/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

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

  *

  * Copyright (C) 2003-2011

  * 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 <lemon/list_graph.h>

 #include <lemon/lgf_reader.h>

 #include <lemon/path.h>

 #include <lemon/suurballe.h>

 #include <lemon/concepts/digraph.h>

 #include "test_tools.h"

 using namespace lemon;

 char test_lgf[] =

   "@nodes\n"

   "label\n"

   "1\n"

   "2\n"

   "3\n"

   "4\n"

   "5\n"

   "6\n"

   "7\n"

   "8\n"

   "9\n"

   "10\n"

   "11\n"

   "12\n"

   "@arcs\n"

   "      length\n"

   " 1  2  70\n"

   " 1  3 150\n"

   " 1  4  80\n"

   " 2  8  80\n"

   " 3  5 140\n"

   " 4  6  60\n"

   " 4  7  80\n"

   " 4  8 110\n"

   " 5  7  60\n"

   " 5 11 120\n"

   " 6  3   0\n"

   " 6  9 140\n"

   " 6 10  90\n"

   " 7  1  30\n"

   " 8 12  60\n"

   " 9 12  50\n"

   "10 12  70\n"

   "10  2 100\n"

   "10  7  60\n"

   "11 10  20\n"

   "12 11  30\n"

   "@attributes\n"

   "source  1\n"

   "target 12\n"

   "@end\n";

 // Check the interface of Suurballe

 void checkSuurballeCompile()

 {

   typedef int VType;

   typedef concepts::Digraph Digraph;

   typedef Digraph::Node Node;

   typedef Digraph::Arc Arc;

   typedef concepts::ReadMap<Arc, VType> LengthMap;

   typedef Suurballe<Digraph, LengthMap> SuurballeType;

   Digraph g;

   Node n;

   Arc e;

   LengthMap len;

   SuurballeType::FlowMap flow(g);

   SuurballeType::PotentialMap pi(g);

   SuurballeType suurb_test(g, len);

   const SuurballeType& const_suurb_test = suurb_test;

   suurb_test

     .flowMap(flow)

     .potentialMap(pi);

   int k;

   k = suurb_test.run(n, n);

   k = suurb_test.run(n, n, k);

   suurb_test.init(n);

   k = suurb_test.findFlow(n);

   k = suurb_test.findFlow(n, k);

   suurb_test.findPaths();

   int f;

   VType c;

   ::lemon::ignore_unused_variable_warning(f,c);

   c = const_suurb_test.totalLength();

   f = const_suurb_test.flow(e);

   const SuurballeType::FlowMap& fm =

     const_suurb_test.flowMap();

   c = const_suurb_test.potential(n);

   const SuurballeType::PotentialMap& pm =

     const_suurb_test.potentialMap();

   k = const_suurb_test.pathNum();

   Path<Digraph> p = const_suurb_test.path(k);

   ::lemon::ignore_unused_variable_warning(fm);

   ::lemon::ignore_unused_variable_warning(pm);

 }

 // 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)

 {

   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 s, t;

   std::istringstream input(test_lgf);

   DigraphReader<ListDigraph>(digraph, input).

     arcMap("length", length).

     node("source", s).

     node("target", t).

     run();

   // Find 2 paths

   {

     Suurballe<ListDigraph> suurballe(digraph, length);

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

     check(checkFlow(digraph, suurballe.flowMap(), s, t, 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), s, t), "Wrong path");

   }

   // Find 3 paths

   {

     Suurballe<ListDigraph> suurballe(digraph, length);

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

     check(checkFlow(digraph, suurballe.flowMap(), s, t, 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), s, t), "Wrong path");

   }

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

   {

     Suurballe<ListDigraph> suurballe(digraph, length);

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

     check(checkFlow(digraph, suurballe.flowMap(), s, t, 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), s, t), "Wrong path");

   }

   return 0;

 }