[345] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #include <iostream> |
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| 20 | #include <fstream> |
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| 21 | |
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| 22 | #include <lemon/list_graph.h> |
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| 23 | #include <lemon/lgf_reader.h> |
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| 24 | #include <lemon/path.h> |
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| 25 | #include <lemon/suurballe.h> |
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| 26 | |
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| 27 | #include "test_tools.h" |
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| 28 | |
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| 29 | using namespace lemon; |
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| 30 | |
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[346] | 31 | // Check the feasibility of the flow |
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[345] | 32 | template <typename Digraph, typename FlowMap> |
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| 33 | bool checkFlow( const Digraph& gr, const FlowMap& flow, |
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| 34 | typename Digraph::Node s, typename Digraph::Node t, |
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| 35 | int value ) |
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| 36 | { |
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| 37 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 38 | for (ArcIt e(gr); e != INVALID; ++e) |
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| 39 | if (!(flow[e] == 0 || flow[e] == 1)) return false; |
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| 40 | |
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| 41 | for (NodeIt n(gr); n != INVALID; ++n) { |
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| 42 | int sum = 0; |
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| 43 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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| 44 | sum += flow[e]; |
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| 45 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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| 46 | sum -= flow[e]; |
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| 47 | if (n == s && sum != value) return false; |
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| 48 | if (n == t && sum != -value) return false; |
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| 49 | if (n != s && n != t && sum != 0) return false; |
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| 50 | } |
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| 51 | |
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| 52 | return true; |
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| 53 | } |
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| 54 | |
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[346] | 55 | // Check the optimalitiy of the flow |
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[345] | 56 | template < typename Digraph, typename CostMap, |
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| 57 | typename FlowMap, typename PotentialMap > |
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| 58 | bool checkOptimality( const Digraph& gr, const CostMap& cost, |
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| 59 | const FlowMap& flow, const PotentialMap& pi ) |
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| 60 | { |
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[346] | 61 | // Check the "Complementary Slackness" optimality condition |
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[345] | 62 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 63 | bool opt = true; |
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| 64 | for (ArcIt e(gr); e != INVALID; ++e) { |
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| 65 | typename CostMap::Value red_cost = |
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| 66 | cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; |
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| 67 | opt = (flow[e] == 0 && red_cost >= 0) || |
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| 68 | (flow[e] == 1 && red_cost <= 0); |
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| 69 | if (!opt) break; |
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| 70 | } |
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| 71 | return opt; |
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| 72 | } |
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| 73 | |
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[346] | 74 | // Check a path |
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| 75 | template <typename Digraph, typename Path> |
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[345] | 76 | bool checkPath( const Digraph& gr, const Path& path, |
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| 77 | typename Digraph::Node s, typename Digraph::Node t) |
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| 78 | { |
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[346] | 79 | // Check the "Complementary Slackness" optimality condition |
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[345] | 80 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 81 | Node n = s; |
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| 82 | for (int i = 0; i < path.length(); ++i) { |
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| 83 | if (gr.source(path.nth(i)) != n) return false; |
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| 84 | n = gr.target(path.nth(i)); |
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| 85 | } |
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| 86 | return n == t; |
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| 87 | } |
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| 88 | |
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| 89 | |
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| 90 | int main() |
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| 91 | { |
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| 92 | DIGRAPH_TYPEDEFS(ListDigraph); |
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| 93 | |
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[346] | 94 | // Read the test digraph |
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[345] | 95 | ListDigraph digraph; |
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| 96 | ListDigraph::ArcMap<int> length(digraph); |
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| 97 | Node source, target; |
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| 98 | |
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| 99 | std::string fname; |
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| 100 | if(getenv("srcdir")) |
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| 101 | fname = std::string(getenv("srcdir")); |
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| 102 | else fname = "."; |
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| 103 | fname += "/test/min_cost_flow_test.lgf"; |
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| 104 | |
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| 105 | std::ifstream input(fname.c_str()); |
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| 106 | check(input, "Input file '" << fname << "' not found"); |
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| 107 | DigraphReader<ListDigraph>(digraph, input). |
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| 108 | arcMap("cost", length). |
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| 109 | node("source", source). |
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| 110 | node("target", target). |
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| 111 | run(); |
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| 112 | input.close(); |
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| 113 | |
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[346] | 114 | // Find 2 paths |
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[345] | 115 | { |
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| 116 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 117 | check(suurballe.run(2) == 2, "Wrong number of paths"); |
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| 118 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 2), |
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| 119 | "The flow is not feasible"); |
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| 120 | check(suurballe.totalLength() == 510, "The flow is not optimal"); |
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| 121 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 122 | suurballe.potentialMap()), |
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| 123 | "Wrong potentials"); |
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| 124 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 125 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 126 | "Wrong path"); |
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| 127 | } |
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| 128 | |
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[346] | 129 | // Find 3 paths |
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[345] | 130 | { |
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| 131 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 132 | check(suurballe.run(3) == 3, "Wrong number of paths"); |
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| 133 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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| 134 | "The flow is not feasible"); |
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| 135 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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| 136 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 137 | suurballe.potentialMap()), |
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| 138 | "Wrong potentials"); |
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| 139 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 140 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 141 | "Wrong path"); |
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| 142 | } |
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| 143 | |
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[346] | 144 | // Find 5 paths (only 3 can be found) |
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[345] | 145 | { |
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| 146 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 147 | check(suurballe.run(5) == 3, "Wrong number of paths"); |
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| 148 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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| 149 | "The flow is not feasible"); |
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| 150 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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| 151 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 152 | suurballe.potentialMap()), |
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| 153 | "Wrong potentials"); |
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| 154 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 155 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 156 | "Wrong path"); |
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| 157 | } |
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| 158 | |
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| 159 | return 0; |
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| 160 | } |
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