[21] | 1 | /* |
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| 2 | preflow_push_max_flow_hh |
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| 3 | by jacint. |
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| 4 | Runs a preflow push algorithm with the modification, |
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| 5 | that we do not push on nodes with level at least n. |
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| 6 | Moreover, if a level gets empty, we put all nodes above that |
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| 7 | level to level n. Hence, in the end, we arrive at a maximum preflow |
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| 8 | with value of a max flow value. An empty level gives a minimum cut. |
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| 9 | |
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| 10 | Member functions: |
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| 11 | |
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| 12 | void run() : runs the algorithm |
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| 13 | |
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| 14 | The following functions should be used after run() was already run. |
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| 15 | |
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| 16 | T maxflow() : returns the value of a maximum flow |
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| 17 | |
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| 18 | node_property_vector<graph_type, bool> mincut(): returns a |
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| 19 | characteristic vector of a minimum cut. |
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| 20 | */ |
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| 21 | |
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| 22 | #ifndef PREFLOW_PUSH_MAX_FLOW_HH |
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| 23 | #define PREFLOW_PUSH_MAX_FLOW_HH |
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| 24 | |
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| 25 | #include <algorithm> |
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| 26 | #include <vector> |
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| 27 | #include <stack> |
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| 28 | |
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| 29 | #include <marci_list_graph.hh> |
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| 30 | #include <marci_graph_traits.hh> |
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| 31 | #include <marci_property_vector.hh> |
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| 32 | #include <reverse_bfs.hh> |
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| 33 | |
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| 34 | |
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| 35 | namespace marci { |
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| 36 | |
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| 37 | template <typename graph_type, typename T> |
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| 38 | class preflow_push_max_flow { |
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| 39 | |
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| 40 | typedef typename graph_traits<graph_type>::node_iterator node_iterator; |
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| 41 | typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator; |
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| 42 | typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator; |
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| 43 | typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator; |
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| 44 | |
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| 45 | graph_type& G; |
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| 46 | node_iterator s; |
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| 47 | node_iterator t; |
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| 48 | edge_property_vector<graph_type, T>& capacity; |
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| 49 | T value; |
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| 50 | node_property_vector<graph_type, bool> mincutvector; |
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| 51 | |
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| 52 | |
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| 53 | |
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| 54 | public: |
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| 55 | |
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| 56 | preflow_push_max_flow(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { } |
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| 57 | |
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| 58 | |
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| 59 | /* |
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| 60 | The run() function runs a modified version of the highest label preflow-push, which only |
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| 61 | finds a maximum preflow, hence giving the value of a maximum flow. |
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| 62 | */ |
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| 63 | void run() { |
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| 64 | |
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| 65 | edge_property_vector<graph_type, T> flow(G, 0); //the flow value, 0 everywhere |
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| 66 | node_property_vector<graph_type, int> level(G); //level of node |
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| 67 | node_property_vector<graph_type, T> excess(G); //excess of node |
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| 68 | |
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| 69 | int n=number_of(G.first_node()); //number of nodes |
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| 70 | int b=n-2; |
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| 71 | /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/ |
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| 72 | |
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| 73 | std::vector<int> numb(n); //The number of nodes on level i < n. |
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| 74 | |
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| 75 | std::vector<std::stack<node_iterator> > stack(2*n-1); //Stack of the active nodes in level i. |
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| 76 | |
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| 77 | |
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| 78 | |
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| 79 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 80 | |
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| 81 | reverse_bfs<list_graph> bfs(G, t); |
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| 82 | bfs.run(); |
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[30] | 83 | for(each_node_iterator v=G.first_node(); v.valid(); ++v) |
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[21] | 84 | { |
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| 85 | int dist=bfs.dist(v); |
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| 86 | level.put(v, dist); |
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| 87 | ++numb[dist]; |
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| 88 | } |
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| 89 | |
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| 90 | /*The level of s is fixed to n*/ |
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| 91 | level.put(s,n); |
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| 92 | |
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| 93 | |
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| 94 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 95 | |
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[30] | 96 | for(out_edge_iterator i=G.first_out_edge(s); i.valid(); ++i) |
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[21] | 97 | { |
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| 98 | node_iterator w=G.head(i); |
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| 99 | flow.put(i, capacity.get(i)); |
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| 100 | stack[bfs.dist(w)].push(w); |
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| 101 | excess.put(w, capacity.get(i)); |
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| 102 | } |
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| 103 | |
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| 104 | |
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| 105 | /* |
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| 106 | End of preprocessing |
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| 107 | */ |
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| 108 | |
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| 109 | |
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| 110 | |
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| 111 | |
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| 112 | /* |
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| 113 | Push/relabel on the highest level active nodes. |
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| 114 | */ |
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| 115 | |
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| 116 | /*While there exists an active node.*/ |
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| 117 | while (b) { |
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| 118 | |
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| 119 | /*We decrease the bound if there is no active node of level b.*/ |
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| 120 | if (stack[b].empty()) { |
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| 121 | --b; |
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| 122 | } else { |
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| 123 | |
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| 124 | node_iterator w=stack[b].top(); //w is the highest label active node. |
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| 125 | stack[b].pop(); //We delete w from the stack. |
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| 126 | |
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| 127 | int newlevel=2*n-2; //In newlevel we maintain the next level of w. |
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| 128 | |
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[30] | 129 | for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) { |
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[21] | 130 | node_iterator v=G.head(e); |
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| 131 | /*e is the edge wv.*/ |
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| 132 | |
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| 133 | if (flow.get(e)<capacity.get(e)) { |
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| 134 | /*e is an edge of the residual graph */ |
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| 135 | |
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| 136 | if(level.get(w)==level.get(v)+1) { |
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| 137 | /*Push is allowed now*/ |
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| 138 | |
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| 139 | if (capacity.get(e)-flow.get(e) > excess.get(w)) { |
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| 140 | /*A nonsaturating push.*/ |
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| 141 | |
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| 142 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 143 | /*v becomes active.*/ |
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| 144 | |
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| 145 | flow.put(e, flow.get(e)+excess.get(w)); |
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| 146 | excess.put(v, excess.get(v)+excess.get(w)); |
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| 147 | excess.put(w,0); |
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| 148 | //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl; |
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| 149 | break; |
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| 150 | } else { |
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| 151 | /*A saturating push.*/ |
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| 152 | |
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| 153 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 154 | /*v becomes active.*/ |
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| 155 | |
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| 156 | excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
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| 157 | excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
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| 158 | flow.put(e, capacity.get(e)); |
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| 159 | //std::cout << w <<" " << v <<" elore elen sat pump " << std::endl; |
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| 160 | if (excess.get(w)==0) break; |
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| 161 | /*If w is not active any more, then we go on to the next node.*/ |
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| 162 | |
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| 163 | } // if (capacity.get(e)-flow.get(e) > excess.get(w)) |
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| 164 | } // if (level.get(w)==level.get(v)+1) |
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| 165 | |
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| 166 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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| 167 | |
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| 168 | } //if (flow.get(e)<capacity.get(e)) |
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| 169 | |
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[30] | 170 | } //for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) |
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[21] | 171 | |
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| 172 | |
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| 173 | |
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[30] | 174 | for(in_edge_iterator e=G.first_in_edge(w); e.valid(); ++e) { |
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[21] | 175 | node_iterator v=G.tail(e); |
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| 176 | /*e is the edge vw.*/ |
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| 177 | |
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| 178 | if (excess.get(w)==0) break; |
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| 179 | /*It may happen, that w became inactive in the first 'for' cycle.*/ |
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| 180 | |
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| 181 | if(flow.get(e)>0) { |
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| 182 | /*e is an edge of the residual graph */ |
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| 183 | |
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| 184 | if(level.get(w)==level.get(v)+1) { |
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| 185 | /*Push is allowed now*/ |
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| 186 | |
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| 187 | if (flow.get(e) > excess.get(w)) { |
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| 188 | /*A nonsaturating push.*/ |
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| 189 | |
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| 190 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 191 | /*v becomes active.*/ |
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| 192 | |
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| 193 | flow.put(e, flow.get(e)-excess.get(w)); |
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| 194 | excess.put(v, excess.get(v)+excess.get(w)); |
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| 195 | excess.put(w,0); |
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| 196 | //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl; |
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| 197 | break; |
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| 198 | } else { |
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| 199 | /*A saturating push.*/ |
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| 200 | |
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| 201 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 202 | /*v becomes active.*/ |
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| 203 | |
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| 204 | flow.put(e,0); |
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| 205 | excess.put(v, excess.get(v)+flow.get(e)); |
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| 206 | excess.put(w, excess.get(w)-flow.get(e)); |
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| 207 | //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl; |
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| 208 | if (excess.get(w)==0) { break;} |
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| 209 | } //if (flow.get(e) > excess.get(v)) |
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| 210 | } //if(level.get(w)==level.get(v)+1) |
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| 211 | |
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| 212 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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| 213 | //std::cout << "Leveldecrease of node " << w << " to " << newlevel << std::endl; |
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| 214 | |
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| 215 | } //if (flow.get(e)>0) |
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| 216 | |
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| 217 | } //for in-edge |
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| 218 | |
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| 219 | |
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| 220 | |
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| 221 | |
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| 222 | /* |
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| 223 | Relabel |
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| 224 | */ |
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| 225 | if (excess.get(w)>0) { |
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| 226 | /*Now newlevel <= n*/ |
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| 227 | |
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| 228 | int l=level.get(w); //l is the old level of w. |
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| 229 | --numb[l]; |
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| 230 | |
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| 231 | if (newlevel == n) { |
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| 232 | level.put(w,n); |
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| 233 | |
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| 234 | } else { |
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| 235 | |
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| 236 | if (numb[l]) { |
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| 237 | /*If the level of w remains nonempty.*/ |
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| 238 | |
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| 239 | level.put(w,++newlevel); |
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| 240 | ++numb[newlevel]; |
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| 241 | stack[newlevel].push(w); |
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| 242 | b=newlevel; |
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| 243 | } else { |
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| 244 | /*If the level of w gets empty.*/ |
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| 245 | |
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[30] | 246 | for (each_node_iterator v=G.first_node() ; v.valid() ; ++v) { |
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[21] | 247 | if (level.get(v) >= l ) { |
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| 248 | level.put(v,n); |
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| 249 | } |
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| 250 | } |
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| 251 | |
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| 252 | for (int i=l+1 ; i!=n ; ++i) numb[i]=0; |
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| 253 | } //if (numb[l]) |
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| 254 | |
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| 255 | } // if (newlevel = n) |
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| 256 | |
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| 257 | } // if (excess.get(w)>0) |
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| 258 | |
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| 259 | |
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| 260 | } //else |
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| 261 | |
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| 262 | } //while(b) |
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| 263 | |
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| 264 | value=excess.get(t); |
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| 265 | /*Max flow value.*/ |
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| 266 | |
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| 267 | |
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| 268 | |
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| 269 | /* |
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| 270 | We find an empty level, e. The nodes above this level give |
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| 271 | a minimum cut. |
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| 272 | */ |
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| 273 | |
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| 274 | int e=1; |
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| 275 | |
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| 276 | while(e) { |
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| 277 | if(numb[e]) ++e; |
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| 278 | else break; |
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| 279 | } |
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[30] | 280 | for (each_node_iterator v=G.first_node(); v.valid(); ++v) { |
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[21] | 281 | if (level.get(v) > e) mincutvector.put(v, true); |
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| 282 | } |
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| 283 | |
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| 284 | |
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| 285 | } // void run() |
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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 | Returns the maximum value of a flow. |
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| 291 | */ |
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| 292 | |
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| 293 | T maxflow() { |
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| 294 | return value; |
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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 a minimum cut. |
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| 301 | */ |
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| 302 | |
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| 303 | node_property_vector<graph_type, bool> mincut() { |
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| 304 | return mincutvector; |
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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 | }//namespace marci |
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| 310 | #endif |
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| 311 | |
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| 312 | |
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| 313 | |
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| 314 | |
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| 315 | |
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