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

  *

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

  *

  * Copyright (C) 2003-2010

  * 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/capacity_scaling.h>

 #include <lemon/cost_scaling.h>

 #include <lemon/cycle_canceling.h>

 #include <lemon/concepts/digraph.h>

 #include <lemon/concepts/heap.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().resetParams()

              .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.resetParams().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.resetParams().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.resetParams().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> >();

   }

   // Check the interface of CapacityScaling

   {

     typedef concepts::Digraph GR;

     checkConcept< McfClassConcept<GR, int, int>,

                   CapacityScaling<GR> >();

     checkConcept< McfClassConcept<GR, double, double>,

                   CapacityScaling<GR, double> >();

     checkConcept< McfClassConcept<GR, int, double>,

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

     typedef CapacityScaling<GR>::

       SetHeap<concepts::Heap<int, RangeMap<int> > >::Create CAS;

     checkConcept< McfClassConcept<GR, int, int>, CAS >();

   }

   // Check the interface of CostScaling

   {

     typedef concepts::Digraph GR;

     checkConcept< McfClassConcept<GR, int, int>,

                   CostScaling<GR> >();

     checkConcept< McfClassConcept<GR, double, double>,

                   CostScaling<GR, double> >();

     checkConcept< McfClassConcept<GR, int, double>,

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

     typedef CostScaling<GR>::

       SetLargeCost<double>::Create COS;

     checkConcept< McfClassConcept<GR, int, int>, COS >();

   }

   // Check the interface of CycleCanceling

   {

     typedef concepts::Digraph GR;

     checkConcept< McfClassConcept<GR, int, int>,

                   CycleCanceling<GR> >();

     checkConcept< McfClassConcept<GR, double, double>,

                   CycleCanceling<GR, double> >();

     checkConcept< McfClassConcept<GR, int, double>,

                   CycleCanceling<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");

   }

   // Test CapacityScaling

   {

     typedef CapacityScaling<Digraph> MCF;

     runMcfGeqTests<MCF>(0, "SSP");

     runMcfGeqTests<MCF>(2, "CAS");

   }

   // Test CostScaling

   {

     typedef CostScaling<Digraph> MCF;

     runMcfGeqTests<MCF>(MCF::PUSH, "COS-PR");

     runMcfGeqTests<MCF>(MCF::AUGMENT, "COS-AR");

     runMcfGeqTests<MCF>(MCF::PARTIAL_AUGMENT, "COS-PAR");

   }

   // Test CycleCanceling

   {

     typedef CycleCanceling<Digraph> MCF;

     runMcfGeqTests<MCF>(MCF::SIMPLE_CYCLE_CANCELING, "SCC");

     runMcfGeqTests<MCF>(MCF::MINIMUM_MEAN_CYCLE_CANCELING, "MMCC");

     runMcfGeqTests<MCF>(MCF::CANCEL_AND_TIGHTEN, "CAT");

   }

   return 0;

 }