/* -*- 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 <lemon/list_graph.h>

 #include <lemon/lgf_reader.h>

 #include <lemon/path.h>

 #include <lemon/suurballe.h>

 #include "test_tools.h"

 using namespace lemon;

 char test_lgf[] =

   "@nodes\n"

   "label supply1 supply2 supply3\n"

   "1     0        20      27\n"

   "2     0       -4        0\n"

   "3     0        0        0\n"

   "4     0        0        0\n"

   "5     0        9        0\n"

   "6     0       -6        0\n"

   "7     0        0        0\n"

   "8     0        0        0\n"

   "9     0        3        0\n"

   "10    0       -2        0\n"

   "11    0        0        0\n"

   "12    0       -20     -27\n"

   "@arcs\n"

   "      cost capacity lower1 lower2\n"

   " 1  2  70  11       0      8\n"

   " 1  3 150   3       0      1\n"

   " 1  4  80  15       0      2\n"

   " 2  8  80  12       0      0\n"

   " 3  5 140   5       0      3\n"

   " 4  6  60  10       0      1\n"

   " 4  7  80   2       0      0\n"

   " 4  8 110   3       0      0\n"

   " 5  7  60  14       0      0\n"

   " 5 11 120  12       0      0\n"

   " 6  3   0   3       0      0\n"

   " 6  9 140   4       0      0\n"

   " 6 10  90   8       0      0\n"

   " 7  1  30   5       0      0\n"

   " 8 12  60  16       0      4\n"

   " 9 12  50   6       0      0\n"

   "10 12  70  13       0      5\n"

   "10  2 100   7       0      0\n"

   "10  7  60  10       0      0\n"

   "11 10  20  14       0      6\n"

   "12 11  30  10       0      0\n"

   "@attributes\n"

   "source  1\n"

   "target 12\n"

   "@end\n";

 // 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::istringstream input(test_lgf);

   DigraphReader<ListDigraph>(digraph, input).

     arcMap("cost", length).

     node("source", source).

     node("target", target).

     run();

   // 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;

 }