[20] | 1 | /* |
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| 2 | preflow_push_hl.hh |
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| 3 | by jacint. |
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| 4 | Runs the highest label variant of the preflow push algorithm with |
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| 5 | running time O(n^2\sqrt(m)). |
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| 6 | |
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| 7 | Member functions: |
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| 8 | |
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| 9 | void run() : runs the algorithm |
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| 10 | |
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| 11 | The following functions should be used after run() was already run. |
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| 12 | |
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| 13 | T maxflow() : returns the value of a maximum flow |
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| 14 | |
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| 15 | T flowonedge(edge_iterator e) : for a fixed maximum flow x it returns x(e) |
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| 16 | |
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| 17 | edge_property_vector<graph_type, T> allflow() : returns the fixed maximum flow x |
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| 18 | |
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| 19 | node_property_vector<graph_type, bool> mincut() : returns a |
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| 20 | characteristic vector of a minimum cut. (An empty level |
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| 21 | in the algorithm gives a minimum cut.) |
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| 22 | */ |
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| 23 | |
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| 24 | #ifndef PREFLOW_PUSH_HL_HH |
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| 25 | #define PREFLOW_PUSH_HL_HH |
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| 26 | |
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| 27 | #include <algorithm> |
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| 28 | #include <vector> |
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| 29 | #include <stack> |
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| 30 | |
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| 31 | #include <marci_graph_traits.hh> |
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| 32 | #include <marci_property_vector.hh> |
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| 33 | #include <reverse_bfs.hh> |
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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_hl { |
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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>::edge_iterator edge_iterator; |
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| 42 | typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator; |
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| 43 | typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator; |
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| 44 | typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator; |
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| 45 | typedef typename graph_traits<graph_type>::each_edge_iterator each_edge_iterator; |
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| 46 | |
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| 47 | |
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| 48 | graph_type& G; |
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| 49 | node_iterator s; |
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| 50 | node_iterator t; |
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| 51 | edge_property_vector<graph_type, T> flow; |
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| 52 | edge_property_vector<graph_type, T>& capacity; |
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| 53 | T value; |
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| 54 | node_property_vector<graph_type, bool> mincutvector; |
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| 55 | |
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| 56 | |
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| 57 | public: |
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| 58 | |
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| 59 | preflow_push_hl(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), mincutvector(_G, true) { } |
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| 60 | |
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| 61 | |
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| 62 | |
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| 63 | |
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| 64 | /* |
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| 65 | The run() function runs the highest label preflow-push, |
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| 66 | running time: O(n^2\sqrt(m)) |
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| 67 | */ |
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| 68 | void run() { |
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| 69 | |
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| 70 | node_property_vector<graph_type, int> level(G); //level of node |
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| 71 | node_property_vector<graph_type, T> excess(G); //excess of node |
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| 72 | |
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| 73 | int n=number_of(G.first_node()); //number of nodes |
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| 74 | int b=n; |
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| 75 | /*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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| 76 | |
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| 77 | std::vector<std::stack<node_iterator> > stack(2*n-1); //Stack of the active nodes in level i. |
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| 78 | |
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| 79 | |
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| 80 | |
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| 81 | |
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| 82 | /*Reverse_bfs from t, to find the starting level.*/ |
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| 83 | |
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| 84 | reverse_bfs<list_graph> bfs(G, t); |
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| 85 | bfs.run(); |
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[30] | 86 | for(each_node_iterator v=G.first_node(); v.valid(); ++v) { |
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[20] | 87 | level.put(v, bfs.dist(v)); |
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| 88 | //std::cout << "the level of " << v << " is " << bfs.dist(v); |
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| 89 | } |
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| 90 | |
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| 91 | /*The level of s is fixed to n*/ |
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| 92 | level.put(s,n); |
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| 93 | |
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| 94 | |
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| 95 | |
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| 96 | |
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| 97 | |
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| 98 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 99 | |
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[30] | 100 | for(out_edge_iterator i=G.first_out_edge(s); i.valid(); ++i) |
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[20] | 101 | { |
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| 102 | node_iterator w=G.head(i); |
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| 103 | flow.put(i, capacity.get(i)); |
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| 104 | stack[bfs.dist(w)].push(w); |
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| 105 | excess.put(w, capacity.get(i)); |
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| 106 | } |
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| 107 | |
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| 108 | |
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| 109 | /* |
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| 110 | End of preprocessing |
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| 111 | */ |
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| 112 | |
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| 113 | |
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| 114 | |
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| 115 | /* |
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| 116 | Push/relabel on the highest level active nodes. |
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| 117 | */ |
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| 118 | |
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| 119 | /*While there exists active node.*/ |
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| 120 | while (b) { |
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| 121 | |
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| 122 | /*We decrease the bound if there is no active node of level b.*/ |
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| 123 | if (stack[b].empty()) { |
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| 124 | --b; |
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| 125 | } else { |
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| 126 | |
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| 127 | node_iterator w=stack[b].top(); //w is the highest label active node. |
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| 128 | stack[b].pop(); //We delete w from the stack. |
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| 129 | |
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| 130 | int newlevel=2*n-2; //In newlevel we maintain the next level of w. |
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| 131 | |
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[30] | 132 | for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) { |
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[20] | 133 | node_iterator v=G.head(e); |
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| 134 | /*e is the edge wv.*/ |
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| 135 | |
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| 136 | if (flow.get(e)<capacity.get(e)) { |
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| 137 | /*e is an edge of the residual graph */ |
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| 138 | |
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| 139 | if(level.get(w)==level.get(v)+1) { |
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| 140 | /*Push is allowed now*/ |
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| 141 | |
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| 142 | if (capacity.get(e)-flow.get(e) > excess.get(w)) { |
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| 143 | /*A nonsaturating push.*/ |
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| 144 | |
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| 145 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 146 | /*v becomes active.*/ |
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| 147 | |
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| 148 | flow.put(e, flow.get(e)+excess.get(w)); |
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| 149 | excess.put(v, excess.get(v)+excess.get(w)); |
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| 150 | excess.put(w,0); |
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| 151 | //std::cout << w << " " << v <<" elore elen nonsat pump " << std::endl; |
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| 152 | break; |
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| 153 | } else { |
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| 154 | /*A saturating push.*/ |
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| 155 | |
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| 156 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 157 | /*v becomes active.*/ |
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| 158 | |
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| 159 | excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
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| 160 | excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
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| 161 | flow.put(e, capacity.get(e)); |
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| 162 | //std::cout << w<<" " <<v<<" elore elen sat pump " << std::endl; |
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| 163 | if (excess.get(w)==0) break; |
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| 164 | /*If w is not active any more, then we go on to the next node.*/ |
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| 165 | |
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| 166 | } // if (capacity.get(e)-flow.get(e) > excess.get(w)) |
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| 167 | } // if(level.get(w)==level.get(v)+1) |
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| 168 | |
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| 169 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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| 170 | |
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| 171 | } //if (flow.get(e)<capacity.get(e)) |
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| 172 | |
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[30] | 173 | } //for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) |
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[20] | 174 | |
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| 175 | |
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| 176 | |
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[30] | 177 | for(in_edge_iterator e=G.first_in_edge(w); e.valid(); ++e) { |
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[20] | 178 | node_iterator v=G.tail(e); |
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| 179 | /*e is the edge vw.*/ |
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| 180 | |
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| 181 | if (excess.get(w)==0) break; |
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| 182 | /*It may happen, that w became inactive in the first for cycle.*/ |
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| 183 | if(flow.get(e)>0) { |
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| 184 | /*e is an edge of the residual graph */ |
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| 185 | |
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| 186 | if(level.get(w)==level.get(v)+1) { |
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| 187 | /*Push is allowed now*/ |
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| 188 | |
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| 189 | if (flow.get(e) > excess.get(w)) { |
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| 190 | /*A nonsaturating push.*/ |
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| 191 | |
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| 192 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 193 | /*v becomes active.*/ |
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| 194 | |
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| 195 | flow.put(e, flow.get(e)-excess.get(w)); |
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| 196 | excess.put(v, excess.get(v)+excess.get(w)); |
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| 197 | excess.put(w,0); |
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| 198 | //std::cout << v << " " << w << " vissza elen nonsat pump " << std::endl; |
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| 199 | break; |
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| 200 | } else { |
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| 201 | /*A saturating push.*/ |
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| 202 | |
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| 203 | if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); |
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| 204 | /*v becomes active.*/ |
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| 205 | |
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| 206 | excess.put(v, excess.get(v)+flow.get(e)); |
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| 207 | excess.put(w, excess.get(w)-flow.get(e)); |
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| 208 | flow.put(e,0); |
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| 209 | //std::cout << v <<" " << w << " vissza elen sat pump " << std::endl; |
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| 210 | if (excess.get(w)==0) { break;} |
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| 211 | } //if (flow.get(e) > excess.get(v)) |
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| 212 | } //if(level.get(w)==level.get(v)+1) |
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| 213 | |
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| 214 | else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);} |
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| 215 | |
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| 216 | |
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| 217 | } //if (flow.get(e)>0) |
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| 218 | |
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| 219 | } //for |
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| 220 | |
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| 221 | |
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| 222 | if (excess.get(w)>0) { |
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| 223 | level.put(w,++newlevel); |
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| 224 | stack[newlevel].push(w); |
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| 225 | b=newlevel; |
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| 226 | //std::cout << "The new level of " << w << " is "<< newlevel <<std::endl; |
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| 227 | } |
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| 228 | |
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| 229 | |
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| 230 | } //else |
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| 231 | |
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| 232 | } //while(b) |
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| 233 | |
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| 234 | value = excess.get(t); |
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| 235 | /*Max flow value.*/ |
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| 236 | |
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| 237 | |
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| 238 | |
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| 239 | |
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| 240 | } //void run() |
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| 241 | |
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| 242 | |
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| 243 | |
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| 244 | |
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| 245 | |
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| 246 | /* |
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| 247 | Returns the maximum value of a flow. |
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| 248 | */ |
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| 249 | |
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| 250 | T maxflow() { |
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| 251 | return value; |
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| 252 | } |
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| 253 | |
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| 254 | |
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| 255 | |
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| 256 | /* |
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| 257 | 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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| 258 | */ |
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| 259 | |
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| 260 | T flowonedge(edge_iterator e) { |
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| 261 | return flow.get(e); |
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| 262 | } |
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| 263 | |
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| 264 | |
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| 265 | |
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| 266 | /* |
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| 267 | Returns the maximum flow x found by the algorithm. |
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| 268 | */ |
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| 269 | |
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| 270 | edge_property_vector<graph_type, T> allflow() { |
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| 271 | return flow; |
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| 272 | } |
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| 273 | |
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| 274 | |
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| 275 | |
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| 276 | /* |
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| 277 | Returns a minimum cut by using a reverse bfs from t in the residual graph. |
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| 278 | */ |
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| 279 | |
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| 280 | node_property_vector<graph_type, bool> mincut() { |
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| 281 | |
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| 282 | std::queue<node_iterator> queue; |
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| 283 | |
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| 284 | mincutvector.put(t,false); |
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| 285 | queue.push(t); |
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| 286 | |
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| 287 | while (!queue.empty()) { |
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| 288 | node_iterator w=queue.front(); |
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| 289 | queue.pop(); |
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| 290 | |
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[30] | 291 | for(in_edge_iterator e=G.first_in_edge(w) ; e.valid(); ++e) { |
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[20] | 292 | node_iterator v=G.tail(e); |
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| 293 | if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 294 | queue.push(v); |
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| 295 | mincutvector.put(v, false); |
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| 296 | } |
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| 297 | } // for |
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| 298 | |
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[30] | 299 | for(out_edge_iterator e=G.first_out_edge(w) ; e.valid(); ++e) { |
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[20] | 300 | node_iterator v=G.head(e); |
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| 301 | if (mincutvector.get(v) && flow.get(e) > 0 ) { |
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| 302 | queue.push(v); |
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| 303 | mincutvector.put(v, false); |
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| 304 | } |
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| 305 | } // for |
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| 306 | |
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| 307 | } |
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| 308 | |
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| 309 | return mincutvector; |
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| 310 | |
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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 | }//namespace marci |
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| 316 | #endif |
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| 317 | |
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| 318 | |
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| 319 | |
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| 320 | |
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