#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>

#include "test_tools.h"

using namespace lemon;

using namespace std;

const int n = 10;

const int e = 22;

int sourceNode = 0;

int sources[e] = {

  1, 0, 2, 4, 4, 3, 9, 8, 9, 8,

  4, 2, 0, 6, 4, 1, 7, 2, 8, 6,

  1, 0

};

int targets[e] = {

  8, 3, 1, 1, 4, 9, 8, 1, 8, 0,

  3, 2, 1, 3, 1, 1, 2, 6, 3, 9,

  1, 3

};

double costs[e] = {

  107.444, 70.3069, 46.0496, 28.3962, 91.4325,

  76.9443, 61.986, 39.3754, 74.9575, 39.3153,

  45.7094, 34.6184, 100.156, 95.726, 22.3429,

  31.587, 51.6972, 29.6773, 115.038, 32.4137,

  60.0038, 40.1237

};

int main() {

  srand(time(0));

  typedef SmartGraph Graph;

  GRAPH_TYPEDEFS(Graph);

  typedef Graph::EdgeMap<double> CostMap;

  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) {

    Edge edge = graph.addEdge(nodes[sources[i]], nodes[targets[i]]);

    cost[edge] = costs[i];

  }

  Node source = nodes[sourceNode];

  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)) {

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

      }

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

    }

  }

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

               "INVALID DUAL");

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

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

    check(!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;

      }

    }

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

  }

  return 0;

}