[72] | 1 | // -*- C++ -*- |
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| 2 | /* |
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[83] | 3 | preflow_push_hl.h |
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[72] | 4 | by jacint. |
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| 5 | Runs the highest label variant of the preflow push algorithm with |
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| 6 | running time O(n^2\sqrt(m)). |
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| 7 | |
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| 8 | Member functions: |
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| 9 | |
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| 10 | void run() : runs the algorithm |
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| 11 | |
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| 12 | The following functions should be used after run() was already run. |
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| 13 | |
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| 14 | T maxflow() : returns the value of a maximum flow |
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| 15 | |
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[83] | 16 | T flowonedge(EdgeIt e) : for a fixed maximum flow x it returns x(e) |
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[72] | 17 | |
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[83] | 18 | Graph::EdgeMap<T> allflow() : returns the fixed maximum flow x |
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[72] | 19 | |
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[83] | 20 | Graph::NodeMap<bool> mincut() : returns a |
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[72] | 21 | characteristic vector of a minimum cut. (An empty level |
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| 22 | in the algorithm gives a minimum cut.) |
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| 23 | */ |
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| 24 | |
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| 25 | #ifndef PREFLOW_PUSH_HL_H |
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| 26 | #define PREFLOW_PUSH_HL_H |
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| 27 | |
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[88] | 28 | #define A 1 |
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| 29 | |
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[72] | 30 | #include <vector> |
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| 31 | #include <stack> |
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| 32 | |
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[78] | 33 | #include <reverse_bfs.h> |
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[72] | 34 | |
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| 35 | namespace marci { |
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| 36 | |
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[78] | 37 | template <typename Graph, typename T> |
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[72] | 38 | class preflow_push_hl { |
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| 39 | |
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| 40 | typedef typename Graph::NodeIt NodeIt; |
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| 41 | typedef typename Graph::EdgeIt EdgeIt; |
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| 42 | typedef typename Graph::EachNodeIt EachNodeIt; |
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| 43 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 44 | typedef typename Graph::InEdgeIt InEdgeIt; |
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| 45 | |
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| 46 | Graph& G; |
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| 47 | NodeIt s; |
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| 48 | NodeIt t; |
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[78] | 49 | typename Graph::EdgeMap<T> flow; |
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| 50 | typename Graph::EdgeMap<T> capacity; |
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[72] | 51 | T value; |
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[78] | 52 | typename Graph::NodeMap<bool> mincutvector; |
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[72] | 53 | |
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| 54 | public: |
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| 55 | |
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| 56 | preflow_push_hl(Graph& _G, NodeIt _s, NodeIt _t, |
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[78] | 57 | typename Graph::EdgeMap<T>& _capacity) : |
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[83] | 58 | G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), |
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| 59 | mincutvector(_G, true) { } |
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[72] | 60 | |
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| 61 | |
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| 62 | /* |
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| 63 | The run() function runs the highest label preflow-push, |
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| 64 | running time: O(n^2\sqrt(m)) |
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| 65 | */ |
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| 66 | void run() { |
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| 67 | |
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[88] | 68 | std::cout<<"A is "<<A<<" "; |
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| 69 | |
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[83] | 70 | typename Graph::NodeMap<int> level(G); |
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[84] | 71 | typename Graph::NodeMap<T> excess(G); |
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[85] | 72 | |
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[84] | 73 | int n=G.nodeNum(); |
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[83] | 74 | int b=n-2; |
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| 75 | /* |
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| 76 | b is a bound on the highest level of an active node. |
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| 77 | In the beginning it is at most n-2. |
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| 78 | */ |
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[72] | 79 | |
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[85] | 80 | std::vector<int> numb(n); //The number of nodes on level i < n. |
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[83] | 81 | std::vector<std::stack<NodeIt> > stack(2*n-1); |
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| 82 | //Stack of the active nodes in level i. |
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[72] | 83 | |
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| 84 | |
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| 85 | /*Reverse_bfs from t, to find the starting level.*/ |
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[78] | 86 | reverse_bfs<Graph> bfs(G, t); |
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[72] | 87 | bfs.run(); |
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[83] | 88 | for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) |
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| 89 | { |
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[85] | 90 | int dist=bfs.dist(v); |
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| 91 | level.set(v, dist); |
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| 92 | ++numb[dist]; |
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[83] | 93 | } |
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[72] | 94 | |
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| 95 | level.set(s,n); |
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| 96 | |
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| 97 | |
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[83] | 98 | /* Starting flow. It is everywhere 0 at the moment. */ |
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| 99 | for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) |
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[72] | 100 | { |
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[83] | 101 | if ( capacity.get(e) > 0 ) { |
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| 102 | NodeIt w=G.head(e); |
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[85] | 103 | if ( w!=s ) { |
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| 104 | if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); |
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| 105 | flow.set(e, capacity.get(e)); |
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| 106 | excess.set(w, excess.get(w)+capacity.get(e)); |
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| 107 | } |
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[83] | 108 | } |
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[72] | 109 | } |
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| 110 | |
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| 111 | /* |
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| 112 | End of preprocessing |
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| 113 | */ |
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| 114 | |
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| 115 | |
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| 116 | |
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| 117 | /* |
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[84] | 118 | Push/relabel on the highest level active nodes. |
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[72] | 119 | */ |
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| 120 | |
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[85] | 121 | /*While there exists an active node.*/ |
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[72] | 122 | while (b) { |
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| 123 | |
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[85] | 124 | /*We decrease the bound if there is no active node of level b.*/ |
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[72] | 125 | if (stack[b].empty()) { |
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| 126 | --b; |
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| 127 | } else { |
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| 128 | |
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[84] | 129 | NodeIt w=stack[b].top(); //w is a highest label active node. |
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| 130 | stack[b].pop(); |
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[72] | 131 | |
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[84] | 132 | int newlevel=2*n-2; //In newlevel we bound the next level of w. |
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[72] | 133 | |
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| 134 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) { |
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[84] | 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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[72] | 138 | |
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[84] | 139 | NodeIt v=G.head(e); /*e is the edge wv.*/ |
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[72] | 140 | |
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[84] | 141 | if( level.get(w) == level.get(v)+1 ) { |
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[72] | 142 | /*Push is allowed now*/ |
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| 143 | |
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[85] | 144 | if ( excess.get(v)==0 && v != s && v !=t ) stack[level.get(v)].push(v); |
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| 145 | /*v becomes active.*/ |
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| 146 | |
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| 147 | if ( capacity.get(e)-flow.get(e) > excess.get(w) ) { |
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[72] | 148 | /*A nonsaturating push.*/ |
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| 149 | |
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| 150 | flow.set(e, flow.get(e)+excess.get(w)); |
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| 151 | excess.set(v, excess.get(v)+excess.get(w)); |
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| 152 | excess.set(w,0); |
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| 153 | break; |
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[85] | 154 | |
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[72] | 155 | } else { |
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| 156 | /*A saturating push.*/ |
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| 157 | |
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| 158 | excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e)); |
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| 159 | excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e)); |
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| 160 | flow.set(e, capacity.get(e)); |
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[85] | 161 | if ( excess.get(w)==0 ) break; |
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| 162 | /*If w is not active any more, then we go on to the next node.*/ |
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[72] | 163 | |
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[85] | 164 | } |
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| 165 | } else { |
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| 166 | newlevel = newlevel < level.get(v) ? newlevel : level.get(v); |
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| 167 | } |
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[72] | 168 | |
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[85] | 169 | } //if the out edge wv is in the res graph |
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[72] | 170 | |
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[85] | 171 | } //for out edges wv |
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[72] | 172 | |
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| 173 | |
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[85] | 174 | if ( excess.get(w) > 0 ) { |
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| 175 | |
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| 176 | for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) { |
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| 177 | NodeIt v=G.tail(e); /*e is the edge vw.*/ |
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[72] | 178 | |
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[85] | 179 | if( flow.get(e) > 0 ) { |
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| 180 | /*e is an edge of the residual graph */ |
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[72] | 181 | |
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[85] | 182 | if( level.get(w)==level.get(v)+1 ) { |
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| 183 | /*Push is allowed now*/ |
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[72] | 184 | |
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[85] | 185 | if ( excess.get(v)==0 && v != s && v !=t) stack[level.get(v)].push(v); |
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[72] | 186 | /*v becomes active.*/ |
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| 187 | |
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[85] | 188 | if ( flow.get(e) > excess.get(w) ) { |
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| 189 | /*A nonsaturating push.*/ |
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[72] | 190 | |
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[85] | 191 | flow.set(e, flow.get(e)-excess.get(w)); |
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| 192 | excess.set(v, excess.get(v)+excess.get(w)); |
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| 193 | excess.set(w,0); |
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| 194 | break; |
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| 195 | } else { |
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| 196 | /*A saturating push.*/ |
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| 197 | |
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| 198 | excess.set(v, excess.get(v)+flow.get(e)); |
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| 199 | excess.set(w, excess.get(w)-flow.get(e)); |
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| 200 | flow.set(e,0); |
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| 201 | if ( excess.get(w)==0 ) break; |
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| 202 | } |
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| 203 | } else { |
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| 204 | newlevel = newlevel < level.get(v) ? newlevel : level.get(v); |
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| 205 | } |
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| 206 | |
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| 207 | } //if in edge vw is in the res graph |
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[72] | 208 | |
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[85] | 209 | } //for in edges vw |
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[72] | 210 | |
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[85] | 211 | } // if w still has excess after the out edge for cycle |
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[72] | 212 | |
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| 213 | |
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[85] | 214 | /* |
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| 215 | Relabel |
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| 216 | */ |
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| 217 | |
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| 218 | if ( excess.get(w) > 0 ) { |
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| 219 | |
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| 220 | int oldlevel=level.get(w); |
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[72] | 221 | level.set(w,++newlevel); |
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[85] | 222 | |
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| 223 | if ( oldlevel < n ) { |
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| 224 | --numb[oldlevel]; |
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| 225 | |
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[88] | 226 | if ( !numb[oldlevel] && oldlevel < A*n ) { //If the level of w gets empty. |
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[85] | 227 | |
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| 228 | for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) { |
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| 229 | if (level.get(v) > oldlevel && level.get(v) < n ) level.set(v,n); |
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| 230 | } |
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| 231 | for (int i=oldlevel+1 ; i!=n ; ++i) numb[i]=0; |
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| 232 | if ( newlevel < n ) newlevel=n; |
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| 233 | } else { |
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| 234 | if ( newlevel < n ) ++numb[newlevel]; |
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| 235 | } |
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| 236 | } else { |
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| 237 | if ( newlevel < n ) ++numb[newlevel]; |
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| 238 | } |
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| 239 | |
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[72] | 240 | stack[newlevel].push(w); |
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| 241 | b=newlevel; |
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[85] | 242 | |
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[72] | 243 | } |
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| 244 | |
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[85] | 245 | } // if stack[b] is nonempty |
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[72] | 246 | |
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[85] | 247 | } // while(b) |
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| 248 | |
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[72] | 249 | |
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| 250 | value = excess.get(t); |
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| 251 | /*Max flow value.*/ |
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| 252 | |
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| 253 | |
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| 254 | } //void run() |
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| 255 | |
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| 256 | |
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| 257 | |
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| 258 | |
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| 259 | |
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| 260 | /* |
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| 261 | Returns the maximum value of a flow. |
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| 262 | */ |
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| 263 | |
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| 264 | T maxflow() { |
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| 265 | return 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 | /* |
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| 271 | 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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| 272 | */ |
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| 273 | |
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[88] | 274 | T flowonedge(EdgeIt e) { |
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[72] | 275 | return flow.get(e); |
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| 276 | } |
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| 277 | |
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| 278 | |
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| 279 | |
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| 280 | /* |
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| 281 | Returns the maximum flow x found by the algorithm. |
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| 282 | */ |
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| 283 | |
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[78] | 284 | typename Graph::EdgeMap<T> allflow() { |
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[72] | 285 | return flow; |
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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 | /* |
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| 291 | Returns a minimum cut by using a reverse bfs from t in the residual graph. |
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| 292 | */ |
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| 293 | |
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[78] | 294 | typename Graph::NodeMap<bool> mincut() { |
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[72] | 295 | |
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| 296 | std::queue<NodeIt> queue; |
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| 297 | |
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| 298 | mincutvector.set(t,false); |
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| 299 | queue.push(t); |
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| 300 | |
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| 301 | while (!queue.empty()) { |
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| 302 | NodeIt w=queue.front(); |
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| 303 | queue.pop(); |
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| 304 | |
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| 305 | for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) { |
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| 306 | NodeIt v=G.tail(e); |
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| 307 | if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) { |
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| 308 | queue.push(v); |
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| 309 | mincutvector.set(v, false); |
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| 310 | } |
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| 311 | } // for |
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| 312 | |
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| 313 | for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) { |
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| 314 | NodeIt v=G.head(e); |
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| 315 | if (mincutvector.get(v) && flow.get(e) > 0 ) { |
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| 316 | queue.push(v); |
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| 317 | mincutvector.set(v, false); |
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| 318 | } |
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| 319 | } // for |
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| 320 | |
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| 321 | } |
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| 322 | |
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| 323 | return mincutvector; |
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| 324 | |
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| 325 | } |
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| 326 | }; |
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| 327 | }//namespace marci |
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| 328 | #endif |
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| 329 | |
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| 330 | |
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| 331 | |
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| 332 | |
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