[357] | 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 | |
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| 21 | #include <lemon/list_graph.h> |
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| 22 | #include <lemon/lgf_reader.h> |
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| 23 | #include <lemon/path.h> |
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| 24 | #include <lemon/suurballe.h> |
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| 25 | |
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| 26 | #include "test_tools.h" |
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| 27 | |
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| 28 | using namespace lemon; |
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| 29 | |
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[442] | 30 | char test_lgf[] = |
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| 31 | "@nodes\n" |
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| 32 | "label supply1 supply2 supply3\n" |
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| 33 | "1 0 20 27\n" |
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| 34 | "2 0 -4 0\n" |
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| 35 | "3 0 0 0\n" |
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| 36 | "4 0 0 0\n" |
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| 37 | "5 0 9 0\n" |
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| 38 | "6 0 -6 0\n" |
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| 39 | "7 0 0 0\n" |
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| 40 | "8 0 0 0\n" |
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| 41 | "9 0 3 0\n" |
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| 42 | "10 0 -2 0\n" |
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| 43 | "11 0 0 0\n" |
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| 44 | "12 0 -20 -27\n" |
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| 45 | "@arcs\n" |
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| 46 | " cost capacity lower1 lower2\n" |
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| 47 | " 1 2 70 11 0 8\n" |
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| 48 | " 1 3 150 3 0 1\n" |
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| 49 | " 1 4 80 15 0 2\n" |
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| 50 | " 2 8 80 12 0 0\n" |
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| 51 | " 3 5 140 5 0 3\n" |
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| 52 | " 4 6 60 10 0 1\n" |
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| 53 | " 4 7 80 2 0 0\n" |
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| 54 | " 4 8 110 3 0 0\n" |
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| 55 | " 5 7 60 14 0 0\n" |
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| 56 | " 5 11 120 12 0 0\n" |
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| 57 | " 6 3 0 3 0 0\n" |
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| 58 | " 6 9 140 4 0 0\n" |
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| 59 | " 6 10 90 8 0 0\n" |
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| 60 | " 7 1 30 5 0 0\n" |
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| 61 | " 8 12 60 16 0 4\n" |
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| 62 | " 9 12 50 6 0 0\n" |
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| 63 | "10 12 70 13 0 5\n" |
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| 64 | "10 2 100 7 0 0\n" |
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| 65 | "10 7 60 10 0 0\n" |
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| 66 | "11 10 20 14 0 6\n" |
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| 67 | "12 11 30 10 0 0\n" |
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| 68 | "@attributes\n" |
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| 69 | "source 1\n" |
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| 70 | "target 12\n" |
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| 71 | "@end\n"; |
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| 72 | |
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[358] | 73 | // Check the feasibility of the flow |
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[357] | 74 | template <typename Digraph, typename FlowMap> |
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| 75 | bool checkFlow( const Digraph& gr, const FlowMap& flow, |
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| 76 | typename Digraph::Node s, typename Digraph::Node t, |
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| 77 | int value ) |
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| 78 | { |
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| 79 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 80 | for (ArcIt e(gr); e != INVALID; ++e) |
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| 81 | if (!(flow[e] == 0 || flow[e] == 1)) return false; |
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| 82 | |
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| 83 | for (NodeIt n(gr); n != INVALID; ++n) { |
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| 84 | int sum = 0; |
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| 85 | for (OutArcIt e(gr, n); e != INVALID; ++e) |
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| 86 | sum += flow[e]; |
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| 87 | for (InArcIt e(gr, n); e != INVALID; ++e) |
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| 88 | sum -= flow[e]; |
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| 89 | if (n == s && sum != value) return false; |
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| 90 | if (n == t && sum != -value) return false; |
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| 91 | if (n != s && n != t && sum != 0) return false; |
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| 92 | } |
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| 93 | |
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| 94 | return true; |
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| 95 | } |
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| 96 | |
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[358] | 97 | // Check the optimalitiy of the flow |
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[357] | 98 | template < typename Digraph, typename CostMap, |
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| 99 | typename FlowMap, typename PotentialMap > |
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| 100 | bool checkOptimality( const Digraph& gr, const CostMap& cost, |
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| 101 | const FlowMap& flow, const PotentialMap& pi ) |
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| 102 | { |
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[358] | 103 | // Check the "Complementary Slackness" optimality condition |
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[357] | 104 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 105 | bool opt = true; |
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| 106 | for (ArcIt e(gr); e != INVALID; ++e) { |
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| 107 | typename CostMap::Value red_cost = |
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| 108 | cost[e] + pi[gr.source(e)] - pi[gr.target(e)]; |
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| 109 | opt = (flow[e] == 0 && red_cost >= 0) || |
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| 110 | (flow[e] == 1 && red_cost <= 0); |
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| 111 | if (!opt) break; |
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| 112 | } |
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| 113 | return opt; |
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| 114 | } |
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| 115 | |
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[358] | 116 | // Check a path |
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| 117 | template <typename Digraph, typename Path> |
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[357] | 118 | bool checkPath( const Digraph& gr, const Path& path, |
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| 119 | typename Digraph::Node s, typename Digraph::Node t) |
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| 120 | { |
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[358] | 121 | // Check the "Complementary Slackness" optimality condition |
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[357] | 122 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 123 | Node n = s; |
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| 124 | for (int i = 0; i < path.length(); ++i) { |
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| 125 | if (gr.source(path.nth(i)) != n) return false; |
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| 126 | n = gr.target(path.nth(i)); |
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| 127 | } |
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| 128 | return n == t; |
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| 129 | } |
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| 130 | |
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| 131 | |
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| 132 | int main() |
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| 133 | { |
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| 134 | DIGRAPH_TYPEDEFS(ListDigraph); |
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| 135 | |
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[358] | 136 | // Read the test digraph |
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[357] | 137 | ListDigraph digraph; |
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| 138 | ListDigraph::ArcMap<int> length(digraph); |
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| 139 | Node source, target; |
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| 140 | |
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[442] | 141 | std::istringstream input(test_lgf); |
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[357] | 142 | DigraphReader<ListDigraph>(digraph, input). |
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| 143 | arcMap("cost", length). |
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| 144 | node("source", source). |
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| 145 | node("target", target). |
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| 146 | run(); |
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| 147 | |
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[358] | 148 | // Find 2 paths |
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[357] | 149 | { |
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| 150 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 151 | check(suurballe.run(2) == 2, "Wrong number of paths"); |
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| 152 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 2), |
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| 153 | "The flow is not feasible"); |
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| 154 | check(suurballe.totalLength() == 510, "The flow is not optimal"); |
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| 155 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 156 | suurballe.potentialMap()), |
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| 157 | "Wrong potentials"); |
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| 158 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 159 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 160 | "Wrong path"); |
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| 161 | } |
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| 162 | |
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[358] | 163 | // Find 3 paths |
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[357] | 164 | { |
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| 165 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 166 | check(suurballe.run(3) == 3, "Wrong number of paths"); |
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| 167 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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| 168 | "The flow is not feasible"); |
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| 169 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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| 170 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 171 | suurballe.potentialMap()), |
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| 172 | "Wrong potentials"); |
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| 173 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 174 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 175 | "Wrong path"); |
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| 176 | } |
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| 177 | |
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[358] | 178 | // Find 5 paths (only 3 can be found) |
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[357] | 179 | { |
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| 180 | Suurballe<ListDigraph> suurballe(digraph, length, source, target); |
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| 181 | check(suurballe.run(5) == 3, "Wrong number of paths"); |
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| 182 | check(checkFlow(digraph, suurballe.flowMap(), source, target, 3), |
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| 183 | "The flow is not feasible"); |
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| 184 | check(suurballe.totalLength() == 1040, "The flow is not optimal"); |
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| 185 | check(checkOptimality(digraph, length, suurballe.flowMap(), |
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| 186 | suurballe.potentialMap()), |
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| 187 | "Wrong potentials"); |
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| 188 | for (int i = 0; i < suurballe.pathNum(); ++i) |
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| 189 | check(checkPath(digraph, suurballe.path(i), source, target), |
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| 190 | "Wrong path"); |
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| 191 | } |
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| 192 | |
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| 193 | return 0; |
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| 194 | } |
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