/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2008
 * 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 <lemon/list_graph.h>
#include <lemon/smart_graph.h>
#include <lemon/graph_reader.h>
#include <lemon/dimacs.h>
#include <lemon/time_measure.h>

#include <lemon/cycle_canceling.h>
#include <lemon/capacity_scaling.h>
#include <lemon/cost_scaling.h>
#include <lemon/network_simplex.h>

#include <lemon/min_cost_flow.h>
#include <lemon/min_cost_max_flow.h>

#include "test_tools.h"

using namespace lemon;

// Checks the feasibility of a flow
template < typename Graph, typename LowerMap, typename CapacityMap,
           typename SupplyMap, typename FlowMap >
bool checkFlow( const Graph& gr,
                const LowerMap& lower, const CapacityMap& upper,
                const SupplyMap& supply, const FlowMap& flow )
{
  GRAPH_TYPEDEFS(typename Graph);
  for (EdgeIt e(gr); e != INVALID; ++e)
    if (flow[e] < lower[e] || flow[e] > upper[e]) return false;

  for (NodeIt n(gr); n != INVALID; ++n) {
    typename SupplyMap::Value sum = 0;
    for (OutEdgeIt e(gr, n); e != INVALID; ++e)
      sum += flow[e];
    for (InEdgeIt e(gr, n); e != INVALID; ++e)
      sum -= flow[e];
    if (sum != supply[n]) return false;
  }

  return true;
}

// Checks the optimalitiy of a flow
template < typename Graph, typename LowerMap, typename CapacityMap,
           typename CostMap, typename FlowMap, typename PotentialMap >
bool checkOptimality( const Graph& gr, const LowerMap& lower,
                      const CapacityMap& upper, const CostMap& cost,
                      const FlowMap& flow, const PotentialMap& pi )
{
  GRAPH_TYPEDEFS(typename Graph);
  // Checking the Complementary Slackness optimality condition
  bool opt = true;
  for (EdgeIt e(gr); e != INVALID; ++e) {
    typename CostMap::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]);
    if (!opt) break;
  }
  return opt;
}

// Runs a minimum cost flow algorithm and checks the results
template < typename MinCostFlowImpl, typename Graph,
           typename LowerMap, typename CapacityMap,
           typename CostMap, typename SupplyMap >
void checkMcf( std::string test_id,
               const MinCostFlowImpl& mcf, const Graph& gr,
               const LowerMap& lower, const CapacityMap& upper,
               const CostMap& cost, const SupplyMap& supply,
               bool mcf_result, bool result,
               typename CostMap::Value total )
{
  check(mcf_result == result, "Wrong result " + test_id);
  if (result) {
    check(checkFlow(gr, lower, upper, supply, mcf.flowMap()),
          "The flow is not feasible " + test_id);
    check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
    check(checkOptimality(gr, lower, upper, cost, mcf.flowMap(), mcf.potentialMap()),
          "Wrong potentials " + test_id);
  }
}

int main()
{
  // Various tests on a small graph
  {
    typedef ListGraph Graph;
    GRAPH_TYPEDEFS(ListGraph);

    // Reading the test graph
    Graph gr;
    Graph::EdgeMap<int> c(gr), l1(gr), l2(gr), u(gr);
    Graph::NodeMap<int> s1(gr), s2(gr), s3(gr);
    Node v, w;

    std::string fname;
    if(getenv("srcdir"))
      fname = std::string(getenv("srcdir"));
    else fname = ".";
    fname += "/test/min_cost_flow_test.lgf";

    std::ifstream input(fname.c_str());
    check(input, "Input file '" << fname << "' not found");
    GraphReader<Graph>(input, gr).
      readEdgeMap("cost", c).
      readEdgeMap("capacity", u).
      readEdgeMap("lower1", l1).
      readEdgeMap("lower2", l2).
      readNodeMap("supply1", s1).
      readNodeMap("supply2", s2).
      readNodeMap("supply3", s3).
      readNode("source", v).
      readNode("target", w).
      run();
    input.close();

    // Testing CapacityScaling (scaling enabled)
    {
      CapacityScaling<Graph> mcf1(gr,u,c,s1);        checkMcf("#A1",mcf1,gr,l1,u,c,s1,mcf1.run(),true,    0);
      CapacityScaling<Graph> mcf2(gr,u,c,s2);        checkMcf("#A2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240);
      CapacityScaling<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#A3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620);
      CapacityScaling<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#A4",mcf4,gr,l2,u,c,s1,mcf4.run(),false,   0);
      CapacityScaling<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#A5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970);
      CapacityScaling<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#A6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010);
    }
    // Testing CapacityScaling (scaling disabled)
    {
      CapacityScaling<Graph> mcf1(gr,u,c,s1);        checkMcf("#B1",mcf1,gr,l1,u,c,s1,mcf1.run(false),true,    0);
      CapacityScaling<Graph> mcf2(gr,u,c,s2);        checkMcf("#B2",mcf2,gr,l1,u,c,s2,mcf2.run(false),true, 5240);
      CapacityScaling<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#B3",mcf3,gr,l1,u,c,s3,mcf3.run(false),true, 7620);
      CapacityScaling<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#B4",mcf4,gr,l2,u,c,s1,mcf4.run(false),false,   0);
      CapacityScaling<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#B5",mcf5,gr,l2,u,c,s2,mcf5.run(false),true, 5970);
      CapacityScaling<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#B6",mcf6,gr,l2,u,c,s3,mcf6.run(false),true, 8010);
    }

    // Testing CostScaling
    {
      CostScaling<Graph> mcf1(gr,u,c,s1);        checkMcf("#C1",mcf1,gr,l1,u,c,s1,mcf1.run(),true,    0);
      CostScaling<Graph> mcf2(gr,u,c,s2);        checkMcf("#C2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240);
      CostScaling<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#C3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620);
      CostScaling<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#C4",mcf4,gr,l2,u,c,s1,mcf4.run(),false,   0);
      CostScaling<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#C5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970);
      CostScaling<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#C6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010);
    }

    // Testing NetworkSimplex (with the default pivot rule)
    {
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#D1",mcf1,gr,l1,u,c,s1,mcf1.run(),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#D2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#D3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#D4",mcf4,gr,l2,u,c,s1,mcf4.run(),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#D5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#D6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010);
    }
    // Testing NetworkSimplex (with FIRST_ELIGIBLE_PIVOT)
    {
      NetworkSimplex<Graph>::PivotRuleEnum pr = NetworkSimplex<Graph>::FIRST_ELIGIBLE_PIVOT;
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#E1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#E2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#E3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#E4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#E5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#E6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010);
    }
    // Testing NetworkSimplex (with BEST_ELIGIBLE_PIVOT)
    {
      NetworkSimplex<Graph>::PivotRuleEnum pr = NetworkSimplex<Graph>::BEST_ELIGIBLE_PIVOT;
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#F1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#F2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#F3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#F4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#F5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#F6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010);
    }
    // Testing NetworkSimplex (with BLOCK_SEARCH_PIVOT)
    {
      NetworkSimplex<Graph>::PivotRuleEnum pr = NetworkSimplex<Graph>::BLOCK_SEARCH_PIVOT;
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#G1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#G2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#G3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#G4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#G5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#G6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010);
    }
    // Testing NetworkSimplex (with CANDIDATE_LIST_PIVOT)
    {
      NetworkSimplex<Graph>::PivotRuleEnum pr = NetworkSimplex<Graph>::CANDIDATE_LIST_PIVOT;
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#I1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#I2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#I3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#I4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#I5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#I6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010);
    }
    // Testing NetworkSimplex (with ALTERING_LIST_PIVOT)
    {
      NetworkSimplex<Graph>::PivotRuleEnum pr = NetworkSimplex<Graph>::ALTERING_LIST_PIVOT;
      NetworkSimplex<Graph> mcf1(gr,u,c,s1);        checkMcf("#H1",mcf1,gr,l1,u,c,s1,mcf1.run(pr),true,    0);
      NetworkSimplex<Graph> mcf2(gr,u,c,s2);        checkMcf("#H2",mcf2,gr,l1,u,c,s2,mcf2.run(pr),true, 5240);
      NetworkSimplex<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#H3",mcf3,gr,l1,u,c,s3,mcf3.run(pr),true, 7620);
      NetworkSimplex<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#H4",mcf4,gr,l2,u,c,s1,mcf4.run(pr),false,   0);
      NetworkSimplex<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#H5",mcf5,gr,l2,u,c,s2,mcf5.run(pr),true, 5970);
      NetworkSimplex<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#H6",mcf6,gr,l2,u,c,s3,mcf6.run(pr),true, 8010);
    }

    // Testing CycleCanceling (with BellmanFord)
    {
      CycleCanceling<Graph> mcf1(gr,u,c,s1);        checkMcf("#J1",mcf1,gr,l1,u,c,s1,mcf1.run(),true,    0);
      CycleCanceling<Graph> mcf2(gr,u,c,s2);        checkMcf("#J2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240);
      CycleCanceling<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#J3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620);
      CycleCanceling<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#J4",mcf4,gr,l2,u,c,s1,mcf4.run(),false,   0);
      CycleCanceling<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#J5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970);
      CycleCanceling<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#J6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010);
    }
    // Testing CycleCanceling (with MinMeanCycle)
    {
      CycleCanceling<Graph> mcf1(gr,u,c,s1);        checkMcf("#K1",mcf1,gr,l1,u,c,s1,mcf1.run(true),true,    0);
      CycleCanceling<Graph> mcf2(gr,u,c,s2);        checkMcf("#K2",mcf2,gr,l1,u,c,s2,mcf2.run(true),true, 5240);
      CycleCanceling<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#K3",mcf3,gr,l1,u,c,s3,mcf3.run(true),true, 7620);
      CycleCanceling<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#K4",mcf4,gr,l2,u,c,s1,mcf4.run(true),false,   0);
      CycleCanceling<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#K5",mcf5,gr,l2,u,c,s2,mcf5.run(true),true, 5970);
      CycleCanceling<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#K6",mcf6,gr,l2,u,c,s3,mcf6.run(true),true, 8010);
    }

    // Testing MinCostFlow
    {
      MinCostFlow<Graph> mcf1(gr,u,c,s1);        checkMcf("#L1",mcf1,gr,l1,u,c,s1,mcf1.run(),true,    0);
      MinCostFlow<Graph> mcf2(gr,u,c,s2);        checkMcf("#L2",mcf2,gr,l1,u,c,s2,mcf2.run(),true, 5240);
      MinCostFlow<Graph> mcf3(gr,u,c,v,w,27);    checkMcf("#L3",mcf3,gr,l1,u,c,s3,mcf3.run(),true, 7620);
      MinCostFlow<Graph> mcf4(gr,l2,u,c,s1);     checkMcf("#L4",mcf4,gr,l2,u,c,s1,mcf4.run(),false,   0);
      MinCostFlow<Graph> mcf5(gr,l2,u,c,s2);     checkMcf("#L5",mcf5,gr,l2,u,c,s2,mcf5.run(),true, 5970);
      MinCostFlow<Graph> mcf6(gr,l2,u,c,v,w,27); checkMcf("#L6",mcf6,gr,l2,u,c,s3,mcf6.run(),true, 8010);
    }

    // Testing MinCostMaxFlow
    {
      MinCostMaxFlow<Graph> mcmf(gr,u,c,v,w);
      mcmf.run();
      checkMcf("#M1",mcmf,gr,l1,u,c,s3,true,true,7620);
    }
  }

  // Benchmark test on a DIMACS network
  {
    typedef SmartGraph Graph;
    GRAPH_TYPEDEFS(SmartGraph);

    // Reading the test graph
    Graph graph;
    Graph::EdgeMap<int> lower(graph), capacity(graph), cost(graph);
    Graph::NodeMap<int> supply(graph);

    std::string fname;
    if(getenv("srcdir"))
      fname = std::string(getenv("srcdir"));
    else fname = ".";
    fname += "/test/min_cost_flow_test.net";

    std::ifstream input(fname.c_str());
    check(input, "Input file '" << fname << "' not found");
    readDimacs(input, graph, lower, capacity, cost, supply);
    input.close();

    // NetworkSimplex
    {
      Timer t;
      NetworkSimplex<Graph> mcf(graph, lower, capacity, cost, supply);
      bool res = mcf.run();
      t.stop();
      checkMcf("#T3", mcf, graph, lower, capacity, cost, supply, res, true, 196587626);
      std::cout << "NetworkSimplex";
      std::cout << std::endl << t << std::endl;
    }
    // CapacityScaling
    {
      Timer t;
      CapacityScaling<Graph> mcf(graph, lower, capacity, cost, supply);
      bool res = mcf.run();
      t.stop();
      checkMcf("#T1", mcf, graph, lower, capacity, cost, supply, res, true, 196587626);
      std::cout << "CapacityScaling";
      std::cout << std::endl << t << std::endl;
    }
    // CostScaling
    {
      Timer t;
      CostScaling<Graph> mcf(graph, lower, capacity, cost, supply);
      bool res = mcf.run();
      t.stop();
      checkMcf("#T2", mcf, graph, lower, capacity, cost, supply, res, true, 196587626);
      std::cout << "CostScaling";
      std::cout << std::endl << t << std::endl;
    }
    // CycleCanceling
    {
      Timer t;
      CycleCanceling<Graph> mcf(graph, lower, capacity, cost, supply);
      bool res = mcf.run();
      t.stop();
      checkMcf("#T4", mcf, graph, lower, capacity, cost, supply, res, true, 196587626);
      std::cout << "CycleCanceling";
      std::cout << std::endl << t << std::endl;
    }
  }

  return 0;
}