// -*- c++ -*-

 #include <iostream>

 #include <fstream>

 #include <lemon/smart_graph.h>

 #include <lemon/list_graph.h>

 #include <lemon/dimacs.h>

 #include <lemon/time_measure.h>

 //#include <graph_wrapper.h>

 #include <lemon/preflow.h>

 #include <augmenting_flow.h>

 //#include <preflow_res.h>

 #include <lp_solver_wrapper.h>

 // Use a DIMACS max flow file as stdin.

 // max_flow_demo < dimacs_max_flow_file

 using namespace lemon;

 namespace lemon {

   template<typename Edge, typename EdgeIndexMap> 

   class PrimalMap {

   protected:

     LPSolverWrapper* lp;

     EdgeIndexMap* edge_index_map;

   public:

     PrimalMap(LPSolverWrapper& _lp, EdgeIndexMap& _edge_index_map) : 

       lp(&_lp), edge_index_map(&_edge_index_map) { }

     double operator[](Edge e) const { 

       return lp->getPrimal((*edge_index_map)[e]);

     }

   };

   // excess: rho-delta

   template <typename Graph, typename Num,

 	    typename Excess=typename Graph::template NodeMap<Num>, 

 	    typename LCapMap=typename Graph::template EdgeMap<Num>,

 	    typename CapMap=typename Graph::template EdgeMap<Num>,

             typename FlowMap=typename Graph::template EdgeMap<Num>,

 	    typename CostMap=typename Graph::template EdgeMap<Num> >

   class MinCostGenFlow {

   protected:

     const Graph& g;

     const Excess& excess;

     const LCapMap& lcapacity;

     const CapMap& capacity;

     FlowMap& flow;

     const CostMap& cost;

   public:

     MinCostGenFlow(const Graph& _g, const Excess& _excess, 

 		   const LCapMap& _lcapacity, const CapMap& _capacity, 

 		   FlowMap& _flow, 

 		   const CostMap& _cost) :

       g(_g), excess(_excess), lcapacity(_lcapacity),

       capacity(_capacity), flow(_flow), cost(_cost) { }

     void run() {

       LPSolverWrapper lp;

       lp.setMinimize();

       typedef LPSolverWrapper::ColIt ColIt;

       typedef LPSolverWrapper::RowIt RowIt;

       typedef typename Graph::template EdgeMap<ColIt> EdgeIndexMap;

       EdgeIndexMap edge_index_map(g);

       PrimalMap<typename Graph::Edge, EdgeIndexMap> lp_flow(lp, edge_index_map);

       for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) {

 	ColIt col_it=lp.addCol();

 	edge_index_map.set(e, col_it);

 	if (lcapacity[e]==capacity[e])

 	  lp.setColBounds(col_it, LPX_FX, lcapacity[e], capacity[e]);

 	else 

 	  lp.setColBounds(col_it, LPX_DB, lcapacity[e], capacity[e]);

 	lp.setObjCoef(col_it, cost[e]);

       }

       for (typename Graph::NodeIt n(g); n!=INVALID; ++n) {

 	typename Graph::template EdgeMap<Num> coeffs(g, 0);

 	for (typename Graph::InEdgeIt e(g, n); e!=INVALID; ++e)

 	coeffs.set(e, coeffs[e]+1);

 	for (typename Graph::OutEdgeIt e(g, n); e!=INVALID; ++e) 

 	coeffs.set(e, coeffs[e]-1);

 	RowIt row_it=lp.addRow();

 	typename std::vector< std::pair<ColIt, double> > row;

 	//std::cout << "node:" <<g.id(n)<<std::endl;

 	for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) {

 	  if (coeffs[e]!=0) {

 	    //std::cout << " edge:" <<g.id(e)<<" "<<coeffs[e];

 	    row.push_back(std::make_pair(edge_index_map[e], coeffs[e]));

 	  }

 	}

 	//std::cout << std::endl;

 	lp.setRowCoeffs(row_it, row.begin(), row.end());

 	lp.setRowBounds(row_it, LPX_FX, 0.0, 0.0);

       }

       lp.solveSimplex();

       //std::cout << lp.colNum() << std::endl;

       //std::cout << lp.rowNum() << std::endl;

       //std::cout << "flow value: "<< lp.getObjVal() << std::endl;

       for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) 

       flow.set(e, lp_flow[e]);

     }

   };

 }

 int main(int, char **) {

   typedef ListGraph MutableGraph;

   typedef SmartGraph Graph;

   typedef Graph::Node Node;

   typedef Graph::Edge Edge;

   typedef Graph::EdgeIt EdgeIt;

   Graph g;

   Node s, t;

   Graph::EdgeMap<int> cap(g);

   //readDimacsMaxFlow(std::cin, g, s, t, cap);

   readDimacs(std::cin, g, cap, s, t);

   Timer ts;

   Graph::EdgeMap<int> flow(g); //0 flow

   Preflow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > 

     max_flow_test(g, s, t, cap, flow);

   AugmentingFlow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> > 

     augmenting_flow_test(g, s, t, cap, flow);

   Graph::NodeMap<bool> cut(g);

   {

     std::cout << "preflow ..." << std::endl;

     ts.reset();

     max_flow_test.run();

     std::cout << "elapsed time: " << ts << std::endl;

     std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

     max_flow_test.minCut(cut);

     for (EdgeIt e(g); e!=INVALID; ++e) {

       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 	std::cout << "Slackness does not hold!" << std::endl;

       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 	std::cout << "Slackness does not hold!" << std::endl;

     }

   }

 //   {

 //     std::cout << "preflow ..." << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

 //     ts.reset();

 //     max_flow_test.preflow(Preflow<Graph, int, Graph::EdgeMap<int>, Graph::EdgeMap<int> >::GEN_FLOW);

 //     std::cout << "elapsed time: " << ts << std::endl;

 //     std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

 //       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //     }

 //   }

 //   {

 //     std::cout << "wrapped preflow ..." << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

 //     ts.reset();

 //     pre_flow_res.run();

 //     std::cout << "elapsed time: " << ts << std::endl;

 //     std::cout << "flow value: "<< pre_flow_test.flowValue() << std::endl;

 //   }

   {

     std::cout << "physical blocking flow augmentation ..." << std::endl;

     for (EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);

     ts.reset();

     int i=0;

     while (augmenting_flow_test.augmentOnBlockingFlow<MutableGraph>()) { ++i; }

     std::cout << "elapsed time: " << ts << std::endl;

     std::cout << "number of augmentation phases: " << i << std::endl; 

     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

     for (EdgeIt e(g); e!=INVALID; ++e) {

       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 	std::cout << "Slackness does not hold!" << std::endl;

       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 	std::cout << "Slackness does not hold!" << std::endl;

     }

   }

 //   {

 //     std::cout << "faster physical blocking flow augmentation ..." << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

 //     ts.reset();

 //     int i=0;

 //     while (max_flow_test.augmentOnBlockingFlow1<MutableGraph>()) { ++i; }

 //     std::cout << "elapsed time: " << ts << std::endl;

 //     std::cout << "number of augmentation phases: " << i << std::endl; 

 //     std::cout << "flow value: "<< max_flow_test.flowValue() << std::endl;

 //   }

   {

     std::cout << "on-the-fly blocking flow augmentation ..." << std::endl;

     for (EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);

     ts.reset();

     int i=0;

     while (augmenting_flow_test.augmentOnBlockingFlow2()) { ++i; }

     std::cout << "elapsed time: " << ts << std::endl;

     std::cout << "number of augmentation phases: " << i << std::endl; 

     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

     for (EdgeIt e(g); e!=INVALID; ++e) {

       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 	std::cout << "Slackness does not hold!" << std::endl;

       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 	std::cout << "Slackness does not hold!" << std::endl;

     }

   }

 //   {

 //     std::cout << "on-the-fly shortest path augmentation ..." << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

 //     ts.reset();

 //     int i=0;

 //     while (augmenting_flow_test.augmentOnShortestPath()) { ++i; }

 //     std::cout << "elapsed time: " << ts << std::endl;

 //     std::cout << "number of augmentation phases: " << i << std::endl; 

 //     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

 //       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //     }

 //   }

 //   {

 //     std::cout << "on-the-fly shortest path augmentation ..." << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) flow.set(e, 0);

 //     ts.reset();

 //     int i=0;

 //     while (augmenting_flow_test.augmentOnShortestPath2()) { ++i; }

 //     std::cout << "elapsed time: " << ts << std::endl;

 //     std::cout << "number of augmentation phases: " << i << std::endl; 

 //     std::cout << "flow value: "<< augmenting_flow_test.flowValue() << std::endl;

 //     FOR_EACH_LOC(Graph::EdgeIt, e, g) {

 //       if (cut[g.source(e)] && !cut[g.target(e)] && !flow[e]==cap[e]) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //       if (!cut[g.source(e)] && cut[g.target(e)] && flow[e]>0) 

 // 	std::cout << "Slackness does not hold!" << std::endl;

 //     }

 //   }

   ts.reset();

   Edge e=g.addEdge(t, s);

   Graph::EdgeMap<int> cost(g, 0);

   cost.set(e, -1);

   cap.set(e, 10000);

   typedef ConstMap<Node, int> Excess;

   Excess excess(0);

   typedef ConstMap<Edge, int> LCap;

   LCap lcap(0);

   MinCostGenFlow<Graph, int, Excess, LCap> 

     min_cost(g, excess, lcap, cap, flow, cost); 

   min_cost.run();

   std::cout << "elapsed time: " << ts << std::endl;

   std::cout << "flow value: "<< flow[e] << std::endl;

 }