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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2009
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#include <iostream>
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#include <fstream>
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#include <lemon/list_graph.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/network_simplex.h>
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#include <lemon/concepts/digraph.h>
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#include <lemon/concept_check.h>
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#include "test_tools.h"
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using namespace lemon;
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char test_lgf[] =
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"@nodes\n"
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"label sup1 sup2 sup3\n"
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" 1 20 27 0\n"
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" 2 -4 0 0\n"
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" 3 0 0 0\n"
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" 4 0 0 0\n"
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" 5 9 0 0\n"
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" 6 -6 0 0\n"
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" 7 0 0 0\n"
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" 8 0 0 0\n"
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" 9 3 0 0\n"
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" 10 -2 0 0\n"
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" 11 0 0 0\n"
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" 12 -20 -27 0\n"
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"\n"
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"@arcs\n"
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" cost cap low1 low2\n"
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" 1 2 70 11 0 8\n"
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" 1 3 150 3 0 1\n"
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" 1 4 80 15 0 2\n"
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" 2 8 80 12 0 0\n"
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" 3 5 140 5 0 3\n"
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" 4 6 60 10 0 1\n"
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" 4 7 80 2 0 0\n"
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" 4 8 110 3 0 0\n"
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" 5 7 60 14 0 0\n"
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" 5 11 120 12 0 0\n"
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" 6 3 0 3 0 0\n"
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" 6 9 140 4 0 0\n"
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" 6 10 90 8 0 0\n"
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" 7 1 30 5 0 0\n"
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" 8 12 60 16 0 4\n"
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" 9 12 50 6 0 0\n"
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"10 12 70 13 0 5\n"
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"10 2 100 7 0 0\n"
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"10 7 60 10 0 0\n"
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"11 10 20 14 0 6\n"
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"12 11 30 10 0 0\n"
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"\n"
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"@attributes\n"
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"source 1\n"
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"target 12\n";
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// Check the interface of an MCF algorithm
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template <typename GR, typename Flow, typename Cost>
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class McfClassConcept
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{
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public:
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template <typename MCF>
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struct Constraints {
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void constraints() {
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checkConcept<concepts::Digraph, GR>();
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MCF mcf(g);
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b = mcf.reset()
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.lowerMap(lower)
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.upperMap(upper)
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.capacityMap(upper)
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.boundMaps(lower, upper)
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.costMap(cost)
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.supplyMap(sup)
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.stSupply(n, n, k)
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.run();
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const typename MCF::FlowMap &fm = mcf.flowMap();
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const typename MCF::PotentialMap &pm = mcf.potentialMap();
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v = mcf.totalCost();
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double x = mcf.template totalCost<double>();
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v = mcf.flow(a);
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v = mcf.potential(n);
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mcf.flowMap(flow);
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mcf.potentialMap(pot);
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ignore_unused_variable_warning(fm);
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ignore_unused_variable_warning(pm);
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ignore_unused_variable_warning(x);
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}
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typedef typename GR::Node Node;
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typedef typename GR::Arc Arc;
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typedef concepts::ReadMap<Node, Flow> NM;
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typedef concepts::ReadMap<Arc, Flow> FAM;
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typedef concepts::ReadMap<Arc, Cost> CAM;
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const GR &g;
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const FAM &lower;
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const FAM &upper;
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const CAM &cost;
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const NM ⊃
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const Node &n;
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const Arc &a;
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const Flow &k;
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Flow v;
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bool b;
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typename MCF::FlowMap &flow;
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typename MCF::PotentialMap &pot;
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};
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};
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// Check the feasibility of the given flow (primal soluiton)
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template < typename GR, typename LM, typename UM,
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typename SM, typename FM >
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bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
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const SM& supply, const FM& flow )
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{
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TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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for (ArcIt e(gr); e != INVALID; ++e) {
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if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
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}
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for (NodeIt n(gr); n != INVALID; ++n) {
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typename SM::Value sum = 0;
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for (OutArcIt e(gr, n); e != INVALID; ++e)
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sum += flow[e];
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for (InArcIt e(gr, n); e != INVALID; ++e)
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sum -= flow[e];
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if (sum != supply[n]) return false;
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}
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return true;
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}
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// Check the feasibility of the given potentials (dual soluiton)
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// using the "Complementary Slackness" optimality condition
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template < typename GR, typename LM, typename UM,
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typename CM, typename FM, typename PM >
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bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
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const CM& cost, const FM& flow, const PM& pi )
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{
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TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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bool opt = true;
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for (ArcIt e(gr); opt && e != INVALID; ++e) {
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typename CM::Value red_cost =
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cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
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opt = red_cost == 0 ||
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(red_cost > 0 && flow[e] == lower[e]) ||
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(red_cost < 0 && flow[e] == upper[e]);
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}
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return opt;
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}
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// Run a minimum cost flow algorithm and check the results
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template < typename MCF, typename GR,
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typename LM, typename UM,
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typename CM, typename SM >
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void checkMcf( const MCF& mcf, bool mcf_result,
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const GR& gr, const LM& lower, const UM& upper,
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const CM& cost, const SM& supply,
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bool result, typename CM::Value total,
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const std::string &test_id = "" )
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{
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check(mcf_result == result, "Wrong result " + test_id);
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if (result) {
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check(checkFlow(gr, lower, upper, supply, mcf.flowMap()),
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"The flow is not feasible " + test_id);
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check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
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check(checkPotential(gr, lower, upper, cost, mcf.flowMap(),
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mcf.potentialMap()),
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"Wrong potentials " + test_id);
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}
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}
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int main()
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{
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// Check the interfaces
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{
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typedef int Flow;
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typedef int Cost;
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// TODO: This typedef should be enabled if the standard maps are
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// reference maps in the graph concepts (See #190).
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/**/
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//typedef concepts::Digraph GR;
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typedef ListDigraph GR;
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/**/
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checkConcept< McfClassConcept<GR, Flow, Cost>,
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NetworkSimplex<GR, Flow, Cost> >();
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}
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// Run various MCF tests
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typedef ListDigraph Digraph;
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DIGRAPH_TYPEDEFS(ListDigraph);
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// Read the test digraph
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Digraph gr;
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Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);
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Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr);
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ConstMap<Arc, int> cc(1), cu(std::numeric_limits<int>::max());
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Node v, w;
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std::istringstream input(test_lgf);
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DigraphReader<Digraph>(gr, input)
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.arcMap("cost", c)
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.arcMap("cap", u)
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.arcMap("low1", l1)
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.arcMap("low2", l2)
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.nodeMap("sup1", s1)
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.nodeMap("sup2", s2)
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.nodeMap("sup3", s3)
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.node("source", v)
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.node("target", w)
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.run();
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// A. Test NetworkSimplex with the default pivot rule
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{
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NetworkSimplex<Digraph> mcf(gr);
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mcf.upperMap(u).costMap(c);
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checkMcf(mcf, mcf.supplyMap(s1).run(),
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gr, l1, u, c, s1, true, 5240, "#A1");
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checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
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gr, l1, u, c, s2, true, 7620, "#A2");
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mcf.lowerMap(l2);
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checkMcf(mcf, mcf.supplyMap(s1).run(),
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gr, l2, u, c, s1, true, 5970, "#A3");
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checkMcf(mcf, mcf.stSupply(v, w, 27).run(),
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gr, l2, u, c, s2, true, 8010, "#A4");
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mcf.reset();
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checkMcf(mcf, mcf.supplyMap(s1).run(),
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gr, l1, cu, cc, s1, true, 74, "#A5");
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checkMcf(mcf, mcf.lowerMap(l2).stSupply(v, w, 27).run(),
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gr, l2, cu, cc, s2, true, 94, "#A6");
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mcf.reset();
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checkMcf(mcf, mcf.run(),
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gr, l1, cu, cc, s3, true, 0, "#A7");
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checkMcf(mcf, mcf.boundMaps(l2, u).run(),
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gr, l2, u, cc, s3, false, 0, "#A8");
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}
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// B. Test NetworkSimplex with each pivot rule
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{
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NetworkSimplex<Digraph> mcf(gr);
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mcf.supplyMap(s1).costMap(c).capacityMap(u).lowerMap(l2);
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checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::FIRST_ELIGIBLE),
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gr, l2, u, c, s1, true, 5970, "#B1");
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checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BEST_ELIGIBLE),
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gr, l2, u, c, s1, true, 5970, "#B2");
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checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::BLOCK_SEARCH),
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gr, l2, u, c, s1, true, 5970, "#B3");
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checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::CANDIDATE_LIST),
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gr, l2, u, c, s1, true, 5970, "#B4");
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checkMcf(mcf, mcf.run(NetworkSimplex<Digraph>::ALTERING_LIST),
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gr, l2, u, c, s1, true, 5970, "#B5");
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}
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return 0;
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}
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