# HG changeset patch # User kpeter # Date 1204167506 0 # Node ID 84ef3c5b36983a0622fbfffe0bd2a8dd004dab51 # Parent 7216b6a52ab902375682bb942fd507094f775464 Test file for the min cost flow algorithms. diff -r 7216b6a52ab9 -r 84ef3c5b3698 test/min_cost_flow_test.cc --- a/test/min_cost_flow_test.cc Thu Feb 28 02:57:36 2008 +0000 +++ b/test/min_cost_flow_test.cc Thu Feb 28 02:58:26 2008 +0000 @@ -17,112 +17,313 @@ */ #include +#include + +#include +#include +#include +#include +#include + +#include +#include +#include +#include + +#include +#include + #include "test_tools.h" -#include -#include -//#include -//#include using namespace lemon; +// Checks the feasibility of a flow +template < typename Graph, typename LowerMap, typename CapacityMap, + typename SupplyMap, typename FlowMap > +bool checkFlow( const Graph& gr, + const LowerMap& lower, const CapacityMap& upper, + const SupplyMap& supply, const FlowMap& flow ) +{ + GRAPH_TYPEDEFS(typename Graph); + for (EdgeIt e(gr); e != INVALID; ++e) + if (flow[e] < lower[e] || flow[e] > upper[e]) return false; -bool passed = true; -/* -void check(bool rc, char *msg="") { - passed = passed && rc; - if(!rc) { - std::cerr << "Test failed! ("<< msg << ")" << std::endl; \ - + for (NodeIt n(gr); n != INVALID; ++n) { + typename SupplyMap::Value sum = 0; + for (OutEdgeIt e(gr, n); e != INVALID; ++e) + sum += flow[e]; + for (InEdgeIt e(gr, n); e != INVALID; ++e) + sum -= flow[e]; + if (sum != supply[n]) return false; + } + return true; +} + +// Checks the optimalitiy of a flow +template < typename Graph, typename LowerMap, typename CapacityMap, + typename CostMap, typename FlowMap, typename PotentialMap > +bool checkOptimality( const Graph& gr, const LowerMap& lower, + const CapacityMap& upper, const CostMap& cost, + const FlowMap& flow, const PotentialMap& pi ) +{ + GRAPH_TYPEDEFS(typename Graph); + // Checking the Complementary Slackness optimality condition + bool opt = true; + for (EdgeIt e(gr); e != INVALID; ++e) { + typename CostMap::Value red_cost = + cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; + opt = red_cost == 0 || + (red_cost > 0 && flow[e] == lower[e]) || + (red_cost < 0 && flow[e] == upper[e]); + if (!opt) break; + } + return opt; +} + +// Runs a minimum cost flow algorithm and checks the results +template < typename MinCostFlowImpl, typename Graph, + typename LowerMap, typename CapacityMap, + typename CostMap, typename SupplyMap > +void checkMcf( std::string test_id, + const MinCostFlowImpl& mcf, const Graph& gr, + const LowerMap& lower, const CapacityMap& upper, + const CostMap& cost, const SupplyMap& supply, + bool mcf_result, bool result, + typename CostMap::Value total ) +{ + check(mcf_result == result, "Wrong result " + test_id); + if (result) { + check(checkFlow(gr, lower, upper, supply, mcf.flowMap()), + "The flow is not feasible " + test_id); + check(mcf.totalCost() == total, "The flow is not optimal " + test_id); + check(checkOptimality(gr, lower, upper, cost, mcf.flowMap(), mcf.potentialMap()), + "Wrong potentials " + test_id); } } -*/ - int main() { - typedef ListGraph Graph; - typedef Graph::Node Node; - typedef Graph::Edge Edge; + // Various tests on a small graph + { + typedef ListGraph Graph; + GRAPH_TYPEDEFS(ListGraph); - Graph graph; + // Reading the test graph + Graph gr; + Graph::EdgeMap c(gr), l1(gr), l2(gr), u(gr); + Graph::NodeMap s1(gr), s2(gr), s3(gr); + Node v, w; - //Ahuja könyv példája + std::string fname; + if(getenv("srcdir")) + fname = std::string(getenv("srcdir")); + else fname = "."; + fname += "/test/min_cost_flow_test.lgf"; - Node s=graph.addNode(); - Node v1=graph.addNode(); - Node v2=graph.addNode(); - Node v3=graph.addNode(); - Node v4=graph.addNode(); - Node v5=graph.addNode(); - Node t=graph.addNode(); + std::ifstream input(fname.c_str()); + check(input, "Input file '" << fname << "' not found"); + GraphReader(input, gr). + readEdgeMap("cost", c). + readEdgeMap("capacity", u). + readEdgeMap("lower1", l1). + readEdgeMap("lower2", l2). + readNodeMap("supply1", s1). + readNodeMap("supply2", s2). + readNodeMap("supply3", s3). + readNode("source", v). + readNode("target", w). + run(); + input.close(); - Edge s_v1=graph.addEdge(s, v1); - Edge v1_v2=graph.addEdge(v1, v2); - Edge s_v3=graph.addEdge(s, v3); - Edge v2_v4=graph.addEdge(v2, v4); - Edge v2_v5=graph.addEdge(v2, v5); - Edge v3_v5=graph.addEdge(v3, v5); - Edge v4_t=graph.addEdge(v4, t); - Edge v5_t=graph.addEdge(v5, t); - + // Testing CapacityScaling (scaling enabled) + { + CapacityScaling mcf1(gr,u,c,s1); checkMcf("#A1",mcf1,gr,l1,u,c,s1,mcf1.run(),true, 0); + CapacityScaling mcf2(gr,u,c,s2); checkMcf("#A2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240); + CapacityScaling mcf3(gr,u,c,v,w,27); checkMcf("#A3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620); + CapacityScaling mcf4(gr,l2,u,c,s1); checkMcf("#A4",mcf4,gr,l2,u,c,s1,mcf4.run(),false, 0); + CapacityScaling mcf5(gr,l2,u,c,s2); checkMcf("#A5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970); + CapacityScaling mcf6(gr,l2,u,c,v,w,27); checkMcf("#A6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010); + } + // Testing CapacityScaling (scaling disabled) + { + CapacityScaling mcf1(gr,u,c,s1); checkMcf("#B1",mcf1,gr,l1,u,c,s1,mcf1.run(false),true, 0); + CapacityScaling mcf2(gr,u,c,s2); checkMcf("#B2",mcf2,gr,l1,u,c,s2,mcf2.run(false),true, 5240); + CapacityScaling mcf3(gr,u,c,v,w,27); checkMcf("#B3",mcf3,gr,l1,u,c,s3,mcf3.run(false),true, 7620); + CapacityScaling mcf4(gr,l2,u,c,s1); checkMcf("#B4",mcf4,gr,l2,u,c,s1,mcf4.run(false),false, 0); + CapacityScaling mcf5(gr,l2,u,c,s2); checkMcf("#B5",mcf5,gr,l2,u,c,s2,mcf5.run(false),true, 5970); + CapacityScaling mcf6(gr,l2,u,c,v,w,27); checkMcf("#B6",mcf6,gr,l2,u,c,s3,mcf6.run(false),true, 8010); + } - Graph::EdgeMap length(graph); + // Testing CostScaling + { + CostScaling mcf1(gr,u,c,s1); checkMcf("#C1",mcf1,gr,l1,u,c,s1,mcf1.run(),true, 0); + CostScaling mcf2(gr,u,c,s2); checkMcf("#C2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240); + CostScaling mcf3(gr,u,c,v,w,27); checkMcf("#C3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620); + CostScaling mcf4(gr,l2,u,c,s1); checkMcf("#C4",mcf4,gr,l2,u,c,s1,mcf4.run(),false, 0); + CostScaling mcf5(gr,l2,u,c,s2); checkMcf("#C5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970); + CostScaling mcf6(gr,l2,u,c,v,w,27); checkMcf("#C6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010); + } - length.set(s_v1, 6); - length.set(v1_v2, 4); - length.set(s_v3, 10); - length.set(v2_v4, 5); - length.set(v2_v5, 1); - length.set(v3_v5, 4); - length.set(v4_t, 8); - length.set(v5_t, 8); + // Testing NetworkSimplex (with the default pivot rule) + { + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#D1",mcf1,gr,l1,u,c,s1,mcf1.run(),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#D2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#D3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#D4",mcf4,gr,l2,u,c,s1,mcf4.run(),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#D5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#D6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010); + } + // Testing NetworkSimplex (with FIRST_ELIGIBLE_PIVOT) + { + NetworkSimplex::PivotRuleEnum pr = NetworkSimplex::FIRST_ELIGIBLE_PIVOT; + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#E1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#E2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#E3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#E4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#E5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#E6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010); + } + // Testing NetworkSimplex (with BEST_ELIGIBLE_PIVOT) + { + NetworkSimplex::PivotRuleEnum pr = NetworkSimplex::BEST_ELIGIBLE_PIVOT; + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#F1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#F2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#F3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#F4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#F5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#F6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010); + } + // Testing NetworkSimplex (with BLOCK_SEARCH_PIVOT) + { + NetworkSimplex::PivotRuleEnum pr = NetworkSimplex::BLOCK_SEARCH_PIVOT; + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#G1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#G2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#G3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#G4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#G5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#G6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010); + } + // Testing NetworkSimplex (with LIMITED_SEARCH_PIVOT) + { + NetworkSimplex::PivotRuleEnum pr = NetworkSimplex::LIMITED_SEARCH_PIVOT; + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#H1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#H2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#H3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#H4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#H5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#H6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010); + } + // Testing NetworkSimplex (with CANDIDATE_LIST_PIVOT) + { + NetworkSimplex::PivotRuleEnum pr = NetworkSimplex::CANDIDATE_LIST_PIVOT; + NetworkSimplex mcf1(gr,u,c,s1); checkMcf("#I1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true, 0); + NetworkSimplex mcf2(gr,u,c,s2); checkMcf("#I2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240); + NetworkSimplex mcf3(gr,u,c,v,w,27); checkMcf("#I3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620); + NetworkSimplex mcf4(gr,l2,u,c,s1); checkMcf("#I4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false, 0); + NetworkSimplex mcf5(gr,l2,u,c,s2); checkMcf("#I5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970); + NetworkSimplex mcf6(gr,l2,u,c,v,w,27); checkMcf("#I6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010); + } - Graph::EdgeMap capacity(graph); + // Testing CycleCanceling (with BellmanFord) + { + CycleCanceling mcf1(gr,u,c,s1); checkMcf("#J1",mcf1,gr,l1,u,c,s1,mcf1.run(),true, 0); + CycleCanceling mcf2(gr,u,c,s2); checkMcf("#J2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240); + CycleCanceling mcf3(gr,u,c,v,w,27); checkMcf("#J3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620); + CycleCanceling mcf4(gr,l2,u,c,s1); checkMcf("#J4",mcf4,gr,l2,u,c,s1,mcf4.run(),false, 0); + CycleCanceling mcf5(gr,l2,u,c,s2); checkMcf("#J5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970); + CycleCanceling mcf6(gr,l2,u,c,v,w,27); checkMcf("#J6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010); + } + // Testing CycleCanceling (with MinMeanCycle) + { + CycleCanceling mcf1(gr,u,c,s1); checkMcf("#K1",mcf1,gr,l1,u,c,s1,mcf1.run(true),true, 0); + CycleCanceling mcf2(gr,u,c,s2); checkMcf("#K2",mcf2,gr,l1,u,c,s2,mcf2.run(true),true, 5240); + CycleCanceling mcf3(gr,u,c,v,w,27); checkMcf("#K3",mcf3,gr,l1,u,c,s3,mcf3.run(true),true, 7620); + CycleCanceling mcf4(gr,l2,u,c,s1); checkMcf("#K4",mcf4,gr,l2,u,c,s1,mcf4.run(true),false, 0); + CycleCanceling mcf5(gr,l2,u,c,s2); checkMcf("#K5",mcf5,gr,l2,u,c,s2,mcf5.run(true),true, 5970); + CycleCanceling mcf6(gr,l2,u,c,v,w,27); checkMcf("#K6",mcf6,gr,l2,u,c,s3,mcf6.run(true),true, 8010); + } - capacity.set(s_v1, 2); - capacity.set(v1_v2, 2); - capacity.set(s_v3, 1); - capacity.set(v2_v4, 1); - capacity.set(v2_v5, 1); - capacity.set(v3_v5, 1); - capacity.set(v4_t, 1); - capacity.set(v5_t, 2); + // Testing MinCostFlow + { + MinCostFlow mcf1(gr,u,c,s1); checkMcf("#L1",mcf1,gr,l1,u,c,s1,mcf1.run(),true, 0); + MinCostFlow mcf2(gr,u,c,s2); checkMcf("#L2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240); + MinCostFlow mcf3(gr,u,c,v,w,27); checkMcf("#L3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620); + MinCostFlow mcf4(gr,l2,u,c,s1); checkMcf("#L4",mcf4,gr,l2,u,c,s1,mcf4.run(),false, 0); + MinCostFlow mcf5(gr,l2,u,c,s2); checkMcf("#L5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970); + MinCostFlow mcf6(gr,l2,u,c,v,w,27); checkMcf("#L6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010); + } - // ConstMap const1map(1); - std::cout << "Mincostflows algorithm test..." << std::endl; + // Testing MinCostMaxFlow + { + MinCostMaxFlow mcmf(gr,u,c,v,w); + mcmf.run(); + checkMcf("#M1",mcmf,gr,l1,u,c,s3,true,true,7620); + } + } - SspMinCostFlow< Graph, Graph::EdgeMap, Graph::EdgeMap > - surb_test(graph, length, capacity, s, t); + // Benchmark test on a DIMACS network + { + typedef SmartGraph Graph; + GRAPH_TYPEDEFS(SmartGraph); - int k=1; + // Reading the test graph + Graph graph; + Graph::EdgeMap lower(graph), capacity(graph), cost(graph); + Graph::NodeMap supply(graph); - surb_test.augment(); - check( surb_test.flowValue() == 1 && surb_test.totalLength() == 19,"One path, total length should be 19"); + std::string fname; + if(getenv("srcdir")) + fname = std::string(getenv("srcdir")); + else fname = "."; + fname += "/test/min_cost_flow_test.net"; - check( surb_test.run(k) == 1 && surb_test.totalLength() == 19,"One path, total length should be 19"); + std::ifstream input(fname.c_str()); + check(input, "Input file '" << fname << "' not found"); + readDimacs(input, graph, lower, capacity, cost, supply); + input.close(); - check(surb_test.checkComplementarySlackness(), "Is the primal-dual solution pair really optimal?"); - - k=2; - - check( surb_test.run(k) == 2 && surb_test.totalLength() == 41,"Two paths, total length should be 41"); + // NetworkSimplex + { + Timer t; + NetworkSimplex mcf(graph, lower, capacity, cost, supply); + bool res = mcf.run(); + t.stop(); + checkMcf("#T3", mcf, graph, lower, capacity, cost, supply, res, true, 196587626); + std::cout << "NetworkSimplex"; + std::cout << std::endl << t << std::endl; + } + // CapacityScaling + { + Timer t; + CapacityScaling mcf(graph, lower, capacity, cost, supply); + bool res = mcf.run(); + t.stop(); + checkMcf("#T1", mcf, graph, lower, capacity, cost, supply, res, true, 196587626); + std::cout << "CapacityScaling"; + std::cout << std::endl << t << std::endl; + } + // CostScaling + { + Timer t; + CostScaling mcf(graph, lower, capacity, cost, supply); + bool res = mcf.run(); + t.stop(); + checkMcf("#T2", mcf, graph, lower, capacity, cost, supply, res, true, 196587626); + std::cout << "CostScaling"; + std::cout << std::endl << t << std::endl; + } + // CycleCanceling + { + Timer t; + CycleCanceling mcf(graph, lower, capacity, cost, supply); + bool res = mcf.run(); + t.stop(); + checkMcf("#T4", mcf, graph, lower, capacity, cost, supply, res, true, 196587626); + std::cout << "CycleCanceling"; + std::cout << std::endl << t << std::endl; + } + } - check(surb_test.checkComplementarySlackness(), "Is the primal-dual solution pair really optimal?"); - - surb_test.augment(); - surb_test.augment(); - surb_test.augment(); - k=4; - - check( surb_test.run(k) == 3 && surb_test.totalLength() == 64,"Three paths, total length should be 64"); - - check(surb_test.checkComplementarySlackness(), "Is the primal-dual solution pair really optimal?"); - - - std::cout << (passed ? "All tests passed." : "Some of the tests failed!!!") - << std::endl; - - return passed ? 0 : 1; - + return 0; } diff -r 7216b6a52ab9 -r 84ef3c5b3698 test/min_cost_flow_test.lgf --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/test/min_cost_flow_test.lgf Thu Feb 28 02:58:26 2008 +0000 @@ -0,0 +1,44 @@ +@nodeset +label supply1 supply2 supply3 +1 0 20 27 +2 0 -4 0 +3 0 0 0 +4 0 0 0 +5 0 9 0 +6 0 -6 0 +7 0 0 0 +8 0 0 0 +9 0 3 0 +10 0 -2 0 +11 0 0 0 +12 0 -20 -27 + +@edgeset + cost capacity lower1 lower2 +1 2 70 11 0 8 +1 3 150 3 0 1 +1 4 80 15 0 2 +2 8 80 12 0 0 +3 5 140 5 0 3 +4 6 60 10 0 1 +4 7 80 2 0 0 +4 8 110 3 0 0 +5 7 60 14 0 0 +5 11 120 12 0 0 +6 3 0 3 0 0 +6 9 140 4 0 0 +6 10 90 8 0 0 +7 1 30 5 0 0 +8 12 60 16 0 4 +9 12 50 6 0 0 +10 12 70 13 0 5 +10 2 100 7 0 0 +10 7 60 10 0 0 +11 10 20 14 0 6 +12 11 30 10 0 0 + +@nodes +source 1 +target 12 + +@end diff -r 7216b6a52ab9 -r 84ef3c5b3698 test/min_cost_flow_test.net --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/test/min_cost_flow_test.net Thu Feb 28 02:58:26 2008 +0000 @@ -0,0 +1,1531 @@ +c NETGEN flow network generator (C version) +c Problem 1 input parameters +c --------------------------- +c Random seed: 13502460 +c Number of nodes: 200 +c Source nodes: 100 +c Sink nodes: 100 +c Number of arcs: 1300 +c Minimum arc cost: 1 +c Maximum arc cost: 10000 +c Total supply: 100000 +c Transshipment - +c Sources: 0 +c Sinks: 0 +c Skeleton arcs - +c With max cost: 0% +c Capacitated: 0% +c Minimum arc capacity: 0 +c Maximum arc capacity: 0 +c +c *** Minimum cost flow *** +c +p min 200 1308 +n 1 286 +n 2 671 +n 3 605 +n 4 195 +n 5 1287 +n 6 497 +n 7 149 +n 8 660 +n 9 676 +n 10 1338 +n 11 222 +n 12 738 +n 13 1819 +n 14 1857 +n 15 1749 +n 16 1479 +n 17 154 +n 18 1897 +n 19 707 +n 20 367 +n 21 917 +n 22 410 +n 23 1000 +n 24 770 +n 25 1122 +n 26 1895 +n 27 1501 +n 28 514 +n 29 2227 +n 30 913 +n 31 947 +n 32 2260 +n 33 996 +n 34 986 +n 35 125 +n 36 362 +n 37 706 +n 38 1262 +n 39 389 +n 40 1410 +n 41 758 +n 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