/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #include <iostream>

 #include <fstream>

 #include <lemon/list_graph.h>

 #include <lemon/lgf_reader.h>

 #include <lemon/path.h>

 #include <lemon/suurballe.h>

 #include "test_tools.h"

 using namespace lemon;

 // Check the feasibility of the flow

 template <typename Digraph, typename FlowMap>

 bool checkFlow( const Digraph& gr, const FlowMap& flow, 

                 typename Digraph::Node s, typename Digraph::Node t,

                 int value )

 {

   TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

   for (ArcIt e(gr); e != INVALID; ++e)

     if (!(flow[e] == 0 || flow[e] == 1)) return false;

   for (NodeIt n(gr); n != INVALID; ++n) {

     int sum = 0;

     for (OutArcIt e(gr, n); e != INVALID; ++e)

       sum += flow[e];

     for (InArcIt e(gr, n); e != INVALID; ++e)

       sum -= flow[e];

     if (n == s && sum != value) return false;

     if (n == t && sum != -value) return false;

     if (n != s && n != t && sum != 0) return false;

   }

   return true;

 }

 // Check the optimalitiy of the flow

 template < typename Digraph, typename CostMap, 

            typename FlowMap, typename PotentialMap >

 bool checkOptimality( const Digraph& gr, const CostMap& cost,

                       const FlowMap& flow, const PotentialMap& pi )

 {

   // Check the "Complementary Slackness" optimality condition

   TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

   bool opt = true;

   for (ArcIt e(gr); e != INVALID; ++e) {

     typename CostMap::Value red_cost =

       cost[e] + pi[gr.source(e)] - pi[gr.target(e)];

     opt = (flow[e] == 0 && red_cost >= 0) ||

           (flow[e] == 1 && red_cost <= 0);

     if (!opt) break;

   }

   return opt;

 }

 // Check a path

 template <typename Digraph, typename Path>

 bool checkPath( const Digraph& gr, const Path& path,

                 typename Digraph::Node s, typename Digraph::Node t)

 {

   // Check the "Complementary Slackness" optimality condition

   TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

   Node n = s;

   for (int i = 0; i < path.length(); ++i) {

     if (gr.source(path.nth(i)) != n) return false;

     n = gr.target(path.nth(i));

   }

   return n == t;

 }

 int main()

 {

   DIGRAPH_TYPEDEFS(ListDigraph);

   // Read the test digraph

   ListDigraph digraph;

   ListDigraph::ArcMap<int> length(digraph);

   Node source, target;

   std::string fname;

   if(getenv("srcdir"))

     fname = std::string(getenv("srcdir"));

   else fname = ".";

   fname += "/test/min_cost_flow_test.lgf";

   std::ifstream input(fname.c_str());

   check(input, "Input file '" << fname << "' not found");

   DigraphReader<ListDigraph>(digraph, input).

     arcMap("cost", length).

     node("source", source).

     node("target", target).

     run();

   input.close();

   // Find 2 paths

   {

     Suurballe<ListDigraph> suurballe(digraph, length, source, target);

     check(suurballe.run(2) == 2, "Wrong number of paths");

     check(checkFlow(digraph, suurballe.flowMap(), source, target, 2),

           "The flow is not feasible");

     check(suurballe.totalLength() == 510, "The flow is not optimal");

     check(checkOptimality(digraph, length, suurballe.flowMap(), 

                           suurballe.potentialMap()),

           "Wrong potentials");

     for (int i = 0; i < suurballe.pathNum(); ++i)

       check(checkPath(digraph, suurballe.path(i), source, target),

             "Wrong path");

   }

   // Find 3 paths

   {

     Suurballe<ListDigraph> suurballe(digraph, length, source, target);

     check(suurballe.run(3) == 3, "Wrong number of paths");

     check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),

           "The flow is not feasible");

     check(suurballe.totalLength() == 1040, "The flow is not optimal");

     check(checkOptimality(digraph, length, suurballe.flowMap(), 

                           suurballe.potentialMap()),

           "Wrong potentials");

     for (int i = 0; i < suurballe.pathNum(); ++i)

       check(checkPath(digraph, suurballe.path(i), source, target),

             "Wrong path");

   }

   // Find 5 paths (only 3 can be found)

   {

     Suurballe<ListDigraph> suurballe(digraph, length, source, target);

     check(suurballe.run(5) == 3, "Wrong number of paths");

     check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),

           "The flow is not feasible");

     check(suurballe.totalLength() == 1040, "The flow is not optimal");

     check(checkOptimality(digraph, length, suurballe.flowMap(), 

                           suurballe.potentialMap()),

           "Wrong potentials");

     for (int i = 0; i < suurballe.pathNum(); ++i)

       check(checkPath(digraph, suurballe.path(i), source, target),

             "Wrong path");

   }

   return 0;

 }