#include"lp_solver_skeleton.h"

 #include"lp_glpk.h"

 #include<lemon/list_graph.h>

 using namespace lemon;

 void lpTest(LpSolverBase & lp)

 {

   typedef LpSolverBase LP;

   std::vector<LP::Col> x;

   for(int i=0;i<10;i++) x.push_back(lp.addCol());

   std::vector<LP::Col> y(10);

   lp.addColSet(y);

   std::map<int,LP::Col> z;

   z.insert(std::make_pair(12,INVALID));

   z.insert(std::make_pair(2,INVALID));

   z.insert(std::make_pair(7,INVALID));

   z.insert(std::make_pair(5,INVALID));

   lp.addColSet(z);

   LP::Expr e,f,g;

   LP::Col p1,p2,p3,p4,p5;

   LP::Constr c;

   e[p1]=2;

   e.constComp()=12;

   e[p1]+=2;

   e.constComp()+=12;

   e[p1]-=2;

   e.constComp()-=12;

   e=2;

   e=2.2;

   e=p1;

   e=f;

   e+=2;

   e+=2.2;

   e+=p1;

   e+=f;

   e-=2;

   e-=2.2;

   e-=p1;

   e-=f;

   e*=2;

   e*=2.2;

   e/=2;

   e/=2.2;

   e=((p1+p2)+(p1-p2)+(p1+12)+(12+p1)+(p1-12)+(12-p1)+

       (f+12)+(12+f)+(p1+f)+(f+p1)+(f+g)+

       (f-12)+(12-f)+(p1-f)+(f-p1)+(f-g)+

       2.2*f+f*2.2+f/2.2+

       2*f+f*2+f/2+

       2.2*p1+p1*2.2+p1/2.2+

       2*p1+p1*2+p1/2

      );

   c = (e  <= f  );

   c = (e  <= 2.2);

   c = (e  <= 2  );

   c = (e  <= p1 );

   c = (2.2<= f  );

   c = (2  <= f  );

   c = (p1 <= f  );

   c = (p1 <= p2 );

   c = (p1 <= 2.2);

   c = (p1 <= 2  );

   c = (2.2<= p2 );

   c = (2  <= p2 );

   c = (e  >= f  );

   c = (e  >= 2.2);

   c = (e  >= 2  );

   c = (e  >= p1 );

   c = (2.2>= f  );

   c = (2  >= f  );

   c = (p1 >= f  );

   c = (p1 >= p2 );

   c = (p1 >= 2.2);

   c = (p1 >= 2  );

   c = (2.2>= p2 );

   c = (2  >= p2 );

   c = (e  == f  );

   c = (e  == 2.2);

   c = (e  == 2  );

   c = (e  == p1 );

   c = (2.2== f  );

   c = (2  == f  );

   c = (p1 == f  );

   //c = (p1 == p2 );

   c = (p1 == 2.2);

   c = (p1 == 2  );

   c = (2.2== p2 );

   c = (2  == p2 );

   c = (2 <= e <= 3);

   c = (2 <= p1<= 3);

   c = (2 >= e >= 3);

   c = (2 >= p1>= 3);

   e[x[3]]=2;

   e[x[3]]=4;

   e[x[3]]=1;

   e.constComp()=12;

   lp.addRow(LP::INF,e,23);

   lp.addRow(LP::INF,3.0*(x[1]+x[2]/2)-x[3],23);

   lp.addRow(LP::INF,3.0*(x[1]+x[2]*2-5*x[3]+12-x[4]/3)+2*x[4]-4,23);

   lp.addRow(x[1]+x[3]<=x[5]-3);

   lp.addRow(-7<=x[1]+x[3]-12<=3);

   lp.addRow(x[1]<=x[5]);

 }

 template<class G,class C>

 double maxFlow(const G &g,const C &cap,typename G::Node s,typename G::Node t)

 {

   LpGlpk lp;

   typedef G Graph;

   typedef typename G::Node Node;

   typedef typename G::NodeIt NodeIt;

   typedef typename G::Edge Edge;

   typedef typename G::EdgeIt EdgeIt;

   typedef typename G::OutEdgeIt OutEdgeIt;

   typedef typename G::InEdgeIt InEdgeIt;

   typename G::template EdgeMap<LpGlpk::Col> x(g);

   lp.addColSet(x);

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

     lp.colUpperBound(x[e],cap[e]);

     lp.colLowerBound(x[e],0);

   }

   for(NodeIt n(g);n!=INVALID;++n) if(n!=s&&n!=t) {

     LpGlpk::Expr ex;

     for(InEdgeIt  e(g,n);e!=INVALID;++e) ex+=x[e];

     for(OutEdgeIt e(g,n);e!=INVALID;++e) ex-=x[e];

     lp.addRow(ex==0);

   }

   {

     LpGlpk::Expr ex;

     for(InEdgeIt  e(g,t);e!=INVALID;++e) ex+=x[e];

     for(OutEdgeIt e(g,t);e!=INVALID;++e) ex-=x[e];

     lp.setObj(ex);

   }

   lp.solve();

   return 0;

 }

 int main() 

 {

   LpSolverSkeleton lp_skel;

   LpGlpk lp_glpk;

   lpTest(lp_skel);

   lpTest(lp_glpk);

   ListGraph g;

   ListGraph::Node s=g.addNode();

   ListGraph::Node t=g.addNode();

   ListGraph::EdgeMap<double> cap(g);

   maxFlow(g,cap,s,t);

 }