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

  *

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

  *

  * Copyright (C) 2003-2013

  * 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 "test_tools.h"

 #include <lemon/smart_graph.h>

 #include <lemon/preflow.h>

 #include <lemon/edmonds_karp.h>

 #include <lemon/concepts/digraph.h>

 #include <lemon/concepts/maps.h>

 #include <lemon/lgf_reader.h>

 #include <lemon/elevator.h>

 #include <lemon/tolerance.h>

 using namespace lemon;

 char test_lgf[] =

   "@nodes\n"

   "label\n"

   "0\n"

   "1\n"

   "2\n"

   "3\n"

   "4\n"

   "5\n"

   "6\n"

   "7\n"

   "8\n"

   "9\n"

   "@arcs\n"

   "    label capacity\n"

   "0 1 0     20\n"

   "0 2 1     0\n"

   "1 1 2     3\n"

   "1 2 3     8\n"

   "1 3 4     8\n"

   "2 5 5     5\n"

   "3 2 6     5\n"

   "3 5 7     5\n"

   "3 6 8     5\n"

   "4 3 9     3\n"

   "5 7 10    3\n"

   "5 6 11    10\n"

   "5 8 12    10\n"

   "6 8 13    8\n"

   "8 9 14    20\n"

   "8 1 15    5\n"

   "9 5 16    5\n"

   "@attributes\n"

   "source 1\n"

   "target 8\n";

 // Checks the general interface of a max flow algorithm

 template <typename GR, typename CAP>

 struct MaxFlowClassConcept

 {

   template <typename MF>

   struct Constraints {

     typedef typename GR::Node Node;

     typedef typename GR::Arc Arc;

     typedef typename CAP::Value Value;

     typedef concepts::ReadWriteMap<Arc, Value> FlowMap;

     typedef concepts::WriteMap<Node, bool> CutMap;

     GR g;

     Node n;

     Arc e;

     CAP cap;

     FlowMap flow;

     CutMap cut;

     Value v;

     bool b;

     void constraints() {

       checkConcept<concepts::Digraph, GR>();

       const Constraints& me = *this;

       typedef typename MF

           ::template SetFlowMap<FlowMap>

           ::Create MaxFlowType;

       typedef typename MF::Create MaxFlowType2;

       MaxFlowType max_flow(me.g, me.cap, me.n, me.n);

       const MaxFlowType& const_max_flow = max_flow;

       max_flow

           .capacityMap(cap)

           .flowMap(flow)

           .source(n)

           .target(n);

       typename MaxFlowType::Tolerance tol = const_max_flow.tolerance();

       max_flow.tolerance(tol);

       max_flow.init();

       max_flow.init(cap);

       max_flow.run();

       v = const_max_flow.flowValue();

       v = const_max_flow.flow(e);

       const FlowMap& fm = const_max_flow.flowMap();

       b = const_max_flow.minCut(n);

       const_max_flow.minCutMap(cut);

       ::lemon::ignore_unused_variable_warning(fm);

     }

   };

 };

 // Checks the specific parts of Preflow's interface

 void checkPreflowCompile()

 {

   typedef int Value;

   typedef concepts::Digraph Digraph;

   typedef concepts::ReadMap<Digraph::Arc, Value> CapMap;

   typedef Elevator<Digraph, Digraph::Node> Elev;

   typedef LinkedElevator<Digraph, Digraph::Node> LinkedElev;

   Digraph g;

   Digraph::Node n;

   CapMap cap;

   typedef Preflow<Digraph, CapMap>

       ::SetElevator<Elev>

       ::SetStandardElevator<LinkedElev>

       ::Create PreflowType;

   PreflowType preflow_test(g, cap, n, n);

   const PreflowType& const_preflow_test = preflow_test;

   const PreflowType::Elevator& elev = const_preflow_test.elevator();

   preflow_test.elevator(const_cast<PreflowType::Elevator&>(elev));

   bool b = preflow_test.init(cap);

   preflow_test.startFirstPhase();

   preflow_test.startSecondPhase();

   preflow_test.runMinCut();

   ::lemon::ignore_unused_variable_warning(b);

 }

 // Checks the specific parts of EdmondsKarp's interface

 void checkEdmondsKarpCompile()

 {

   typedef int Value;

   typedef concepts::Digraph Digraph;

   typedef concepts::ReadMap<Digraph::Arc, Value> CapMap;

   Digraph g;

   Digraph::Node n;

   CapMap cap;

   EdmondsKarp<Digraph, CapMap> ek_test(g, cap, n, n);

   ek_test.init(cap);

   bool b = ek_test.checkedInit(cap);

   b = ek_test.augment();

   ek_test.start();

   ::lemon::ignore_unused_variable_warning(b);

 }

 template <typename T>

 T cutValue(const SmartDigraph& g,

            const SmartDigraph::NodeMap<bool>& cut,

            const SmartDigraph::ArcMap<T>& cap) {

   T c = 0;

   for (SmartDigraph::ArcIt e(g); e != INVALID; ++e) {

     if (cut[g.source(e)] && !cut[g.target(e)]) c += cap[e];

   }

   return c;

 }

 template <typename T>

 bool checkFlow(const SmartDigraph& g,

                const SmartDigraph::ArcMap<T>& flow,

                const SmartDigraph::ArcMap<T>& cap,

                SmartDigraph::Node s, SmartDigraph::Node t,

                const Tolerance<T>& tol) {

   for (SmartDigraph::ArcIt e(g); e != INVALID; ++e) {

     if (tol.negative(flow[e]) || tol.less(cap[e], flow[e])) return false;

   }

   for (SmartDigraph::NodeIt n(g); n != INVALID; ++n) {

     if (n == s || n == t) continue;

     T sum = 0;

     for (SmartDigraph::OutArcIt e(g, n); e != INVALID; ++e) {

       sum += flow[e];

     }

     for (SmartDigraph::InArcIt e(g, n); e != INVALID; ++e) {

       sum -= flow[e];

     }

     if (tol.nonZero(sum)) return false;

   }

   return true;

 }

 void checkInitPreflow()

 {

   DIGRAPH_TYPEDEFS(SmartDigraph);

   SmartDigraph g;

   SmartDigraph::ArcMap<int> cap(g), iflow(g);

   Node s = g.addNode(); Node t = g.addNode();

   Node n1 = g.addNode(); Node n2 = g.addNode();

   Arc a;

   a = g.addArc(s, n1); cap[a] = 20; iflow[a] = 20;

   a = g.addArc(n1, n2); cap[a] = 10; iflow[a] = 0;

   a = g.addArc(n2, t); cap[a] = 20; iflow[a] = 0;

   Preflow<SmartDigraph> pre(g, cap, s, t);

   pre.init(iflow);

   pre.startFirstPhase();

   check(pre.flowValue() == 10, "Incorrect max flow value.");

   check(pre.minCut(s), "Wrong min cut (Node s).");

   check(pre.minCut(n1), "Wrong min cut (Node n1).");

   check(!pre.minCut(n2), "Wrong min cut (Node n2).");

   check(!pre.minCut(t), "Wrong min cut (Node t).");

 }

 template <typename MF, typename SF>

 void checkMaxFlowAlg(const char *input_lgf,  typename MF::Value expected) {

   typedef SmartDigraph Digraph;

   DIGRAPH_TYPEDEFS(Digraph);

   typedef typename MF::Value Value;

   typedef Digraph::ArcMap<Value> CapMap;

   typedef CapMap FlowMap;

   typedef BoolNodeMap CutMap;

   Tolerance<Value> tol;

   Digraph g;

   Node s, t;

   CapMap cap(g);

   std::istringstream input(input_lgf);

   DigraphReader<Digraph>(g,input)

       .arcMap("capacity", cap)

       .node("source",s)

       .node("target",t)

       .run();

   MF max_flow(g, cap, s, t);

   max_flow.run();

   check(!tol.different(expected, max_flow.flowValue()),

         "Incorrect max flow value.");

   check(checkFlow(g, max_flow.flowMap(), cap, s, t, tol),

         "The flow is not feasible.");

   CutMap min_cut(g);

   max_flow.minCutMap(min_cut);

   Value min_cut_value = cutValue(g, min_cut, cap);

   check(!tol.different(expected, min_cut_value),

         "Incorrect min cut value.");

   FlowMap flow(g);

   for (ArcIt e(g); e != INVALID; ++e) flow[e] = max_flow.flowMap()[e];

   for (ArcIt e(g); e != INVALID; ++e) cap[e] = 2 * cap[e];

   max_flow.init(flow);

   SF::startFirstPhase(max_flow);       // start first phase of the algorithm

   CutMap min_cut1(g);

   max_flow.minCutMap(min_cut1);

   min_cut_value = cutValue(g, min_cut1, cap);

   check(!tol.different(2 * expected, max_flow.flowValue()),

         "Incorrect max flow value.");

   check(!tol.different(2 * expected, min_cut_value),

         "Incorrect min cut value.");

   SF::startSecondPhase(max_flow);       // start second phase of the algorithm

   check(checkFlow(g, max_flow.flowMap(), cap, s, t, tol),

         "The flow is not feasible.");

   CutMap min_cut2(g);

   max_flow.minCutMap(min_cut2);

   min_cut_value = cutValue(g, min_cut2, cap);

   check(!tol.different(2 * expected, max_flow.flowValue()),

         "Incorrect max flow value.");

   check(!tol.different(2 * expected, min_cut_value),

         "Incorrect min cut value.");

   max_flow.flowMap(flow);

   NodeIt tmp1(g, s);

   ++tmp1;

   if (tmp1 != INVALID) s = tmp1;

   NodeIt tmp2(g, t);

   ++tmp2;

   if (tmp2 != INVALID) t = tmp2;

   max_flow.source(s);

   max_flow.target(t);

   max_flow.run();

   CutMap min_cut3(g);

   max_flow.minCutMap(min_cut3);

   min_cut_value = cutValue(g, min_cut3, cap);

   check(!tol.different(max_flow.flowValue(), min_cut_value),

         "The max flow value or the min cut value is wrong.");

 }

 // Struct for calling start functions of a general max flow algorithm

 template <typename MF>

 struct GeneralStartFunctions {

   static void startFirstPhase(MF& mf) {

     mf.start();

   }

   static void startSecondPhase(MF& mf) {

     ::lemon::ignore_unused_variable_warning(mf);

   }

 };

 // Struct for calling start functions of Preflow

 template <typename MF>

 struct PreflowStartFunctions {

   static void startFirstPhase(MF& mf) {

     mf.startFirstPhase();

   }

   static void startSecondPhase(MF& mf) {

     mf.startSecondPhase();

   }

 };

 int main() {

   typedef concepts::Digraph GR;

   typedef concepts::ReadMap<GR::Arc, int> CM1;

   typedef concepts::ReadMap<GR::Arc, double> CM2;

   // Check the interface of Preflow

   checkConcept< MaxFlowClassConcept<GR, CM1>,

                 Preflow<GR, CM1> >();

   checkConcept< MaxFlowClassConcept<GR, CM2>,

                 Preflow<GR, CM2> >();

   // Check the interface of EdmondsKarp

   checkConcept< MaxFlowClassConcept<GR, CM1>,

                 EdmondsKarp<GR, CM1> >();

   checkConcept< MaxFlowClassConcept<GR, CM2>,

                 EdmondsKarp<GR, CM2> >();

   // Check Preflow

   typedef Preflow<SmartDigraph, SmartDigraph::ArcMap<int> > PType1;

   typedef Preflow<SmartDigraph, SmartDigraph::ArcMap<float> > PType2;

   typedef Preflow<SmartDigraph, SmartDigraph::ArcMap<double> > PType3;

   checkMaxFlowAlg<PType1, PreflowStartFunctions<PType1> >(test_lgf, 13);

   checkMaxFlowAlg<PType2, PreflowStartFunctions<PType2> >(test_lgf, 13);

   checkMaxFlowAlg<PType3, PreflowStartFunctions<PType3> >(test_lgf, 13);

   checkInitPreflow();

   // Check EdmondsKarp

   typedef EdmondsKarp<SmartDigraph, SmartDigraph::ArcMap<int> > EKType1;

   typedef EdmondsKarp<SmartDigraph, SmartDigraph::ArcMap<float> > EKType2;

   typedef EdmondsKarp<SmartDigraph, SmartDigraph::ArcMap<double> > EKType3;

   checkMaxFlowAlg<EKType1, GeneralStartFunctions<EKType1> >(test_lgf, 13);

   checkMaxFlowAlg<EKType2, GeneralStartFunctions<EKType2> >(test_lgf, 13);

   checkMaxFlowAlg<EKType3, GeneralStartFunctions<EKType3> >(test_lgf, 13);

   return 0;

 }