/* -*- 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;

 }