); |
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| 289 | NodeIt left_n=left.get(w); |
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| 290 | |
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| 291 | if ( right_n != 0 ) { |
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| 292 | if ( left_n != 0 ) { |
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| 293 | right.set(left_n, right_n); |
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| 294 | left.set(right_n, left_n); |
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| 295 | } else { |
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| 296 | level_list[lev]=right_n; |
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| 297 | left.set(right_n, 0); |
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| 298 | } |
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| 299 | } else { |
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| 300 | if ( left_n != 0 ) { |
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| 301 | right.set(left_n, 0); |
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| 302 | } else { |
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| 303 | level_list[lev]=0; |
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| 304 | } |
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| 305 | } |
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| 306 | |
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| 307 | |
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| 308 | if ( level_list[lev]==0 ) { |
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| 309 | |
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| 310 | for (int i=lev; i!=k ; ) { |
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| 311 | NodeIt v=level_list[++i]; |
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| 312 | while ( v != 0 ) { |
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| 313 | level.set(v,n); |
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| 314 | v=right.get(v); |
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| 315 | } |
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| 316 | level_list[i]=0; |
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| 317 | } |
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| 318 | |
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| 319 | level.set(w,n); |
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| 320 | |
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| 321 | b=--lev; |
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| 322 | k=b; |
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| 323 | |
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| 324 | } else { |
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| 325 | |
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| 326 | if ( newlevel == n ) { |
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| 327 | level.set(w,n); |
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| 328 | } else { |
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| 329 | |
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| 330 | level.set(w,++newlevel); |
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| 331 | stack[newlevel].push(w); |
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| 332 | b=newlevel; |
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| 333 | if ( k < newlevel ) ++k; |
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| 334 | NodeIt first=level_list[newlevel]; |
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| 335 | if ( first != 0 ) left.set(first,w); |
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| 336 | right.set(w,first); |
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| 337 | left.set(w,0); |
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| 338 | level_list[newlevel]=w; |
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| 339 | } |
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| 340 | } |
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| 341 | } //phase 0 |
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| 342 | } // if ( exc > 0 ) |
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| 343 | |
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| 344 | |
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| 345 | } // if stack[b] is nonempty |
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| 346 | |
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| 347 | } // while(true) |
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| 348 | |
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| 349 | |
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| 350 | value = excess.get(t); |
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| 351 | /*Max flow value.*/ |
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| 352 | |
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| 353 | |
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| 354 | } //void run() |
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| 355 | |
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| 356 | |
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| 357 | |
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| 358 | |
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| 359 | |
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| 360 | /* |
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| 361 | Returns the maximum value of a flow. |
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| 362 | */ |
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| 363 | |
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| 364 | T maxflow() { |
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| 365 | return value; |
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| 366 | } |
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| 367 | |
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| 368 | |
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| 369 | |
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| 370 | /* |
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| 371 | 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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| 372 | */ |
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| 373 | |
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| 374 | T flowonedge(EdgeIt e) { |
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| 375 | return flow.get(e); |
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| 376 | } |
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| 377 | |
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| 378 | |
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| 379 | |
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| 380 | FlowMap allflow() { |
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| 381 | return flow; |
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| 382 | } |
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| 383 | |
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| 384 | |
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| 385 | |
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| 386 | void allflow(FlowMap& _flow ) { |
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| 387 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) |
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| 388 | _flow.set(v,flow.get(v)); |
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| 389 | } |
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| 390 | |
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| 391 | |
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| 392 | |
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| 393 | /* |
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| 394 | Returns the minimum min cut, by a bfs from s in the residual graph. |
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| 395 | */ |
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| 396 | |
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| 397 | template<typename CutMap> |
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| 398 | void mincut(CutMap& M) { |
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| 399 | |
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| 400 | std::queue<NodeIt> queue; |
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| 401 | |
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| 402 | M.set(s,true); |
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| 403 | queue.push(s); |
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| 404 | |
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| 405 | while (!queue.empty()) { |
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| 406 | NodeIt w=queue.front(); |
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| 407 | queue.pop(); |
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| 408 | |
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| 409 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 410 | NodeIt v=G.head(e); |
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| 411 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 412 | queue.push(v); |
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| 413 | M.set(v, true); |
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| 414 | } |
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| 415 | } |
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| 416 | |
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| 417 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 418 | NodeIt v=G.tail(e); |
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| 419 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 420 | queue.push(v); |
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| 421 | M.set(v, true); |
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| 422 | } |
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| 423 | } |
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| 424 | |
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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 | |
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| 430 | |
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| 431 | /* |
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| 432 | Returns the maximum min cut, by a reverse bfs |
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| 433 | from t in the residual graph. |
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| 434 | */ |
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| 435 | |
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| 436 | template<typename CutMap> |
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| 437 | void max_mincut(CutMap& M) { |
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| 438 | |
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| 439 | std::queue<NodeIt> queue; |
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| 440 | |
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| 441 | M.set(t,true); |
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| 442 | queue.push(t); |
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| 443 | |
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| 444 | while (!queue.empty()) { |
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| 445 | NodeIt w=queue.front(); |
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| 446 | queue.pop(); |
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| 447 | |
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| 448 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 449 | NodeIt v=G.tail(e); |
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| 450 | if (!M.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 451 | queue.push(v); |
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| 452 | M.set(v, true); |
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| 453 | } |
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| 454 | } |
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| 455 | |
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| 456 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 457 | NodeIt v=G.head(e); |
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| 458 | if (!M.get(v) && flow.get(e) > 0 ) { |
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| 459 | queue.push(v); |
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| 460 | M.set(v, true); |
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| 461 | } |
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| 462 | } |
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| 463 | } |
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| 464 | |
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| 465 | for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) { |
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| 466 | M.set(v, !M.get(v)); |
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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 | |
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| 473 | template<typename CutMap> |
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| 474 | void min_mincut(CutMap& M) { |
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| 475 | mincut(M); |
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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 | }//namespace marci |
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| 482 | #endif |
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| 483 | |
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| 484 | |
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| 485 | |
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| 486 | |
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