/* -*- 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;

  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);

  ignore_unused_variable_warning(fm);

  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;

}