/* -*- 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;

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";

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>();

      MCF mcf(g);

      const MCF& const_mcf = mcf;

      b = mcf.reset()

             .lowerMap(lower)

             .upperMap(upper)

             .costMap(cost)

             .supplyMap(sup)

             .stSupply(n, n, k)

             .run();

      c = const_mcf.totalCost();

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

      v = const_mcf.flow(a);

      c = const_mcf.potential(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;

    const GR &g;

    const VAM &lower;

    const VAM &upper;

    const CAM &cost;

    const NM ⊃

    const Node &n;

    const Arc &a;

    const 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);

  }

}

int main()

{

  // Check the interfaces

  {

    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> >();

  }

  // Run various MCF tests

  typedef ListDigraph Digraph;

  DIGRAPH_TYPEDEFS(ListDigraph);

  // Read the test digraph

  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;

  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();

  // Build test digraphs with negative costs

  Digraph neg_gr;

  Node n1 = neg_gr.addNode();

  Node n2 = neg_gr.addNode();

  Node n3 = neg_gr.addNode();

  Node n4 = neg_gr.addNode();

  Node n5 = neg_gr.addNode();

  Node n6 = neg_gr.addNode();

  Node n7 = neg_gr.addNode();

  Arc a1 = neg_gr.addArc(n1, n2);

  Arc a2 = neg_gr.addArc(n1, n3);

  Arc a3 = neg_gr.addArc(n2, n4);

  Arc a4 = neg_gr.addArc(n3, n4);

  Arc a5 = neg_gr.addArc(n3, n2);

  Arc a6 = neg_gr.addArc(n5, n3);

  Arc a7 = neg_gr.addArc(n5, n6);

  Arc a8 = neg_gr.addArc(n6, n7);

  Arc a9 = neg_gr.addArc(n7, n5);

  Digraph::ArcMap<int> neg_c(neg_gr), neg_l1(neg_gr, 0), neg_l2(neg_gr, 0);

  ConstMap<Arc, int> neg_u1(std::numeric_limits<int>::max()), neg_u2(5000);

  Digraph::NodeMap<int> neg_s(neg_gr, 0);

  neg_l2[a7] =  1000;

  neg_l2[a8] = -1000;

  neg_s[n1] =  100;

  neg_s[n4] = -100;

  neg_c[a1] =  100;

  neg_c[a2] =   30;

  neg_c[a3] =   20;

  neg_c[a4] =   80;

  neg_c[a5] =   50;

  neg_c[a6] =   10;

  neg_c[a7] =   80;

  neg_c[a8] =   30;

  neg_c[a9] = -120;

  Digraph negs_gr;

  Digraph::NodeMap<int> negs_s(negs_gr);

  Digraph::ArcMap<int> negs_c(negs_gr);

  ConstMap<Arc, int> negs_l(0), negs_u(1000);

  n1 = negs_gr.addNode();

  n2 = negs_gr.addNode();

  negs_s[n1] = 100;

  negs_s[n2] = -300;

  negs_c[negs_gr.addArc(n1, n2)] = -1;

  // A. Test NetworkSimplex with the default pivot rule

  {

    NetworkSimplex<Digraph> mcf(gr);

    // Check the equality form

    mcf.upperMap(u).costMap(c);

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l1, u, c, s1, mcf.OPTIMAL, true,   5240, "#A1");

    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),

             gr, l1, u, c, s2, mcf.OPTIMAL, true,   7620, "#A2");

    mcf.lowerMap(l2);

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#A3");

    checkMcf(mcf, mcf.stSupply(v, w, 27).run(),

             gr, l2, u, c, s2, mcf.OPTIMAL, true,   8010, "#A4");

    mcf.reset();

    checkMcf(mcf, mcf.supplyMap(s1).run(),

             gr, l1, cu, cc, s1, mcf.OPTIMAL, true,   74, "#A5");

    checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(),

             gr, l2, cu, cc, s2, mcf.OPTIMAL, true,   94, "#A6");

    mcf.reset();

    checkMcf(mcf, mcf.run(),

             gr, l1, cu, cc, s3, mcf.OPTIMAL, true,    0, "#A7");

    checkMcf(mcf, mcf.lowerMap(l2).upperMap(u).run(),

             gr, l2, u, cc, s3, mcf.INFEASIBLE, false, 0, "#A8");

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

    checkMcf(mcf, mcf.run(),

             gr, l3, u, c, s4, mcf.OPTIMAL, true,   6360, "#A9");

    // Check the GEQ form

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

    checkMcf(mcf, mcf.run(),

             gr, l1, u, c, s5, mcf.OPTIMAL, true,   3530, "#A10", GEQ);

    mcf.supplyType(mcf.GEQ);

    checkMcf(mcf, mcf.lowerMap(l2).run(),

             gr, l2, u, c, s5, mcf.OPTIMAL, true,   4540, "#A11", GEQ);

    mcf.supplyMap(s6);

    checkMcf(mcf, mcf.run(),

             gr, l2, u, c, s6, mcf.INFEASIBLE, false,  0, "#A12", GEQ);

    // Check the LEQ form

    mcf.reset().supplyType(mcf.LEQ);

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

    checkMcf(mcf, mcf.run(),

             gr, l1, u, c, s6, mcf.OPTIMAL, true,   5080, "#A13", LEQ);

    checkMcf(mcf, mcf.lowerMap(l2).run(),

             gr, l2, u, c, s6, mcf.OPTIMAL, true,   5930, "#A14", LEQ);

    mcf.supplyMap(s5);

    checkMcf(mcf, mcf.run(),

             gr, l2, u, c, s5, mcf.INFEASIBLE, false,  0, "#A15", LEQ);

    // Check negative costs

    NetworkSimplex<Digraph> neg_mcf(neg_gr);

    neg_mcf.lowerMap(neg_l1).costMap(neg_c).supplyMap(neg_s);

    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u1,

      neg_c, neg_s, neg_mcf.UNBOUNDED, false,    0, "#A16");

    neg_mcf.upperMap(neg_u2);

    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l1, neg_u2,

      neg_c, neg_s, neg_mcf.OPTIMAL, true,  -40000, "#A17");

    neg_mcf.reset().lowerMap(neg_l2).costMap(neg_c).supplyMap(neg_s);

    checkMcf(neg_mcf, neg_mcf.run(), neg_gr, neg_l2, neg_u1,

      neg_c, neg_s, neg_mcf.UNBOUNDED, false,    0, "#A18");

    NetworkSimplex<Digraph> negs_mcf(negs_gr);

    negs_mcf.costMap(negs_c).supplyMap(negs_s);

    checkMcf(negs_mcf, negs_mcf.run(), negs_gr, negs_l, negs_u,

      negs_c, negs_s, negs_mcf.OPTIMAL, true, -300, "#A19", GEQ);

  }

  // B. Test NetworkSimplex with each pivot rule

  {

    NetworkSimplex<Digraph> mcf(gr);

    mcf.supplyMap(s1).costMap(c).upperMap(u).lowerMap(l2);

    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::FIRST_ELIGIBLE),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B1");

    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BEST_ELIGIBLE),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B2");

    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BLOCK_SEARCH),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B3");

    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::CANDIDATE_LIST),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B4");

    checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::ALTERING_LIST),

             gr, l2, u, c, s1, mcf.OPTIMAL, true,   5970, "#B5");

  }

  return 0;

}