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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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 <limits>

#include <lemon/list_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/network_simplex.h>

#include <lemon/concepts/digraph.h>

#include <lemon/concept_check.h>

#include "test_tools.h"

using namespace lemon;

// Test networks

char test_lgf[] =

  "@nodes\n"

  "label  sup1 sup2 sup3 sup4 sup5 sup6\n"

  "    1    20   27    0   30   20   30\n"

  "    2    -4    0    0    0   -8   -3\n"

  "    3     0    0    0    0    0    0\n"

  "    4     0    0    0    0    0    0\n"

  "    5     9    0    0    0    6   11\n"

  "    6    -6    0    0    0   -5   -6\n"

  "    7     0    0    0    0    0    0\n"

  "    8     0    0    0    0    0    3\n"

  "    9     3    0    0    0    0    0\n"

  "   10    -2    0    0    0   -7   -2\n"

  "   11     0    0    0    0  -10    0\n"

  "   12   -20  -27    0  -30  -30  -20\n"

  "\n"                

  "@arcs\n"

  "       cost  cap low1 low2 low3\n"

  " 1  2    70   11    0    8    8\n"

  " 1  3   150    3    0    1    0\n"

  " 1  4    80   15    0    2    2\n"

  " 2  8    80   12    0    0    0\n"

  " 3  5   140    5    0    3    1\n"

  " 4  6    60   10    0    1    0\n"

  " 4  7    80    2    0    0    0\n"

  " 4  8   110    3    0    0    0\n"

  " 5  7    60   14    0    0    0\n"

  " 5 11   120   12    0    0    0\n"

  " 6  3     0    3    0    0    0\n"

  " 6  9   140    4    0    0    0\n"

  " 6 10    90    8    0    0    0\n"

  " 7  1    30    5    0    0   -5\n"

  " 8 12    60   16    0    4    3\n"

  " 9 12    50    6    0    0    0\n"

  "10 12    70   13    0    5    2\n"

  "10  2   100    7    0    0    0\n"

  "10  7    60   10    0    0   -3\n"

  "11 10    20   14    0    6  -20\n"

  "12 11    30   10    0    0  -10\n"

  "\n"

  "@attributes\n"

  "source 1\n"

  "target 12\n";

char test_neg1_lgf[] =

  "@nodes\n"

  "label   sup\n"

  "    1   100\n"

  "    2     0\n"

  "    3     0\n"

  "    4  -100\n"

  "    5     0\n"

  "    6     0\n"

  "    7     0\n"

  "@arcs\n"

  "      cost   low1   low2\n"

  "1 2    100      0      0\n"

  "1 3     30      0      0\n"

  "2 4     20      0      0\n"

  "3 4     80      0      0\n"

  "3 2     50      0      0\n"

  "5 3     10      0      0\n"

  "5 6     80      0   1000\n"

  "6 7     30      0  -1000\n"

  "7 5   -120      0      0\n";

char test_neg2_lgf[] =

  "@nodes\n"

  "label   sup\n"

  "    1   100\n"

  "    2  -300\n"

  "@arcs\n"

  "      cost\n"

  "1 2     -1\n";

// Test data

typedef ListDigraph Digraph;

DIGRAPH_TYPEDEFS(ListDigraph);

Digraph gr;

Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), l3(gr), u(gr);

Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr), s4(gr), s5(gr), s6(gr);

ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());

Node v, w;

Digraph neg1_gr;

Digraph::ArcMap<int> neg1_c(neg1_gr), neg1_l1(neg1_gr), neg1_l2(neg1_gr);

ConstMap<Arc, int> neg1_u1(std::numeric_limits<int>::max()), neg1_u2(5000);

Digraph::NodeMap<int> neg1_s(neg1_gr);

Digraph neg2_gr;

Digraph::ArcMap<int> neg2_c(neg2_gr);

ConstMap<Arc, int> neg2_l(0), neg2_u(1000);

Digraph::NodeMap<int> neg2_s(neg2_gr);

enum SupplyType {

  EQ,

  GEQ,

  LEQ

};

// Check the interface of an MCF algorithm

template <typename GR, typename Value, typename Cost>

class McfClassConcept

{

public:

  template <typename MCF>

  struct Constraints {

    void constraints() {

      checkConcept<concepts::Digraph, GR>();

      const Constraints& me = *this;

      MCF mcf(me.g);

      const MCF& const_mcf = mcf;

      b = mcf.reset()

             .lowerMap(me.lower)

             .upperMap(me.upper)

             .costMap(me.cost)

             .supplyMap(me.sup)

             .stSupply(me.n, me.n, me.k)

             .run();

      c = const_mcf.totalCost();

      x = const_mcf.template totalCost<double>();

      v = const_mcf.flow(me.a);

      c = const_mcf.potential(me.n);

      const_mcf.flowMap(fm);

      const_mcf.potentialMap(pm);

    }

    typedef typename GR::Node Node;

    typedef typename GR::Arc Arc;

    typedef concepts::ReadMap<Node, Value> NM;

    typedef concepts::ReadMap<Arc, Value> VAM;

    typedef concepts::ReadMap<Arc, Cost> CAM;

    typedef concepts::WriteMap<Arc, Value> FlowMap;

    typedef concepts::WriteMap<Node, Cost> PotMap;

    GR g;

    VAM lower;

    VAM upper;

    CAM cost;

    NM sup;

    Node n;

    Arc a;

    Value k;

    FlowMap fm;

    PotMap pm;

    bool b;

    double x;

    typename MCF::Value v;

    typename MCF::Cost c;

  };

};

// Check the feasibility of the given flow (primal soluiton)

template < typename GR, typename LM, typename UM,

           typename SM, typename FM >

bool checkFlow( const GR& gr, const LM& lower, const UM& upper,

                const SM& supply, const FM& flow,

                SupplyType type = EQ )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);

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

    if (flow[e] < lower[e] || flow[e] > upper[e]) return false;

  }

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

    typename SM::Value sum = 0;

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

      sum += flow[e];

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

      sum -= flow[e];

    bool b = (type ==  EQ && sum == supply[n]) ||

             (type == GEQ && sum >= supply[n]) ||

             (type == LEQ && sum <= supply[n]);

    if (!b) return false;

  }

  return true;

}

// Check the feasibility of the given potentials (dual soluiton)

// using the "Complementary Slackness" optimality condition

template < typename GR, typename LM, typename UM,

           typename CM, typename SM, typename FM, typename PM >

bool checkPotential( const GR& gr, const LM& lower, const UM& upper,

                     const CM& cost, const SM& supply, const FM& flow, 

                     const PM& pi, SupplyType type )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);

  bool opt = true;

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

    typename CM::Value red_cost =

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

    opt = red_cost == 0 ||

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

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

  }

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

    typename SM::Value 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 (type != LEQ) {

      opt = (pi[n] <= 0) && (sum == supply[n] || pi[n] == 0);

    } else {

      opt = (pi[n] >= 0) && (sum == supply[n] || pi[n] == 0);

    }

  }

  return opt;

}

// Check whether the dual cost is equal to the primal cost

template < typename GR, typename LM, typename UM,

           typename CM, typename SM, typename PM >

bool checkDualCost( const GR& gr, const LM& lower, const UM& upper,

                    const CM& cost, const SM& supply, const PM& pi,

                    typename CM::Value total )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);

  typename CM::Value dual_cost = 0;

  SM red_supply(gr);

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

    red_supply[n] = supply[n];

  }

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

    if (lower[a] != 0) {

      dual_cost += lower[a] * cost[a];

      red_supply[gr.source(a)] -= lower[a];

      red_supply[gr.target(a)] += lower[a];

    }

  }

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

    dual_cost -= red_supply[n] * pi[n];

  }

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

    typename CM::Value red_cost =

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

    dual_cost -= (upper[a] - lower[a]) * std::max(-red_cost, 0);

  }

  return dual_cost == total;

}

// Run a minimum cost flow algorithm and check the results

template < typename MCF, typename GR,

           typename LM, typename UM,

           typename CM, typename SM,

           typename PT >

void checkMcf( const MCF& mcf, PT mcf_result,

               const GR& gr, const LM& lower, const UM& upper,

               const CM& cost, const SM& supply,

               PT result, bool optimal, typename CM::Value total,

               const std::string &test_id = "",

               SupplyType type = EQ )

{

  check(mcf_result == result, "Wrong result " + test_id);

  if (optimal) {

    typename GR::template ArcMap<typename SM::Value> flow(gr);

    typename GR::template NodeMap<typename CM::Value> pi(gr);

    mcf.flowMap(flow);

    mcf.potentialMap(pi);

    check(checkFlow(gr, lower, upper, supply, flow, type),

          "The flow is not feasible " + test_id);

    check(mcf.totalCost() == total, "The flow is not optimal " + test_id);

    check(checkPotential(gr, lower, upper, cost, supply, flow, pi, type),

          "Wrong potentials " + test_id);

    check(checkDualCost(gr, lower, upper, cost, supply, pi, total),

          "Wrong dual cost " + test_id);

  }

}

template < typename MCF, typename Param >

void runMcfGeqTests( Param param,

                     const std::string &test_str = "",

                     bool full_neg_cost_support = false )

{

  MCF mcf1(gr), mcf2(neg1_gr), mcf3(neg2_gr);

  // Basic tests

  mcf1.upperMap(u).costMap(c).supplyMap(s1);

  checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s1,

           mcf1.OPTIMAL, true,     5240, test_str + "-1");

  mcf1.stSupply(v, w, 27);

  checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s2,

           mcf1.OPTIMAL, true,     7620, test_str + "-2");

  mcf1.lowerMap(l2).supplyMap(s1);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s1,

           mcf1.OPTIMAL, true,     5970, test_str + "-3");

  mcf1.stSupply(v, w, 27);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s2,

           mcf1.OPTIMAL, true,     8010, test_str + "-4");

  mcf1.reset().supplyMap(s1);

  checkMcf(mcf1, mcf1.run(param), gr, l1, cu, cc, s1,

           mcf1.OPTIMAL, true,       74, test_str + "-5");

  mcf1.lowerMap(l2).stSupply(v, w, 27);

  checkMcf(mcf1, mcf1.run(param), gr, l2, cu, cc, s2,

           mcf1.OPTIMAL, true,       94, test_str + "-6");

  mcf1.reset();

  checkMcf(mcf1, mcf1.run(param), gr, l1, cu, cc, s3,

           mcf1.OPTIMAL, true,        0, test_str + "-7");

  mcf1.lowerMap(l2).upperMap(u);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, cc, s3,

           mcf1.INFEASIBLE, false,    0, test_str + "-8");

  mcf1.lowerMap(l3).upperMap(u).costMap(c).supplyMap(s4);

  checkMcf(mcf1, mcf1.run(param), gr, l3, u, c, s4,

           mcf1.OPTIMAL, true,     6360, test_str + "-9");

  // Tests for the GEQ form

  mcf1.reset().upperMap(u).costMap(c).supplyMap(s5);

  checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s5,

           mcf1.OPTIMAL, true,     3530, test_str + "-10", GEQ);

  mcf1.lowerMap(l2);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s5,

           mcf1.OPTIMAL, true,     4540, test_str + "-11", GEQ);

  mcf1.supplyMap(s6);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s6,

           mcf1.INFEASIBLE, false,    0, test_str + "-12", GEQ);

  // Tests with negative costs

  mcf2.lowerMap(neg1_l1).costMap(neg1_c).supplyMap(neg1_s);

  checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l1, neg1_u1, neg1_c, neg1_s,

           mcf2.UNBOUNDED, false,     0, test_str + "-13");

  mcf2.upperMap(neg1_u2);

  checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l1, neg1_u2, neg1_c, neg1_s,

           mcf2.OPTIMAL, true,   -40000, test_str + "-14");

  mcf2.reset().lowerMap(neg1_l2).costMap(neg1_c).supplyMap(neg1_s);

  checkMcf(mcf2, mcf2.run(param), neg1_gr, neg1_l2, neg1_u1, neg1_c, neg1_s,

           mcf2.UNBOUNDED, false,     0, test_str + "-15");

  mcf3.costMap(neg2_c).supplyMap(neg2_s);

  if (full_neg_cost_support) {

    checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,

             mcf3.OPTIMAL, true,   -300, test_str + "-16", GEQ);

  } else {

    checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,

             mcf3.UNBOUNDED, false,   0, test_str + "-17", GEQ);

  }

  mcf3.upperMap(neg2_u);

  checkMcf(mcf3, mcf3.run(param), neg2_gr, neg2_l, neg2_u, neg2_c, neg2_s,

           mcf3.OPTIMAL, true,     -300, test_str + "-18", GEQ);

}

template < typename MCF, typename Param >

void runMcfLeqTests( Param param,

                     const std::string &test_str = "" )

{

  // Tests for the LEQ form

  MCF mcf1(gr);

  mcf1.supplyType(mcf1.LEQ);

  mcf1.upperMap(u).costMap(c).supplyMap(s6);

  checkMcf(mcf1, mcf1.run(param), gr, l1, u, c, s6,

           mcf1.OPTIMAL, true,   5080, test_str + "-19", LEQ);

  mcf1.lowerMap(l2);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s6,

           mcf1.OPTIMAL, true,   5930, test_str + "-20", LEQ);

  mcf1.supplyMap(s5);

  checkMcf(mcf1, mcf1.run(param), gr, l2, u, c, s5,

           mcf1.INFEASIBLE, false,  0, test_str + "-21", LEQ);

}

int main()

{

  // Read the test networks

  std::istringstream input(test_lgf);

  DigraphReader<Digraph>(gr, input)

    .arcMap("cost", c)

    .arcMap("cap", u)

    .arcMap("low1", l1)

    .arcMap("low2", l2)

    .arcMap("low3", l3)

    .nodeMap("sup1", s1)

    .nodeMap("sup2", s2)

    .nodeMap("sup3", s3)

    .nodeMap("sup4", s4)

    .nodeMap("sup5", s5)

    .nodeMap("sup6", s6)

    .node("source", v)

    .node("target", w)

    .run();

  std::istringstream neg_inp1(test_neg1_lgf);

  DigraphReader<Digraph>(neg1_gr, neg_inp1)

    .arcMap("cost", neg1_c)

    .arcMap("low1", neg1_l1)

    .arcMap("low2", neg1_l2)

    .nodeMap("sup", neg1_s)

    .run();

  std::istringstream neg_inp2(test_neg2_lgf);

  DigraphReader<Digraph>(neg2_gr, neg_inp2)

    .arcMap("cost", neg2_c)

    .nodeMap("sup", neg2_s)

    .run();

  // Check the interface of NetworkSimplex

  {

    typedef concepts::Digraph GR;

    checkConcept< McfClassConcept<GR, int, int>,

                  NetworkSimplex<GR> >();

    checkConcept< McfClassConcept<GR, double, double>,

                  NetworkSimplex<GR, double> >();

    checkConcept< McfClassConcept<GR, int, double>,

                  NetworkSimplex<GR, int, double> >();

  }

  // Test NetworkSimplex

  { 

    typedef NetworkSimplex<Digraph> MCF;

    runMcfGeqTests<MCF>(MCF::FIRST_ELIGIBLE, "NS-FE", true);

    runMcfLeqTests<MCF>(MCF::FIRST_ELIGIBLE, "NS-FE");

    runMcfGeqTests<MCF>(MCF::BEST_ELIGIBLE,  "NS-BE", true);

    runMcfLeqTests<MCF>(MCF::BEST_ELIGIBLE,  "NS-BE");

    runMcfGeqTests<MCF>(MCF::BLOCK_SEARCH,   "NS-BS", true);

    runMcfLeqTests<MCF>(MCF::BLOCK_SEARCH,   "NS-BS");

    runMcfGeqTests<MCF>(MCF::CANDIDATE_LIST, "NS-CL", true);

    runMcfLeqTests<MCF>(MCF::CANDIDATE_LIST, "NS-CL");

    runMcfGeqTests<MCF>(MCF::ALTERING_LIST,  "NS-AL", true);

    runMcfLeqTests<MCF>(MCF::ALTERING_LIST,  "NS-AL");

  }

  return 0;

}