#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;
}