/* -*- 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;

}