/* -*- 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;

 }