#include <iostream>

 #include <set>

 #include <vector>

 #include <iterator>

 #include <cmath>

 #include <cstdlib>

 #include <lemon/smart_graph.h>

 #include <lemon/min_cost_arborescence.h>

 #include <lemon/graph_utils.h>

 #include <lemon/time_measure.h>

 #include <lemon/tolerance.h>

 using namespace lemon;

 using namespace std;

 int main(int argc, const char *argv[]) {

   srand(time(0));

   typedef SmartGraph Graph;

   GRAPH_TYPEDEFS(Graph);

   typedef Graph::EdgeMap<double> CostMap;

   const int n = argc > 1 ? atoi(argv[1]) : 100;

   const int e = argc > 2 ? atoi(argv[2]) : (int)(n * log(n));

   Graph graph;

   CostMap cost(graph);

   vector<Node> nodes;

   for (int i = 0; i < n; ++i) {

     nodes.push_back(graph.addNode());

   }

   for (int i = 0; i < e; ++i) {

     int s = (int)(n * (double)rand() / (RAND_MAX + 1.0));

     int t = (int)(n * (double)rand() / (RAND_MAX + 1.0));

     double c = rand() / (1.0 + RAND_MAX) * 100.0 + 20.0;

     Edge edge = graph.addEdge(nodes[s], nodes[t]);

     cost[edge] = c;

   }

   Node source = nodes[(int)(n * (double)rand() / (RAND_MAX + 1.0))];

   MinCostArborescence<Graph, CostMap> mca(graph, cost);

   mca.run(source);

   vector<pair<double, set<Node> > > dualSolution(mca.dualSize());

   for (int i = 0; i < mca.dualSize(); ++i) {

     dualSolution[i].first = mca.dualValue(i);

     for (MinCostArborescence<Graph, CostMap>::DualIt it(mca, i); 

          it != INVALID; ++it) {

       dualSolution[i].second.insert(it);

     }

   }

   Tolerance<double> tolerance;

   for (EdgeIt it(graph); it != INVALID; ++it) {

     if (mca.reached(graph.source(it))) {

       double sum = 0.0;

       for (int i = 0; i < (int)dualSolution.size(); ++i) {

         if (dualSolution[i].second.find(graph.target(it)) 

             != dualSolution[i].second.end() &&

             dualSolution[i].second.find(graph.source(it)) 

             == dualSolution[i].second.end()) {

           sum += dualSolution[i].first;

         }

       }

       if (mca.arborescence(it)) {

         LEMON_ASSERT(!tolerance.less(sum, cost[it]), "INVALID DUAL");

       }

       LEMON_ASSERT(!tolerance.less(cost[it], sum), "INVALID DUAL");

     }

   }

   LEMON_ASSERT(!tolerance.different(mca.dualValue(), mca.arborescenceValue()),

                "INVALID DUAL");

   LEMON_ASSERT(mca.reached(source), "INVALID ARBORESCENCE");

   for (EdgeIt it(graph); it != INVALID; ++it) {

     LEMON_ASSERT(!mca.reached(graph.source(it)) || 

                  mca.reached(graph.target(it)), "INVALID ARBORESCENCE");

   }

   for (NodeIt it(graph); it != INVALID; ++it) {

     if (!mca.reached(it)) continue;

     int cnt = 0;

     for (InEdgeIt jt(graph, it); jt != INVALID; ++jt) {

       if (mca.arborescence(jt)) {

         ++cnt;

       }

     }

     LEMON_ASSERT((it == source ? cnt == 0 : cnt == 1), "INVALID ARBORESCENCE");

   }

   return 0;

 }