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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) 2003-2011
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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 <lemon/list_graph.h>
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#include <lemon/lgf_reader.h>
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#include <lemon/path.h>
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#include <lemon/suurballe.h>
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#include <lemon/concepts/digraph.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\n"
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"1\n"
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"2\n"
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"3\n"
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"4\n"
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"5\n"
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"6\n"
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"7\n"
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"8\n"
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"9\n"
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"10\n"
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"11\n"
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"12\n"
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"@arcs\n"
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" length\n"
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" 1 2 70\n"
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" 1 3 150\n"
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" 1 4 80\n"
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" 2 8 80\n"
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" 3 5 140\n"
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" 4 6 60\n"
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" 4 7 80\n"
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" 4 8 110\n"
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" 5 7 60\n"
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" 5 11 120\n"
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" 6 3 0\n"
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" 6 9 140\n"
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" 6 10 90\n"
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" 7 1 30\n"
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" 8 12 60\n"
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" 9 12 50\n"
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"10 12 70\n"
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"10 2 100\n"
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"10 7 60\n"
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"11 10 20\n"
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"12 11 30\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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"@end\n";
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// Check the interface of Suurballe
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void checkSuurballeCompile()
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{
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typedef int VType;
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typedef concepts::Digraph Digraph;
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typedef Digraph::Node Node;
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typedef Digraph::Arc Arc;
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typedef concepts::ReadMap<Arc, VType> LengthMap;
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typedef Suurballe<Digraph, LengthMap> SuurballeType;
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Digraph g;
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Node n;
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Arc e;
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LengthMap len;
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SuurballeType::FlowMap flow(g);
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SuurballeType::PotentialMap pi(g);
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SuurballeType suurb_test(g, len);
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const SuurballeType& const_suurb_test = suurb_test;
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suurb_test
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.flowMap(flow)
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.potentialMap(pi);
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int k;
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k = suurb_test.run(n, n);
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k = suurb_test.run(n, n, k);
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suurb_test.init(n);
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k = suurb_test.findFlow(n);
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k = suurb_test.findFlow(n, k);
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suurb_test.findPaths();
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int f;
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VType c;
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ignore_unused_variable_warning(f,c);
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c = const_suurb_test.totalLength();
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f = const_suurb_test.flow(e);
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const SuurballeType::FlowMap& fm =
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const_suurb_test.flowMap();
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c = const_suurb_test.potential(n);
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const SuurballeType::PotentialMap& pm =
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const_suurb_test.potentialMap();
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k = const_suurb_test.pathNum();
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Path<Digraph> p = const_suurb_test.path(k);
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ignore_unused_variable_warning(fm);
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ignore_unused_variable_warning(pm);
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}
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// Check the feasibility of the flow
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template <typename Digraph, typename FlowMap>
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bool checkFlow( const Digraph& gr, const FlowMap& flow,
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typename Digraph::Node s, typename Digraph::Node t,
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int value )
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{
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TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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for (ArcIt e(gr); e != INVALID; ++e)
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if (!(flow[e] == 0 || flow[e] == 1)) return false;
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for (NodeIt n(gr); n != INVALID; ++n) {
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int 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 (n == s && sum != value) return false;
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if (n == t && sum != -value) return false;
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if (n != s && n != t && sum != 0) return false;
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}
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return true;
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}
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// Check the optimalitiy of the flow
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template < typename Digraph, typename CostMap,
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typename FlowMap, typename PotentialMap >
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bool checkOptimality( const Digraph& gr, const CostMap& cost,
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const FlowMap& flow, const PotentialMap& pi )
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{
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// Check the "Complementary Slackness" optimality condition
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TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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bool opt = true;
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for (ArcIt e(gr); e != INVALID; ++e) {
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typename CostMap::Value red_cost =
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cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
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opt = (flow[e] == 0 && red_cost >= 0) ||
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(flow[e] == 1 && red_cost <= 0);
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if (!opt) break;
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}
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return opt;
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}
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// Check a path
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template <typename Digraph, typename Path>
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bool checkPath( const Digraph& gr, const Path& path,
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typename Digraph::Node s, typename Digraph::Node t)
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{
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TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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Node n = s;
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for (int i = 0; i < path.length(); ++i) {
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if (gr.source(path.nth(i)) != n) return false;
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n = gr.target(path.nth(i));
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}
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return n == t;
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}
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int main()
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{
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DIGRAPH_TYPEDEFS(ListDigraph);
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// Read the test digraph
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ListDigraph digraph;
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ListDigraph::ArcMap<int> length(digraph);
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Node s, t;
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std::istringstream input(test_lgf);
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DigraphReader<ListDigraph>(digraph, input).
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arcMap("length", length).
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node("source", s).
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node("target", t).
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run();
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// Find 2 paths
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{
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Suurballe<ListDigraph> suurballe(digraph, length);
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check(suurballe.run(s, t) == 2, "Wrong number of paths");
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check(checkFlow(digraph, suurballe.flowMap(), s, t, 2),
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"The flow is not feasible");
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check(suurballe.totalLength() == 510, "The flow is not optimal");
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check(checkOptimality(digraph, length, suurballe.flowMap(),
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suurballe.potentialMap()),
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"Wrong potentials");
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for (int i = 0; i < suurballe.pathNum(); ++i)
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check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path");
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}
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// Find 3 paths
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{
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Suurballe<ListDigraph> suurballe(digraph, length);
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check(suurballe.run(s, t, 3) == 3, "Wrong number of paths");
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check(checkFlow(digraph, suurballe.flowMap(), s, t, 3),
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"The flow is not feasible");
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check(suurballe.totalLength() == 1040, "The flow is not optimal");
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check(checkOptimality(digraph, length, suurballe.flowMap(),
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suurballe.potentialMap()),
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"Wrong potentials");
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for (int i = 0; i < suurballe.pathNum(); ++i)
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check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path");
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}
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// Find 5 paths (only 3 can be found)
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{
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Suurballe<ListDigraph> suurballe(digraph, length);
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check(suurballe.run(s, t, 5) == 3, "Wrong number of paths");
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check(checkFlow(digraph, suurballe.flowMap(), s, t, 3),
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"The flow is not feasible");
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check(suurballe.totalLength() == 1040, "The flow is not optimal");
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check(checkOptimality(digraph, length, suurballe.flowMap(),
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suurballe.potentialMap()),
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"Wrong potentials");
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for (int i = 0; i < suurballe.pathNum(); ++i)
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check(checkPath(digraph, suurballe.path(i), s, t), "Wrong path");
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}
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return 0;
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}
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