[2025] | 1 | #include <iostream> |
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| 2 | #include <set> |
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| 3 | #include <vector> |
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| 4 | #include <iterator> |
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| 5 | |
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| 6 | #include <cmath> |
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| 7 | #include <cstdlib> |
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| 8 | |
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| 9 | #include <lemon/smart_graph.h> |
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| 10 | #include <lemon/min_cost_arborescence.h> |
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| 11 | |
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| 12 | #include <lemon/graph_utils.h> |
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| 13 | #include <lemon/time_measure.h> |
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| 14 | |
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| 15 | #include <lemon/tolerance.h> |
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| 16 | |
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| 17 | using namespace lemon; |
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| 18 | using namespace std; |
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| 19 | |
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| 20 | int main(int argc, const char *argv[]) { |
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| 21 | srand(time(0)); |
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| 22 | typedef SmartGraph Graph; |
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| 23 | GRAPH_TYPEDEFS(Graph); |
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| 24 | |
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| 25 | typedef Graph::EdgeMap<double> CostMap; |
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| 26 | |
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| 27 | const int n = argc > 1 ? atoi(argv[1]) : 100; |
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| 28 | const int e = argc > 2 ? atoi(argv[2]) : (int)(n * log(n)); |
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| 29 | |
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| 30 | Graph graph; |
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| 31 | CostMap cost(graph); |
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| 32 | vector<Node> nodes; |
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| 33 | |
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| 34 | for (int i = 0; i < n; ++i) { |
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| 35 | nodes.push_back(graph.addNode()); |
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| 36 | } |
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| 37 | |
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| 38 | for (int i = 0; i < e; ++i) { |
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| 39 | int s = (int)(n * (double)rand() / (RAND_MAX + 1.0)); |
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| 40 | int t = (int)(n * (double)rand() / (RAND_MAX + 1.0)); |
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| 41 | double c = rand() / (1.0 + RAND_MAX) * 100.0 + 20.0; |
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| 42 | Edge edge = graph.addEdge(nodes[s], nodes[t]); |
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| 43 | cost[edge] = c; |
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| 44 | } |
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| 45 | |
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| 46 | Node source = nodes[(int)(n * (double)rand() / (RAND_MAX + 1.0))]; |
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| 47 | |
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| 48 | MinCostArborescence<Graph, CostMap> mca(graph, cost); |
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| 49 | mca.run(source); |
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| 50 | |
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| 51 | vector<pair<double, set<Node> > > dualSolution(mca.dualSize()); |
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| 52 | |
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| 53 | for (int i = 0; i < mca.dualSize(); ++i) { |
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| 54 | dualSolution[i].first = mca.dualValue(i); |
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| 55 | for (MinCostArborescence<Graph, CostMap>::DualIt it(mca, i); |
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| 56 | it != INVALID; ++it) { |
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| 57 | dualSolution[i].second.insert(it); |
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| 58 | } |
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| 59 | } |
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| 60 | |
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| 61 | Tolerance<double> tolerance; |
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| 62 | |
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| 63 | for (EdgeIt it(graph); it != INVALID; ++it) { |
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| 64 | if (mca.reached(graph.source(it))) { |
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| 65 | double sum = 0.0; |
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| 66 | for (int i = 0; i < (int)dualSolution.size(); ++i) { |
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| 67 | if (dualSolution[i].second.find(graph.target(it)) |
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| 68 | != dualSolution[i].second.end() && |
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| 69 | dualSolution[i].second.find(graph.source(it)) |
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| 70 | == dualSolution[i].second.end()) { |
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| 71 | sum += dualSolution[i].first; |
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| 72 | } |
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| 73 | } |
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| 74 | if (mca.arborescence(it)) { |
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| 75 | LEMON_ASSERT(!tolerance.less(sum, cost[it]), "INVALID DUAL"); |
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| 76 | } |
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| 77 | LEMON_ASSERT(!tolerance.less(cost[it], sum), "INVALID DUAL"); |
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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 | LEMON_ASSERT(!tolerance.different(mca.dualValue(), mca.arborescenceValue()), |
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| 83 | "INVALID DUAL"); |
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| 84 | |
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| 85 | |
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| 86 | LEMON_ASSERT(mca.reached(source), "INVALID ARBORESCENCE"); |
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| 87 | for (EdgeIt it(graph); it != INVALID; ++it) { |
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| 88 | LEMON_ASSERT(!mca.reached(graph.source(it)) || |
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| 89 | mca.reached(graph.target(it)), "INVALID ARBORESCENCE"); |
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| 90 | } |
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| 91 | |
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| 92 | for (NodeIt it(graph); it != INVALID; ++it) { |
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| 93 | if (!mca.reached(it)) continue; |
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| 94 | int cnt = 0; |
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| 95 | for (InEdgeIt jt(graph, it); jt != INVALID; ++jt) { |
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| 96 | if (mca.arborescence(jt)) { |
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| 97 | ++cnt; |
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| 98 | } |
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| 99 | } |
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| 100 | LEMON_ASSERT((it == source ? cnt == 0 : cnt == 1), "INVALID ARBORESCENCE"); |
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| 101 | } |
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| 102 | |
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| 103 | return 0; |
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| 104 | } |
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